<%BANNER%>

Robust Adaptive Methods and Their Applications in Quadrupole Resonance

xml version 1.0 encoding UTF-8
REPORT xmlns http:www.fcla.edudlsmddaitss xmlns:xsi http:www.w3.org2001XMLSchema-instance xsi:schemaLocation http:www.fcla.edudlsmddaitssdaitssReport.xsd
INGEST IEID E20110221_AAAACO INGEST_TIME 2011-02-21T20:45:11Z PACKAGE UFE0013387_00001
AGREEMENT_INFO ACCOUNT UF PROJECT UFDC
FILES
FILE SIZE 8904 DFID F20110221_AAAEJX ORIGIN DEPOSITOR PATH xiong_h_Page_043.QC.jpg GLOBAL false PRESERVATION BIT MESSAGE_DIGEST ALGORITHM MD5
23aabb94703ba71f8c62dadafa270ebf
SHA-1
782c9e6520dea5ee4d9c6d77a4b2dd3f5d2f8736
22688 F20110221_AAAELA xiong_h_Page_095.QC.jpg
8e780f60916d5b714c3e8283d66dc62c
3ad24575f718e7a1a959b19ce6c1760710aab15e
27478 F20110221_AAAEKM xiong_h_Page_066.jpg
4c6cdeefdb261565345be0d101219629
a17403b1e24809fa2fac44128be2842ada5de574
63165 F20110221_AAAEJY xiong_h_Page_044.jpg
c3572143498578bc89dda1ca3e9b2d10
09c6b3e44b6b7629fcf5642ff71fc3c18d242b4b
14026 F20110221_AAAELB xiong_h_Page_099.QC.jpg
854d75c4565b0c3c2afd25797edb0aeb
93e5c4db993b4853fd06dab34b9c920ef5ff1760
35288 F20110221_AAAEKN xiong_h_Page_072.jpg
80f021fbc4e0f24558076deeb55d6118
5651487d500d2a05ccf3e67002308b1bff335405
20233 F20110221_AAAEJZ xiong_h_Page_045.QC.jpg
5b4c0e57acec510d99d01bd741eb25c0
1a17e6b999078a4222241fa15eb83e54b1aeafb9
18615 F20110221_AAAELC xiong_h_Page_100.jpg
cd5f92a98c26de31df71aa31bc5fec44
0374148b005064d18acd2b82aec432a5ddcc64c3
25533 F20110221_AAAEKO xiong_h_Page_074.jpg
9f647c3e310f732ded4839ae3885dc6f
6f050ada8a1e8d6a3934f0be7912e45db8b96b47
7902 F20110221_AAAELD xiong_h_Page_102.jpg
bcdc5301beceef14c752bbe17cdf7bc4
d8975da4cf7fdfcd86b238588151ecc24fa85bf0
18841 F20110221_AAAEKP xiong_h_Page_075.QC.jpg
e2a62b373b2bfe2328f1a1b2a2fa55de
9855ab1691684755da2185518c4d0d142f1a424a
36731 F20110221_AAAELE xiong_h_Page_103.jpg
78d03d9ac34bc69f529914db9f836486
75bd665edd8aee6c0f2a53150af94470e659ff83
16389 F20110221_AAAEKQ xiong_h_Page_076.jpg
c5f21eccd4347461db8d16af99b378cf
907d0a980da8135b2dbb7744fd99aeb16c08e0ea
21082 F20110221_AAAELF xiong_h_Page_106.jpg
1d2cd692034118334317701ddbcc0b9c
2673651c9f61bf85046f6cf39303ae639fc8c7f7
22899 F20110221_AAAEKR xiong_h_Page_079.QC.jpg
e75e9aed52ab9098efa7239cd0092404
da1a9c37433591732114eb234d11d6aa21a17175
6833 F20110221_AAAELG xiong_h_Page_106.QC.jpg
1a7bcf78863ea106b6f1956103c8190e
81359f3d00649332fcc51ccc1d3a5c4f32b151f8
83369 F20110221_AAAEKS xiong_h_Page_080.jpg
217d97d7a75cb3e9ae7808abe6dbea4a
dd96d3eb549ad2fca18f6a5d7f7265f9bf2bcdcc
5441 F20110221_AAAELH xiong_h_Page_107.QC.jpg
dc637257379acb5cd81abff77b779d8c
2c37fafbb5c702b37dff1ed1e2a8a2bd9eeb412f
61914 F20110221_AAAEKT xiong_h_Page_081.jpg
6bc5f548d7ed536f2ccf4dfdfd0a9e81
0768abdaab931071370908ac505b25fb65a28c9c
89026 F20110221_AAAELI xiong_h_Page_108.jpg
5e039bbd25fca71cd6578a3cacd9b201
8b974c41f09bdb7d66ae1a356e67ee1ac1df37bc
15892 F20110221_AAAEKU xiong_h_Page_084.QC.jpg
ebd16944d6ce04c2a1bd84944528db4a
e8257abee2b7b74acd4a8b2aa663d5ca6a697594
99323 F20110221_AAAELJ xiong_h_Page_109.jpg
cc08e2adee3d03ba3601b32e6a901f74
98a12abd70af322de2cda5ba0dd734d35f923dc8
13012 F20110221_AAAEKV xiong_h_Page_085.QC.jpg
dfbeddd5d38324fb8185136f188aaf64
85eafb729ba5726b656a975d1021f7b880d50e9e
27809 F20110221_AAAELK xiong_h_Page_112.QC.jpg
53fd58bf7119aee0125318b8e2c141f5
c50bde1e85c26e0cb0a095358ed32c5518355076
14078 F20110221_AAAEKW xiong_h_Page_086.QC.jpg
ef871047e58c2323433061280ac043be
650316f4e3ab21dea7a76b200d4711be8983efa0
25923 F20110221_AAAELL xiong_h_Page_113.QC.jpg
ba2a0aa5b5762a085449dc2e8a0fac52
8f8a91d4dec4f6f2fa0732df055145cf6a687516
17867 F20110221_AAAEKX xiong_h_Page_088.QC.jpg
9a51a5353a6c714d4f73cd75fbed5887
ced3961a59f8f7db012b8823e88cece3e1780eec
943663 F20110221_AAAEMA xiong_h_Page_040.jp2
82505aff9e4a435076a6be056e469c0c
652b27238dac72a47f4308e9543c1baa063007f8
718736 F20110221_AAAELM xiong_h_Page_003.jp2
f2c17a3df76df4c74e6cf3ce98cfefab
2fb2624c5994ee6c74ba1b067748c40260fdbaef
14535 F20110221_AAAEKY xiong_h_Page_090.QC.jpg
1724a2f05ac2d177abbf974e5b584764
e7ed95e3218a45a8799f188b6f51c2ad1de5ebbc
264954 F20110221_AAAEMB xiong_h_Page_043.jp2
4aefded3fe631b4c95af677be1b81748
12c96f5fb151d05d60fa07368e6d9aeff78708a1
85195 F20110221_AAAEKZ xiong_h_Page_092.jpg
17ec4f4d098dd5bd53e8a3f0dc07b3b8
49de5d4ef8c2ddc40a4f533edd2ff549c9d81c7d
601456 F20110221_AAAEMC xiong_h_Page_054.jp2
725c1ca4ab91729e292e5b3d573d08d0
5bcf056212c1692d0151dbe98fc192b66664d5f3
965886 F20110221_AAAELN xiong_h_Page_009.jp2
af3a1918c61a855542611066f827980d
43846df15d03e580b5127b606bbdcd7d39c68079
954671 F20110221_AAAEMD xiong_h_Page_060.jp2
ae9fa35832fd2d786e83843a314cb8e6
bb081d2fba270788008b1d509c32d0977c1b10cc
1051958 F20110221_AAAELO xiong_h_Page_012.jp2
bd002c2c4f46adca644d8488a70f22b6
097b81fdb9516f4de9d00fb0f47e8fa2161bd80e
526095 F20110221_AAAEME xiong_h_Page_061.jp2
3ea88816af202d545cd610cc95902ba4
2a16a3bd5831e97e188d8509bc3b36af60077ad2
940579 F20110221_AAAELP xiong_h_Page_015.jp2
4747c62536804ef186f44c0239f6193b
32a09f9d6d5aeee9d6bd392671b4da3432d26352
746955 F20110221_AAAEMF xiong_h_Page_062.jp2
a31710235076ad559972815a12ec12f2
300d8a09bc6f5b01f5797045b33a02ad4f395b06
1051969 F20110221_AAAELQ xiong_h_Page_022.jp2
c3a5e45592d293ff7c9aaa9a8eb13b2f
157b9aa2b23e296b466c6d83b901bd43b4504612
735723 F20110221_AAAEMG xiong_h_Page_064.jp2
621cfa9820016a5a597f749fea3a8c61
c3fbc1dc0d04555e6bcb80635950cf08f1a6972b
1051965 F20110221_AAAELR xiong_h_Page_023.jp2
6829f0afc4ddf357fcf66cc413a79019
5d32211b3cbf9cf9d947fa557f7e983d6a18a1ed
294793 F20110221_AAAEMH xiong_h_Page_066.jp2
f72c9711a8d7e8ae09c71eb2866f9449
acc72b4f3c7ca767b389038f67d5a5738aa355e4
1028245 F20110221_AAAELS xiong_h_Page_026.jp2
ee3547d26b842c45d6d9e7e884df41f6
6feadef82ef31afb09f6b8c9c12b0f6ab2414044
380643 F20110221_AAAEMI xiong_h_Page_068.jp2
1f17dcd7bb2edeef1b92d7d45bd5a4a0
69159a2023f87bb4187f98b4330f6cfc3bc1f11b
677213 F20110221_AAAELT xiong_h_Page_027.jp2
4aef5ffa502f1e71e73dc1a57c1a7230
76b5622ff8f7e170ca7cfb293cad3f1660593e92
269507 F20110221_AAAEMJ xiong_h_Page_069.jp2
0bf5da506fed990aab40252513ad8866
4f32ebc03613cf2acb3bdfab80da03d03cca6fc8
607852 F20110221_AAAELU xiong_h_Page_030.jp2
720ee31689a3b4b3ce0ed9b4de1282ef
25bfd4f877865f59a75774da93620bd2825c11d5
297835 F20110221_AAAEMK xiong_h_Page_073.jp2
0593008cab73b02909253f74f952a1be
a3c28e5cde150e2378e5c5e4e04828b916bbeda4
718784 F20110221_AAAELV xiong_h_Page_031.jp2
a172dd4168b873f927df20e30a9bcb52
bcb8611df3d50cbe3a84f985b92e14191f876144
804644 F20110221_AAAEML xiong_h_Page_075.jp2
a461f7596b6ffba7a769faeb162248bf
e668a906b44e510e908e0c44c21db757bb975cca
441278 F20110221_AAAELW xiong_h_Page_032.jp2
09cf329470969f2676d5423c17aa3fda
87814e5f7c25ea1d934eabb62c1190e07337dc6f
4512 F20110221_AAAENA xiong_h_Page_009thm.jpg
414046d48bdf61a1d4f08f6cd3a2e4f9
8d608841fca094f21d97677b4a1dde431198ef55
1051978 F20110221_AAAEMM xiong_h_Page_079.jp2
13c9e57f7603f10282dd2982661ac082
0e0c3cca62a6179d5a00b10ae328c3fdd8e1ceaf
701705 F20110221_AAAELX xiong_h_Page_035.jp2
48a4518e8120bf5cf63505065872195a
892d4f1494279de0b18cbc7907c5e783233669ec
5852 F20110221_AAAENB xiong_h_Page_012thm.jpg
02ac879b76870d66460c1cdcf0fcb098
9c6a074376bc5c87c4bb9e2bb553862179e60cfb
778016 F20110221_AAAEMN xiong_h_Page_081.jp2
18ee7203586e97a580f7b08838f8d005
1d0ec5d773bae213ea6b2b262ec7e3c950431688
509606 F20110221_AAAELY xiong_h_Page_036.jp2
7ac80e31b3d8bc4b9d93fe311648a37c
52f45bd4a55974880c3bb8de7e6438c0e4e54412
15938 F20110221_AAADKA xiong_h_Page_039.QC.jpg
751dfb41b7ce777dcd999df25cb295d7
8e4fb2954405c0d6bebe49ef670cfb0314050262
5405 F20110221_AAAENC xiong_h_Page_014thm.jpg
43b08a734d5a85e01060c923692a0943
6f8a3a53195261a6f25cb02c9ab2670669b96da6
651184 F20110221_AAAELZ xiong_h_Page_039.jp2
3595bb5efdb419bb8ee6d15b93165aba
9dea8691bdc8044fc97bf3ad53001bbe62959581
2198 F20110221_AAADKB xiong_h_Page_022.txt
50aab7db915b7d47fd6436c7a966d3ad
9392edfeb247260d631f165f277f87061c4f01ff
5614 F20110221_AAAEND xiong_h_Page_021thm.jpg
4b4963a895244d5afe1217f9b1ca1a3d
c06e23267cba3c55c6c31a7ba70c45fff48df25a
472327 F20110221_AAAEMO xiong_h_Page_082.jp2
b6e3a44a108948213f31ed3e702e39df
3236da955949536c81d907f74bb4908a78389ffc
866 F20110221_AAADKC xiong_h_Page_008.txt
393b33ac269e6fcdf262b83d95ad23d7
d0efe480af26f165bd35523c7c80bbaa1d85003f
5639 F20110221_AAAENE xiong_h_Page_022thm.jpg
3e57f164c07aa97309292d60ab982b91
d186cc7f937d4bbaf6d6fe21965c7c427f52dfa0
683677 F20110221_AAAEMP xiong_h_Page_089.jp2
da8dd06b5e6116e400c55526c26ee861
73c859031a71d004d618071206ba013da64342d2
23955 F20110221_AAADKD xiong_h_Page_014.QC.jpg
3661beca0fd089ec1784cc78a52bcb59
cc105e7488d6cd56770d722191f556b94a660324
5646 F20110221_AAAENF xiong_h_Page_023thm.jpg
5d5b1694dcf1a94db79ec7d426c4a98a
b16043a593ca9f1e57d13f744af5d57b03992c37
1051962 F20110221_AAAEMQ xiong_h_Page_096.jp2
e9713d9c31cbfe1c510ae4ac38dbca3a
a12bf36494cfa077e071291d262359cd1244bf1e
5574 F20110221_AAAENG xiong_h_Page_024thm.jpg
b36f0b991c3a1138150e72a72b5332bc
58ac274b4f4a2c7057ad33d5a922d8fa1cdbedfe
50006 F20110221_AAADJP xiong_h_Page_039.jpg
9f0bb37cbe1a34d27b3486910c0934ac
ee542e09bc38ac86c68dca882ebfe0337dddf57a
F20110221_AAAEMR xiong_h_Page_097.jp2
9448ac7618dbf4733e88d9a1c622d0c4
39f73a8a883ac0ee9bc71ee7064233d703e39d51
997669 F20110221_AAADKE xiong_h_Page_007.jp2
256a2bca658c6c961db3aed0ffd7e21f
637694f70647f85c6ec6b2eb31913b1ca1fd966b
5227 F20110221_AAAENH xiong_h_Page_025thm.jpg
5913a862749223556a9d006b8dc50883
95d90d1cfd043366ffc2d8b7d922e11642e11df8
691184 F20110221_AAADJQ xiong_h_Page_057.jp2
5a58aeda6f7ca3fac42b95c969b7119a
fb8757abd74e7b87b66f184192d7e01e0c462adc
87389 F20110221_AAAEMS xiong_h_Page_102.jp2
03d40ed9e550994c02b03126665ac142
4e640e883b604a2706cb2ccecc7c12de45646278
49231 F20110221_AAADKF xiong_h_Page_079.pro
4be2a126ba21d2ae5126d4e31038915b
0cba518a8d55eecf7d10405bd211d488637ccda7
3985 F20110221_AAAENI xiong_h_Page_027thm.jpg
a5ecce10e698333a09a255f1d17d16cf
0821622e8a3baff0e92031ba24aad0436d70f2e3
51187 F20110221_AAADJR xiong_h_Page_018.pro
5ab315a09a8c6bc1100ce77be6b9896e
31504a58b339b9ed672dfd195134d9a09bf6d5f4
596425 F20110221_AAAEMT xiong_h_Page_105.jp2
bcff1a47ef2bc6b8a6abb38f9bed289e
cfec3211cdeca14a1a895943ee2a2a6fd1e86b74
8423998 F20110221_AAADKG xiong_h_Page_003.tif
926704d314e9abacb81d3db53bbd82db
d151aa3f08019ace9f85404c53d7f6286004dfd6
4421 F20110221_AAAENJ xiong_h_Page_035thm.jpg
946feac772139968f82ece83da9d6fca
a108cf4210b49f2d136972b025fd94b7e689d0a0
41088 F20110221_AAADJS xiong_h_Page_047.jpg
87cf0ca36d6dde5b5d611b8337f45371
dab39c750e9544e1d45a99cd582c3278d0672aad
269924 F20110221_AAAEMU xiong_h_Page_106.jp2
d7909e735d72b83038d8a51a8a971334
cbe0273a477823eaa42e62dc148888e7017f1fbd
24723 F20110221_AAADKH xiong_h_Page_080.QC.jpg
0b5c7f49fd9f21f66a67312131bd228f
a633e27b33de2c51a7830b4b9724c03e213e8624
3453 F20110221_AAAENK xiong_h_Page_036thm.jpg
ab87862ae6f8bc48df16c0ffcc1a67f9
8670765ae6d7097f38e01fb9ab62374b7ac23c42
23636 F20110221_AAADJT xiong_h_Page_108.QC.jpg
d99d8b41553e9d14205607b67f82b14e
fb5a116313221c1f1f8c59eddb878f97f2850655
192504 F20110221_AAAEMV xiong_h_Page_107.jp2
71d000aa16ed330bbbf2203b1e50871a
f852817ab4a90bf98fc40fb338fcac29fb7be3b7
1618 F20110221_AAADKI xiong_h_Page_028.txt
d5fd52f5202826d9b531c64e6e5c21eb
42879c4876c88a2893b9c1d3894a2b24f4844aa0
5557 F20110221_AAAENL xiong_h_Page_041thm.jpg
88317abc90a57db635f69b114d26998e
2a022f9dadebe656dac49b0636e02794bc2347b5
819142 F20110221_AAADJU xiong_h_Page_044.jp2
a44563b71f33b54fb2027eb2679e1405
68d57e169408af2ded454d742ba81e5746c65eff
1051985 F20110221_AAAEMW xiong_h_Page_108.jp2
4fb3e3248c1b0bec6d4d46db4c8aa118
60713b73b792f7d7b077de4c6407f9a19e3baa03
4898 F20110221_AAADKJ xiong_h_Page_045thm.jpg
d6852a6f2a44b38058063833b6cd60c7
6e5d191c3e927cd11c13dc21b9f012bc463cd1df
5390 F20110221_AAAEOA xiong_h_Page_079thm.jpg
68aead4a6357b12661b3d9d39678a0e4
dc9a69b464a9f05df3c078c1d8f78d88312c560a
4598 F20110221_AAAENM xiong_h_Page_044thm.jpg
2bb3b80dae1b5dafa347f15dec255892
ce42dffe6615ba4c000302161b4e154058c7c0d5
60980 F20110221_AAADJV xiong_h_Page_075.jpg
319e58d8db47b4d55b48d1753889b11b
020544df23a48a41ca19fd1cb60d45379716c6e5
1051944 F20110221_AAAEMX xiong_h_Page_109.jp2
f2b8a3f65d3e7c1a8acd4bb6bfc2b01b
b8f009cf16cb2c31eb61252cf4937ffea35f3c6d
F20110221_AAADKK xiong_h_Page_107.tif
246a6b4fc867eb049409475754429c13
4c791d8f3fa7cbf1a244092dca191b8cb9f98175
F20110221_AAAEOB xiong_h_Page_080thm.jpg
6b67ee638b9ebecfcb763c7da22eb585
cd306f0e2e60f7490d7fb287a7d2409939390b9a
5721 F20110221_AAAENN xiong_h_Page_050thm.jpg
dfe098020e5d612068376c35bcfb2f21
aeccd70e69aeb782cebf11e5e17c5d5749c5c155
830003 F20110221_AAADJW xiong_h_Page_045.jp2
ed4089485d27b4a04d6920fc8866cabb
edb7181abb329d594fd753803177f42a50a051a3
1051932 F20110221_AAAEMY xiong_h_Page_111.jp2
d42e1e20b0c72be036bb563ef6574d73
736afc6ddb3facabc23d0a1273da6bee581ffa49
4658 F20110221_AAADKL xiong_h_Page_037thm.jpg
1c68b71eeec55ae6a972a3263f1ecf81
07c8daf737eb5c9e1f59f64e514b890c739318a4
5087 F20110221_AAAEOC xiong_h_Page_081thm.jpg
da06112a965e146f6b3b2a5c36e61a87
93cbd91130d812c241c303b5322b65ef2cfc08d5
4055 F20110221_AAAENO xiong_h_Page_053thm.jpg
1eec5283b6b7928932c59589281b23ca
4b26502423cf21701d7271a0295e7f3f6747d876
9370 F20110221_AAADJX xiong_h_Page_074.QC.jpg
607b78c3c502109dc4013a4ac70c1299
0fa1af327dcccacc6256bcbf2b76c5d43fa2593e
1583 F20110221_AAAEMZ xiong_h_Page_001thm.jpg
d35970bb9e5d3a6b25d3851f3bbebbb1
270ec8f3a6efc4e5a09ab4397893fa535bd5258a
82030 F20110221_AAADLA xiong_h_Page_020.jpg
81546235731e84b3df1ee910722dea9a
df6e73c585ef85a58f506391a11bffee86fae5a9
69404 F20110221_AAADKM xiong_h_Page_060.jpg
7529dda9b7de64289c26680602660d96
d3a3a397223732763dfd078603a3dcd0435cb491
3328 F20110221_AAAEOD xiong_h_Page_082thm.jpg
0c7aff2282c9ced7bef64a8759d83c57
bdc598f8f74fbf7b71b0c5f7918818822511e44f
9811 F20110221_AAADJY xiong_h_Page_073.QC.jpg
dad736b171ba52650cb2409dfaad7ac8
ff394a34bcc935d397d529c54644c2ba71c228fe
5667 F20110221_AAADLB xiong_h_Page_076.QC.jpg
404b765a5246a8522af0ae23330fa29d
3c8373937c8e62b07d995cfe40a283b215d7bbfd
3355 F20110221_AAAEOE xiong_h_Page_083thm.jpg
4edba078fba8e9600ed60344934a03cf
34852f4f75461b373d9612526325767daaab734a
F20110221_AAADJZ xiong_h_Page_078.tif
209f8cc831223e5d1755509c51bfc6d4
8214e995c23c2c3fe69303ccd1a9d4afd06e7e2b
51018 F20110221_AAADLC xiong_h_Page_027.jpg
5e9c33326deda4dcfb93946333ae7e39
1925277ddd6df92f9c6e7992ce5bd46c91008cfc
F20110221_AAADKN xiong_h_Page_111.tif
a0e33f595e7b462fc025dfa56d9da150
02e98fa6b1e46964ccecbfc29a26a7b59b411530
4521 F20110221_AAAENP xiong_h_Page_055thm.jpg
30e39eedb60a0427bcb464b904826115
a1774fec8e34b5db169f59e195b7ae372e3dece0
3544 F20110221_AAAEOF xiong_h_Page_085thm.jpg
506b53bad9249d01ea7eaf88bb926155
5abf87dad82874242069b75f24405e63ef029c99
132905 F20110221_AAADLD xiong_h_Page_104.jp2
51ca37281a569a635964840b72af7e32
0298fdbdf2165d70ef2b6c2f7410d3f9dbc36669
F20110221_AAADKO xiong_h_Page_012.tif
6f96b657138e182e5a8e55946c71c4ab
79e26231bb15ac716451ccae090d4742d3e0f110
4195 F20110221_AAAENQ xiong_h_Page_057thm.jpg
43a75fad90b4382c5ac3be8f7cdf9ccd
cdf65ee3b4838a9178bf47cd66320d8259dcb1e9
3765 F20110221_AAAEOG xiong_h_Page_086thm.jpg
db9946190c8f35ff4620f69c2c03abed
115af1b61586a66f0bb6c0b3133683b4495e28e0
67257 F20110221_AAADLE xiong_h_Page_093.jpg
893b1b08f20daad8e73e779e410b4ebc
4e36537cf730ae9790392208a010629f973c7b1f
639895 F20110221_AAADKP xiong_h_Page_084.jp2
d5589a5bc8f5c5a60c7681fd5eedcd66
d7d1c261dd28d48fabe34c03ddb595fa8eb01b94
4838 F20110221_AAAENR xiong_h_Page_059thm.jpg
890d98f6c346fa4e8f8599690c457794
22eacf0e4a65151dd7e1c17a62c2dacc1065245f
3934 F20110221_AAAEOH xiong_h_Page_087thm.jpg
f21a972371425cb02636d3715d9d7a55
f2eaab051a1859e75373be747d0d2671580bb4d7
728575 F20110221_AAADLF xiong_h_Page_056.jp2
18101b43319389b593cbb0adaa478082
b7d445e4b165c911c4c469d5f5eb27855c856fdf
4470 F20110221_AAADKQ xiong_h_Page_019thm.jpg
d5c97e7aaa35e757b40b37f0bc5eba42
e629fb87eea153c7caac17b43ccea24780255e20
4729 F20110221_AAAENS xiong_h_Page_060thm.jpg
311bf649bf3953438507a0189f54b50f
8456056e9143b64d453d6aefefbb8c93dafde6bd
4978 F20110221_AAAEOI xiong_h_Page_095thm.jpg
b0b01aa3a9797455d7671006e8260b3e
e8e8336fb29cd5bd5a9b381a6bf7de090d9c71b3
3581 F20110221_AAADLG xiong_h_Page_072thm.jpg
4fa7cd3642639cdde29e47d2ab50ed1d
b8155c6193710c804cc5fae83373889175d0c71c
809307 F20110221_AAADKR xiong_h_Page_038.jp2
0933bbb0a50dd961238b79b3f22b1f9f
032cbd84248f86800b38f3953896ed9218d81a85
3757 F20110221_AAAENT xiong_h_Page_061thm.jpg
c24633d5dec40a989a4a56aab7f08d76
18632209cb920d0df37e545cb53260a992e3a1f8
5098 F20110221_AAAEOJ xiong_h_Page_096thm.jpg
d0de55caddda6f4c4da3756f0be524ba
3ac0cb380ddfa48e4244141212b9b57e389ffc8b
F20110221_AAADLH xiong_h_Page_001.tif
17e267048548df15d674a59bde6212ce
389e7773e0e5b82ba20bf4e78ad4ed4c81759b64
1051980 F20110221_AAADKS xiong_h_Page_017.jp2
94ae6e0dbf72c8cf02a9419e70c62008
ec513b89907eb6b52f9a3502664f4be91605de95
4642 F20110221_AAAENU xiong_h_Page_063thm.jpg
635d4ad6abb2e026d6d4bcf63d47e9a4
1829a125c8b308860d9d6452c03ccb64891bac8e
3248 F20110221_AAAEOK xiong_h_Page_103thm.jpg
324fcb57ff2d12c29265e393d6e08464
1e584f0e43df2b4efd26dcbe34f42748d7710fc1
4472 F20110221_AAAENV xiong_h_Page_064thm.jpg
1176a01fe50b6ca46e450cebe0a21625
a4f05163b4deb56159fba01f8aae1e1e06ee07e7
20420 F20110221_AAADLI xiong_h_Page_007.QC.jpg
0a2d766e4077022e5235dd98442b445c
c1b57b981e40339be8dbfe1288f0546d00d2cc76
F20110221_AAADKT xiong_h_Page_002.tif
1af35be6029cca9a4cc36d2201f342c9
619e237b7f29b86f08b874428a89e5fb4cb2f368
1014 F20110221_AAAEOL xiong_h_Page_104thm.jpg
63e0eafdc5ef0d20c9859760fd658672
741ffdd8fc1ea53038322da66b628f4d33bc2875
5761 F20110221_AAAENW xiong_h_Page_071thm.jpg
7497194f93f1c2a80d5675807f201498
8acb436400a636121a0db18e0b1056b4e9a247d9
68118 F20110221_AAADLJ xiong_h_Page_112.pro
a8e24ba54b3ba3ad3e6fe85a2beba908
ad19e29f356afc36f35995adcf3e13d9b8dc9ef5
3458 F20110221_AAADKU xiong_h_Page_004thm.jpg
096cffcb47c3a43e2fcbcd4669ba1377
f4e5a76e60429d3fec7ce3b3fb88dbd04af6739a
1632 F20110221_AAAEOM xiong_h_Page_106thm.jpg
9f2b57ce2c6d90f5834d3f2ff8ff984b
72238491e0b39ca49906b3c92acb295316746931
3372 F20110221_AAAENX xiong_h_Page_073thm.jpg
7b46c895ef97554d676f4b5d38083870
04f912e4ca71f1df6c2ab76640b2c20d461ecc37
1768 F20110221_AAADLK xiong_h_Page_063.txt
d66e6e35de4b9b7b385f7c9b543583a2
bc792c19da49a8d5c2ee8ad758413101b1eb172f
1151 F20110221_AAADKV xiong_h_Page_066.txt
3796d4cc80063e8001827d9379933cf1
b8c4a5b9a01c7ef2c56e6c3ea784e19397c51218
1731 F20110221_AAAEON xiong_h_Page_107thm.jpg
79ba66a23fd4f2e6cf61f02eb2554e89
022d2a700fe193bbba9930d729730dca83f1393a
5138 F20110221_AAAENY xiong_h_Page_077thm.jpg
c88bdaa4e38a3b63580507fdb05f7a67
21f382197aad16de28b8347f3e9878fae8ed2f06
4007 F20110221_AAADLL xiong_h_Page_039thm.jpg
3d62df3110e78578371abb4cfd112148
30551eeb34e421a2a7b5f236a588296f2057f76c
30948 F20110221_AAADKW xiong_h_Page_052.pro
fb18409cffa2f0ac0d5335a244520777
fd215920cd19a7ab1f5f326034721dc1b5dd0481
6036 F20110221_AAAEOO xiong_h_Page_109thm.jpg
fd71eab95e8823ec2cf0dba01ace8e50
bcf831b4d4711d41a22abe31006c7f8da612e15c
5587 F20110221_AAAENZ xiong_h_Page_078thm.jpg
2665e082feb512e0a8184f3f3501cb82
d8e0709315c991c283d85829195c49262a176fc9
41694 F20110221_AAADMA xiong_h_Page_061.jpg
127d9e1393728930af18f171eaa47439
9dabf644226508e8565893ca4474db0ae55c8036
25477 F20110221_AAADLM xiong_h_Page_022.QC.jpg
36a09d0002e3d6d58c64d33d6400f35c
8d6008e9e99260d90eef955d555f3030e3087169
4170 F20110221_AAADKX xiong_h_Page_033thm.jpg
8dfe603f5c13a979b9c32d403822ba75
08ea1201fddbcd97b2f37fe2631c4fb49e1faea8
5733 F20110221_AAAEOP xiong_h_Page_110thm.jpg
119a2d9d122e65b6994fe9a8c3707803
7afb5c64fa2ad2ceea97e901d27088e1baa67ba3
24984 F20110221_AAADMB xiong_h_Page_099.pro
8c476354e83b8487f6a9e9ae49145030
41aa6ce8f5f181c6ae72b40072a0983154e05105
F20110221_AAADLN xiong_h_Page_050.tif
d0189ff2b2d09dd18122fa83b695f782
5ca6644428decfda56abec7207f5a6cbfa93332e
1008430 F20110221_AAADKY xiong_h_Page_016.jp2
ad39c49a5cab8fece394a47d11735a38
1e481f3ddab5c25b483fd013fb2c6d560702e396
4448 F20110221_AAADMC xiong_h_Page_088thm.jpg
8f5ec4f7933ebbf62667c859ada68a83
55df0118c514034c57dae1edf63c3bdb5a2ac5ef
F20110221_AAADKZ xiong_h_Page_046.tif
804e5703992ad3e7218f29456351055a
385395718c534996a5986482005522f1ef092c93
6097 F20110221_AAAEOQ xiong_h_Page_112thm.jpg
b8f5e98a8f755cb1a5c05155d32ad898
a75de4d4e5c49560eedf9fc232d72990e0c07709
1051955 F20110221_AAADMD xiong_h_Page_020.jp2
ca9c51b53153a4621332525a88df8f15
3351ae048af91a0213ee9e4da156ff522b708962
20541 F20110221_AAADLO xiong_h_Page_015.QC.jpg
197d5fcfac012816e45e65356df5079b
91eb78e1f63e5e9333d9d677936fb54beb075921
789521 F20110221_AAAEOR xiong_h.pdf
1f79b63d5efe0586d79603e485415f1d
8ae0952a8896f210312c62283559b060216bba55
35067 F20110221_AAADME xiong_h_Page_094.pro
0e6420d1326c7a40a14829e87c44b733
6c37346081fe394c49de09a500ef5ae9d7178554
1665 F20110221_AAADLP xiong_h_Page_056.txt
57446315b6e0609f92e0b0f1a2044b7a
fc175bab0f9487df356c11b913aa1794d0915e92
135428 F20110221_AAAEOS UFE0013387_00001.mets FULL
2c2aee3f7ee8e2d2b70a71b51ab149a3
fa84accdfa3343450159120c651f1b24110bcc03
F20110221_AAADMF xiong_h_Page_017.tif
6e9c5dc41e8815ff8b862112674cb532
f4c2d37cd51f2da9218eca7d6a598a64c34db37a
5541 F20110221_AAADLQ xiong_h_Page_049thm.jpg
5173a06cd33c09dc1828a8c417e6e3ca
405f0f3da6c3c8c3eb935fdcbe83686763fa238a
8356 F20110221_AAADMG xiong_h_Page_076.pro
a334160abfb00f513bd1c27b64683f47
6f503c7b8f1a7456868aab5f033f40391e6cb720
1776 F20110221_AAADLR xiong_h_Page_051.txt
8442a54357134b7f26239dc1cfd15d0d
467eefa166153b3a5f9d3368d555d2c2263fa389
33269 F20110221_AAADMH xiong_h_Page_056.pro
0972254f5ac49d8705c062c0227afc82
7c8997c74836bf873d8f84973a74f70213af3b08
56839 F20110221_AAADLS xiong_h_Page_019.jpg
43e8e0e7580a4ef203488169ece88a5f
358d72314cbb5cb6a04b5f20d9eb4db0d2667d39
89204 F20110221_AAADMI xiong_h_Page_071.jpg
4d5f69fc99ce003b5fa20b6a2208347b
ea31f231f58f98787c9e2602d2382d41188d10be
28791 F20110221_AAADLT xiong_h_Page_053.pro
f2eb3dac43c52c23a155aaa7ba783d27
27aaf150cc216a2881c32c7026c158ef2455b00f
746222 F20110221_AAADMJ xiong_h_Page_004.jp2
3484178bce90aae9709b5fd39dae5a32
8cb2b57cd5d228dd12056b844f0e77fd431821ec
57708 F20110221_AAADLU xiong_h_Page_012.pro
a57f3fcd85fb5b40b2cccc629b0d9b23
41fe8d20525086b6b8cdcf7c4e0bef5858da0d1d
960 F20110221_AAADMK xiong_h_Page_098.txt
4511c4d5bdc9ebf137e41589e32087a3
cb3440095fe55f4b00ec20e733b3e8e0c8a347e4
F20110221_AAADLV xiong_h_Page_010.tif
c019b3151d9cf7b5b681ae1f670f30f6
2832148812be538a7bee0041e7bfc63b13eb874d
2664 F20110221_AAADML xiong_h_Page_046thm.jpg
cbb1fe92eaf3e69f7e271ab7fe550ef0
8805cab37950e33a5871cb35701c99a6b5c333df
55479 F20110221_AAADLW xiong_h_Page_071.pro
1f94c02985f6fe17527c7d26e3888c1c
2b5c127b900a63ec10497537c346778bcc08943a
26726 F20110221_AAADMM xiong_h_Page_042.jpg
00af299c81b56e2307943769d655b1f0
a967e163b448857f1877681a23c3a8f8d2400030
F20110221_AAADLX xiong_h_Page_047.tif
a14bdc8620058aead560d999940dd160
738b0be3c4a29e4b63059fb44b65256c43de7dcb
F20110221_AAADNA xiong_h_Page_100.tif
f1e27456b1d356c3d5797d3a23bde40f
4a8871589c574c6b7df3cda172c9b7bf33dc5421
16045 F20110221_AAADMN xiong_h_Page_033.QC.jpg
ffb091aea157c4a995491b923661ee05
b19240ccc90d34f13f05d107c5ab27da01dbccfe
1051952 F20110221_AAADLY xiong_h_Page_092.jp2
3e1f9c5a374f9989c211b1269f932b84
92397caf23222d8118d3d6aa5d7e76c8008eed90
59094 F20110221_AAADNB xiong_h_Page_088.jpg
61292e753238a775c3a2c23ff371597e
0d3e2baba79de4e67125a371e34dadb35d43bf3a
F20110221_AAADMO xiong_h_Page_081.tif
7f2e861caab7c1f5fc963021c6ed9c30
0666dcdaebd447ff2da8d7be9af217d8a00726c4
25718 F20110221_AAADLZ xiong_h_Page_092.QC.jpg
78870c22f24b830e0b5f280bcdd90470
c0ebb8cf2fcffc779a5ece2c04d7d9273dad1bec
2615 F20110221_AAADNC xiong_h_Page_102.QC.jpg
092dfce7d8db9690d61da7d0ba169bf8
719830d7a8f0c4fbb847c71d73b61902889ca433
9956 F20110221_AAADND xiong_h_Page_068.QC.jpg
9600f8a0efed31f87f8a1d2399cd2990
fd06aaf4d6461c1287ef5663f7378ee77edb9153
23584 F20110221_AAADMP xiong_h_Page_021.QC.jpg
963560b0b0d735a9c1aabbd45c39fba0
750e483fbdf26d685332b2ffe813a841e5b4ef5f
94963 F20110221_AAADNE xiong_h_Page_113.jpg
96e484123773353f488b3b516375b783
f8c1fec0e677896ec37687b0c34abfb29f499105
29059 F20110221_AAADMQ xiong_h_Page_090.pro
7a2f884de49b3140af5342a231503f1b
761dea3f5be18a97b551846e4d1ad1119eda8169
464 F20110221_AAADNF xiong_h_Page_002thm.jpg
192d7770375ecf61286d47e3f69a7528
08cee9243baaf1adb38fc7b81a2ba4c13d2ac921
2606 F20110221_AAADMR xiong_h_Page_109.txt
42d213f5ec8ff41a4ab75d29b0e32341
04dd33cc3b3a8feb34712778513f098a362c3be1
4733 F20110221_AAADNG xiong_h_Page_051thm.jpg
83eef40f21edab61d329a1be2cc9ad36
a611ab3715fb599d31915836854ca66492378665
86464 F20110221_AAADMS xiong_h_Page_024.jpg
2f28f16a87fcc7079371990b43fc868b
bbfda4515363447c803073272f541981b5f87cd9
1463 F20110221_AAADNH xiong_h_Page_090.txt
fae16fdee0ae92ade2fe3eb6636cea07
65af129ff4585db467921251a3e97ad27a57a62b
19983 F20110221_AAADMT xiong_h_Page_093.QC.jpg
99b0ae6de19a7ee9f835f2610e54d0ed
1c4eaa7fcf4c9bdc65cc0d1c32feb87f34c73ff3
961 F20110221_AAADNI xiong_h_Page_082.txt
9761e7b82b60d7a17db2469341fbc93c
1ee9877a40a6a5fa391c392bccde4938726c8104
F20110221_AAADMU xiong_h_Page_026.tif
9bae9844870caf870c2ff390316e8fa9
ad2a69d5a3e37696017c7cf6b5047f8987a2514b
2457 F20110221_AAADNJ xiong_h_Page_113.txt
c39254ea342fc8a74ef975cb28d873a0
cde8ca5a55b97f3e26329c43c7d8c229c13520fc
62145 F20110221_AAADMV xiong_h_Page_110.pro
ecaf1d7e429cf77f94580ebd8de069e6
f3a2901010981744c0b3cca7d49b90c1e8e71de9
51723 F20110221_AAADNK xiong_h_Page_033.jpg
cd837e35aeb9d4cbcd08f75dcc6d0099
4730027a0022d65a32b6bf84655587a518684a3d
51321 F20110221_AAADMW xiong_h_Page_021.pro
0194f3684929ab15f7f73626b7d89204
a8c25c3583b9576e60c0d87acd35fd0a8aec1058
35013 F20110221_AAADNL xiong_h_Page_083.jpg
180aef42fbfc50e7500605c5ff1949cb
84d32260c7bc71e73b06d315b5bfd691d55b0c44
31729 F20110221_AAADMX xiong_h_Page_044.pro
589fba049689fa41d55b8b439a165a6e
685043e97304af96d397c32e309072468ae467c2
967101 F20110221_AAADOA xiong_h_Page_065.jp2
376acaf588ff2faefd83e9d6d33c4c62
fe741cfbb5af20ca369b5acad3dff604da3e1a88
F20110221_AAADNM xiong_h_Page_023.QC.jpg
c76960d302844349ca3d92edc8344034
b7f8e5e7a93dcf72170a07c500c2211285671005
25665 F20110221_AAADMY xiong_h_Page_069.jpg
ef33ef12d4d1fd5edaf263d76b5e22e2
72ecd551da3fd634c8d20fba6c397d18e82b2dac
83961 F20110221_AAADOB xiong_h_Page_114.jpg
1795d9ec2188a1ed0ed87e206651c000
16b2f41722e24794d060878ebfb3e09fe8a89754
F20110221_AAADNN xiong_h_Page_004.tif
71ae9f12a9b8054df0b51291db09ba82
c48188e6663625a499ce5f36d72ebbecea6be0f4
9227 F20110221_AAADMZ xiong_h_Page_008.QC.jpg
2aa7e539efe3498b9b597670bbc86c62
ef526e436dd2c15b2084448cb63da7949712f916
612 F20110221_AAADOC xiong_h_Page_076.txt
682b87078aab3f8817574053e256a8fa
405e23ca424f978d4811b265f31331dbbaeb271b
77358 F20110221_AAADNO xiong_h_Page_079.jpg
0291137661b9802042f2b08cb92e9361
ed958e51f79ddff920849f807db886e6277c1a2f
2181 F20110221_AAADOD xiong_h_Page_007.txt
2eddc8f2875adc8062a5c50708fb5d58
7073537c8141f225c9d66fa56bf3b448ee7bcd4c
17521 F20110221_AAADNP xiong_h_Page_062.QC.jpg
cc088bceaf6cf8ac60dc861ea0e3dbb3
a16e63bbdee9ca41d4e6f7233043fa508e2665a6
15175 F20110221_AAADOE xiong_h_Page_034.QC.jpg
f0602dff5dd77b2f30f5b7ec607087a5
585fcb20c7b9096c6c8e1d1d6a6e0746c42cf2c3
5214 F20110221_AAADOF xiong_h_Page_040thm.jpg
36e71ba7c012e5c8005ea60f981ecafc
141e8dc19088c276e7694da059cc07abdf0dac9c
39449 F20110221_AAADNQ xiong_h_Page_058.jpg
c4cdcd789a6daaf55498f7b94071013d
5811f3d192b4ddd98d35f905565197a5cc378cf3
54198 F20110221_AAADOG xiong_h_Page_049.pro
a3b2463f102840ad1c34b5a5c6c0a28b
c864fc0755b7f94461721d45480906a7008b82e0
22705 F20110221_AAADNR xiong_h_Page_114.QC.jpg
2524d9d34a79c3f0161bfa2bcf21bb50
b4a02a9e8255c7c8fce0633e5281a8912700a673
4329 F20110221_AAADOH xiong_h_Page_089thm.jpg
d1b3f1b710dd240919558c3ac8d4b2a1
cb475a97de4c715c4b27e1b2a12498cbb33b2257
F20110221_AAADNS xiong_h_Page_034.tif
95db4e40619fa4bbf295b6e7081524d9
9f76aa697a251e8a2e5070d64221835765d0bef3
5846 F20110221_AAADOI xiong_h_Page_013thm.jpg
dce56ceae4d3b79313a8dbfd5c4e95eb
8f56c97cc42a9a77f295f93edebdf6b000f0b25a
11959 F20110221_AAADNT xiong_h_Page_103.QC.jpg
23a837b5dd8105619615a0b8590a2345
70dfa0741e5b0dcb9e0a155d9e014671d7c37a75
524143 F20110221_AAADOJ xiong_h_Page_085.jp2
483da0e3d676a0586d4f4372568153c8
ab16cf563072f3197cb02c08830eeddf95bf06ca
F20110221_AAADNU xiong_h_Page_113.tif
55d3fac75b96d9f8e0d0e2bbb9e62478
ae8022ba57b8ee803b95e0d3370560372951d91f
F20110221_AAADOK xiong_h_Page_007.tif
fcf951ce595b8a3d7ab66a1b4907fd4f
87d42249d07dc59b96fbc3f971e9ee1062a3030f
86219 F20110221_AAADNV xiong_h_Page_023.jpg
4d66dc4f4270a5e4694c6211219fb196
4f8edf3c6dd80cec78709b6753cc2e236e07802d
1051984 F20110221_AAADOL xiong_h_Page_049.jp2
f599473824cea2c43e86a7b8806a7cf0
1eb8261fe3dc8bdea22b072b11ca7f6069f47277
F20110221_AAADNW xiong_h_Page_018.jp2
def11a298271073a9510efdd2fa3207a
68823f84bd277ef51015bab811dfa5f96d5103db
1889 F20110221_AAADPA xiong_h_Page_026.txt
f6492f90262ba2efa6aa0767fd5a5953
85df0056e3032b2f5efe4511fae0373630f919fe
1620 F20110221_AAADOM xiong_h_Page_053.txt
cd36d154eece2610faf58fc3411b0b6e
cefe0724d0d8b84b9170fe6b1821f8e33a7d76a7
F20110221_AAADNX xiong_h_Page_067.jp2
7b8a2d39c536504c7676ccce4d4dcd93
7ab41f76f1862369b291995fc8bb05123678d290
26593 F20110221_AAADON xiong_h_Page_109.QC.jpg
e7c4a42d5b4d9d95e729f5b316c0d415
ef634995efc58dc06207f5709020d7e41ecde25d
F20110221_AAADNY xiong_h_Page_095.jp2
76c3b877a1da456b162392cb381f2515
6ce929d80e7b06e83965a58443d5c1ac0963f7ce
29255 F20110221_AAADPB xiong_h_Page_028.pro
cd675c7ed1425aadbb4f0d98b28e0233
1c01fb7f1baa92b0fd9cd654628517ca6bc18341
595487 F20110221_AAADOO xiong_h_Page_028.jp2
0aa366e2a3df923f843369e0992f1c4a
f696080bcfa51e31e788c68330b82c5a2e156eb2
17853 F20110221_AAADNZ xiong_h_Page_115.pro
5ca21f9c84fc6d0d4f0b41c178255f67
55bacb2852a2f54cb8dc7afeda9291b9c94d0ed5
F20110221_AAADPC xiong_h_Page_096.tif
07da3a312394cc077fcb228e644b632c
2abb32644c37de1a7af1e1183b7cdba3f75df260
79736 F20110221_AAADOP xiong_h_Page_025.jpg
035b126a2707bc9240a348e7f2a3747e
80c75785bfec8657648c1f8717badba0792647f9
46429 F20110221_AAADPD xiong_h_Page_016.pro
43965b6b4a112c829e9a5620efced4f1
faccc0a7bcff352b02b1be503925186391437def
2121 F20110221_AAADOQ xiong_h_Page_080.txt
88f42b6b42adc904f83a81602557c0a8
3a0bde00e5b3b11ba466c3dc120a69ce279bae0c
1490 F20110221_AAADPE xiong_h_Page_058.txt
02e1ec340e360577f69abb1be4eba783
2d85809efaeeb6e6ce8a162f5af8f2b45782a9f6
805 F20110221_AAADPF xiong_h_Page_102thm.jpg
f54203d6e35656ed335914639b623b29
bb5e8419c7c297094e94b2125d5f8a190e7d8af2
3692 F20110221_AAADOR xiong_h_Page_003thm.jpg
ddd182a980eafea92ad2dbf6e0f41bf7
593a289437a6ba8219ef3dc43ce7a36b460b7cb4
42459 F20110221_AAADPG xiong_h_Page_009.pro
7731eb32fa34c0cffa7e2e307f5a3145
5ee100ceb2d35d0fd5691527dfef243c4b825c49
77438 F20110221_AAADOS xiong_h_Page_018.jpg
f2bbc582fa64fe5f6a12f8c61d1b68fd
1fdc626e5b4e3852ebf6dc85fe4e9613c6d695df
212658 F20110221_AAADPH xiong_h_Page_100.jp2
07c4c2ac127a332a14d78b253df4bfa3
8dd9f09def5b746038ef06e72fc36e0aa033f693
2629 F20110221_AAADOT xiong_h_Page_070thm.jpg
15f0714db03576cf452d2381f899687d
467ebb3b3254e33abd48db7352d3f3cf13288e2f
F20110221_AAADPI xiong_h_Page_069.tif
f6b57992ce0379b9e145f7b280293711
6c9333c5f047ea002e12da73596700398b5033d9
1246 F20110221_AAADOU xiong_h_Page_002.QC.jpg
15c2255f29d56deec8e46f49ba8abe35
fae1f0fcd1c4158db26578a9b3e2a213fc95d58c
61132 F20110221_AAADPJ xiong_h_Page_038.jpg
a87c4fdff1894f0c5112e11c0aa8c391
0081b1f620d7834c4cb2728c31f6a97e7276ae42
4720 F20110221_AAADOV xiong_h_Page_026thm.jpg
1f06260681a3f116f5b824cfaa80f1cd
576c29336524f72478f01b5396bdc1563829390b
14530 F20110221_AAADPK xiong_h_Page_030.QC.jpg
e0374cfe7084bc2b72fea10ae65c6a06
366f2c0fed574292439fb6f7b44d56d8196e2c6c
72740 F20110221_AAADOW xiong_h_Page_077.jpg
d8027d3ba04fbfbcbd1c891fb1335d4b
f5010604446ec121e34e80623af7868e62abb03c
F20110221_AAADPL xiong_h_Page_006.tif
cfdd0c135a57eb278e6e182e725b611b
b52875df24a014720253dbdfa075af2587eab8f7
40453 F20110221_AAADOX xiong_h_Page_036.jpg
5062622885a645266d32f9c774eb8a43
41e667eca4addc0dab1b838f924cd4dab785f7a7
85947 F20110221_AAADQA xiong_h_Page_078.jpg
3cf0e0cb52f66b39b1fba49ad592424e
b8ef30a538ac979d91f4b89205fb51d943056aef
F20110221_AAADPM xiong_h_Page_018.tif
b9dd534c111c738274d04919c3c83617
5a3aeca7d865b2a3d646c2060f79a9bb594d6af6
53618 F20110221_AAADOY xiong_h_Page_080.pro
0af2c62e264e2178ee3205791e0986dc
8d532e86ecb2e55d1cc8a0a9ddd8e5075ad3bc51
29643 F20110221_AAADQB xiong_h_Page_010.pro
a6e6af5ca113bbb126fcc465aaa24d60
f8340ac8abb32b48fd1d39ba2ed49f366c8e5c6f
23694 F20110221_AAADPN xiong_h_Page_097.QC.jpg
06f3a8ab6206523596c39fd2010328f8
f16cd0ea7150edaebc1ac7c55edcf9bcf4eac562
24685 F20110221_AAADOZ xiong_h_Page_020.QC.jpg
ded371a5e9b595802ffc3a613a99ace0
ac30d26300c27202ef982467019ac55de3af884c
F20110221_AAADQC xiong_h_Page_095.tif
c1fdf8cd7747bcbd194fbe85b51551a3
362d515f7019641bdd6f58ee711142e12b0a6a7b
22745 F20110221_AAADPO xiong_h_Page_070.jpg
a7fe82a1847714893872efc6b1cd0741
ade78cf1aa6dd201d3f84bb743e6d5d6d8fd7c8b
1950 F20110221_AAADQD xiong_h_Page_062.txt
209318db3b91810cd526c7f731bdbf4c
cb716999053d58063d6add8b505f99e6e843535c
2157 F20110221_AAADPP xiong_h_Page_114.txt
6563b4ce985b798d8e26099662f104e8
86e88e30cebd9be1047fc627afddadcdf5323c6b
12628 F20110221_AAADQE xiong_h_Page_106.pro
520121761f6a7c50e7c5b04ec0bc9024
d1484b96f60cccf3029279298255835f54f4b1f9
1051977 F20110221_AAADPQ xiong_h_Page_078.jp2
2f20238552605973bb82b08983beb559
1787bb9f245e388898f505a9c25d3166f7416210
F20110221_AAADQF xiong_h_Page_039.tif
e1730932111dd6e3b1f051986d724af5
e986840f703977d6c2e97fad4bd73c9a48637d7d
675278 F20110221_AAADPR xiong_h_Page_010.jp2
639491894ff0662d30b15cb144e2827e
fc653809a98ee7e6de32ef748f27615c6a0e7eef
57586 F20110221_AAADQG xiong_h_Page_067.pro
ae447b0b9bfe7c1b6015d83f70962198
dbb911440f282cc18a4955c31153421766bb399d
4233 F20110221_AAADQH xiong_h_Page_031thm.jpg
0671555201e75ed83fc50ed3162e2ddf
d5955771cd826a03e625508268f191d4097b2d6e
F20110221_AAADPS xiong_h_Page_089.tif
8191ea2e5fcf58da122a22fe5642da8b
633170b1b4e2a77329d7a1006f901760ae423fde
18268 F20110221_AAADQI xiong_h_Page_094.QC.jpg
c57c54a23e8807b63096362c2d970f66
2cf3947644522573591765a9b1a0bc47562e6dd1
1051972 F20110221_AAADPT xiong_h_Page_080.jp2
a1adad58dada9cb6f6892f715c9c3ce3
26f97d5302c0b7e964164490d2850e585b4044b9
F20110221_AAADQJ xiong_h_Page_051.tif
dcd795aa8415fe4e16cd8a4b26d565f5
da1e8e3e0c6fd4c38941ea934cceebd7c69a6131
2835 F20110221_AAADPU xiong_h_Page_066thm.jpg
cf0d430e3bc9a2adf84ea6f183354ce1
f92c2e1b58d406542003296ddc5bf62abafba465
30552 F20110221_AAADQK xiong_h_Page_033.pro
d8fe5548e65439cac3c81e8b07b9b806
fe4d87ebe875b806f03c108110d0112fbba25d2f
F20110221_AAADPV xiong_h_Page_090.tif
b63dbb24c40ed082615d47c052e73643
6a0faf6424c4c9a1aac09f64155d2ea5aad534f2
26862 F20110221_AAADQL xiong_h_Page_030.pro
b27bbdc792776251cc6509ae2f774b76
4178ab71d87132ebd01da877b675f5ae804d7e69
1051982 F20110221_AAADPW xiong_h_Page_014.jp2
b9d08a3989eba73dbf79d1fbce923a21
c841d8e1e253f935da3c85be9189e6c0fb7c86d2
412952 F20110221_AAADRA xiong_h_Page_098.jp2
8c94cdae155884a8bde6ace9db221329
b8f035054b0090b7ef14e605ae38786904078656
2184 F20110221_AAADQM xiong_h_Page_071.txt
cf2a8b239c54fec2f0ce37e53661dda8
6be78d685d5745cab5f8841211c078f9fa5fd118
411461 F20110221_AAADPX xiong_h_Page_115.jp2
57e1e292e6c76f4e7edb9ff9d1ea67d4
c3f34cb0bbea20186745b0bfea4b2da4c0daced9
F20110221_AAADRB xiong_h_Page_020.tif
25a18bc2cafd87f7bffe2f494e023d1e
52fc2e3782510b44efeb0ee95a995fe7698c58de
2046 F20110221_AAADQN xiong_h_Page_014.txt
8c2a6cc3e64c66d07f28afafcde2a843
b3141ca141c30cd821760d5ec1fbb7170f2d0a25
1976 F20110221_AAADPY xiong_h_Page_095.txt
7abe35b37503e005f52a8896eb471e19
498fa2acc76807b58f7fb9eb501849869d361fe2
4684 F20110221_AAADRC xiong_h_Page_038thm.jpg
147af6c684fdf8ad3dba6821652a0d5c
79e143a78a993ae13a96670ef0f308286e361ba9
32714 F20110221_AAADQO xiong_h_Page_057.pro
17ee7c7711db0977a2b6849a6ef35b16
7172589fa8e4f1eee539ff7543fe1227e56597e7
1763 F20110221_AAADPZ xiong_h_Page_036.txt
395eac63fcbee3198b303aa1a92ead67
e1c9ad5c82793d019b5dcbf5cfcef99ecd376cb2
1780 F20110221_AAADRD xiong_h_Page_059.txt
8e5bcb60b66156ed5c3a1aac4685ce69
f7a2ed3c5df32cc6cce7d6dcbb668a8b9ceb5c9e
53657 F20110221_AAADQP xiong_h_Page_078.pro
96f70c3ccc85c08f67471fb86bfb25b0
b5a06f2c63c9fcf1462dae04b82c1a662b26d82d
21362 F20110221_AAADRE xiong_h_Page_008.pro
147a37dc0a43b8da1074d398fe432daa
9c85ece721c4d4a9e6d8f43dbf4503acb2480735
2147 F20110221_AAADQQ xiong_h_Page_078.txt
bfc11d0f72c675b27666569b386f096d
17fc6902e877b1f7d227162fadee50afc39b9a48
57316 F20110221_AAADRF xiong_h_Page_108.pro
1ba698b73703dabc7d2889cb51dbfbd2
7139bb9094e34747a4b2ecbe35e9deea617104de
76456 F20110221_AAADQR xiong_h_Page_005.jpg
8a518606513f6e75c7b2b4114b19b71c
67a16d52fc08d278c6a1f91de4a5069fffcc33f7
1732 F20110221_AAADRG xiong_h_Page_087.txt
053d12cb9792db22af7e84237335e74d
475fb332046a7597e48587a583bfebfdebca4340
1635 F20110221_AAADQS xiong_h_Page_031.txt
e59390eb69a80d3212f3319524fd0e17
c401fea547f14df851cccef49b11f20200a050d1
24070 F20110221_AAADRH xiong_h_Page_096.QC.jpg
39cf33824275167a36623b9ca543c6f2
ebcbfcd47baae42e97b02fd7cfd9567bfc144208
3885 F20110221_AAADRI xiong_h_Page_090thm.jpg
cb533a5a9f4fcb19ae766a186b49269e
dc049b086e1292abba183d106c43720a336b38e7
18254 F20110221_AAADQT xiong_h_Page_070.pro
be7d74090c4d9d34f4a7dd0b5a9db3ef
b295dace237b4a9923f39f4168c06178cad3d691
F20110221_AAADRJ xiong_h_Page_054.tif
148ad29aa16192a2c64b769888c89d58
b72db5d93be8afc44af5a5e91cbdc3ae8c13b9e3
2264 F20110221_AAADQU xiong_h_Page_067.txt
10d413e3a9f230f012fd05b4b63bea9f
13227ca7cf376f306203f4fde69c015454e28b76
16768 F20110221_AAADRK xiong_h_Page_035.QC.jpg
52e1e42ecba3b598eea7fe26afb37d23
dc53cfb07b46dcaccb3b28efad62bd5c7ceab3e0
15428 F20110221_AAADQV xiong_h_Page_053.QC.jpg
49596c607300791bd87ac2b586fda38e
9faf1ad226a9b0a0db9e5af7fcb7a2800c55754d
3131 F20110221_AAADRL xiong_h_Page_069thm.jpg
36c02ff9fd2e0b6ca28ee334c33b0771
25f6a76f5138918bba856f2d84cefb8d519ca2e3
19505 F20110221_AAADQW xiong_h_Page_081.QC.jpg
29d774600a471f950f7ed7c1c1df358a
78f2f220de30c478012437898109ffa41f25b711
32898 F20110221_AAADRM xiong_h_Page_098.jpg
2f0f76fcc17537a9968b0ab13db7022a
1641e6500ab20c28dffef93e6e118f1a7a691c36
841566 F20110221_AAADQX xiong_h_Page_063.jp2
de8eae9d9da9dc7538fe9a497bbae041
fa9634b461d0ed3d079a47ea98336abd893dc07d
6183 F20110221_AAADSA xiong_h_Page_111thm.jpg
7d09e5bc4812cbd7b648ddddd0b2b281
99009e4630ee5c3bda07bb634b11c8f492262f0d
F20110221_AAADRN xiong_h_Page_058.tif
1f3ca461209d081ed517d833a3057a93
bf81785f58df73b2e947249be44a30ed671e60ad
57635 F20110221_AAADQY xiong_h_Page_005.pro
2a96458c9c76f8ae0100d1bcf839b368
999d8345126415a3558ba0a535f457b6ddb778b3
52246 F20110221_AAADSB xiong_h_Page_057.jpg
d8b23c57c73c1bbd39760439d0b3e0d9
cf15db1a0a4ea33c70675ec4c59c8cde0b7e5a56
F20110221_AAADRO xiong_h_Page_112.jp2
8b3e1ce222ac74f00421305a6a267133
bb0bd960797394c6bec035437bdcb989327443a3
2262 F20110221_AAADQZ xiong_h_Page_004.txt
89d0b95704e48be2609bc260359eb70d
2fd779fba5f6805956a27c99857b26715809831f
32357 F20110221_AAADSC xiong_h_Page_003.pro
483ff520483c3fc5e7b9df6928575c6b
93a715d41850b67b9c3fd31d94c743d2f82db454
F20110221_AAADRP xiong_h_Page_109.tif
ca1b8d114b9638b82173422690d8c7b0
a5e2ba6f0ea8f84fd1c16978236324168dec96be
18055 F20110221_AAADSD xiong_h_Page_004.QC.jpg
cd099d3d2e30b4b24bffb17f783a943e
fc12745f5042dbcf11aae83688e483eba95202ff
681451 F20110221_AAADRQ xiong_h_Page_087.jp2
fb34d92cb4e513ac9634ddc53d1b3249
6a8b45705056097a004aa277b5175e9a49ec39cb
F20110221_AAADSE xiong_h_Page_042.tif
7c18836b453b1845ebd2609a73d248d1
ed602e12b44a321e1f948f6de760d9f2dcf5706c
26767 F20110221_AAADRR xiong_h_Page_071.QC.jpg
d6a1028ef7148c99e128e08d3c651b91
53a97ee5c638d5e804c7547ed8f91f51f0fcefe8
887147 F20110221_AAADSF xiong_h_Page_093.jp2
0b56aa96bdafbfe9b8e30a05cdaeb503
62c747576749a4356a9bd0e53836cd6cae0afb29
25770 F20110221_AAADRS xiong_h_Page_078.QC.jpg
8bfe9fc68e2d79ef8ccb97847c88718d
db76d6141d3d62e2e1bd6cd8651c5cc1af39c846
2245 F20110221_AAADSG xiong_h_Page_115thm.jpg
c681eb363496b533951bca16d7bd9c5e
592589b8adf4674b904fb45bd7f616f96d08bb12
50823 F20110221_AAADRT xiong_h_Page_004.pro
9d4e319e32f66ae1c3a0f87bc3da13f6
136929ca1571c667a18922f32b7b551bb96a7ef1
31518 F20110221_AAADSH xiong_h_Page_087.pro
b6308eeab036addb6bcd27fe431e22c3
e4b1fd8aa16a3f185a53b85f2a334123c01e3601
2960 F20110221_AAADSI xiong_h_Page_074thm.jpg
803b591d41537830c956e36e88035837
f21d4fe065cb63d7cbdfb6da55b750ec280cd3d0
1376 F20110221_AAADRU xiong_h_Page_103.txt
4a06f9db375429a16f8ad1c82d29f54e
af0be5df78ef5a8654ac0b61f643417233e4740d
89083 F20110221_AAADSJ xiong_h_Page_050.jpg
3576484c6a8702286c5b801bd4774f56
c23e7d1cbf188b8f650837d6bd88446264e8abe2
609 F20110221_AAADRV xiong_h_Page_006thm.jpg
1c32431500fb9bbc81f61aa1c738a95a
b2006ac271fcc8e82de1f7cf9bdd5a03905ffbbd
21250 F20110221_AAADSK xiong_h_Page_077.QC.jpg
75cef61940861bd4284460a6c7a900ec
c4ba3b29d73633d6bc405d99e213793a36004cbf
F20110221_AAADRW xiong_h_Page_030.tif
6f40d7b11a528d12cda85506fc26f818
88e599b5efb9ef619518eeb83a40b58514f73e41
863202 F20110221_AAADSL xiong_h_Page_051.jp2
87bd79fed1591a89311579be968acf39
eca5acd01948a6609f66fc0eb7d2dce9eab2dffc
610243 F20110221_AAADRX xiong_h_Page_034.jp2
06c21be381a8a813c84e8f7a8cae297a
633620ae051d265b675a6a8cd6a8d17731eea4d4
4447 F20110221_AAADTA xiong_h_Page_007thm.jpg
668527b02c619de66b3e1b3f7e63d0d3
10cdbc7b711a533322e68f78b697277bfaa1c685
63210 F20110221_AAADSM xiong_h_Page_045.jpg
8abe890b1877ff0d12ca240524a48f2e
db06ae2d8693bec203b9f044028b3f618ec822b0
2573 F20110221_AAADRY xiong_h_Page_042thm.jpg
3b87b16afd41e6e05e7b23e12c8342b4
7a7b0528f369332c8877f0faa49fd3bade9ca00c
2161 F20110221_AAADTB xiong_h_Page_041.txt
4c3f3f9528adf4409d368058317a0a88
31a02b796e022149295413dcd93cda55413b497f
21956 F20110221_AAADSN xiong_h_Page_001.jpg
6e1b5a5a0f2f6eaf19fc5760080de43f
51f31607f1aa0126dbbda49b0596ee1d0d8b684c
32334 F20110221_AAADTC xiong_h_Page_027.pro
c58e70032400466f322c9505c3dbabd0
5e38411b346c81ec84846c0499c6ca8939e2b1df
3932 F20110221_AAADSO xiong_h_Page_054thm.jpg
5a84db58b01477511ef01d3158c64d6f
903a7df2e08bf015875318fe2e3629de09cfb687
55826 F20110221_AAADRZ xiong_h_Page_022.pro
98f700cfefe67ea5703d1449ac926332
49aa6034480d50c2fbe2a5643a83db4fbfad07dd
16871 F20110221_AAADTD xiong_h_Page_107.jpg
e8b9f1d8ab1531f800d50a3c0ef768c5
6b764aa62a4f37fc9db8f6154f0a0b49a1a0feaa
17726 F20110221_AAADSP xiong_h_Page_056.QC.jpg
98bc13692b06c3aeb49f22a8e3dd03f2
2a9869d2bc07ab493cc5b9c0e9ba914074e4d751
F20110221_AAADTE xiong_h_Page_088.tif
7aa07c78fb51b5986c6ca7415be6618e
192e599aca7ff847b511a6808623acff4143d403
54200 F20110221_AAADSQ xiong_h_Page_091.jpg
35e2cfc249f8e2694a2b6b61df3f2c1f
b210c7c873d65350e76864882aeee69b981d8962
16096 F20110221_AAADTF xiong_h_Page_031.QC.jpg
44a7f38ddc773792028965369da02a7a
a4eac056f9ad3ab4b433ec338dad8821f5b585d7
1015550 F20110221_AAADSR xiong_h_Page_011.jp2
ff76fd60ed8bfb1de6a692837d4d7fda
794249812e4affe51eb507b95c9db808b273d0b1
22246 F20110221_AAADTG xiong_h_Page_016.QC.jpg
f284af73220a0314d3a8c220acfec98d
a7be49c6c54d1e727746b003cf9c39f9c6e3818c
F20110221_AAADSS xiong_h_Page_114.jp2
70d00edf880339c6b780cde4204656e7
91b43200e1a313cf60bc7a0e6fae7a8ae7f84066
397144 F20110221_AAADTH xiong_h_Page_008.jp2
9f6500b87cc1fc1157703fb4dd899204
27848cedeac418570c5809efdbe8363ff366af7d
F20110221_AAADST xiong_h_Page_079.txt
782f6c5691916c14a60dc7f27d0828d0
e06432a273b56f2c590d0b524b37f4ffbd5c0c70
1659 F20110221_AAADTI xiong_h_Page_019.txt
774ee793c6f07d8eb4e521f21ae1ffdf
2ee1e5a75e5b4cd467809ad999e9b6c9b72f0b5d
2318 F20110221_AAADSU xiong_h_Page_108.txt
5fd3b87278d7f1e033003e384af55236
f23f68d33ece8ce001a0538b0e30753f3fdd9e26
72597 F20110221_AAADTJ xiong_h_Page_011.jpg
d8cc57846fdbafad74e234d118848daf
a5a9161cd91f460ff0592cc9fc8456f9ec69bd73
61671 F20110221_AAADTK xiong_h_Page_063.jpg
2a811e2edec2e6285743912df1f8e351
5b83ac679194a91514c91691487d1c4222f6c19c
1738 F20110221_AAADSV xiong_h_Page_054.txt
2fb9f65644252322a5ef39867e7bdc4c
9e290f46bb2f840ae4b2d663d2370b7b1255aea3
4431 F20110221_AAADTL xiong_h_Page_056thm.jpg
6c7934f8f578eabfaf18ffc2d8a35057
cd3d2befafcefeb158aafb6aa2bec130240dc2bb
5729 F20110221_AAADSW xiong_h_Page_017thm.jpg
50af5d58867b8f402c3e384d3defc8eb
ee7538edad15d7bca78c107073b0a19bbf98937c
25699 F20110221_AAADTM xiong_h_Page_110.QC.jpg
806e147a1d569f1f9176ed128691bc75
9ffb7b1e0b3d8af1d1bb926b417e87267e1cdc17
21947 F20110221_AAADSX xiong_h_Page_040.QC.jpg
c697ca92cbc90bc74ca972d286f21fbe
ac6e64eb6e4c667ea2816aa5b40f9f2df6be37d8
17050 F20110221_AAADUA xiong_h_Page_098.pro
f37cf5841915e7fed0b4485ffa402de6
d76e1a3bfed5ed4c78fd194f23bb36c246e901bb
21019 F20110221_AAADTN xiong_h_Page_065.QC.jpg
671dfb21f9b8cb5d848dd4cb2b5b11d2
1eab1d082a516ba76eb093309d75b25311b6d5e5
F20110221_AAADSY xiong_h_Page_094.tif
3c818756bb429fb8b298022634d31381
8c0939225a6f1fb7c37eb86f996b8845d3eee927
52614 F20110221_AAADUB xiong_h_Page_089.jpg
4d9f13f8e3255f037c569770ac1bf43d
bde26bda6b3762f2930a46a176ca545c12cccf54
27135 F20110221_AAADTO xiong_h_Page_067.QC.jpg
97eb8e6054103669a12bc08494f8d36e
327c9fd0ebfed711c24f39e393233305327b84a9
203 F20110221_AAADSZ xiong_h_Page_102.txt
02c20f2d177a37180d9ccef177f73dd2
323e4561c7f5db0c01fc576ef02d10ff6f0320fd
4792 F20110221_AAADUC xiong_h_Page_075thm.jpg
33bd5ff7f060db4b6ea5eb50b7d29eb7
e7e5b0dd7ff6b63df8fbb4bb2e7d558386fb5fb2
3517 F20110221_AAADTP xiong_h_Page_099thm.jpg
f42520f5de881689646e2a0278d4cff2
bcb095da256918495c97c976116a259694715419
13592 F20110221_AAADUD xiong_h_Page_061.QC.jpg
227e56baac5f7228bb040b59e11856fe
26a71457179ded1d54753d49b03fe01131468b1d
45274 F20110221_AAADTQ xiong_h_Page_090.jpg
de67a3c5620c2cfb2c7aac2c3f828217
5e205daf4b2662359d268b487c35488593b31017
1549 F20110221_AAADUE xiong_h_Page_052.txt
553e817f8d205c03d9220314ba522908
f3d5efa1f58667b8f598cbf1ccce018ab3bdd91c
75616 F20110221_AAADTR xiong_h_Page_007.jpg
5174021dff9bd1d0fd5685c14e682be4
dd4f58c0ff571f3dc0a3acd4fde6d64d271c8f86
3964 F20110221_AAAEAA xiong_h_Page_101thm.jpg
38ff401d156753075b1b0301c2d93712
feb7c2536fdb28e741a1542e34d7f05b110949ba
13474 F20110221_AAADUF xiong_h_Page_069.pro
e9eeff419084d5d5e4c20ebb1efdf5e6
2d9512e9379c4405b8bfc5ac421cde759b3d6c1c
77212 F20110221_AAADTS xiong_h_Page_095.jpg
4455860bb99319f02d512c429367bdcb
d9d0ef7510a2c6c3d079e1bf656cb92e2f9a20c2
1608 F20110221_AAAEAB xiong_h_Page_035.txt
69a213804d20246a651a505e0f283a4c
220d75267a4896630cd2af407391d679f6edc3dd
48528 F20110221_AAADUG xiong_h_Page_053.jpg
c6caef2613491dc11d55c235e036c86f
9b76af01582ee1f68109b8cc9f4fd37ea458ed54
5904 F20110221_AAADTT xiong_h_Page_067thm.jpg
1a1928a7826f8b292277bcf31d3ff04a
17f525aaf17ee0b3af69adb8f7cf5e6f6c3ebbd0
41307 F20110221_AAADUH xiong_h_Page_085.jpg
dae0158ce6947b9d1fe3031bc8438823
4bb709297b60d37d9c3628a0049105b382e6a937
876927 F20110221_AAADTU xiong_h_Page_005.jp2
4e2f19a4f330f3ac6256d40af958a1f6
7548b500273df3c9b9b8e91d35f258ae8f112d52
96804 F20110221_AAAEAC xiong_h_Page_110.jpg
44cafef4978648c5ff92864c8d157d91
2b6969505e12b552182786e537e06a76831bd61b
737092 F20110221_AAADUI xiong_h_Page_094.jp2
35fbdf26f94eaba789e937eea0859052
b8c93b6b97d977a8d7e6cbb48cf99c61468366f8
F20110221_AAADTV xiong_h_Page_112.tif
d6706728c9343e6d2a348f3734ba3811
2553f0c554d8084847837d268703d311faf7682e
45197 F20110221_AAAEAD xiong_h_Page_026.pro
4fad93effcb1f8f0dee77753bf4a8827
6e896456e7c3a82f64e358c3f4c4513106d61231
35318 F20110221_AAADUJ xiong_h_Page_032.jpg
2bc88fc5a5d4e7da7a3a8c126d85f049
17fd11e897551beb6b53a9d683176c5627740fdb
F20110221_AAAEAE xiong_h_Page_014.tif
620faee20c2efa5f9cd148e0816ea339
c25b73dad6ca01200ca4ddf40fc4e1af59c60a80
3727 F20110221_AAADUK xiong_h_Page_028thm.jpg
fd34b71042b65b778a93ae38376101c2
21d76da276eaff51aa961ef1caac8b86e06666b8
8710 F20110221_AAADTW xiong_h_Page_107.pro
d9e5a147fc997f1873edfca725e3a9bd
aa12749ba0c3a54895f34fff8d2c5623032047dd
37768 F20110221_AAAEAF xiong_h_Page_045.pro
d0a76c8ddad7b574defc6b9519e539b2
0ff209d95fa57d1ce08257ff4699a99ea9c8e311
5165 F20110221_AAADUL xiong_h_Page_048thm.jpg
1d25ce9db1c44cacc90278be51fb9d52
f29db43504ecc3969d03dac9cca98ad3470f87a5
8229 F20110221_AAADTX xiong_h_Page_069.QC.jpg
70b2efd838b89c51b14c62669d5ed160
6e20a990900940a83fbd8005295a7015c6feb29f
11528 F20110221_AAAEAG xiong_h_Page_046.pro
283a3d3bc9508eb5b8eb56afb74f98cc
b18b21fed549585cbcaf70a925c2139d051c7a0d
54060 F20110221_AAADVA xiong_h_Page_056.jpg
61265345380b1ab9470d5026c05ca2ba
8cee69bc4423ed1b578fa5aaff3ca8b2b61a6b7f
1918 F20110221_AAADUM xiong_h_Page_088.txt
a32a71b8db50d0663fd564d5985fcd0b
70a031a68e3279eb8f0e76cf7954040f6f81f901
248038 F20110221_AAADTY xiong_h_Page_070.jp2
8f797e47e5a3a3bc6f597debac900b0c
f7c002f6d9b04646f509e8916eb1cf8de39964d0
25407 F20110221_AAAEAH xiong_h_Page_085.pro
d13b7a3249ffeb6395c35980a9f71589
940dc0f7f2007cdd93e3bda663ec8fb1fb5b7402
21712 F20110221_AAADVB xiong_h_Page_026.QC.jpg
4322219a863d6d52bd8573548dda5699
8f99d6c4f429ff8207eb035538e3db819ce9832c
16066 F20110221_AAADUN xiong_h_Page_091.QC.jpg
3264f994bb00fb27ee241a2db7e19e71
dd4b501dfbf3f6fff44a9a8fb94c38a225cf1104
52867 F20110221_AAADTZ xiong_h_Page_003.jpg
ce2add551f265b6291e1b508ce455725
16aabd27838799a97d9fd6071c0a98a39bda36ae
592797 F20110221_AAAEAI xiong_h_Page_086.jp2
679e962c6097393764b283d3fc073844
98d1ca92cc22b68469bf240c40273d67e4b75e6a
50799 F20110221_AAADVC xiong_h_Page_048.pro
17266298486d607de8cb2e8401b4e632
66cb2866021b7aeaf7d68cd0d8935ac3d7650ec0
4059 F20110221_AAADUO xiong_h_Page_052thm.jpg
49eb36992597ad6b7c059d157d4d4f3a
1df6ed94dbe08943f1d5136d419428a1510d52dc
2593 F20110221_AAAEAJ xiong_h_Page_043thm.jpg
12417d4fe19c70da0c71b7454e360264
ad4d6f32f8792f7c09e52f2606ad629cd49052fc
67298 F20110221_AAADVD xiong_h_Page_004.jpg
8c31780383a913966d30ae0b4502060e
bee30e5b4389c12069ac64a2d870848182274991
F20110221_AAADUP xiong_h_Page_052.tif
a2139f7a72f3f7f556bff750b3fa2471
17a85a2de920f508ea04d2053a2d9edc0da32c6b
28100 F20110221_AAAEAK xiong_h_Page_089.pro
12f505a0076c5f1d7538bc589ff639b7
bdf83e2a34fabfada6bfc03f4faa52854db31925
9619 F20110221_AAADVE xiong_h_Page_115.QC.jpg
ca56f676041ee8fbdb7333b166f86f07
0e155b051b1acfbf1359081a78996f5c3e20e8b1
F20110221_AAADUQ xiong_h_Page_073.tif
967a58b5ec17de48df5b5aac6a148198
1aff9f71da806328c92d3e09fbf75410b00e9588
58440 F20110221_AAAEAL xiong_h_Page_055.jpg
06241f698ad1217ddde9e8785285ea56
7321fcce27885f18b0e27420f1c585540af998d9
494933 F20110221_AAADVF xiong_h_Page_058.jp2
23a72e84a95af1a0f993be44ca91e5e8
4a33ba1bd5318818ec7b03d9e4df73304a882fc1
14489 F20110221_AAADUR xiong_h_Page_105.QC.jpg
3953533aa424f53d6f49321e9c51f32f
d3ea715b1d726206cb80d338583e9f127bd873f8
F20110221_AAAEBA xiong_h_Page_103.tif
a0ded1075c3b8cac67584f8d43c334d3
fd9d6a34b136b1c899438fcef118c85572126bc7
4852 F20110221_AAAEAM xiong_h_Page_093thm.jpg
645a65569d4f780d564525086b6e6bb4
62e2f2679e64b181990f748370fb8eb162342aa5
3719 F20110221_AAADVG xiong_h_Page_002.jpg
e85aca65a766b747fd2b7e45bd8a02e1
79159e5958fa9dde6cada95ee0842449bc300572
1935 F20110221_AAADUS xiong_h_Page_025.txt
b9117b8e129d83c53a9e846d9fec6d4c
014f10e9444555984f658c1f2bbcf93d2bf53fb5
F20110221_AAAEBB xiong_h_Page_047thm.jpg
294b21566a8165e67a369cec2b4c93f0
8b9ee6ea9c9701afe7445bcf9108ea2221847e7e
F20110221_AAAEAN xiong_h_Page_031.tif
f78f3364a71cce92d5912f5783aac4ff
a3f887b8b72d4bcc64819cccd98c1ffd791a6bf4
2162 F20110221_AAADVH xiong_h_Page_070.txt
172f8ba416e7c3e6fdd5ad0a61d0e38d
e45dd3957dab70a0a3ea761fd2cea8088d4b6e25
1051927 F20110221_AAADUT xiong_h_Page_110.jp2
1c66a865c4ce13920497f7307e08c50f
61a436733fe9bfe64caa8018332e9bde07c39621
46458 F20110221_AAAEBC xiong_h_Page_028.jpg
a032607f9fb9f5819f7e946b160f9c59
159a1ee55ee36c152fee28b7edd130e6999fc14a
104964 F20110221_AAAEAO xiong_h_Page_112.jpg
58c8d39ec454d619e7a2cf28e88ab810
7e7c5d8b043830256f1ddba0c4054a9ef15f8e94
53924 F20110221_AAADVI xiong_h_Page_035.jpg
757cd28bcf0c87f70d6e56c10131140a
e1d7ad40b68dadd5525e4510902ad6dd0676de73
F20110221_AAADUU xiong_h_Page_072.tif
0330bec15481548cd29c06d208f0350c
38d83cc858a4f61f7bef91225b3c3dea814b6ba5
5609 F20110221_AAAEAP xiong_h_Page_020thm.jpg
b9bc525f56298a7b8478b7121a6409df
58b30a099c8ccc789d63d533b5cc23ecb02b1895
57874 F20110221_AAADVJ xiong_h_Page_094.jpg
1879b4334c3bff56b7f343edf2bfbd55
05648af7d09bc0aeedb61d2c07e6e4e5ac78ee44
108965 F20110221_AAADUV xiong_h_Page_111.jpg
bc6378a6f13c1d48380d5acfab3a9ae6
920f091e9dca0dff7cb5ba567ecf5c36c50f6f92
45598 F20110221_AAAEBD xiong_h_Page_101.jpg
8cb10a0a4a11da7a60c07b9d252809e7
c3fc2de09796206453715b217284ebcc2da5d5d8
46078 F20110221_AAAEAQ xiong_h_Page_011.pro
d15a736b7b6f428287ba5609061633a7
beffb4d4e4af2e95cc3c2f423ddfedd4e08daf1f
9413 F20110221_AAADVK xiong_h_Page_042.QC.jpg
1fa3487c784a465badf50a9e7411d87d
45a01fc4f9e6bbbfbcdab51d8c2126ebdb847d72
37540 F20110221_AAADUW xiong_h_Page_082.jpg
bc9e46400da2f6ec687e834d89eaed71
7b0efbaee4d6387aa22ae211740f15654ff3651c
3948 F20110221_AAAEBE xiong_h_Page_034thm.jpg
3d3d5f21e6d14c0dea499d575269123d
528b6c7b377005dcbe035a800ae6eeca6c948208
37742 F20110221_AAAEAR xiong_h_Page_038.pro
8a907788b19dec8cef10e49600fb743c
1980f51f15802c3e48104ffa0bd4d211d243fc4f
4457 F20110221_AAADVL xiong_h_Page_094thm.jpg
b75ffdbddbb455071ff453f7c6ec5148
4feea4e7a06095b4cfad85cf252aa51624e93052
33525 F20110221_AAAEBF xiong_h_Page_019.pro
80f6dcd8f8d5678d6a8afde99aa770e7
dd27de0234785a27a36d4f0d2c7d7cd5ca6afea3
F20110221_AAADWA xiong_h_Page_015.tif
edcf1fdbf91c9a29674c8850fe62d520
90c9b5f7d9f1b8b47a2a2744e67cdea9419e3e05
11974 F20110221_AAAEAS xiong_h_Page_047.QC.jpg
77163552f9876f9a9e1a46d880923ed3
62d20cc5562232343422bd2d1d00963c44cfed3d
F20110221_AAADVM xiong_h_Page_071.jp2
c76190af1884478e356416786e93ba0f
cbd4aacc0a17a1bc207df358b2fd5a373a168700
F20110221_AAADUX xiong_h_Page_106.tif
5b6ef971d116e049ffda70e03f71cc42
58ac5e9105fc79cafd6d97e6134c3343898fa718
28106 F20110221_AAAEBG xiong_h_Page_073.jpg
ff7a1508d1b87a6e4f07dd3ae37c6909
986480d0062ca284410bb6dfbae0f94e8929087d
22927 F20110221_AAADWB xiong_h_Page_047.pro
9472d24bae4ceb6199c5833674f500ed
f729c9be2aa7cdf30c5d943f9e31c38e3224380d
604 F20110221_AAAEAT xiong_h_Page_106.txt
893c4c9fd9abf16cec96d14e7e742ebd
00fe60213ea29945eda093154a434b90c1854c4a
49115 F20110221_AAADVN xiong_h_Page_010.jpg
199259e9facceeab1f8f792c38e0f055
2a5174be8cafcf26db0193a18febed4e604548d5
627340 F20110221_AAADUY xiong_h_Page_052.jp2
a7f3f1b811b5bb8dd1237167de35849e
8d5744074a0b5df4caab6f85f6820e644a8d01e4
F20110221_AAAEBH xiong_h_Page_011.tif
53d8be351e545ea6766736591240097f
4e2610f0f0ad7d2f624075047cb7e87a81b8af28
1051975 F20110221_AAADWC xiong_h_Page_013.jp2
f19eee8cb784d9801c25fc6fe1f9e795
8128bbdcb04beec67969c1a4d78ebea500f28c30
22681 F20110221_AAAEAU xiong_h_Page_103.pro
cdd3192767e0359da17dc4fb075ba467
c3f87c7dbc593b74abb7044b49f4a6a2a646eb6b
1174 F20110221_AAADVO xiong_h_Page_032.txt
02c25bb150cde72f250c7f842bb55d06
1e7ac9348ac78d377ee5421d463fab9d9e993313
7966 F20110221_AAADUZ xiong_h_Page_070.QC.jpg
639564096b75a4a602e7d680fde1d401
af8b6a7c98fbc50bc31db1cdc056bf042ca5dbee
16198 F20110221_AAAEBI xiong_h_Page_057.QC.jpg
4032bb5f2a1daa9217f793138559dce9
c49c772111a9c725ceb890e4a0363e004b9b4b4a
1908 F20110221_AAADWD xiong_h_Page_011.txt
0a2680987a6e5ef6850efbdb1689cf05
bf7440ce3ba1f62175d47e2a474f2aed341a9acd
5573 F20110221_AAAEAV xiong_h_Page_100.QC.jpg
e6d7ce49b5a68a0d3bd918b78e9d6160
a48f3d86ef6434197847cbcf18459b3aa80862e0
48848 F20110221_AAADVP xiong_h_Page_096.pro
8e08a177e3e5674e0b0dc8a52f401d28
f7d661ad953219b21202cde47cc407d4718f0cb6
1473 F20110221_AAAEBJ xiong_h_Page_093.txt
596841b7d8502a12cb9e1b98f9af8491
a36a3de2877a58bb15fae7e3300daf1beb85287b
53208 F20110221_AAADWE xiong_h_Page_007.pro
67fa44d1c1e311c1797af5bf3606986c
2d2751611507481d475737e4f3b888aefaa20219
11624 F20110221_AAAEAW xiong_h_Page_083.QC.jpg
4e51f3b427fbe5019d34770aa754694e
9d75705b8a6d6897380fe9df64cc1bbfffce522a
236142 F20110221_AAADVQ xiong_h_Page_001.jp2
ddd80403baaf031c8a6106e448e7ddb2
b336f8564c86a001b2b814624638aad7da37ce68
10193 F20110221_AAAEBK xiong_h_Page_098.QC.jpg
bbdea61398025768507834b282fde624
d61bc3bff191e0baed72b4bb52c686fa392c191d
50449 F20110221_AAADWF xiong_h_Page_020.pro
fcd233846f1214e0d385f17228534349
a8af128cde8da977a22d4f7355f0da861fd8851a
467611 F20110221_AAAEAX xiong_h_Page_083.jp2
3146679f87a98957622769b6c051b990
bcbb5a6b5903cdd3afbb350b1d64f69ead5071d4
19335 F20110221_AAADVR xiong_h_Page_044.QC.jpg
390f915a911601f4bc30dda2a89c3bca
48958094bd8b063bf5efa1e68c6bcef39e678944
F20110221_AAAECA xiong_h_Page_041.jp2
4acb6640791515c8be47e8ff04a04fa2
f3cd2b3dc262d74eeb1f3b2fd352e80fdb0fcfae
F20110221_AAAEBL xiong_h_Page_053.tif
ca7690401995fc3176bb7c10a4b5c4ca
51bf6c04fc4f022b19d526c515b01d0752a36d77
14927 F20110221_AAADWG xiong_h_Page_054.QC.jpg
853fb6e19d7b4290ee2cd96784f3c507
b25c4ac24dbfd0f2996fb6058c6daba704dd9a17
F20110221_AAAEAY xiong_h_Page_027.tif
b8c1d803e1add7bb00fcb1ddc3f821f2
7d51b3fec787ecadfa5814eae3bb6ae03775791b
1256 F20110221_AAADVS xiong_h_Page_064.txt
a90fc5be813064e01462dd1162b3d41e
4fdeff3884d66f29a78320fb2c5383573246320a
28255 F20110221_AAAECB xiong_h_Page_054.pro
f4b50293818b85d937b2b68bb0e45ca1
fbd97ecb7f2f56eefbb384696a869349a9d2431a
70266 F20110221_AAAEBM xiong_h_Page_111.pro
d12bfc5dec41efef055a27d12122ca2c
84cb98b984aa35a990af30f84794e570c64a0273
755804 F20110221_AAADWH xiong_h_Page_055.jp2
b3c3ae62d9a7c02dcb6630c8a35c09ce
09151b3327398674f72bfc682d0a05db18b10ce0
55914 F20110221_AAAEAZ xiong_h_Page_023.pro
b4731e8494cc70e6afd182a372ad69f4
0bb79e847d728d92a56dfb7bd4ce8f70d3fd80c3
18415 F20110221_AAADVT xiong_h_Page_038.QC.jpg
9beaf0b9d3a868ecb788886908e19a0f
0b2b34334755c415db7a144faf5917028fbbf262
24012 F20110221_AAAECC xiong_h_Page_048.QC.jpg
052f4ced75b89cecbd8d9ce9d9fe73c4
84f8de474b46276fda4a8b8724db45a1bff12fc6
55157 F20110221_AAAEBN xiong_h_Page_024.pro
45f57ef2753daa26279e5992952a2fc6
5a0d8cae9e34c662b2e29d4029e662887d54a8e5
27980 F20110221_AAADWI xiong_h_Page_002.jp2
cc0a7c6c40a261631a2579c27127e2d2
4ced502c14fec74e55ce05aa5c95e0d64766b8d1
31776 F20110221_AAADVU xiong_h_Page_115.jpg
8f7b4ec10a094deace01bf9b3e96e09b
987a1248848feb0be356763fd5dafd3e79ad76cb
1716 F20110221_AAAECD xiong_h_Page_086.txt
00ae1cd6f0f9671d242da1b4eb6d5a93
a052247a8b217afed6d3089b5c48539b5acee799
1051971 F20110221_AAAEBO xiong_h_Page_021.jp2
7ee772346c0bae5d1fdea2e29a826726
6dda52203215188fb7887b0d1aca312b02a3ea52
F20110221_AAADWJ xiong_h_Page_070.tif
f969d5dc973d5df0c9a393912a3959a2
81c287e73166f1984168516ebe6f07d72260dc58
42405 F20110221_AAADVV xiong_h_Page_015.pro
453a632448410d7f8658c42f3cf52a25
e8e2379535e8b7d94faa8dd2f2cffff42912a214
F20110221_AAAEBP xiong_h_Page_102.tif
acb64ae194918f66a723d80deee2acee
cf9dd645b3307c6b914a55bbbc48c0139264b997
1682 F20110221_AAADWK xiong_h_Page_100thm.jpg
a65a43f7c19412e098915063f0bc67fa
89c197053f8e1d8249507198a1c5ba3f445f6272
46743 F20110221_AAADVW xiong_h_Page_030.jpg
2a7388f60eb46560375442eb93638485
a038c959f8d42e529952c7c32bb71ad98d31cae6
98 F20110221_AAAECE xiong_h_Page_074.txt
4a416104ff1110ca1ec31130c5279dfb
c29437117cc33ffc621c263750a96bb2a79524cc
4244 F20110221_AAAEBQ xiong_h_Page_091thm.jpg
c98a59bd1a6bfd5a09ffb2341b178c54
c135fdee68f152044ae9ef14bfb57a1da4b4ea3f
668223 F20110221_AAADWL xiong_h_Page_033.jp2
edb377a7c456e61a79cd223247395c2d
a84a332e8832d0d49d83f8a3d1afed3ba013b904
46517 F20110221_AAADVX xiong_h_Page_099.jpg
807c2be06cbb5d85ae05f7afa9dc015d
929041691f947bc07b2e1eac60adf3ff80688198
536560 F20110221_AAAECF xiong_h_Page_029.jp2
77321289e30693554308f6620a17da5d
f16eaf0903c3e4345dd5392e1da54482955c1d7b
F20110221_AAAEBR xiong_h_Page_024.jp2
c4fa475ab677fe6b3da68ece55ec80a6
35fafbae323d5aea9fdd88cc0f37c20e32f46178
72642 F20110221_AAADWM xiong_h_Page_016.jpg
b57cffffcc83ea4e62689e585496b764
6f881760a6271c0586a9cfc2c48e29412af16b60
2051 F20110221_AAAECG xiong_h_Page_008thm.jpg
a9739f8f91b07b4eee18d097212cdd15
507ac0aea4a61aa461f7d613cf8a57f8f5e5a611
1478 F20110221_AAADXA xiong_h_Page_027.txt
5de304871a93ae091b4876532ebc0b3c
fe74cec483c365431f43f1d90fdf270099bc6d9f
34080 F20110221_AAAEBS xiong_h_Page_068.jpg
d5ae370ea21eae67f934ab77c69d243c
cef0b67cd9d097c3814243758eb367b573ab561f
3973 F20110221_AAADWN xiong_h_Page_030thm.jpg
cb04a5830bc6572aecac98e745771b1e
ec2ffe80020031479e578cf0230bc8e64fc08eb7
186309 F20110221_AAADVY xiong_h_Page_076.jp2
5238976a09a90fbfe6fd484ee6f1c7f5
346cf0c6315de7f0c22afc461f703f11d1375568
5893 F20110221_AAAECH xiong_h_Page_113thm.jpg
fa84da3a8d9cc34d2f162014d15161a4
38a1625c8bec2bcd54896e332b5cc01c675a7df7
866453 F20110221_AAADXB xiong_h_Page_037.jp2
cecc82b867173d7da298b4afc58a37fa
e528470c064b8294d6e0ce31515adf65dcec8ff0
271571 F20110221_AAAEBT xiong_h_Page_042.jp2
bbd3457697f29c3568d73b164da2b654
6e6d32221d9b3efabd329e0b88ed50cf1b4b4194
81202 F20110221_AAADWO xiong_h_Page_048.jpg
44dab8c2c1210f85f8d59b85ac8af4be
c724d0b08e3799664d1157ec06bb91ee076e7b7c
12630 F20110221_AAADVZ xiong_h_Page_029.QC.jpg
66935f6d993d54c9afd7e76518ec72a2
64b10ed3b9a258b5d261e5be79c286d8cc9fe9c5
11740 F20110221_AAAECI xiong_h_Page_082.QC.jpg
01c250767d38f62d4ed25dfe78226a35
eb8d58a6aebec971d1df9a7f60bdd0123fe75170
432 F20110221_AAADXC xiong_h_Page_001.txt
6e918d6f3c1fb2aae17c19614b45e27a
bddf08b84ba3168268a64da16138f2837e75900d
25610 F20110221_AAAEBU xiong_h_Page_024.QC.jpg
3c3619bba5f4034cd9950cee03a0ef1c
62c3a49911bd7976a961aa90ca69312877e18601
626316 F20110221_AAADWP xiong_h_Page_090.jp2
2195da0f941c2ea1d1f07e470677982a
61da04bed1ea09e7cc257ef67546b5804e7467fb
F20110221_AAAECJ xiong_h_Page_032.tif
2b05b3a41e602d33c6e7a8ee6389e0d1
66ea86811b762f5824a7c13d2c31da59d1a3c1da
5168 F20110221_AAADXD xiong_h_Page_097thm.jpg
6676545eaf2527ba4aed5a8c88e1a645
6ea459ec8490b8c2b5138f70478cce6d34589f55
2172 F20110221_AAAEBV xiong_h_Page_024.txt
a88a23e3863cf60dcf86ab31c794e615
09844283de500ff881676fc44c9a42b25cc496f4
70603 F20110221_AAADWQ xiong_h_Page_040.jpg
474723499fc90fc8ecba6f6afbc49d2e
7f9cbdb9b301c0c910ed092c673ade7c3c95abfd
803391 F20110221_AAAECK xiong_h_Page_088.jp2
9b21b88463034f968f0edb5e79d60bd7
49c1a259fa1e66e0466e3c9f34c5c51e4e654b75
90952 F20110221_AAADXE xiong_h_Page_067.jpg
2459de9c8dad2f34ae08810e0b0c7a6c
34403537acc78428ac650a1f31399fa482ddfd58
52224 F20110221_AAAEBW xiong_h_Page_087.jpg
a841534131814c6d6d663292f25a5037
28c4bd109efa45f63aad9de7d03c45a30752969d
63121 F20110221_AAADWR xiong_h_Page_051.jpg
15c3aa4a79103a06945bcfc08696327a
b6083b5b4dac537b0555ce728b91ad6b2054cf5b
2224 F20110221_AAAEDA xiong_h_Page_023.txt
d57450ca8fdfc3f5fd8f4781a047ebb2
6382295cff46f2d69a555a06051608438af44d0a
21774 F20110221_AAAECL xiong_h_Page_083.pro
e86ccb37fb3c2b5a947900ce4c38590b
2219522c379623ea9a54cbe926c3abd6ffd72a7c
F20110221_AAADXF xiong_h_Page_049.tif
52a3a66cacd9f7c98400fe7f5202c4eb
54b361163a4202752f5886d35bee00f51a25be96
1051959 F20110221_AAAEBX xiong_h_Page_048.jp2
c4a7a54c3390e3a81985d8ba2d5e304a
aad9384bb2120815077f313fd2e0932efcd12c42
3047 F20110221_AAADWS xiong_h_Page_098thm.jpg
3be05f79a042cf1927f3bbee1c9195c4
7ad3a1d79b0138c1c85d0020e92f84349f221d7c
25171 F20110221_AAAEDB xiong_h_Page_029.pro
9c962602038b040ab2f3d14c273bb258
53aa0f7dec68f31f671879d95d6a762e65e00f40
48383 F20110221_AAAECM xiong_h_Page_052.jpg
631bdade3e16b2fdb06efbf5c9889176
05d8f602320db0c10a9a8653dd7833b3415fe4ce
5111 F20110221_AAADXG xiong_h_Page_018thm.jpg
0adfa206f66fe91477547ca1c26c40ef
077b0e6b5a502ffb70047f8220797ca6a50c04ed
34387 F20110221_AAAEBY xiong_h_Page_075.pro
37661fc7301cf60bcfddb533faca0a5e
9b96b3aa46379261b7158b7c8e05579800ce438d
F20110221_AAADWT xiong_h_Page_021.tif
10c057b1ebf559ae9a7a0c4cb1737e02
b92a50e56114bce8c5d1d074099cce22af1f0ea3
2141 F20110221_AAAEDC xiong_h_Page_049.txt
9e7bf7554d7861bd1f8c4987deeadbfa
3c1b6969126e0b89a3679da542e6d0c3c7b630c4
738576 F20110221_AAAECN xiong_h_Page_019.jp2
197ccfe88dccbd523956992ce4d5c8ab
a44acc4bd001a8d77b368190c2c8c88552ccaed6
4449 F20110221_AAADXH xiong_h_Page_015thm.jpg
34686554b9fd26ad6078d30989f1f4c4
d8c1c334f2e605bf54f3d5081378010e3d8b7dfa
18528 F20110221_AAAEBZ xiong_h_Page_063.QC.jpg
b117877c70b11008d0a59d30e24ed9f4
445edcd70aa267338f28565551d252050fb6e374
3348 F20110221_AAADWU xiong_h_Page_010thm.jpg
4bc1d056342e31fa8ff8aa106b225fcb
f36d8e0af2a6a360486c0c02fd6ede5c4c1441ca
1891 F20110221_AAAEDD xiong_h_Page_076thm.jpg
272ffd2ac6841e79c4fffc1a3ebb1e76
bd44e9ac72207f07933189e3c86db7e4c7c032a3
58920 F20110221_AAAECO xiong_h_Page_013.pro
b90cfc402cafcef5213119fc065e1f4c
f27a3405fc26e7465fddf6ee41f140ca49a347db
33194 F20110221_AAADXI xiong_h_Page_031.pro
1c38de59c230181ed9d8298f1d682517
65050c4ed4c2f0c315a6486dc5800e340060e9c1
31005 F20110221_AAADWV xiong_h_Page_105.pro
b0bbd9170299260a1dba6cd22ddce5f5
d87cc0d499950dbc89717d3bf4692076839980a0
5800 F20110221_AAAEDE xiong_h_Page_001.QC.jpg
40b1776f5da81bc405740d511b995f3b
496e01b56a471d8cd5964f202869b4365de4122e
F20110221_AAAECP xiong_h_Page_099.tif
a11ce69d73f7731ebbca7eff9accb0a0
dbee859885fb9eb2d96f905c479be65aada840d8
5001 F20110221_AAADXJ xiong_h_Page_065thm.jpg
d526b67b2b75719f48d95f0e3417c420
5126b0464691f261f6f12a9498c7570738173cb8
F20110221_AAADWW xiong_h_Page_057.tif
615706ae9868de59413ec1e7c57920e4
7d91c04ab989bf9bfec72f864b55f52339702e52
4175 F20110221_AAAECQ xiong_h_Page_084thm.jpg
9dfd4f76317911751b25fadd3b2e251e
e90de2ef9b4234773ac48d90e74e168c02ff9a37
F20110221_AAADXK xiong_h_Page_098.tif
32a52784f2d2d50efabe2c3752cc8f4d
9a331e51e8ceffbcd9a12bfc4d7f97643ec17b9c
605124 F20110221_AAAEDF xiong_h_Page_101.jp2
b94e1c53c63acd545080015185e9337c
30dc856116ed2279c9680ee4ae52cabac83b1266
635 F20110221_AAAECR xiong_h_Page_068.txt
eac82829553c0a9fb0ce63c197f50dfd
993434d54ed2172e14ea530deb0cdc0ff69ba1ac
F20110221_AAADXL xiong_h_Page_074.tif
bdd9f76d048fdd4e65657da4a0b76d6a
632e8fb7d802035e142ea2946d172496de765b8d
1228 F20110221_AAADWX xiong_h_Page_089.txt
c169e3a99f3bcc6b6a2924eebffa4416
2f10b3693d5e6687b7c473f3b11d2a9fa1003128
F20110221_AAAEDG xiong_h_Page_066.tif
2ceeb71d72834a3174f33b976e2f807e
6eb03b9f338790c07c0f17807ac765e69ea25d4e
3684 F20110221_AAADYA xiong_h_Page_104.QC.jpg
34049b8ae256114a131f171aabe20c29
29d97e87207ad050a2629bef219eed8c1a481511
2137 F20110221_AAAECS xiong_h_Page_006.QC.jpg
4d48e85f8fae5fce755a81f858aea5e5
c06c8c7e7f900367a902a6617fcb08c5dd67c392
1340 F20110221_AAADXM xiong_h_Page_003.txt
bc444380b5264e67143d6ab6d225666a
48878e9a702bd3dbab036eeb2111c6300be35e3f
45425 F20110221_AAADWY xiong_h_Page_086.jpg
0bc1a02d55f932114e845833c0fdbb35
375e4ca7ae6713555e59be3855deb7bd68c89b85
1476 F20110221_AAAEDH xiong_h_Page_040.txt
2fd5d838a13cf38900aef49e3b15752b
b67c9718a742966f988b2990051b5a6ca9c8367c
604081 F20110221_AAADYB xiong_h_Page_099.jp2
c62b188186a4065abb400f6673176dd1
c3cceba854db079c48bdf898624f857eec48459e
64931 F20110221_AAAECT xiong_h_Page_109.pro
435517e564978ef9d69eef0d3fda1a58
b4ef0f1bac84fd97779fa4873dc6f1bf8a157377
F20110221_AAADXN xiong_h_Page_065.tif
3a2715fcefff2e2ec762e846766d2932
f09a191c973bfde7ed47b1b795f9d259361eaf24
401246 F20110221_AAAEDI xiong_h_Page_072.jp2
f97229e3b2bf247d735cc2b1ab95f38f
729d26bd75a5cb9143decfbd2a6c3dc25b33a0d4
F20110221_AAADYC xiong_h_Page_046.txt
c9eb69d3c911f9afe1bb147a0bed017d
0e8736a6ede1992fc8d35f5ae7f5c72521937500
6016 F20110221_AAAECU xiong_h_Page_072.pro
c17e2a90d97126af71e8cb812bae5cbd
e5c1aa886d86f0a13e93ea270f09d1e6483419d2
41999 F20110221_AAADXO xiong_h_Page_029.jpg
7613453cbca00f1ceee3c3a4d0c9f4c0
8bbc8b56e739cb658f6c138bc950001a07d6bdd2
F20110221_AAADWZ xiong_h_Page_097.tif
804668a93182c498b0e6671525cb873a
77b932ed2cc07e9b3318f0e52504d0ce4e1ea414
3276 F20110221_AAAEDJ xiong_h_Page_032thm.jpg
ec0775a55c742c6fea418d420995abbd
080d349ccab4dc1846ee72c89363adb4a79deb4e
526925 F20110221_AAADYD xiong_h_Page_047.jp2
0c53875280359414423cd988250d88f8
79d2a4c4ad33192aba7cc2da6162f595cd4fd61f
9210 F20110221_AAAECV xiong_h_Page_066.QC.jpg
23c6e8417830057ae7c723a597444142
2e2370bff976993f2f75e47abd41e31565d3c64e
1381 F20110221_AAADXP xiong_h_Page_039.txt
4be53dd25021005437dabf05c53975bb
1d4739e8631d2610696e9cc106e1af53699a24c9
46425 F20110221_AAAEDK xiong_h_Page_105.jpg
821de2a7126943cbcc5d16d71faa99bd
cb9275c06161e81f99948d86450bdc9b1b16a1ed
287 F20110221_AAADYE xiong_h_Page_104.txt
3c4e3a4369fa0b3f6664fedf13133ffb
7ee64e10b3594bcba234ecaeade1e8a9e5a87220
F20110221_AAAECW xiong_h_Page_043.tif
a9cc39f29ed1067d2073b915ace05848
7ea0be23a310b993bb921669a96d243f65e74c35
11398 F20110221_AAADXQ xiong_h_Page_072.QC.jpg
cbd2c1f476da3e3d964c03f2a7e14641
6334e678d90444a292055401551940c8b49f9ae3
F20110221_AAAEDL xiong_h_Page_061.tif
77e74b653e22329b7905dde5a9975a7a
dad80458bc5b675b805d84cf627861bb02ab554a
F20110221_AAADYF xiong_h_Page_050.jp2
dca98ac3dd9840f8e1b9228837265297
5a136c33e144f82f9f5bee85c9bd80c3e3634d47
1865 F20110221_AAAECX xiong_h_Page_094.txt
9749069a140108d89c11487542954d14
f9606a8eb29457ef5d39acce6e62f219a7c3b305
512 F20110221_AAADXR xiong_h_Page_107.txt
0491e1df1fd6445c538ac10b971b6708
7d7ea40eb20237b9c16ca013658630f4db1cfcde
15847 F20110221_AAAEDM xiong_h_Page_087.QC.jpg
ff828db028048d11e15a6ef13463642c
3a9049b4e42f191d06e1b408f19967dc9e60d035
F20110221_AAADYG xiong_h_Page_105.tif
441bd512ac396b29a1796958b9b80fdd
23ada720eca992a473232548cdeb79df0c4bf8a5
F20110221_AAAECY xiong_h_Page_101.tif
47b26c50b3337045ccbf49c91b5aa970
f3a7af2d250a80e07b9becb552b0f4140da404e0
49791 F20110221_AAADXS xiong_h_Page_084.jpg
c6b8d3c15cdb66fc2359b5a51e21e612
d7413fe73ebca720d0af5fe5f76a567184a3e9d4
87194 F20110221_AAAEDN xiong_h_Page_022.jpg
3a052d5671e71d7f11c0ae3ff9a6441d
d0ffbc3cba659bfeaa2e84dbb0433781ab5e5c1a
3540 F20110221_AAADYH xiong_h_Page_058thm.jpg
21810f2ae0f87da0f67c62a03dd08bbc
d4666da6656cce8b380cfdc3c995ec97c46ca652
71200 F20110221_AAAECZ xiong_h_Page_009.jpg
46a655f43f91128a1eb1e92530c12cb8
0e271cf17cd339e89978793993095b64952931f7
1298 F20110221_AAADXT xiong_h_Page_044.txt
6a263837adde8164ed103f21b7a4caa8
93717f79adc3c6eefb16ce38ca8008e0ee1955e7
F20110221_AAAEEC xiong_h_Page_005.tif
603fbf07d7ccaa25b97d8466f962ef07
7dadcb7c26160789ff0beedcae19f2b18af87774
F20110221_AAAEDO xiong_h_Page_037.tif
0d84bcafd12187344ccf0f805ac2d034
a958dc0a7f50f9a88bee52b109d3bef01d954017
277577 F20110221_AAADYI xiong_h_Page_074.jp2
d3d29e2a6eecb60061f0b7eb6bccb428
736b08ee7a28d39b1c87030054d0705bbd667f0c
F20110221_AAADXU xiong_h_Page_033.tif
dab3fca05b97266491fed2e96300a986
d22614939fcc2aedf83b5737fddbdd34542b85bc
F20110221_AAAEED xiong_h_Page_009.tif
e493965e7ca633f970b0c7510b871498
df81c5730a222baa10b02c2bb4042feb30ada40c
14268 F20110221_AAAEDP xiong_h_Page_101.QC.jpg
29d8ebad79b187713dc63a6e52160945
74f97de357629a13e33e40683ff1c6e229b742c6
28267 F20110221_AAADYJ xiong_h_Page_111.QC.jpg
b9dafb533b3c31d9b5a8adf6dc68d2f1
137f48a72d129a7e487f972a0781585cf1173ff9
27166 F20110221_AAADXV xiong_h_Page_046.jpg
fa681cfc6d4f8e122cde38392c303019
a47989eda5ff35ed4bdc2bdc87360621f283de11
F20110221_AAAEEE xiong_h_Page_013.tif
2c1a5f5cb953951fe11dc9b6b4c90196
db220202102c941ed21f44962ebc6361bef57332
4290 F20110221_AAAEDQ xiong_h_Page_062thm.jpg
c51cf0d9cc82df94df8feb216a379387
cecaaad3faefed836aa0acc49256ac964b54549b
5878 F20110221_AAADYK xiong_h_Page_092thm.jpg
b85d7aa1890605d4efc596a25d2934cd
5172a8595ce88bec7f6876ab9aa7a3c3448e4cc5
1927 F20110221_AAADXW xiong_h_Page_016.txt
e7c43dd0ec40dc30641cddf97e05b372
5f205d693b5c1bb80576eafedd8239b45127086e
F20110221_AAAEEF xiong_h_Page_016.tif
b9dc7c995b692638d36fa5e5b1aeb482
1884747358263b91ae2b74f0920ff8f075cf0984
53207 F20110221_AAAEDR xiong_h_Page_114.pro
41b33482caad86c9535af975e3ba6f20
1175c33601747fc7bbbf17bd39e9fb62349f0cdf
11131 F20110221_AAADYL xiong_h_Page_104.jpg
eec5231c71a9b229de112bdf27656b12
db4c55618c987c979da3ff19f7706a88ed1fa14e
54813 F20110221_AAADXX xiong_h_Page_041.pro
b2535c4d2c69b7a2ffa65187bb2742dd
bce4fcb98a26d028357ca9f092e3f740801df254
F20110221_AAAEDS xiong_h_Page_085.tif
29f5e8db3627f6b67761f3094e58f785
d9938ed2f838f1be8b3903bb7a0115c2bff5ffb4
92139 F20110221_AAADYM xiong_h_Page_012.jpg
94de1519669a4a7b6ba59adccb88dc22
7f6a13e342405feb31dc6595d984eebac13972dd
680917 F20110221_AAADXY xiong_h_Page_091.jp2
b9aa606ab5f1589fca999c824b869063
0554c99c8cf93037576a28b1832192d8b663a9c9
F20110221_AAAEEG xiong_h_Page_019.tif
fd49a09f5bf59049c38d6f007801f2e9
725ae197912b91449900d80a4021ea0fbfbd1125
F20110221_AAADZA xiong_h_Page_008.tif
340cc1bd5cd70848e7c1bc926eef001a
213a236134b03e4aa78f4d9675d8ee04333e6b87
54349 F20110221_AAAEDT xiong_h_Page_006.jp2
67b17e06b602fd65c235a73b7665c95b
c6f37e58c66b0a01977b44bb415867723ef76396
125 F20110221_AAADYN xiong_h_Page_006.txt
02bc146b73cba4adc651dc3f6079d38d
1958145496c3545727ddc3957d1779290c545b91
91065 F20110221_AAADXZ xiong_h_Page_013.jpg
af09ea159768d84393b65cebe8d5f899
f0bb9101e97fc233a93e54756aeedce400400c69
F20110221_AAAEEH xiong_h_Page_023.tif
57317e8abcc3833c89846ca8af30011a
2dccaf2cec4ac91aebcaf8b655a4d115fb02718b
1956 F20110221_AAADZB xiong_h_Page_097.txt
eb0b5cdae067baca49c19b9683cdf02f
2bf630452c9d944d201ff231d11bb5aa0e23c9fa
F20110221_AAADYO xiong_h_Page_022.tif
17d52081d284169e3073d0b64fb65825
6e81b7b059d6e1fa0b9c74c0561af9ee69b0fc77
F20110221_AAAEEI xiong_h_Page_024.tif
508b2ece2fdd5a67380ccc6894db27f1
fafde662e0fc7194b064e9a9836cb73b304696f5
2501 F20110221_AAADZC xiong_h_Page_110.txt
c2d5b1f2fcf24f8c66a2b7c500e89ae6
10308d2167198c63cffea0665e11ab1e36eed77e
9344 F20110221_AAAEDU xiong_h_Page_100.pro
c92d155cb63d384691458f573c179f3f
d4de90bee410156125154eaec30ba35b1e4e06fd
2311 F20110221_AAADYP xiong_h_Page_013.txt
16c37d120eca11f1f6261ce69ced3210
193a13f62541af83b52ba883d57262c43e5930df
F20110221_AAAEEJ xiong_h_Page_025.tif
e8c674ab286faedf9686126b1c437d98
623bd83ff28d6e7e00e95b7d598cd2df56ef0866
281975 F20110221_AAADZD xiong_h_Page_046.jp2
7f9912cc501f89a3bacb70eed22b3cec
0fc9ee0cb5d04bdd3a3104f3eebe23d6e00d5125
912 F20110221_AAAEDV xiong_h_Page_047.txt
caaf587010abc696fb0c85db37ce02bd
9878996a3a5400d5a1016a1b8dbc0c4ff44d2474
5069 F20110221_AAADYQ xiong_h_Page_016thm.jpg
f2e19a25f4c07b3bced74f56c926f749
e3f77dbb5bc22167463962a3088c2955fc0b04c3
F20110221_AAAEEK xiong_h_Page_028.tif
9719799154ddce727615c739007e1bfa
3e5a11021c69623ee9a5edaa98cb94d5f34f1b5d
988800 F20110221_AAADZE xiong_h_Page_077.jp2
350b9dfe32fd6368d2bdc30d61c761c7
944b608888b4e203f8f42d7e5f911d4c880c5200
37291 F20110221_AAAEDW xiong_h_Page_037.pro
1a16f359162a40f35319df2eee46c738
dbf28efd35612d4c46c7ee7ec8430caac1a736e7
16285 F20110221_AAADYR xiong_h_Page_089.QC.jpg
f95cbe8cbd0fca634cbaf9a1269206ae
ecfdfb4c0dac46ac67ae4e7230682798c2f3bb35
F20110221_AAAEFA xiong_h_Page_067.tif
3a691ee6ea82abd3273921d294e3aa70
635ca072b04d99b6ecaafe8684dbf93ca21dc304
F20110221_AAAEEL xiong_h_Page_035.tif
44584cc2de973319f88dbdb24752e299
ece1acf963ad28b82973d9a317601832831af7ff
7943 F20110221_AAADZF xiong_h_Page_001.pro
8167628a0136898e906ab2c1f71913af
86e4878823d67dff040e999cd059f664af013f1e
844158 F20110221_AAAEDX xiong_h_Page_059.jp2
89d6a3d891b8a890c16f95b62de2d537
56f5dc12d266086359860cfdb2acedd4e24acfa1
F20110221_AAADYS xiong_h_Page_104.tif
299bf984ed0b73edf4064e34adaee689
73cbe490c4bc7ca06544058822c7de553b59869c
F20110221_AAAEFB xiong_h_Page_068.tif
cde2c206b44d90d5bf9bcbb51382741b
467cbbf0308e358c64e16958ec18d0895c85a2de
F20110221_AAAEEM xiong_h_Page_036.tif
1fd3deb6901d8380e8c8039627133335
c594c0e7b32a8c97f1667adfa08baa0a638b9f9b
3194 F20110221_AAADZG xiong_h_Page_068thm.jpg
d1730f5ed94a486ea842bd041c8bdc22
3dcbad8a5ca5acbd1624742134d72764f4596745
12489 F20110221_AAAEDY xiong_h_Page_058.QC.jpg
672aa53edcf6e1f298a5b87bd1ddc2c8
7cb0d5dcb46df1ddc42024ac925c8ecc75a13f33
4906 F20110221_AAADYT xiong_h_Page_011thm.jpg
d4b025adddcd18d8bc48527a6bd13734
6076044841aceeb6c2eafa5f0857d3f93b1810a1
F20110221_AAAEFC xiong_h_Page_071.tif
a7af441ad4d33bf56dc06de4e5ff4e87
05a96a627aad17ed992a6133f29df69ff5130237
F20110221_AAAEEN xiong_h_Page_038.tif
7b0935a6a2d37fb2bf36bf19cbaacac3
e559371eb6a86d7b8a0ef5812d52de6537109f1f
48262 F20110221_AAADZH xiong_h_Page_097.pro
2a1cad6a4397231cd03292e0eedcd0f4
9ad07e7a453205c8bd623d9b02d572c01a42458d
185166 F20110221_AAAEDZ UFE0013387_00001.xml
c5781482711bcc4e3a6d3da19f33b966
101be8cb478035b22b33347380807fcbe71a3955
1051981 F20110221_AAADYU xiong_h_Page_113.jp2
bd1461fe75fc693a82c7b96de81d0bb3
5fba0ed045939af00c43a5e81dc9b2fb3e14be85
F20110221_AAAEFD xiong_h_Page_075.tif
bbdb885ae882494b8a3d7503d4380544
7f39c097817af983a9f6ab2e6b805f99dc215e3e
F20110221_AAAEEO xiong_h_Page_040.tif
b84d59c7239cf7394a4b78017248dd80
792587b77b8086e72ae15f473798b114475a6f3b
481718 F20110221_AAADZI xiong_h_Page_103.jp2
a565c1f32c776fd9a2f099908c55b944
0a846a089c316d05b1a505ece163c5b3798458b7
14152 F20110221_AAADYV xiong_h_Page_028.QC.jpg
41378a0b130b75e4c48939c5c33befe3
21ad9df2afc27fee61d89d57eeac85048f53566a
F20110221_AAAEFE xiong_h_Page_076.tif
ad368846c41b3c0b9becf02422b476d3
1b5de4aec849d10952c27cff5637fb501ea871ad
F20110221_AAAEEP xiong_h_Page_041.tif
2a7170a7b9bef3077348df725960df26
652b118844441ced8902ecc9c183918a405eb355
5186 F20110221_AAADZJ xiong_h_Page_114thm.jpg
1b880421618ad67096b17878d1537043
fb338bfa30f0dd3ef903f8fddd0599270800f8f8
21800 F20110221_AAADYW xiong_h_Page_011.QC.jpg
9fe0b20a29fac4e3d8a4b0c07712ab56
c183d2205f9ec475f64a5e70fbcba632487ccb57
F20110221_AAAEFF xiong_h_Page_077.tif
a1666ef584c2105c2c1b1ba783dc9d4f
98dca154af659eb10983a663bf93ef6635cf2d90
F20110221_AAAEEQ xiong_h_Page_044.tif
170f7a0111ca646b564445e0507e1204
caae8db32620a564d42810bd994dd8a68e7a19d2
1479 F20110221_AAADZK xiong_h_Page_101.txt
6a0105a8444d4aead026d33c1a58ec78
381647eb18e4471a89f9b72ce347f38d3dc7c6ca
647085 F20110221_AAADYX xiong_h_Page_053.jp2
0a934d3ed8a16bfd6aa524a82a2ca891
4ac20c3ca7e94414b0e8f18d3a72c809fc4f098d
F20110221_AAAEFG xiong_h_Page_080.tif
21671a9bd4a7737b68fe9aac69b8a8eb
e1bbb95ed23a37a79a7bbd5ce0e6eb93018626fb
F20110221_AAAEER xiong_h_Page_045.tif
515ea1e2985622a050c196ae8f251ac6
34b1bfa3fbea7e71fd5ca0cef3f395b34aa6ce43
F20110221_AAADZL xiong_h_Page_079.tif
e276a6ae1d7a2b0bf68f50a9828fcf55
c7ea617d7f0a070f77c7bf9742e386669e60d82f
F20110221_AAADYY xiong_h_Page_029.tif
22dda80e43dd80a25c49e5e8ea8ed608
db771638de21c97eeb78f6c440173011e41db401
F20110221_AAAEES xiong_h_Page_048.tif
458fbc31d6032ec9c5f1742e6969b245
382372746c29c63087a44b80fc74fe31c1fdc7f1
52301 F20110221_AAADZM xiong_h_Page_031.jpg
27ddfc93f08924b1d32a3176531dccce
0f394d50f4ee7f65ce8165c0435855f11456c9ae
80816 F20110221_AAADYZ xiong_h_Page_096.jpg
55ed1e586bfcfcbd73a770b0549e8310
7d558b3897a8ce092f1002b413c506d5ecfe01b6
F20110221_AAAEFH xiong_h_Page_082.tif
b0154022c46730c9b8f9b13266df3eba
f6e6f13dff15b149eaae20044fdda6c523af884f
F20110221_AAAEET xiong_h_Page_055.tif
40c8bea09aea6b940d6fb8ba31edb0d8
5f0971d80fb6b5db3d17cc2821f11026f1392afa
3505 F20110221_AAADZN xiong_h_Page_029thm.jpg
ab99fa70fe740ccc08e0410bf7d963ef
f4de8d457a770e1c93353ed98c53b8812d119784
F20110221_AAAEFI xiong_h_Page_083.tif
8d3bf1a9a49172964799f0e8d9d487c1
d62af57b5254a7f7cf2ab0900f56f2752fbfbeff
F20110221_AAAEEU xiong_h_Page_056.tif
f4844a37cf86b109451e703fda0619bb
da21a1e1c63b11553e33320fbae1e51a64f3e6b1
81051 F20110221_AAADZO xiong_h_Page_014.jpg
2a710bc5954e163de31f620771696bc7
3e3b73a618c3cde20f7f6cbebbc12c08aba5b74a
F20110221_AAAEFJ xiong_h_Page_086.tif
1e2dedca3e67bb77ec2a4d62fa801cc2
895058f6b44239f73a1437fe7416f250d2119dfc
F20110221_AAAEEV xiong_h_Page_059.tif
4e184dfee80c171ab09c33ce59a79c96
3f7e08f4afdb34f96a152de59beee100ac21bbdb
56586 F20110221_AAADZP xiong_h_Page_062.jpg
1f0b6bd06aecb2416abc813f2638473e
9bad0b50658ccde73dab0dc1174909040443fbb7
F20110221_AAAEFK xiong_h_Page_087.tif
daf77aac255fe21db743857c3cf66307
e81b7b386702a03ab849be0d5811f39ec9800833
F20110221_AAAEEW xiong_h_Page_060.tif
9f85795ce1700708499af26bc6cce576
8c0709d7372fcbb7e50c3a48f361572b9f051ca6
56207 F20110221_AAADZQ xiong_h_Page_064.jpg
2bd995fe5797fcc9b113206af042f042
8578baae077568e4bcbba13aa54466982b861dce
F20110221_AAAEFL xiong_h_Page_091.tif
dc1dfab463b4b923074a2d1e2ca81bca
77762e1d80e9cd97a515c048dd929f38f533b66d
F20110221_AAAEEX xiong_h_Page_062.tif
2e81c319f5157811dbc9c5a59646dce8
1b445a5238a84c59fceebe95548e4f8ab100fff6
1808 F20110221_AAADZR xiong_h_Page_105.txt
47c8632beeff903a3060498279571ccb
ce4bd1003eb0b79e2b7a278f46bea1f591d28381
1996 F20110221_AAAEGA xiong_h_Page_020.txt
22677fa9db38d22c29399d0cf9ad09f4
70a173aec84b58825791bf077582ef4c688a00a3
F20110221_AAAEFM xiong_h_Page_092.tif
c415c5aa55621cc30953269c13e1501a
884c7f8810f0cec8aa084d61fa5386beb65dad59
F20110221_AAAEEY xiong_h_Page_063.tif
6dd1bd7773283f87fc6de8e0d9dfe7ee
cc583c726401dfb61bbef9d67b55959ec05a0b52
4063 F20110221_AAADZS xiong_h_Page_005thm.jpg
65b4549743cfc0c2a8b5a38abae4de38
9daba393e5e679d4c7a8013ffb95504ab510bfb7
2064 F20110221_AAAEGB xiong_h_Page_021.txt
4fce949fa17562e38acd31b5e704af74
d5c4a0bc4fe6dd4723672611da33a71a88a2da8c
F20110221_AAAEFN xiong_h_Page_093.tif
aeb9e82e0e30ae82c1dfa6d136b9decf
a40fd0013d2e72457840d37008c80d0048d7537d
F20110221_AAAEEZ xiong_h_Page_064.tif
7d659acf842954e3ff801a3dc979206d
9b081887a996cc6f2b6af627cab07905578a5ae7
80509 F20110221_AAADZT xiong_h_Page_097.jpg
3a5daa69d70029f54f105673ca1d780b
24852a1f6248bfa4108fc67265b02606a819108f
1493 F20110221_AAAEGC xiong_h_Page_029.txt
d7be0eaa74a562a0b1395ba27c93a7ea
b0682facabcf8a23a79731b8b70eebf78b3b601f
F20110221_AAAEFO xiong_h_Page_108.tif
8ca2aa5576b28f5b30026d5f8dfaed17
53e1e5f1737753ce73b80da1056b959fcc03d087
3889 F20110221_AAADZU xiong_h_Page_105thm.jpg
c4ec187edb28bdec634fe9ce6b69fdd3
48634b6935fb0ed8f004895cca01238bdbf8b34e
1674 F20110221_AAAEGD xiong_h_Page_030.txt
bfbb1af51c544516a4dcea7fe8b67ea4
b1481891b3f541cb370da14e6793be14e4b8edcd
F20110221_AAAEFP xiong_h_Page_110.tif
4b9e7a931534963215cbf1d89b84074a
0ca68132d9f52e244a735ab40ba32f8baf75a340
F20110221_AAADZV xiong_h_Page_025.jp2
6dbee0dc4ca76f40433c9ba28e676a80
af6b208e5b1d044a866c3da0d7ec8a041387a89e
1562 F20110221_AAAEGE xiong_h_Page_033.txt
ffb4d7ed2178cb3a4550b0262a827f9a
11308894d2188cc97f651b11a22e233fa4ccf48b
F20110221_AAAEFQ xiong_h_Page_114.tif
d14e97ecd113e33316190e72888bb61e
3c28d80f80369df8da2712f408f492c31a3d6a6f
5207 F20110221_AAADZW xiong_h_Page_108thm.jpg
451eff6763dba88d02768f734bcb0f6d
6334daa32915bfec35b25ed3ec738772b0cf3b12
1592 F20110221_AAAEGF xiong_h_Page_034.txt
e2e7106cee4dbbe05471c6da714f0f87
3d4cd5a3aa2ddeacc71204164224a55b273e5272
F20110221_AAAEFR xiong_h_Page_115.tif
b5ea7beb6a0831530533e3bd9ff11d70
e4ed64a9ead64d51af50e4fc73521bc2eed32a62
F20110221_AAADZX xiong_h_Page_084.tif
a892f2d8df5b7e412e41a553e1d27a2c
7b80640c2bb471c078d3c1732cd1ec7477142f3b
1846 F20110221_AAAEGG xiong_h_Page_037.txt
f16cfe694cfa1b0e36c3e5e6237b5753
9de307690858bce5194f789db8fc02209b9446f0
71 F20110221_AAAEFS xiong_h_Page_002.txt
24ef53dd84ad2882ac4e59cb6a81bfe0
9edc1602886d2b5866a0e3be51f46d60c1bb0b8e
15317 F20110221_AAADZY xiong_h_Page_052.QC.jpg
eb68bd9228cb34325d01c730504130da
6cb569e0174b267cbb97c3cc0df542316131e67e
F20110221_AAAEGH xiong_h_Page_038.txt
bf83bbb1655d5330f35054300411711a
0268c1368d6bfc2045ef9ec5464698eee0f5f3ad
2456 F20110221_AAAEFT xiong_h_Page_005.txt
94472db83e27f3b017c3545bf4e46738
c7efb7e2c579c370ceae0a01a7392063f5d93fb2
2070 F20110221_AAADZZ xiong_h_Page_048.txt
619bbbf4b27b219d9a832a93dca330aa
bfcd5e62ba3fd6203795a28856031a74beecb5a2
1863 F20110221_AAAEFU xiong_h_Page_009.txt
fa879bc637c184516587da6d08653a97
fa86ea8c00f22d259a1479f286a3a268c37b42b3
720 F20110221_AAAEGI xiong_h_Page_042.txt
c59cfcf47c791926447d6da50fd19373
d7ff69b8a940f7357dffe37b35b01979e268b8de
1188 F20110221_AAAEFV xiong_h_Page_010.txt
347869e901da426040df06560919423e
490dd01c21e74f2426a4c331504409e4587a52b3
963 F20110221_AAAEGJ xiong_h_Page_043.txt
c12eee04a94861cc4be2050a24ef71ee
1b53247dd96c4f02f9000971d19b83af227a4d8c
2277 F20110221_AAAEFW xiong_h_Page_012.txt
cb1484a19e65752e849a847fa96c132f
d40dd781dc31e18bfdbad66c3d199e17408d7321
1621 F20110221_AAAEGK xiong_h_Page_045.txt
bd360c01debc11808a5c8f36db49dac8
3b05927a6d798943bb07c1ff7505d69192a0a625
1750 F20110221_AAAEFX xiong_h_Page_015.txt
16609ee9140795c7a578f894226e56a6
67642260db265f95966293af262eef304ac94e86
1205 F20110221_AAAEHA xiong_h_Page_091.txt
183d88fe1e5fd46f445af8eda3a64e15
42281d72db79d53223a4b405cceacbc0f7a8270f
2212 F20110221_AAAEGL xiong_h_Page_050.txt
63baf728b4170f11c4eaca90dd379553
5784ca5a0c1902b446927b6315124fb1dfc3323a
2221 F20110221_AAAEFY xiong_h_Page_017.txt
4e3d705fd18092ad5c800120ef434f41
1704a07e0be0ae127a1e5943997fcda62274fbc6
2129 F20110221_AAAEHB xiong_h_Page_092.txt
6c6e374415ab6f19f88813c691ce788b
efa9d076b8c6257bed94ef42291a3e63992d935d
1643 F20110221_AAAEGM xiong_h_Page_055.txt
5a49db5a1ef66ee08253d66f40705501
080dfbfb7ad88e18a366340d8bd4f7cb10ae379a
2050 F20110221_AAAEFZ xiong_h_Page_018.txt
75173426b23e5f4e509fafc4cc73b23b
7d1dc31ccc6603417027cbe43dd83601dc0564e6
1936 F20110221_AAAEHC xiong_h_Page_096.txt
1dd6b91d694fa9d5d6d2f0c4582e7244
6241c2b43ecae73f86955fa174a211d386caa543
1636 F20110221_AAAEGN xiong_h_Page_057.txt
4396c5562cf822869a3e62c138bf16d8
661b417a3b45e327afb8aa4a65b218cb25152881
1319 F20110221_AAAEHD xiong_h_Page_099.txt
827cefea098ea98674f3c4b8dfe0c1c1
19993c4ae82961e87c7f88fc5ff08026a6916775
1886 F20110221_AAAEGO xiong_h_Page_060.txt
635f739e060f2079f0649e510c07c88d
5c27eba8868f44c4f83cd570557204bde9495f08
415 F20110221_AAAEHE xiong_h_Page_100.txt
f6646fb992caf7bf2d475f6dfbd333ff
9afa8b4b3b438251afb46739ad628da6706a2199
1304 F20110221_AAAEGP xiong_h_Page_061.txt
66bc811cb67d0d7dce3daec5fa158959
bc77dec28ec2a9ce2ea1d2a4c61af85ac565da5d
2813 F20110221_AAAEHF xiong_h_Page_111.txt
ef3158df749c2f0fc3e51bf8eddf2179
6c252a6e4daf6979f3583d9c610b866f022bf093
1943 F20110221_AAAEGQ xiong_h_Page_065.txt
48a4f92e315c888a2e192e4d57fd1928
e8950c91102a341f236d20851574bec4dd8ea351
2725 F20110221_AAAEHG xiong_h_Page_112.txt
ba4079f8f9a70a1edc3a00cb60a606a9
dae86683a51a65d3cb83e5bd80cbdab3aecea12b
922 F20110221_AAAEGR xiong_h_Page_069.txt
9d9a0cc38d0a686d9d0db3fa964cb80e
fd12f4d2edcae72b717487dccc92c334eb04e25b
754 F20110221_AAAEHH xiong_h_Page_115.txt
7152b16754a7893d969c032ba07962a0
60a823388d817532f89a91d28b708613f702a049
325 F20110221_AAAEGS xiong_h_Page_072.txt
c4037a0e743c677d3c93a7b3d2597f60
c1a0462071cc0ad550f6a28d2139ea1f6318e030
1274 F20110221_AAAEHI xiong_h_Page_002.pro
1390012756ac560ba0fb1c2fbe6e90be
a3682388c22cdbcec8af162807955d5717025633
94 F20110221_AAAEGT xiong_h_Page_073.txt
1973c056831e630b46e98e4916a61c34
a89d3f8be016b5d36c662d16dd2ea70937484f01
1774 F20110221_AAAEGU xiong_h_Page_075.txt
2e03ed9072cd7eeb1f6c8480bd116f8e
0c8b855ef885948862a69a60ec581db1ff2f0212
3023 F20110221_AAAEHJ xiong_h_Page_006.pro
00ed489db3d87d41458d5d51aed61e63
59db5bb0fd8503722e816e8c70f1ef581c8ae956
1816 F20110221_AAAEGV xiong_h_Page_077.txt
ca4a8ce4979425424993445b4400b075
00635ba86c8342c44431b90553ac769e60330e92
50963 F20110221_AAAEHK xiong_h_Page_014.pro
c88f97b0e4d9f07595cf1f75bc3b30c2
7345e4fc9502faf9864c761320992821bef0f6c8
1762 F20110221_AAAEGW xiong_h_Page_081.txt
75b8b15a1dcb245c0c636a6a5d54205a
a3ed9b7a15337ba526470acf997b79113a4f5053
44510 F20110221_AAAEIA xiong_h_Page_060.pro
fcf760dce1a7d08bf38183cba87ba728
096ec849f702c0259f758366c141ea78ff1cd2f3
55708 F20110221_AAAEHL xiong_h_Page_017.pro
34abd27ee26f94e21802f24d35d000e5
ffac21856d1b0e2a299e964bc0d9dfa60273a649
1172 F20110221_AAAEGX xiong_h_Page_083.txt
75355fd5944e8bd4912192226b0240f1
c676eaec743fe4875af9ea2b8a3681c63ae324c2
22141 F20110221_AAAEIB xiong_h_Page_061.pro
641ebd091adb6529fae0c943af820f63
51f3d8169caad172138428f22e1e7f51c404b1f6
48703 F20110221_AAAEHM xiong_h_Page_025.pro
a8c3ae63013b7af4823048a71a2ed7fd
8cd5e86c22ec20dc2a92f874c8d210497aa84dad
1564 F20110221_AAAEGY xiong_h_Page_084.txt
3b0b23954f40a4b0da9b6e53f64236e3
c61cc825d7b5a481e64c0a7fa1956cd8c3ec15c1
36598 F20110221_AAAEIC xiong_h_Page_062.pro
e838caff87d8da5553e7e789153f5a57
32ce77ebaaa9374d6341a94691a3912d07777c99
19442 F20110221_AAAEHN xiong_h_Page_032.pro
2fa4f0338e779c0aa4ad6b90d300c4f1
d06c316e63809a9030128b64ad43dd0381b1f234
1676 F20110221_AAAEGZ xiong_h_Page_085.txt
b9192f755c1caa59fe55db14d43c7740
ec98abb2fd7e246097dd5365af63a39acd55e043
38199 F20110221_AAAEID xiong_h_Page_063.pro
9e68481abbc994502af97e9a5b790d60
3dab59a88fe56774b79687f0f61f5f15d3292732
29326 F20110221_AAAEHO xiong_h_Page_034.pro
0fb3474eae6fedeacd454c66e637641f
df9bbd83caf431cd4626e952d1b2e443c84c9dd3
28892 F20110221_AAAEIE xiong_h_Page_064.pro
2317a9c63abcd11e01e8585497e1be50
5d35bbca6afff75589abd959a35d010c3dc85c1f
31434 F20110221_AAAEHP xiong_h_Page_035.pro
a139011dcbd790f1f0af664eede94b5b
9013d3a8fae22a59956e4fbfbfc596265e0477f6
44330 F20110221_AAAEIF xiong_h_Page_065.pro
ca35e9eeb9a6e7ccc4dec9c9eb588069
80b09f7ed2b884526ae55fc7f9be8a81ca643d6e
24479 F20110221_AAAEHQ xiong_h_Page_036.pro
884dec5d0bd99281162a68c7caec3fda
bd4970145a131e050c015da912c783be78d73c0e
10337 F20110221_AAAEIG xiong_h_Page_066.pro
268d8733e849ebcd37f02f6b2edaa847
39fb8248facb7b3d1a32bdba25cb8e77538b3347
28197 F20110221_AAAEHR xiong_h_Page_039.pro
981f2aef89a538603ff6ff7f635615ff
6e2e6d1dbdcb7deaa7a607f4c50e87f681a01a31
11347 F20110221_AAAEIH xiong_h_Page_068.pro
bb6c8863c0174f5f3a9d11d1a9da8c8f
d86fbdaf5dd225463754ae42170f9b623a989ff1
36603 F20110221_AAAEHS xiong_h_Page_040.pro
14a62d271454dd839e22de33f37c2eb1
a50fd71712d46def24f01b4bc423a1b2e62ea41d
1183 F20110221_AAAEII xiong_h_Page_073.pro
f27c407bf67298d370c110b74230fc56
3b51a964f45663b7489c2d18c17fb7794f2b234e
10356 F20110221_AAAEHT xiong_h_Page_042.pro
693e4c2cfb7702d4dbaa855de2c53516
662645f7b009557bb33e74b860d06dfb53a6a911
F20110221_AAAEIJ xiong_h_Page_074.pro
bfe5fe8915c4a7e4998306274202dfd4
623a2e9040af4d0e9c1b67ccb5d1cdcb2bce6a82
15216 F20110221_AAAEHU xiong_h_Page_043.pro
896d11115a676fa477c157bbd108ce3e
50b90da57052e3b7214fbd9f3f8933e16fcc9a15
55670 F20110221_AAAEHV xiong_h_Page_050.pro
4eb7e05ad90cf3f302b150c040ae485a
fefa9458821fb8eb70fbd4b4f7da2452640e8cb1
43636 F20110221_AAAEIK xiong_h_Page_077.pro
3b5efc387210c295d90fd8eca0bbafb9
c64bb9d9984a09d8bde4bc36270caa00738a88f3
40776 F20110221_AAAEHW xiong_h_Page_051.pro
23911012461de8660dfb9d24fb462ec7
da0f6acf2f2363cf621588781a434bbe4c07b62d
35278 F20110221_AAAEIL xiong_h_Page_081.pro
f44af33a8cf0191151e3ddb6ac4901cf
c981a082f050c9dd370dce73e66fa169004c43b6
36126 F20110221_AAAEHX xiong_h_Page_055.pro
855367627802ced5166f77b25374b794
119c923e2424491ef524fe379bcb60570fc8cfcd
7036 F20110221_AAAEJA xiong_h_Page_006.jpg
6b1a6f4f21973943b031018110aba3eb
ec4c371ec05b9a13a4e76f4c5d7482260b377dd2
21578 F20110221_AAAEIM xiong_h_Page_082.pro
fdc44704789a86c27ef6a7763ce4febe
240447f0f3c08289ea923b6b4c3cf9a43dd7a662
23919 F20110221_AAAEHY xiong_h_Page_058.pro
5e4f2709aa33d340acbf47b7fdc70685
14033b68d6f1659a3318d4c773e868a76a834df1
30354 F20110221_AAAEJB xiong_h_Page_008.jpg
60de155fb6c23f8bf2019d593d439f75
fe6bffa139e033fcddf6847055acdfa8d5816079
29399 F20110221_AAAEIN xiong_h_Page_084.pro
aae9d6e95e98cdceca2f73167a4de0f2
6c15901dd82a3326fe094001fb44518b6c35692d
39135 F20110221_AAAEHZ xiong_h_Page_059.pro
660887c6449f10c6a59d248b16fe7ee5
ed015114719b01151e80fa2b8842455a25a4a1a4
20546 F20110221_AAAEJC xiong_h_Page_009.QC.jpg
36a76617eeafda7cedd96165c085ad30
1a169673b38fdc70f4baf8ed73122558422841e8
28125 F20110221_AAAEIO xiong_h_Page_086.pro
1f323ae0ab31c8d68143daa11502003f
2376d4c6c7a9d77a28e30a4f806d7794d4c22298
14782 F20110221_AAAEJD xiong_h_Page_010.QC.jpg
c65657cdba5a756a865bba4ed590e07c
61894a6690371d61009424acd4cde6686a55cbcc
38040 F20110221_AAAEIP xiong_h_Page_088.pro
1895b88d1a44a9b5945ab1c8b57eac34
9d9fcfc49ac7402e0c21f59b1371c15b2a003a28
27104 F20110221_AAAEJE xiong_h_Page_012.QC.jpg
5265ed2237b17d57144af71810cf36f7
c263bebbfb28bf4d6562b76bb57ef541e7439cad
27396 F20110221_AAAEIQ xiong_h_Page_091.pro
b1a08eb9499fa2dfb8bbf7210aacc57a
25a2a3cb9c22d308a5edcbe9bf447eac09eeadc3
26773 F20110221_AAAEJF xiong_h_Page_013.QC.jpg
ef70fc20a5b4244fcc6a73150f0085aa
963ff294d66cfe5155881c3c738e6d8c8c599d39
68524 F20110221_AAAEJG xiong_h_Page_015.jpg
cb722db6c013050ce332198bd1d1fd04
3363303575c549e335191c4d0b6d06038570a221
52929 F20110221_AAAEIR xiong_h_Page_092.pro
72ca0a832b24ec92ab8c51c2c391cc7d
409b4b9814a1df536ee1a0829f645cea6a4c0e03
86837 F20110221_AAAEJH xiong_h_Page_017.jpg
95aacd680c9eebabd8db82ebc63bfae0
7197603a17b23f4aef60c65be725114051296625
36397 F20110221_AAAEIS xiong_h_Page_093.pro
c0631f6f9dad74b0748e7b75467a6d32
a29db13487d0dedab70d470c1ef8e620fbf8e244
26006 F20110221_AAAEJI xiong_h_Page_017.QC.jpg
2bc600a2c1e5b6b175e95c4114fd04d3
539a9a6db1171836d1b1225d19713e01b59384f9
47708 F20110221_AAAEIT xiong_h_Page_095.pro
76e64382ee0bf63f695bb7c7a1e5b8e7
4cb914b8b729f46962a47c1f0309306ba431f915
22496 F20110221_AAAEJJ xiong_h_Page_018.QC.jpg
a061070aa7b2a2cd32bfd84ace2633fb
8ba47137267c69a23595d74a3a51612aecd8cd54
26472 F20110221_AAAEIU xiong_h_Page_101.pro
c04abf52d268c88548c4a7355450d30b
e2e633a2fd822284e5fb2343e37b54897f4551b5
17882 F20110221_AAAEJK xiong_h_Page_019.QC.jpg
71675af2c244eb729be4341a49a9d46d
555c00e9ab737b6b58f9abd73f8fbeeb21c9db42
4053 F20110221_AAAEIV xiong_h_Page_102.pro
3348f71b88dc4723186c2e581e07ea93
14dd42500cc5fbb96ab26d66d8f861aed6eaf657
6043 F20110221_AAAEIW xiong_h_Page_104.pro
d95761075b2a3e3a1b98872296efff45
c96df4f2152bef51ba526b3deb03b6975ebf4079
9219 F20110221_AAAEKA xiong_h_Page_046.QC.jpg
e408e4d67253ebeb55d9a75a552a2746
ac3518178097e98d5ad87a688ee6c5b5b49d427f
79961 F20110221_AAAEJL xiong_h_Page_021.jpg
da6f115a322cfa0c1624626234b9d7f5
7582126ad6d4b28c6dd7b910e41e1017ecb686af
61202 F20110221_AAAEIX xiong_h_Page_113.pro
bb2cdb0e86d6f0505638acb184635719
56afc9e367945654634a9e23168caa0b592c84a8
84972 F20110221_AAAEKB xiong_h_Page_049.jpg
7248b588d117b98f932e878177806b2d
79b5945f771de3936b0f4b630f7d9ff7960746d1
23577 F20110221_AAAEJM xiong_h_Page_025.QC.jpg
f01f3f2a4e716cc673a681d17a330049
6f64f3183aa37a668342d482f5c86d744ac75d22
15939 F20110221_AAAEIY xiong_h_Page_003.QC.jpg
9178ec0460aab27b3aa9fb24be5f5787
0401d32447b1ee9fa2f863a4a6f70cf2ab6a9890
24869 F20110221_AAAEKC xiong_h_Page_049.QC.jpg
d1d38bcfbfc20ce3f1069d53626c14ce
d89144bfdfb4dca6f2b8cc45a65c86ec7d899106
72388 F20110221_AAAEJN xiong_h_Page_026.jpg
1a47d8290964a3bcf344cb00762f6b60
54f436e189b82470477dae801c2bddc87c62393c
21465 F20110221_AAAEIZ xiong_h_Page_005.QC.jpg
672b7263b762d02b25a774b283723767
75191ea237616d456f30f84dbcf622a571ad8b57
26227 F20110221_AAAEKD xiong_h_Page_050.QC.jpg
fd34ec2d7e69613885069d3cffaee32c
3d3593702dd5e46b2dbf1b692fec74e8c68c5990
15117 F20110221_AAAEJO xiong_h_Page_027.QC.jpg
407e14174d0ad21ad7f84fc97bff72f4
cdc0f1fa9ae0a86b54a764a28676ee5c615858db
18933 F20110221_AAAEKE xiong_h_Page_051.QC.jpg
924dcd12ab89421b5f44eb6cb0171653
c859e6f0e98885e71a19e23d20071d6242e6995d
11288 F20110221_AAAEJP xiong_h_Page_032.QC.jpg
0a85c06f090b1ab38eb06b6f526ac474
97dca008d53f603d68458b8ab94bf7a2eafa83bf
47437 F20110221_AAAEKF xiong_h_Page_054.jpg
6704b6bb7918db8e7f96ee58a4f91ca8
b0c9c99b6dbf8d1b36b4b02c1a5768ede731fe7b
46976 F20110221_AAAEJQ xiong_h_Page_034.jpg
4858cc73adafe8dd423e7b1a3ef14bcd
4fbcf30fdd2a8c970fbdb0df5f7b3930e60f5641
16626 F20110221_AAAEKG xiong_h_Page_055.QC.jpg
c975a4d3df7a29abb2c71d0d6f9b2b70
7f9186d020cd595caf71d76c3706aa6bf71cfe51
11863 F20110221_AAAEJR xiong_h_Page_036.QC.jpg
7aae29cd10def9c66740cfae1fea1579
9d0276a6bce6ff1add00fbcdabf2f4b313a8c0d5
61949 F20110221_AAAEKH xiong_h_Page_059.jpg
c0dda0e42297f9a59e47bdfb8ebc2e4e
2523bd6133eafe9b430009f8a809efd99a446419
65938 F20110221_AAAEJS xiong_h_Page_037.jpg
d7bb8ca3bfea89d4c4f1753319eb68a9
d6dc5cbda0004516d8c9f9dcd29c97967c40cc47
19640 F20110221_AAAEKI xiong_h_Page_059.QC.jpg
84109ac546f4ff05fe06c3602a111b36
888776dda23c2e7a5f0f91ce124b4480499f4492
18349 F20110221_AAAEJT xiong_h_Page_037.QC.jpg
586c5a4b55ce1eb539450631d0a01e56
aed9924b726a6bc29ee23a255b8e3f7dd809a731
20689 F20110221_AAAEKJ xiong_h_Page_060.QC.jpg
1f9e50a1d48dd8d8e7e64ce7c195d89a
81c2d0774cedcfc9ca5c3e269d1d2bf7f3364a9f
87057 F20110221_AAAEJU xiong_h_Page_041.jpg
6fc4edb4b364f760a0822388adcc7d29
d75b4a3523e106eae79e133227b41fd05b52f2da
17501 F20110221_AAAEKK xiong_h_Page_064.QC.jpg
2dfc00cd4750034aac3d4c63cc7426b1
66e4ccedb804fcc4029a7f0da45c70c96a8100d0
25711 F20110221_AAAEJV xiong_h_Page_041.QC.jpg
fd3cd3d810185db3a9459fbd569edef8
be86ee7ceef88db05597feba400a391af0739bc8
71095 F20110221_AAAEKL xiong_h_Page_065.jpg
ee5e9dc6d94256623513a0991c8380a7
b393ac9b96bbafe7fc2da3fe6fb50e38b3d9a72a
25797 F20110221_AAAEJW xiong_h_Page_043.jpg
1b8b91ce938b3d32c8faac8d150b9ef1
b70e958307b3b777618f90df3b88b4eff694d125



PAGE 3

Iwouldliketoexpressmysinceregratitudetomyadvisor,Dr.JianLi,forhersupport,encouragement,inspiration,andpatienceinguidingthisresearch.Iamdeeplyindebtedtoherforprovidingnumerousinsightfulremarksandsuggestionswhichfundamentallyinuencedtheresearchprocess.MyspecialappreciationisduetoDr.ChunrongAi,Dr.DapengWu,andDr.LiuqingYangforservingonmysupervisorycommitteeandfortheircontributiontomygraduateeducationattheUniversityofFlorida.Iamalsogratefulfortheirvaluablediscussions,commentsandsuggestionsonmywork.IamdeeplygratefultoDr.PetreStoicaforhiscommentsandsuggestionswhichinuencedpartofthework.IgratefullyacknowledgeMr.LuzhouXuforhishelpfuldiscussionsandvaluablecommentsthatsubstantiallyimprovedthiswork.IwishtothankDr.ZhisongWangforhishelpduringthiswork.IalsothankallthefellowgraduatestudentsintheSALgroupwithwhomIhadthegreatpleasureofinteracting.Iamdeeplythankfultomyparents,myhusbandandmysonfortheirhelp,encouragement,andsupport.Finally,IwouldliketothankallthepeoplewhohelpedmeduringmyPh.D.study. iii

PAGE 4

page ACKNOWLEDGMENTS ............................. iii LISTOFFIGURES ................................ vii ABSTRACT .................................... ix CHAPTER 1INTRODUCTION .............................. 1 1.1QRTechnologyforExplosiveDetection ................ 1 1.2SignalAmplitudeEstimationinQRApplication ........... 2 1.3ScopeoftheWork ........................... 4 1.4OrganizationoftheDissertation .................... 5 2BACKGROUND ............................... 6 2.1ExplosiveDetectionTechnologies ................... 6 2.2BasicsofQR .............................. 7 2.2.1PrinciplesofQR ......................... 8 2.2.2PulseSequences ......................... 9 2.2.3ObservedSignals ........................ 10 2.3AdvantagesandChallengesofQR ................... 11 2.4QRSignalProcessingMethods .................... 13 3SINGLEANTENNABASEDSIGNALAMPLITUDEESTIMATIONANDDETECTION ....... 16 3.1Introduction ............................... 16 3.2ProblemFormulationandPreliminaries ................ 17 3.3AdaptiveFIRFilterBasedEstimationMethods ........... 20 3.3.1GeneralizedCapon(GC)Filter ................ 20 3.3.2RobustGeneralizedCapon(RGC)Filter ........... 21 3.3.3ApproximateRobustGeneralizedCapon(ARGC)Filter ... 23 3.4Detection ................................ 25 3.5SummaryofImplementationSteps .................. 27 3.6NumericalExamples .......................... 28 3.6.1FirstExample .......................... 28 3.6.2SecondExample ......................... 34 3.7Summary ................................ 35 iv

PAGE 5

38 4.1Introduction ............................... 38 4.2DataModelandProblemFormulation ................ 40 4.3AdaptiveBeamformingMethods .................... 43 4.3.1KnownArraySteeringVector ................. 43 4.3.1.1SCBBasedApproach:SCB1 ............ 44 4.3.1.2SCBBasedApproach:SCB2 ............ 45 4.3.1.3APESBasedApproach:APES1 ........... 46 4.3.2UncertainArraySteeringVector ................ 47 4.3.2.1RCBBasedApproaches:RCB1andRCB2 ..... 47 4.3.2.2GeneralizedRobustAPESBeamformingApproach:GRAPES ....................... 51 4.4Detection ................................ 52 4.5SummaryofImplementationSteps .................. 53 4.6NumericalExamples .......................... 54 4.7Summary ................................ 65 5JOINTCOMPOUNDEXPLOSIVEDETECTION ............ 67 5.1Introduction ............................... 67 5.2ProblemFormulation .......................... 68 5.3RFIMitigationbyGRAPES ...................... 72 5.4JointTNT/RDXDetection ...................... 74 5.4.1Detection ............................. 74 5.4.2DetectorThresholdDetermination ............... 77 5.4.3SummaryoftheDetectionSteps ................ 81 5.5ExperimentalResults .......................... 82 5.6Summary ................................ 84 6SUMMARYANDFUTUREWORK .................... 85 6.1Summary ................................ 85 6.2FutureWork ............................... 87 APPENDIX APROOFOF4142USEDINSECTION 4.3.1.2 ............ 88 BDERVIATIONOF( 4{61 ) .......................... 89 CSTATISTICALPROPERTIESOF~zdIN( 4{63 ) .............. 91 DCFARPROPERTYOFIN( 5{33 ) .................... 93 EPROOFOF( 5{35 ) .............................. 95 FPROOFOF( 5{39 ) .............................. 97 v

PAGE 6

................................... 98 BIOGRAPHICALSKETCH ............................ 105 vi

PAGE 7

Figure page 2{1QRSpectrumof14N[11]. .......................... 9 3{1Anexampleofsignalwaveformversussamplenumber. .......... 29 3{2Anexampleofthemodulusofthereceivedsignalspectra. ........ 30 3{3BiasesandMSEsoftheestimatedamplitudesversustheSNRwhenN=12,ISR1=ISR2=20dB,andL=4.(a)Biases,and(b)MSEs. ..... 32 3{4BiasesandMSEsoftheestimatedamplitudesversustheSNRwhenN=12,ISR1=40dB,ISR2=20dB,andL=4.(a)Biases,and(b)MSEs. 33 3{5Detectionperformance(ROC)comparisonofLS,GC,ARGC,andRGCwhenN=12,ISR1=40dB,ISR2=20dB,SNR=5dB,andL=4. ... 34 3{6Thesignalwaveformversussamplenumber(secondexample). ...... 35 3{7BiasesandMSEsoftheestimatedamplitudesversustheSNR(secondexample)whenN=12,L=4,ISR1=ISR2=20dB.(a)Biases,and(b)MSEs. ..................................... 36 4{1QRsignalvs.samplenumber(obtainedbyscanningaTNTmineinalownoiseandRFI-freeexperiment). ..................... 54 4{2Anexampleofthemainchanneloutput:(a)thereal-partoftheoutputinthetimedomain,and(b)themodulusofthespectrumoftheoutput. 56 4{3Detectionperformance(ROC)comparisonsbetweenthecaseswithandwithoutsteeringvectorerrorsfor(a)SCB1andRCB1,(b)SCB2andRCB2,(c)APES1andGRAPES,and(d)SCB1andSCB2. ....... 58 4{4Detectionperformance(ROC)withdierentvaluesfor(a)RCB1,(b)RCB2,and(c)GRAPES. .......................... 60 4{5Detectionperformance(ROC)withvarioustemporallterorderLinthepresenceofsteeringvectorerrorsfor(a)SCB1,(b)RCB1,(c)SCB2,(d)RCB2,(e)APES1,and(f)GRAPES. .................... 62 4{6Detectionperformance(ROC)comparisonamongthenewmethodsinthepresenceofsteeringvectorerrors. ...................... 65 vii

PAGE 8

............. 66 5{1DatacubefromQRdatacollection ..................... 71 5{2SignalprocessingowchartforjointTNT/RDXdetection. ........ 72 5{3PDFof~z2kand~kforvariousdatalengthN 79 5{4Probabilityoffalsealarmversusdetectionthresholdforthe2-mixturedistributionforthejointTNT/RDXdetectionaswellasindividualTNTorRDXdetection. .............................. 81 5{5TNTfast-timewaveform(obtainedbyscanningaTNTmineinahighSNRandRFI-freeexperiment)andnon-symmetricHanningwindow. .. 83 5{6ROCcurvesfortheGRAPES-GLRTdetector. ............... 84 viii

PAGE 9

Signalamplitudeestimationanddetectionproblemshavebeenencounteredinmanypracticalapplicationsincludingtheemergingquadrupoleresonance(QR)tech-nologyforthedetectionofsubstanceofinterest(e.g.,explosives).IntheQRap-plication,thesignalwaveformisknownapriori.ThemainchallengeofapplyingQRtothedetectionofsubstanceofinterestisthatthereturnedQRsignalisoftenunavoidablycorruptedbystrongradiofrequencyinterferences(RFIs). MotivatedbytheQRapplication,thisdissertationinvestigatesrobustadaptivemethodsfortheamplitudeestimationofasignalwithknownarbitrarywaveforminthepresenceofstrongRFIsandnoise.ThemainobjectiveistofundamentallyaddressthesignalprocessingperspectivesforexplosivedetectionbyQR.Thefocusistoestablishrealisticdatamodels,deviseinnovativesignalprocessingalgorithms,andevaluatetheirperformances. Forthesingleantennabasedapplication,weconsidertheamplitudeestimationofasignalwitharbitraryknownwaveforminthepresenceofstronginterferencesandnoise.Threeadaptivenite-impulseresponselterbasedmethodsarepresentedtosuppressthestronginterferences.WerstextendthegeneralizedCapon(GC) ix

PAGE 10

Fortheantennaarraybasedapplication,weproposeseveraladaptivebeamform-ingapproachestoimprovetheQRsignaldetectionperformanceviaexploitingboththespatialandtemporalcorrelationsofRFIs.Weoperateintheframeworkofsignalamplitudeestimationwithknownsignalwaveformandmakeuseofthreeadaptivebeamformingapproaches,viz.,thestandardCaponbeamformer(SCB),therobustCaponbeamformer(RCB),andtheamplitudeandphaseestimation(APES)algo-rithm,todevelopseveralnewapproachesformitigatingthespatiallyandtemporallycorrelatedRFIs. Forthedetectionofcompoundexplosives,wederiveajointgeneralizedlikelihoodratiotest(GLRT)detectorbasedontheoutputsofRFImitigationltersdesignedforindividualQRexplosiveprobings.WealsoconductadetailedstatisticalanalysisonthejointGLRTdetectorandshowthatithasaconstantfalsealarmrateproperty. x

PAGE 11

1 ].Sincethen,theQRtechnologyhasbeenreceivingincreasingattentionformanyapplications[ 1 ]-[ 9 ]includinghumanitariandeminingandhomelandsecuritybecauseitprovidesauniquesignatureofthesubstanceofinterest. QRissimilartoNMRsincetheyarebothmagneticresonancephenomena[ 1 ].Howevertheyhaveasignicantdierence.Insteadofusinganexternal(static)magneticeld,likeanNMRdevice,aQRdevicemakesuseofthenaturalcrystallineelectricaleldgradientwithinthematerials[ 1 ].Hence,itisunderstoodthatQRissimilartoNMRwithoutamagnet[ 1 ].Asaresult,QRbasedequipmentissaferandmorereliabletouseandtransportthanitsNMRcounterpart. Inrecentyears,theurgentdemandforhomelandsecurityandtheghtagainstterrorismmakesexplosivedetectionahottopic.Asweknow,traineddogshavebeenrecognizedasthequickestandmostreliabledetectorsforexplosives.However,theyeasilybecometiredandtheresourceofdogsthatcanbetrainedforthispurposeisverylimited.Hence,theneedtodevelopmachinebaseddetectorsbecomesurgent[ 10 ].TheInVision(nowpartofGE)baggagescreenerisanexamplewhichisusedinmanyairportsforaviationsecurity.ThebaggagescreenerisashieldeddevicebuiltbasedontheQRtechnology.However,whencost,size,andweightareconcerned,unshieldedQRsystemsarepreferredovertheirshieldedcounterparts,suchashandheldQR 1

PAGE 12

wandsforscreeningpersonnelandQRshoescanners[ 11 ].However,radiofrequencyinterference(RFI)suppressioniscriticalforunshieldedQRsystems[ 1 ]. LandminedetectionisanotherimportantapplicationoftheQRtechnology.Be-causeofthehugeeconomiclossandseverethreattohumanlifecausedbylandmines,landminedetectionhasreceivedsignicantattentionfrommanygovernmentsandhumanitariangroupsinrecentdecades[ 12 ].Itisestimatedthattherearemorethan100millionlandminesinover70countriesaroundtheworldandthataninjuryordeathfromlandminesoccursevery20minutes[ 3 9 ],[ 12 ]-[ 14 ].Byusingexistingtechnologies,itwouldtakemorethan500yearsand$33billiontocleanthemupassumingnomoremineswouldbeburied[ 15 16 ].Hence,itisurgenttodevelopecientandrobustmethodstodetectlandmines.TheuniquespectralsignaturesofexplosivesprovidedbyQRmakeQRapromisingmethodforlandminedetection[ 1 ]. 1 ],[ 17 ]-[ 19 ].IntheQRapplication,thesignalwaveformisknownaprioritowithinamultiplicativeconstant[ 17 ].ThemainchallengeofapplyingQRtothedetectionofsubstanceofinterestisthattheQRprobingisoftenunavoidablycorruptedbystrongRFIsthatareusuallyspatiallyandtemporallycorrelated.Forinstance,theQRfrequencyforthetrinitrotoluene(TNT)explosiveisaround842KHzatnormalroomtemperature[ 1 ].Sincethisfrequencyfallswithintheamplitudemodulation(AM)radiofrequencybandandcannotbechangedbyothermeans,theAMradiosignalscanappearasstrongRFIsthatcanseriouslydegradetheQRsignaldetectionperformance.HencetodetecttheveryweakQRsignal,theRFIsmustbeeectivelysuppressedinordertoattainaccuratesignalamplitudeestimationandachievesatisfactorydetectionperformance.MotivatedbytheQRapplication,thisdissertationinvestigatesrobustadaptiveamplitudeestimationforasignalwithaknownarbitrarywaveforminthepresenceofstrongRFIsandnoise.

PAGE 13

Manymethodshavebeenproposedforsignalamplitudeestimation([ 17 ],[ 20 ]-[ 22 ]andthereferencestherein).Oneofthemistheleast-squares(LS)method[ 21 22 ],whichiswidelyusedforsignalamplitudeestimationduetoitssimplicity.However,inthepresenceofstrongcoloredinterferencesandnoise,theperformanceofLSdegradessignicantly.Severaladaptivenonparametricmethods,includingstandardCaponbeamformer(SCB)[ 23 ],AmplitudeandPhaseEstimation(APES)[ 20 ],andMAtchedFIlter(MAFI)[ 21 ],wereproposedforestimatingthecomplexamplitudesofsinusoidalsignals[ 21 ].However,thesemethodsarenotdirectlyapplicabletotheQRproblemduetothesignalwaveformbeingnon-sinusoidal.Furthermore,inthearraybasedapplications,theseapproachesassumethataprecisesteeringvectorisavailable.Theyarenotimmunetothesteeringvectorerrorandthussuerfromlowrobustnessproblem.Theymayperformpoorlywhenthenumberofsnapshotsissmalland/ornon-stationaryinterferenceandnoiseexist.Thesetwofactorscanbeviewedasequivalenttosteeringvectorerrorsevenwhenthearraysteeringvectorhasnoerror[ 24 ]-[ 26 ].Therefore,newrobustadaptivemethodsareneededfortheQRapplicationundertheframeworkofsignalamplitudeestimationwithanarbitraryknownsignalwaveform[ 19 ]. Inadditiontothearbitraryknownsignalwaveformandrobustnessissues,an-otherimportantissuethatneedstobetakenintoaccountintheQRapplicationisthespatialandtemporalcorrelationsofRFIs[ 17 18 ].Referenceantennas,whichreceiveRFIsonly,canbeusedtogetherwiththemainantenna,whichreceivesboththeQRsignalandtheRFIs,forimprovedRFImitigation[ 1 17 ],[ 27 ]-[ 30 ].Bytakingadvan-tageofthespatialcorrelationoftheRFIsreceivedbytheantennaarray,theRFIscanbereducedsignicantly.However,theRFIsareusuallycoloredbothspatiallyandtemporally[ 31 32 ],andhenceexploitingonlythespatialdiversityoftheantennaarraymaynotgivethebestperformance.Althoughseveralapproacheshavebeenpro-posedtoreducethenegativeeectofRFIsonlandminedetection[ 1 17 18 29 33 ],

PAGE 14

exploitingboththespatialandtemporalcorrelationsoftheinterferenceshasnotbeenfullyinvestigated.Inthisstudy,wewillexploitboththespatialandtemporalcorrelationsofRFIstoimprovetheexplosivedetectionperformance. First,weinvestigatethesingleantennabasedamplitudeestimationofasignalwithanarbitraryknownwaveforminthepresenceofstronginterferencesandnoise.Threeadaptivenite-impulseresponse(FIR)lterbasedmethodsarepresentedtosuppressthestronginterferences.WerstextendthegeneralizedCapon(GC)esti-matortotheproblemofsignalamplitudeestimation.Thenwedevisetworobustiedmethodstomitigatethesmallsnapshotproblemsbyallowinganuncertaintysetforthesignalcovariancematrix. Second,weconsidertheantennaarraybasedsignalamplitudeestimationanddetectionproblem.WepresentseveraladaptivebeamformingapproachestoimprovetheQRsignaldetectionperformanceviaexploitingboththespatialandtemporalcorrelationsoftheRFIs.Weoperateintheframeworkofsignalamplitudeestimationwithknownsignalwaveformandmakeuseofthreeadaptivebeamformingapproaches,viz.,SCB,therobustCaponbeamformer(RCB),andAPESalgorithm,todevelopseveralnewapproachesformitigatingthespatiallyandtemporallycorrelatedRFIseectively.

PAGE 15

Third,weinvestigatethecompoundexplosivedetectionproblem.Sinceasingleminecancontainmorethanonetypeofexplosives(e.g.,TNTandRoyalDemolitioneXplosive(RDX)compound),adetectordesignedtodetectonlyonetypeofexplosivemaynotprovidethebestdetection.Inthisaspect,wefocusonthejointdetectionofTNTandRDXexplosivesforthelandminedetectionviatheQRsensor.Wederiveageneralizedlikelihoodratiotest(GLRT)detectorforthejointcompounddetectionbasedontheoutputsofRFImitigationforindividualQRexplosiveprobings,whichisreferredtoasthejointGLRTdetector.WealsoconductadetailedstatisticalanalysisonthejointGLRTdetectorandshowthatourdetectorhasaconstantfalsealarmrate(CFAR)propertyandthatthedetectionvariableobeysa2-mixturedistributioninthemine-freescenario. 2 brieyin-troducesthebackgroundofexplosivedetectionviaQR.InChapter 3 ,threeadaptivemethodsarepresentedtodealwiththesingleantennabasedsignalamplitudeesti-mationproblem.InChapter 4 ,severaladaptivebeamformingapproachesandtheirrobustiedversionsareproposedtoimprovetheQRsignaldetectionperformance,whichexploitbothspatialandtemporalcorrelationsoftheRFIs.Chapter 5 presentsajointGLRTdetectorforthecompoundexplosivedetectionandconductsatheoret-icalanalysisofthedetectionstatistics.Finally,wesummarizethisworkandoutlinethefutureworkinChapter 6

PAGE 16

Inthischapter,wewillbrieyintroducethebackgroundofexplosivedetectionviaQR.First,wewillintroducetheexistingexplosivedetectiontechnologies,espe-ciallyforthelandminedetection;second,wewillbrieyreviewsomebasicsofQR,whichincludestheprincipleofQR,somecommonlyusedpulsesequences,andtheobservationsignalsinQR;third,wewillpresentanoverviewoftheadvantagesandthechallengesofQR;nally,aliteraturereviewoftheexistingQRsignalprocessingmethodswillbegiven. 3 ]. Aconventionaltechnologyforthelandminedetectionistheelectromagnetic(EM)basedmetaldetector.Becauseitischeapandeasytooperate,ithasbeenwidelyusedinpractice.Themetaldetectorcanprovideahighprobabilityofde-tection(Pd)foranti-tank(AT)mines,whichcontainabout510kgofexplosivesandareburiedwithin10cmdepth[ 1 ].However,itishardlyusefultodetecttheburiedanti-personnel(AP)mines,whichareusuallyverysmall,contain50100gofexplosives,andareburiedunderthesurface[ 1 ].ThereectedEMsignalfromanAPmineisveryweakcomparedwiththatfromanATmine[ 1 ].Thismakesitdiculttodistinguishlandminesfromothermetaldetritus(clutter),suchasshellfragments,rustynails,etc.[ 1 ].Asaresult,metaldetectorsinevitablysuerfromahighfalsealarmrate(FAR).Usually100-1000falsealarmsforeachrealminewillbeproducedbysuchkindsofmetalclutter[ 13 ]. 6

PAGE 17

Asweknow,thebasicrequirementforthelandminedetectionistoachieveahighPd(>99%)withareasonablylowFAR,andthedetectionsystemsshouldbecapableofoperatingundervariousenvironments[ 3 ].Moreover,mostofthemodernlandminesarenotmetal-casedbutplastic-orwood-cased.Theycontainverylittleorevennometalandthuscanhardlybedetectedbymetaldetectors.Hence,themetaldetectorcannotsatisfythesebasicrequirements,anddevelopingnewtechnologiestodetectlandminebecomesveryurgent. Inthepastfewdecades,manytechnologieshavebeeninvestigatedfordetectingbothmetalandnon-metallandmines.Theseinclude,forexample,groundpenetratingradar(GPR)[ 34 ]-[ 37 ],thermalneutronactivation(TNA)[ 38 ],QRsensor[ 1 ],traceexplosivedetector[ 39 ],acousticdetector[ 40 ],advancedmetaldetector,X-ray[ 41 ],infrared[ 42 ]andmultispectralimaging[ 43 ]methods,andminedetectingdogs[ 13 ].Amongthem,QRisapromisingtechnologybecauseaQRdetectorintendstodetectthecontentinsteadofthecaseofthelandmine.Explosives(e.g.,TNTandRDX)areusuallyrichin14NthatisassociatedwithhighlyspecicQRsignalsatparticularfrequencies[ 1 29 33 ],[ 44 ]-[ 46 ].Hence,QRcanbeusedasaconrmationsensorassistingothersensorsforFARreduction. 3 4 47 ].SmithandhiscolleaguesatKing'sCollegeoftheUniversityofLondonhavebeenworkingextensivelyonexplosivedetectionsince1980[ 48 ]-[ 51 ].TheyproducedcommercialQRdetectionsystemsfornarcoticsandexplosivedetectionforairlinebaggageinspection[ 3 ].Schianoetal.atPennsylvaniaStateUniversityproposedafeedbackoptimizationmethodtoachieve

PAGE 18

theoptimalperformanceofthedetectionsystem[ 52 53 ].Theirmethodcanreachthemaximumsignal-to-noiseratio(SNR)byadaptivelyadjustingthepulsewidth,andtherebyimprovingthedetectabilityoflandminesbyQR[ 52 ]. Intherecentdecade,QuantumMagnetics(QM),Inc.hasworkedonprojectsre-latedtoexplosivedetectionbyQR[ 1 11 ],[ 44 ]-[ 46 ],[ 54 ],whichincludenon-destructiveevaluation,landminedetection,andsomesecurityapplications.QMhasalsobuiltcommercialQRdetectionsystemsforexplosivedetectionusedinairports[ 11 ]. 2 ].ItissimilartoNMRandthemagneticresonanceimaging(MRI)techniqueusedinthemedicalindustrybutwith-outusingamagnet[ 1 ].Itprovidesquitespecialpossibilitiesfordetectingchemicalsubstancesinsolidform. ThebasicdetectionprinciplebyQRissimple([ 1 ],p.1110):\applyingapulseorseriesofRFpulsesresonantattheappropriateQRfrequencyofthematerialofinterestandlookingforthepresence(orabsence)ofareturnsignal."ThedetectionbyQRincludesthefollowingsteps[ 55 ].

PAGE 19

Sincethefrequencyoftheechofromthenucleidependsonthemolecularstruc-tureoftheatoms,itisuniqueforeachtypeofexplosive.Hence,QRcanbeusedtoaccuratelydetectthepresenceofexplosive,duetoitshighsensitivitytothetarget'schemicalsubstance.Figure 2{1 showstheQRfrequenciesofsomeexplosivesandnarcotics[ 11 ]. Figure2{1. QRSpectrumof14N[11]. 2 ].Listedbelowareseveralcommonlyusedmulti-pulsesequences. 3 ]toenhancetheSNR.ItistherstsequencethatproducesaseriesofQR

PAGE 20

signalsinashorttimeforcoherentlyaveraging,whichwasintroducedinthelate1970s[ 3 56 ]. 53 ],p.85).TheSORCsequencecanproducethestablespin-echoessuchthatthereceivedsignalscanbecoherentlyadded[ 3 ].OneadvantageoftheSORCsequenceisthatthegeneratedsignalhasthecomparableamplitudewiththatofthefreeinductiondecaysignal[ 53 ].Itwasintroducedintheearly1980s[ 57 ]. 3 58 ].ThiscombinedpulsesequencecanbeusedtoreducethedirectcurrentosetandremovethesystemcorrelatednoisebyvaryingthephaseoftheQRsignalinapredictablemannertoseparateitfromotherartifacts[ 3 ].ThePAPSisrepeatedntimes,followedbynrepetitionsofNPAPS.Theentiresequencemayberepeatedmtimesinordertoim-provesensitivity.SimilartoSORC,thiscombinedsequencecanalsoproducestablesignals,whichcanbecoherentlyaveragedtoimprovetheSNR[ 3 ]. 16 ],[ 48 ]-[ 51 ]. 49 ],p.289).DuetothefastdecayingoftheFIDsignalandthestrongringingaftertheRFpulse,FIDcanhardlybeusedfortheQRsignaldetection.

PAGE 21

16 ].However,particularpulsesequencescanbeusedtotakethembacktoinphaseandusefulspinechoescanbeobtainedduringalongertimethanFID[ 16 ].Therefore,spinechoesarewidelyusedinthepracticalQRapplications. 1 ]-[ 3 ],whicharesummarizedasfollows. Despitetheaforementionedadvantages,severalchallengesneedtobeaddressedbeforeQRcanbeused.ThemainrestrictionisthatthemeasuredSNRislowbecausethereturnedQRsignalisweakcomparedwiththeambientnoise[ 16 ],especiallyforsmallAPlandmines.SomeeortshavebeenmadetoenhancetheSNRofQRbyimprovingthehardwaredesignincludingthesearchcoilandantennas([ 1 ]andthereferencestherein). SueringfromthestrongRFIsisanotherchallengeforthepracticalQRapplica-tion.SincethefrequencyoftheQRsignalislow(0.56MHz)[ 51 ],itisunavoidablycorruptedbyRFIslocatedinthisfrequencyband.Forexample,thefrequencyoftheTNTQRsignalis0.842MHz,whichiswithinthefrequencybandofAMradio.Hence

PAGE 22

theAMradiosignalcanappearasstrongRFIsthatcanseriouslydegradetheexplo-sivedetectionbyQR.Therefore,todetecttheveryweakQRsignal,itisessentialtomitigatetheRFIs[ 1 16 17 59 ]. Theringingproducedbythesearchcoilandassociatedhardwareisalsoaprob-lemofQRsystem[ 1 16 ].Althoughtheexcitingpulsehasended,thecoilcannotimmediatelyobtaintheusefulQRsignalbecauseoftheringproblem[ 16 ].Usingthephasecyclingofthepulsesequenceisanecientwaytoreducetheringingproblem[ 1 8 16 ]. UsingthesignalaverageisanotherecientmethodtoimproveSNR[ 1 3 ].In-steadoftransmittingonepulse,thetransmittersendsoutamulti-pulsesequence.ThentheobtainedQRsignalscanbecoherentlyaveragedovertheentirepulsese-quence.Inaddition,theRFpulsesequencesalsoneedtobecarefullydesignedtomaximizetheSNRinaunittime[ 2 ].Fortheuncorrelatednoise,theSNRwillbeincreasedbythenumberoftheaveragedQRsignals[ 3 ].However,thismethodisnoteectiveinthepresenceofcorrelatednoiseorinterferences[ 3 ]. OptimizingthesearchcoildesignisalsoanecientwaytoincreaseSNRandhenceimprovetheQRsignaldetectionperformance[ 60 ].Inthelandminedetectionapplication,surfacecoilsarewidelyused.Suitsetal.haveaddressedmanycoildesignissuesandproposedseveralmethodstoimprovethecoildesign[ 60 ]-[ 63 ]. ReducingRFIsisanotherwaytoenhancetheSNR.InthehardwaredesignbothpassiveandactivestrategieshavebeenconsideredtoreduceRFIs[ 1 ].TheNavalResearchLaboratory(NRL)designedaQRgradiometercoil[ 60 ],whichisapassiveapproach.Itisreportedthatthegradiometercoilcanreducethefareldmagneticinterferenceby30dB[ 1 ].However,theacquiredQRsignalmayalsobereducedatthesametime[ 60 ].AsymmetricgradiometershavebeenproposedtopartlysolvetheQRsignallossproblem[ 16 ].QMdevelopedanecientQRcoil(usedasthemainantenna)andasetofexternalremoteantennas(usedasreferenceantennas)toreduce

PAGE 23

RFIs[ 1 ].ThemainantennaisdesignedandplacedtoreceivebothRFIsandQRsignalwhilethereferenceantennasreceiveRFIsonly[ 1 ].RFIsinthemainantennacanbesignicantlyreducedbysubtractingtheestimatedRFIsfromthereferenceantennas[ 1 ].Thedrawbackofthisactiveapproachisthatitrequireshighdynamicrangeandaccuratebalanceoftheantennas[ 1 ]. Theenergydetectoristhemostwidelyusedsignaldetectionmethodbecauseitissimpleandeasytoimplement.Itworksasfollows:rst,ittransformsthecollectedQRsignalintothefrequencydomainandcalculatesthepowerofthefrequencybinofinterest;then,apresetthresholdisusedtodeterminethepresenceofthetargetofinterest,suchasalandmine.Thisapproachworksquitewellwhenthesignal-to-inference-plus-noiseratio(SINR)ishigh[ 16 ].However,inthepracticallandminedetection,wheretheSINRisusuallylow,itisdiculttoobtainagooddetectionperformancebyusingthismethodalone. AnadaptivenoisecancellationmethodhasbeenusedbyTantumetal.[ 33 ]toreducetheRFIsforQR.TheirmethodisusedinasimilarfashiontotheQM'sactiveapproachforRFIreduction[ 1 ].Itisreportedthatbyusinga1-tapleastmeansquaresalgorithm,theadaptivenoisecancellationmethod[ 64 65 ]canreducetheRFIsbymorethan50dB[ 33 ].However,thismethodmayamplifythewhitenoiseanditmaysuerfromthesignalcancellationduetominimizingthetotaloutputpower[ 64 ]. AnaveragepowerdetectorbasedonpowerspectralestimationalgorithmshasbeenproposedbyTanetal.in[ 29 ].TheexperimentalresultsinTanetal.[ 29 ]show

PAGE 24

thattheaveragepowerdetectoroutperformsthenon-adaptiveBayesiandetector,andcanproviderobustdetectionperformancebythedistinguishablefeaturesoftheQRsignalandtheRFIinthefrequencydomain[ 59 ].However,wenotethattheaveragepowerdetectorispreferredaftertheRFImitigation.ItmaysuerfromthelowSINRjustastheconventionalenergydetector.ByconsideringtheRFIasacolorednon-Gaussianprocess,Tanetal.[ 66 ]derivedaCramer-Raolowerbound.Morerecently,theyproposedatwo-stepadaptiveKalmanltertoestimateanddetecttheQRsignalinthepost-mitigationsignal[ 59 67 ].AsshownwithnumericalresultsinTanetal.[ 67 ]thismethodcanproviderobustlandminedetectionperformance.However,toobtainthecoecientandcovariancematrices[ 67 ],thismethodrequirestrainingdata,whichmaynotbeavailableinrealapplication. Jiangetal.[ 17 68 ]investigatedthelandminedetectionbyQRundertheframe-workofsignalamplitudeestimationwithknownsignalwaveformandsteeringvector.Theyproposedamaximumlikelihood(ML)estimatorandaCaponestimatorandderivedclosed-formexpressionsforthebiasandmean-squarederrors(MSE)ofbothestimatorsinthepresenceofspatiallycoloredbuttemporallywhiteinterferenceandnoise[ 17 ].Theyalsoshowedthatbothestimatorsareasymptoticallystatisticallyecientforlargedatasnapshots.TheMLestimatorisunbiasedwhiletheCaponestimatorisbiaseddownward.Analternativeleastsquare(ALS)methodisalsopro-posedtoconsideramoregeneralcase,inwhichtheinterferenceandnoisearebothtemporallyandspatiallycolored.ThenumericalresultsinJiangetal.[ 17 ]showthatinmostcases,theALSmethodissuperiortothemodel-mismatchedmaximumlike-lihood(M3L)method,whichignoresthetemporalcorrelationoftheinterferenceandnoise[ 17 ].However,ALSisslightlyworsethanM3Lformorechallengingcases,wherethedesiredsignalandtheinterferencearecloselyspacedinthetemporalfrequencydomain.

PAGE 25

StegenainvestigatedseveraldetectionalgorithmsforQRsignals[ 9 ],whichin-cludeBayesianmethod,matchedlter(MF),andmaximumentropy(ME)method.ItisobservedthattheBayesianmethodisthemostrobustmethodagainstnoise;however,itrequiresaprioriinformation.TheperformanceofMFandMEdegradesrapidlyastheSNRdecreases.Inaddition,theMEmethodisfoundtobemostcomputationallyintensiveamongthesethreemethods. ByexploitingthetemperaturedependencyoftheQRfrequencies,Jakobssonetal.developedseveralnewmethods,whichincludeanon-linearleastsquaresmethod,anapproximatemaximumlikelihooddetector(AML),andafrequencyselectiveAMLdetector,toenhancetheSNRandimprovetheQRsignaldetectionperformance[ 14 15 27 ]. WehaveinvestigatedtheRFImitigationforlandminedetectionbyQRinLiuetal.[ 18 ].ByexploitingboththespatialandtemporalcorrelationoftheRFIs,weproposeacombinedapproachtomitigatetheRFIsecientlyandeectivelyandimprovetheTNTdetectionperformance.FirstweconsideredexploitingthespatialcorrelationoftheRFIsonlyandproposedamaximumlikelihood(ML)estimatorforsignalamplitudeestimationandaCFARdetectorforTNTdetection;second,weadoptedamulti-channelautoregressive(MAR)modeltotakeintoaccountthetemporalcorrelationoftheRFIs;third,wemadeuseofthespatialandtemporalcor-relationsbyusingatwo-dimensional(2-D)robustRCBfollowedbytheMLmethodforimprovedRFImitigation.Finally,wecombinedthemeritsofallthreemethodsforTNTdetection.Theexperimentalresultsshowthatthecombinedapproachout-performsallthethreeproposedmethods,anditsrobustnesshasbeendemonstratedaswellbyusingdatasetscollectedatdierenttimesandconditions.

PAGE 26

21 ],ournewmethodsaredesignedtosuppressthestronginterferencesandnoisebypassingtheobserveddatasamplesthroughanadaptiveniteimpulseresponse(FIR)lter.ThenthesignalamplitudeisestimatedfromtheFIRlteroutputusingasimpleLSmethod.ThreeadaptiveFIRltersareprovidedinthischapterbasedonthegeneralizedCaponprinciple[ 69 ].WerstextendthegeneralizedCapon(GC)estimatorin[ 69 ]totheproblemofsignalamplitudeestimation.Thenbyallowinganuncertaintysetforthesignalcovariancematrix,weproposearobustGC(RGC)estimatortomitigatethesmallsnapshotnumberproblems.TosimplifythecomputationalcomplexityoftheRGCestimator,wealsodeviseanapproximaterobustGC(ARGC)estimatorforsignalamplitudeestimation.NumericalexamplesshowthattheadaptivemethodsoutperformtheLSmethodsignicantlyandthattherobustiedadaptivemethodsoutperformtheirnon-robustiedcounterpart. Theremainderofthischapterisorganizedasfollows.InSection 3.2 ,wefor-mulatetheproblemofinterestandprovidesomepreliminaryresults.Section 3.3 presentstheadaptiveapproaches.Section 3.4 providesadetectionscheme.Section 3.5 summarizestheimplementationstepsoftheproposedmethods.Numericalex-amplesareprovidedinSection 3.6 todemonstratetheperformanceandeectivenessofthesignalamplitudeestimators.Finally,Section 3.7 containsthesummary. 16

PAGE 27

wherex(n)2Cisthenthmeasureddatasample,s(n)2Cisthenthsampleoftheknownsignalwaveform,istheunknownsignalamplitude(tobeestimated),e(n)2Cdenotestheinterferenceandnoiseterm(whichisassumedtobeuncorrelatedwiththeknownsignal),andNisthetotalnumberofdatasamples.Theproblemofinteresthereinistoestimatethesignalamplitudefromtheobserveddatasequencefx(n)gNn=1inthepresenceofinterferencesandnoise. Todealwiththecorrelatedinterferenceandnoise,weadoptthe\stacking"tech-niqueusedin[ 20 21 ].Bypartitioningfx(n)gNn=1intoeNoverlappingsubvectors,referredtoassnapshots,withlengthL=N)]TJ/F8 11.95 Tf 14.32 3.02 TD[(eN+1,thedatamodelin( 3{1 )canberewrittenas: where and with()Tdenotingthetranspose. Wenotethatwhenthesignalwaveformsatises

PAGE 28

withcpbeingaconstantindependentofn(forexample,( 3{6 )satisedbyacomplex-valuedsinusoid),Equation( 3{2 )reducestothestandardformin[ 17 ],i.e., with Thenthemethodsproposedin[ 17 21 ]canbeapplieddirectlytoestimate.Inthischapter,however,weconsiderthegeneralcasewheretheknownsignalwaveformisarbitrary,forexample,liketheoneshowninFigure 3{1 ,whichoccursintheapplicationofusingQRtechnologyforexplosivedetection. Let denotethecoecientvectorofanFIRlteroflengthL,whosedeterminationwillbeaddressedinthenextsection.Passingthesignalx(n)throughthelterhyields (3{10) =sF(n)+hHe(n);n=1;;eN; where()Hdenotestheconjugatetransposeand ApplyingtheLSmethodto( 3{11 )givesthefollowingestimateof =hHXsh hHbRsh;

PAGE 29

where and isthesamplecovariancematrixofthesignalvector,and()denotesthecomplexconjugate.Notefrom( 3{14 )thatascalingfactorofhdoesnotaect~. Whenisknowntobereal-valued,theestimateofisgivenby ~R=Re(~);(3{17) whereRe()denotestherealpart.Whenisknowntobereal-valuedandnon-negative,theestimateofisgivenby ^=8><>:Re(~);ifRe(~)>00;ifRe(~)0:(3{18) ThestandardLSmethodcanbeviewedasaspecialcaseof( 3{14 )-( 3{18 )corre-spondingtohbeingascalar(i.e.,L=1).Forcomplex-valued, ~LS=PNn=1x(n)s(n) TheLSestimatesofwhenisknowntobereal-valuedorreal-valuedandnon-negativearegiven,respectively,by ~LSR=Re(~LS);(3{20) and ^LS=8><>:Re(~LS);ifRe(~LS)>00;ifRe(~LS)0:(3{21)

PAGE 30

3{14 )fortheestimationofthesignalamplitude. 3{11 ),theaveragepoweroftheFIRlteroutputcanbeexpressedas (3{22) =hHbRh; where isthesamplecovariancematrixoffx(n)g.From( 3{2 ),wehaveapproximatelythat where20=jj2,andbQdenotesthesamplecovariancematrixoftheinterferenceandnoiseterm. TheGClterisobtainedbysolvingthefollowingmaximumsignal-to-interference-plus-noise(SINR)problem[ 19 ] maxhhHbRsh hHbRh:(3{26) Notethat( 3{26 )isapproximatelyequivalentto minh20hHbRsh+hHbQh hHbRsh()minhhHbQh hHbRsh()maxhhHbRsh hHbQh: Asiswell-known,thesolutiontotheoptimizationproblemaboveisgivenby ^hGC=Pmax(bR)]TJ/F3 7.97 Tf 6.58 0 TD[(1bRs);(3{28)

PAGE 31

wherePmax()denotestheprincipaleigenvectorcorrespondingtothelargesteigen-valueofamatrix.Werefertotheestimatorof(see( 3{14 ))obtainedbyusingthelterin( 3{28 )astheGCestimator. Usingthe^hGCin( 3{28 )yieldsthefollowingestimateof20: ^20=hHGCbRhHGC=1 (3{29) wheremax()denotesthemaximumeigenvalueofamatrix. 70 ]thatallowsanuncertaintyinthesignalcovariancematrix,andthenderivesarobustgeneralizedCapon(RGC)lter. Let whereD0denotesasquarerootofbRs.Weassumethatthe\true"squarerootmatrixDbelongstotheuncertaintyset: wheredenotestheradiusofthe\uncertaintysphere"andjjjjFdenotestheFrobeniusnormofamatrix. SimilartotherobustCaponbeamformer(RCB)in[ 70 ],weadoptthecovariancettingframeworkandformulatetheRGCoptimizationproblemas: max20;D20subjecttobR)]TJ/F4 11.95 Tf 11.96 0 TD[(20DDH0jjD)]TJ/F7 11.95 Tf 11.95 0 TD[(D0jj2F: ToexcludethetrivialsolutionD=0,theparametermustsatisfythefollowinginequality

PAGE 32

ForanygivenD,thesolution20to( 3{32 )isreadilyobtainedbynotingfollowingequivalences: 2DDHbR)]TJ/F11 5.98 Tf 7.78 3.26 TD[(1 20 (3{34) 2DDHbR)]TJ/F11 5.98 Tf 7.78 3.26 TD[(1 2)0,201 ~20=1 whichisthesameastheonein( 3{29 ). Byusing( 3{35 ),theoptimizationproblemin( 3{32 )canbesimpliedas: minDmax(DHbR)]TJ/F3 7.97 Tf 6.59 0 TD[(1D)subjecttojjD)]TJ/F7 11.95 Tf 11.95 0 TD[(D0jj2F:(3{36) Viarelativelysimplealgebraicmanipulations,wecanreformulate( 3{36 )asaSemi-DeniteProgramming(SDP)problem[ 71 ]: minsubjecttomax(DHbR)]TJ/F3 7.97 Tf 6.58 0 TD[(1D)jjD)]TJ/F7 11.95 Tf 11.96 0 TD[(D0jj2F; whichisequivalentto minsubjecttoI)]TJ/F7 11.95 Tf 11.96 0 TD[(DHbR)]TJ/F3 7.97 Tf 6.58 0 TD[(1D0jjD)]TJ/F7 11.95 Tf 11.95 0 TD[(D0jj2F;

PAGE 33

andhenceequivalentto minsubjectto264IDHDbR3750264vecH(D)]TJ/F7 11.95 Tf 11.95 0 TD[(D0)vec(D)]TJ/F7 11.95 Tf 11.95 0 TD[(D0)I3750; wherevec()denotesthevectorizationoperator(stackingthecolumnsofamatrixontopofeachother).However,theso-obtainedSDPproblemhaslargedimensionsandthereforeitscomputationalcomplexityissomewhathigh[ 71 ].UsingthebDobtainedbysolving( 3{39 )in( 3{28 ),weobtaintherobustgeneralizedCapon(RGC)lter ^hRGC=Pmax(bR)]TJ/F3 7.97 Tf 6.59 0 TD[(1bDbDH):(3{40) ThecorrespondingestimatorofisreferredtoastheRGCestimator. 3{36 )withitsupperboundtr(DHbR)]TJ/F3 7.97 Tf 6.58 0 TD[(1D),wheretr()denotesthetraceofamatrix: minDtr(DHbR)]TJ/F3 7.97 Tf 6.59 0 TD[(1D)subjecttojjD)]TJ/F7 11.95 Tf 11.95 0 TD[(D0jj2F:(3{41) Itiseasytocheckthatthesolutionto( 3{41 )occursontheboundaryoftheconstraintset[ 70 ].Hencetheproblemin( 3{41 )canbesimpliedasfollows: minDtr(DHbR)]TJ/F3 7.97 Tf 6.58 0 TD[(1D)subjecttojjD)]TJ/F7 11.95 Tf 11.95 0 TD[(D0jj2F=:(3{42) UsingtheLagrangianmultipliermethodology,weconstructafunction#as

PAGE 34

where0istheLagrangemultiplier.Minimizing#respecttoDyields wherethematrixinversionlemma[ 25 ]hasbeenusedtoobtainthesecondequalityin( 3{44 ).TheLagrangemultiplierin( 3{44 )canbeobtainedasthesolutionofthefollowingconstraintequation: Let wherethecolumnsofUcontaintheeigenvectorsofbR,and)]TJ/F1 11.95 Tf 12.61 0 TD[(isadiagonalmatrixwithitsdiagonalelementsbeingthecorrespondingeigenvalues12L.Let andletzTldenotethelthrowofZ,thenwehave Hence,theconstraintequation( 3{45 )canbewrittenas: Sincetherst-orderderivativeof$()withrespecttoislessthanzero,forany0thefunction$()isstrictlymonotonicallydecreasingfunctionfor0.Furthermore,$(0)=PLl=1jjzljj2>0,andwenotealsothatfor6=0,

PAGE 35

lim!1$()=0<.Hence,thereisauniquesolution>0to( 3{49 ).Alowerboundandanupperboundoncanbeobtainedasfollows.Replacinglin( 3{49 )by1andbyL,respectively,yields From( 3{50 ),weobtainthefollowinglowerandupperboundson: 1p Lp From( 3{49 ),wecanalsoobtainanotherupperboundonby(droppingthe\1"inthedenominatorof( 3{49 )) Therefore 1p Lp Equation( 3{49 )canbesolvedecientlybyusingtheNewtonmethodinitializedwithavalueofintheintervalgivenby( 3{53 ).ThentheestimatedeDisobtainedbyinsertingtheso-obtainedinto( 3{44 ).UsingthiseDin( 3{28 ),weobtainanapproximaterobustGC(ARGC)lteras ^hARGC=Pmax(bR)]TJ/F3 7.97 Tf 6.59 0 TD[(1eDeDH);(3{54) andtheassociatedestimatorofisreferredtoastheARGCestimator. 3{14 )directlyforsignaldetectiondoesnotyieldaconstantfalsealarmrate(CFAR)detector[ 18 ].Instead

PAGE 36

wemightthinkofusingthefollowingdetectionvariable(seeSection 4.4 fordetails): ~zd,Re(~) cvar[Re(~)]; wherecvar[Re(~)]isanapproximatevarianceofRe(~). Inserting( 3{2 )into(3-17)yields ~=+hHPeNn=1e(n)sF(n) Thenwecancalculatethevarianceof~,whichisgivenby var(~)=E[j~)]TJ/F4 11.95 Tf 11.95 0 TD[(j2]=E264hHPeNn=1e(n)sF(n)PeNn1=1sF(n1)eH(n1)h Assuminghisindependentofe(n)andhHe(n)isawhitesequence,( 3{57 )canbeapproximatedas var(~)E264hHPeNn=1jsF(n)j2e(n)eH(n)h where UsingthestatisticalpropertyofcircularlysymmetriccomplexGaussiannoise,wehave var[Re(~)]=1 2var(~)1 2hHQh

PAGE 37

whereQisanestimateofQobtainedbyusing^in( 3{18 )toreplacein( 3{2 ): Q=1 whichisguaranteedtobenon-negativedenite. Inserting(3-17)and( 3{60 )into( 3{55 )yields ~zd=p q Substituting(3-14)into( 3{62 )gives ~zd=p q Underthenullhypothesis=0(i.e.,nosignalofinterestispresent),itcanbeeasilyshownthatthedistributionof~zdisapproximatelyN(0;1).ThisleadsdirectlytoadetectionrulethathasaCFARpropertysincethestatisticalpropertiesof~zdareindependentoftheinterferenceandnoisescenario. 3{3 )andcalculateitssamplecovariancematrixbRusing( 3{24 ).Similarly,formfs(n)geNn=1accordingto( 3{4 )andcalcu-latebRsusing( 3{16 );thencalculateXsusing( 3{15 ); 3{28 ),RGC( 3{40 ),andARGC( 3{54 ))inSection 3.3 ; 3{17 )and( 3{18 );

PAGE 38

3{61 ); 3{63 ). 3{1 )containsstrongnarrowbandinterferencesandnoise,i.e., wherev0(n)denotesthenoise,andtheinterferencetermi0(n)isasumofcomplexsinusoids: withbn0,fn0,andn0beingtheamplitude,frequency,andphaseofthen0thin-terference,respectively,andN0beingthetotalnumberofinterferingsignals.Theinterference-to-signalratio(ISR)ofthen0thinterferenceisdenedas ISRn0=10log10jbn0j2 wherePsistheaveragesignalpowerdenedas 3{1 ,whichisatypicalsignalwaveformintheQRbasedTNTdetectionapplication[ 18 ].Weassumethatthesignalamplitudeisknowntobereal-valuedandnon-negative.Wesetthetruevalueofthesignalamplitudetobe=1,thesnapshotnumbertobeN=12,thelterordertobeL=4,andthenumberofinterferences

PAGE 39

Figure3{1. Anexampleofsignalwaveformversussamplenumber. tobeN0=2;theinterferencesarelocatedatf1=0:08Hzandf2=0:1HzwithISR1=ISR2=20dB(exceptwhenspeciedotherwise).Wechoose=0:01kD0k2fortheuncertaintysetofthesignalcovariancematrixfortherobustiedestimators(RGCandARGC).WeusetheSeDuMisoftware[ 72 ]tondthesolutiontotheSDPproblemin( 3{39 )fortheRGCestimator. Totally500independentbackgrounddatasets,obtainedbyusingtherealQRmeasurements,areusedasthecolorednoiserealizationsv0(n)in( 3{64 ),andthesimulatedsignalandinterferencesareaddedtothescaledbackgroundmeasurementstogeneratetheobserveddatasequencefx(n)gNn=1invarioussimulationtrials;thescalingfactorofthebackgrounddata0isdeterminedbytheinputSNR,whichisdenedas SNR=10log10(Ps where denotestheaveragepowerofthemeasuredbackgrounddata.

PAGE 40

Figure3{2. Anexampleofthemodulusofthereceivedsignalspectra. Figure 3{2 showsthemodulusofthesimulatedsignalspectrawhenSNR=0dB.InFigure 3{2 ,thesolidlinedenotesthemodulusofthespectrumofthesimulatedsignalx(n),thedotsdenotethemodulusofspectrumoftheinterferencesplusnoise,andthedashedlinedenotesthemodulusofthespectrumofthedesiredsignal.FromFigure 3{2 ,weseethattherearestrongpeaksaroundthezerofrequency,andthatthefrequencylocationofthesignalofinterestisalsoaroundzero. First,weexaminetheperformanceoftheLSandthethreeadaptivemethods(GC,RGC,andARGC)discussedhereinastheSNRvaries.Figures 3{3 (a)and 3{3 (b)showthebiasesandmean-squared-errors(MSEs)oftheestimatedsignalam-plitudesasfunctionsoftheSNR.ItisobservedfromFigure 3{3 (a)thattherobustiedestimators,RGCandARGC,havethesimilarbiasesthataremuchlowerthanthoseoftheLSandnon-robustiedGCestimators.FromFigure 3{3 (b),wenotethatallnewmethodshavemuchlowerMSEsthanthatoftheLSmethod.AlthoughtheGCmethodgivesasimilarMSEwiththoseoftheRGCandARGCmethodswhentheSNRislow(<-2dB),whentheSNRishigh(>)]TJ/F1 11.95 Tf 9.3 0 TD[(2dB),theRGCandARGCmeth-odsgivemuchlowerMSEsthanthatoftheGCmethod.TheMSEofLSmethod

PAGE 41

isverylargeprobablyduetothepresenceofthestrongcoloredinterferences.Theseresultsshowthat,byallowinganuncertaintysetforthesignalcovariancematrixtomitigatethesmallsnapshotnumberproblems,therobustiedmethodscanbeusedtoimprovetheperformanceofthesignalamplitudeestimation. Next,weexaminetheimpactoftheinterferencepoweronthesignalamplitudeestimationperformanceforthesemethods.AsimilarscenariototheexampleinFig-ure 3{3 isconsidered,exceptthatweincreasethepoweroftherstinterferencetoISR1=40dB.Figures 3{4 (a)and 3{4 (b)showthebiasesandMSEsoftheesti-matedamplitudesasfunctionsoftheSNR,respectively.TheperformanceofthenewmethodsissimilartothatinFigure 3{3 .Thisshowsthattheadaptivemethodscaneectivelysuppresstheinterferencesandthereforetheyarenotseriouslyaectedbytheinterferencepowers.However,wenotethattheperformanceoftheLSmethodisseverelydegradedduetotheincreaseoftheinterferencepower. Then,weturntoevaluatingthedetectionperformancesoftheLSandthepro-posedmethodsintermsofreceiveroperatingcharacteristics(ROC)(probabilityofdetection(Pd)versusprobabilityoffalsealarm(Pf)).Inthisexample,wextheSNR=5dB.Anensembleofdataconsistingof500separatebackgroundmeasurementsisusedinthisexample.Tosimulatethedatasamplesinthepresenceofthetarget,weaddtheQRsignaltotherst250backgroundmeasurements.Theremainder250measurementsareusedasthedatasampleswithoutthetarget.ThenweapplytheLSmethodandthethreeadaptivemethodstoallthe500setstoestimatethesignalamplitudeandcalculatethecorrespondingPdandPf.Theso-obtainedROCcurvesareplottedinFigure 3{5 .FromFigure 3{5 ,wecanclearlyseethatthethreeadaptivemethodsoutperformtheLSmethodsignicantly,andthattherobustiedmethods,RGCandARGC,havethesimilardetectionperformancebuttheyoutperformtheGCmethod,especiallyforPf<0:2.

PAGE 42

(a) (b) Figure3{3. BiasesandMSEsoftheestimatedamplitudesversustheSNRwhenN=12,ISR1=ISR2=20dB,andL=4.(a)Biases,and(b)MSEs.

PAGE 43

(a) (b) Figure3{4. BiasesandMSEsoftheestimatedamplitudesversustheSNRwhenN=12,ISR1=40dB,ISR2=20dB,andL=4.(a)Biases,and(b)MSEs.

PAGE 44

Figure3{5. Detectionperformance(ROC)comparisonofLS,GC,ARGC,andRGCwhenN=12,ISR1=40dB,ISR2=20dB,SNR=5dB,andL=4. Finally,wecomparethecomputationalcomplexityoftherobustiedmethods.AcomputationalcomparisonbetweenRGCandARGCshowsthatthelatteriscompu-tationallymuchmoreecientthantheformer;inoneofthetrials,forexample,andwithoutoptimizingourMATLABcodes,wenoticedthatARGCneedsonlyabout0.05secondswhileRGCrunsover8.3secondsoftheCPUtimeofatypicalSunBlade100workstation. 3{6 ,whichisatypicalbinarysignalwaveformwidelyusedinthecode-divisionmultipleaccess(CDMA)system.Thesamescenarioisusedasintherstexampleexceptforadierentsignalwaveform. Now,weexaminetheperformanceoftheLS(non-adaptive)andthethreeadap-tivemethods(GC,RGC,andARGC)discusssedinthischapterastheSNRvaries.Figures 3{7 (a)and 3{7 (b)showthebiasesandMSEsoftheestimatedsignalampli-tudesasfunctionsoftheSNR.FromFigure 3{7 (a),wenotethatalltheproposed

PAGE 45

Figure3{6. Thesignalwaveformversussamplenumber(secondexample). methodssignicantlyoutperformtheLSmethod.ItisalsoobservedfromFigure 3{7 (a)thattheadaptivemethodshavesimilarbiaseswhentheSNRislessthan-10dB.However,whentheSNRisgreaterthan-10dB,thebiasesofRGCandARGCmethodsaresmallerthanthatofGCmethodwhileRGCandARGChavesimilarbiases.FromFigure 3{7 (a)wenotethattherobustiedmethodsARGCandRGCgivemuchsmallerbiasthanthatofthenon-robustiedmethodGC. FromFigure 3{7 (b),wenotethatthenewmethodsgivemuchlowerMSEsthanthatoftheLSmethod.WealsonotethattheproposedmethodshavesimilarMSEswhentheSNRislessthan-10dB.ForSNR>-10dB,therobustiedmethods(RGCandARGC)worksimilarlywellandtheybothsignicantlyoutperformthenon-robustiedGCmethod.Thisconrmsagainthatbytakingintoaccounttheuncertaintyofthesignalcovariancematrix,therobustiedmethodscansignicantlymitigatethenegativeeectduetothesmallsnapshotnumbers.

PAGE 46

(a) (b) Figure3{7. BiasesandMSEsoftheestimatedamplitudesversustheSNR(secondexample)whenN=12,L=4,ISR1=ISR2=20dB.(a)Biases,and(b)MSEs.

PAGE 47

interferencesandnoise.Theseestimators,includingthegeneralizedCapon(GC),therobustGC(RGC),andtheapproximateRGC(ARGC)estimators,arebasedontheprincipleofgeneralizedCaponbeamforming.Therobustiedadaptiveestima-tors,includingRGCandARGC,canbeusedtomitigatethesmallsnapshotnumberproblemsbyallowinganuncertaintysetforthesignalcovariancematrix.Oursimu-lationresultshaveshownthattheproposedmethodscaneectivelysuppressstronginterferencesandachievemuchbetterperformancesthanthedata-independentLSmethod.Ithasalsobeendemonstratedthattherobustiedmethodscanprovidebetterperformancethantheirnon-robustiedcounterpart.Asforthetworobustiedmethods,RGCandARGC,theyhavebeenshowntoperformsimilarlybutthelatterhasmuchlesscomputationalcomplexitythantheformer.

PAGE 48

1 14 ].TheQRfrequencyofTNT,however,islocatedwithintheAMradiofrequencyband[ 1 17 18 29 ].ConsequentlytheAMradiosignalsappearasstrongRFIsthatcanseriouslydegradetheQRsignaldetectionperformance.AnantennaarraycanbeusedtomitigatethestrongRFIs[ 1 17 ],[ 27 ]-[ 29 ].RFIscanbereducedsignicantlybytakingadvantageofthespatialcorrelationsofRFIs.However,theinterferencesandnoiseareusuallybothspatiallyandtemporallycolored[ 31 32 ].AlthoughseveralapproacheshavebeenproposedtoreducethenegativeeectofRFIsonlandminedetection[ 1 17 18 29 33 ],exploitingboththespatialandtemporalcorrelationsoftheinterferenceshasnotbeenfullyinvestigated.Inthischapter,weexploitboththespatialandtemporalcorrelationsofRFIstoimprovetheexplosivedetectionperformance. TheQRproblemofestimatingthecomplexamplitudeofasignalwithknownwaveformandknownsteeringvectorwasconsideredin[ 17 ].Specically,signalampli-tudeestimationinthepresenceofspatiallycoloredbuttemporallywhiteinterferenceandnoise,aswellasparameterestimationinthecaseofbothspatiallyandtemporallycorrelatedinterferenceandnoisewereconsidered.Inthelattercase,bymodellingtheinterferenceandnoisevectorasamultichannelautoregressiverandomprocess,analternatingleastsquares(ALS)methodwasproposedin[ 17 ].Ithasbeenshownviasimulationsthatinmostcases,theALSmethodissuperiortothemodel-mismatched 38

PAGE 49

maximumlikelihood(M3L)method,whichignoresthetemporalcorrelationofthein-terferenceandnoise.However,ALSisslightlyworsethanM3Linchallengingcases,forinstancewhenthedesiredsignalandtheinterferencearecloselyspacedinthetemporalfrequencydomain. Inthischapter,wewillworkintheframeworkofsignalamplitudeestimationwithknownsignalwaveformandmakeuseofthreeadaptivebeamformingapproaches,viz.,thestandardCaponbeamformer(SCB)[ 23 73 ],therobustCaponbeamformer(RCB)[ 70 74 ],andtheamplitudeandphaseestimation(APES)method[ 20 75 ],todevelopseveralnewapproachesformitigatingthespatiallyandtemporallycorrelatedRFIs. SCBisadata-adaptivebeamformerthathasabetterresolutionandmuchbetterinterferencerejectioncapabilitythanthedataindependentmethods,suchasthedelay-and-summethod,providedthatthearraysteeringvectorisaccuratelyknown[ 70 ].HowevertheperformanceofSCBdegradesdrasticallywhenevertheknowledgeofthesteeringvectorisimprecise,thesnapshotnumberissmall,ornon-stationaryinterferenceandnoiseexist[ 70 ]. SeveralmethodshavebeenproposedtoimprovetherobustnessofSCB([ 24 70 74 ],[ 76 ]-[ 79 ]andthereferencestherein).RCBisanaturalextensionofSCBtothecaseofuncertainsteeringvectors,thatisrobustagainststeeringvectorerrorsandyetithashighresolutionandstronginterferencerejectioncapability[ 70 ]. APESisaneectivenon-parametricspectralanalysisapproach([ 20 25 75 80 ]andthereferencestherein).ExtensiveempiricalandanalyticalstudiesofSCBandAPEShaveshownthatalthoughAPESyieldssomewhatwiderspectralpeaksthanSCB,itsamplitudeestimateismuchmoreaccuratethantheSCBestimate[ 20 81 ]:inparticular,thelatterisbiaseddownwardswhiletheformerisunbiased[ 82 ]. StraightforwardextensionsofSCBandAPEStoourproblemofsignalamplitudeestimationwithknownsignalwaveform,inthepresenceofbothtemporallyand

PAGE 50

spatiallycorrelatedRFIs,leadtotwoSCB-basedapproaches,referredtoasSCB1andSCB2,andoneAPES-basedapproach,referredtoasAPES1.SimilartoSCBandAPES,allthesethreenewapproachesassumepreciseknowledgeofthearraysteeringvector.SCB1maximizesthesignal-to-interference-plus-noiseratio(SINR)andgiveshighresolution,butitissensitivetothemodellingerrorslikeSCB.SCB2isamodiedversionofSCB1obtainedbymeansofasub-optimaldesign.SCB2giveslowerresolutionthanSCB1butismorerobust.APES1isderivedusingtheAPESprinciple[ 75 ],andismorerobustthanbothSCB1andSCB2. Next,consideringthepresenceofthesteeringvectoruncertainty,wedeveloptworobustapproachesbasedontheRCBprinciple,whichwerefertoasRCB1andRCB2.RCB1andRCB2areobtainedbyrobustifyingSCB1andSCB2,respectively.TheyaremorerobusttosteeringvectorerrorsthantheirSCBcounterparts.WealsodeviseageneralizedrobustAPESbeamforming(GRAPES)methodusingtheAPESprinciplebuttakingintoaccountthesteeringvectoruncertaintyinmuchthesamefashionasinthederivationofRCB.TherobustnessofGRAPESisbetterthanthatofAPES1atthecostofsomeresolutionloss.Thetrade-obetweenresolutionandrobustnessforvariousmethodsisalsodiscussedinthischapter. Theremainderofthischapterisorganizedasfollows.InSection 4.2 ,weintroducethedatamodelandformulatetheproblemofinterest.Section 4.3 presentsthenewadaptivebeamformingapproaches.Section 4.4 providesadetectionscheme.Section 4.5 givesasummaryoftheimplementationsteps.SimulatedandexperimentalresultsareprovidedinSection 4.6 todemonstratetheeectivenessoftheproposedapproaches.Finally,Section 4.7 containsoursummary.

PAGE 51

RFIs.TheQRmeasurementscanbecharacterizedbythefollowingdatamodel[ 17 18 ] wherex(n)2CeNc1(witheNc=Nc+1)isthenthobserveddatasnapshot;0istheunknownsignalamplitude;a2CeNc1isthesteeringvectorwiththerstelementequaltooneandtheothersequaltozeros(duetothefactthatthemainantennareceivesboththeQRsignalandRFIswhilethereferenceantennasreceiveonlyRFIs);s(n)2Cistheknownsignalwaveform;Nisthenumberofsnapshots;ande(n)2CeNc1denotestheinterferenceandnoise.Theproblemofinteresthereinistoestimatefromtheobserveddatasequencefx(n)gNn=1inthepresenceoftemporallyandspatiallycorrelatedinterferenceandnoisefe(n)gNn=1. Themaximumlikelihoodmethodof[ 17 ],derivedundertheassumptionthate(n)istemporallywhite,performswellwhene(n)satisestheassumption.However,itcannotbeexpectedtoperformsatisfactorilywhenitisapplieddirectlyto( 4{1 )byignoringthepossibletemporalcorrelationoftheinterferenceandnoise.Todealwiththetemporalcorrelationofe(n),weadoptthe\stacking"techniqueof[ 20 ]thatisbasedonthefollowingspatial-temporaldatamodel, ~x(n)=as(n)+v(n);n=1;;eN; where ~x(n)=[xT(n)xT(n+L)]TJ/F1 11.95 Tf 11.95 0 TD[(1)]T;(4{3)

PAGE 52

Wenotethatforsomespecialwaveforms(forexample,acomplexsinusoid)satisfyingtheequation withcpbeingaconstantthatdoesnotdependonn,( 4{2 )reducestothestandardformin[ 17 ], ~x(n)=acs(n)+v(n);n=1;;eN;(4{7) whereac=aTc0aTcL)]TJ/F3 7.97 Tf 6.58 0 TD[(1T.ThenSCB,RCB,andAPESin[ 17 70 75 ]canbeapplieddirectly.However,inthischapter,weconsiderthegeneralcaseofanarbitrarysignalwaveform,whichoccursinmanyapplicationsincludingtheQRapplicationconsideredherein. Let denoteaniteimpulseresponse(FIR)ltercoecientvectorofdimensionLeNc1,wherehl,l=1;;L;isaneNc1vector.Thedeterminationofhwillbediscussedinthenextsection.Herewediscussbrieyhowwewillusehforestimatingtheamplitude.Passingthesignal~x(n)throughthelterhyields, (4{9) =sF(n)+hHv(n);n=1;;eN; where()Hdenotestheconjugatetranspose, and

PAGE 53

From( 4{10 ),byusingtheleastsquares(LS)methodandthefactthat0,anestimateofcanbeobtainedas ^=8><>:Re(~);ifRe(~)>0;0;ifRe(~)0; where ~=PeNn=1yF(n)sF(n) HereRe()denotestherealpartofacomplexscalar,and()denotesthecomplexconjugate. and

PAGE 54

withs(n)=[s(n)s(n+L)]TJ/F1 11.95 Tf 11.95 0 TD[(1)]T.Wealsolet 23 ],whichaimsatmaximizingtheoutputSINR,theSCB1methodobtainstheFIRlterbymaximizinganestimatedoutputSINR(orjustcallitSINRinshort)asfollows: maxhhHbRsh hHbQh;(4{18) wherebQisanestimateofQ,whichisthecovariancematrixoftheinterferenceandnoisevectorv(n).From( 4{2 ),Qcanbeestimatedas: where Byusing( 4{17 )and( 4{19 ),theoptimizationproblemin( 4{18 )canberewrittenas maxhhH)]TJ/F7 11.95 Tf 5.48 -9.68 TD[(AAHh hHbRh:(4{21) Solvingtheoptimizationproblemin( 4{21 )yields[ 22 ], wherePmax()istheeigenvectorcorrespondingtothelargesteigenvalueofamatrix.Themaximumvalueof( 4{21 )correspondingto( 4{22 )is

PAGE 55

wheremax()denotesthelargesteigenvalueofamatrix. NotethatinthecaseofL=1,wehaveA=a,and( 4{22 )reducesto withcbeingaconstant.WhenhisscaledtosatisfyhHa=1,wegettheSCB[ 17 ].Notealsothathcanbearbitrarilyscaledbecauseascalingofhleaves^in( 4{14 )unchanged.SimilartoSCB,SCB1maybesensitivetomodelingerrors,sowemaywanttorelaxtheoptimizationproblemin( 4{21 )toseekamorerobustsolution,asexplainedinthefollowing. 4{21 )bythefollowingtwosteps: 4{21 )); 4{21 )). Let wherelhasbeendenedin( 4{12 ).Thenthesignalpowerofthelteroutputisproportionalto Undertheconstraintthatjjjj2=1,( 4{26 )achievesitsmaximumvalueat Nowtheremainingproblemistosolve minhhHbRhsubjecttoAHh=:(4{28)

PAGE 56

Bysolvingtheoptimizationproblemin( 4{28 ),theSCB2beamformerisreadilyobtainedas[ 25 ] Thevalueof( 4{21 )achievedbybhSCB2in( 4{29 )is WenotethatfromamaximumSINRviewpoint,bhSCB1isanoptimalsolutionwhilebhSCB2isonlyasuboptimalone(inthesensethat4241,seeAppendix A fortheproof).However,SCB2maybemorerobusttomodelingerrorsthanSCB1sincethesignaloutputpowerismaximizedrstinSCB2,whichoerssomeprotectionagainstthenullingofthedesiredsignalsueredbySCB1,aswewillalsoshowvianumericalexamplesinSection6. 75 ],theAPES1methodisformulatedasfollows, minh;eNXn=1hH~x(n))]TJ/F4 11.95 Tf 11.95 0 TD[(LXl=1ls(n+l)]TJ/F1 11.95 Tf 11.95 0 TD[(1)2subjecttoAHh=;(4{31) whereisgivenby( 4{27 ).Minimizingthecostfunctionin( 4{31 )withrespectto(assumedcomplex-valuedforthelterdesignpurpose)yields =hHPeNn=1~x(n)sF(n) andthereforetheoptimizationproblemin( 4{31 )reducesto minhhHeQhsubjecttoAHh=;(4{33) where

PAGE 57

and ~g=PeNn=1~x(n)sF(n) Thesolutiontotheproblemin( 4{33 )is[ 25 ] whichissimilartobhSCB2in( 4{29 ),butwithbRreplacedbyeQ. 70 ] whereaandaregiven(isauserparameterwhichisusedtodescribethesizeofthesteeringvectoruncertainty).Althoughinsomeapplicationswemayknowaexactly,suchasa=a=[100]TintheQRapplication[ 1 ],wecanstillconsideraasbeinganuncertainvectorduetothesamplingerrorsinbR[ 24 25 ]. 74 25 ]).Todoso,observefrom( 4{2 )that where2=2.Hencethecovariancettingproblembecomes maxa;22subjecttobR)]TJ/F4 11.95 Tf 11.95 0 TD[(2AAH0ka)]TJ/F1 11.95 Tf 12.29 0.17 TD[(ak2: Wenotethattherstinequalityin( 4{39 )isequivalentto

PAGE 58

whichyields 12max(bR)]TJ/F3 7.97 Tf 6.58 0 TD[(1=2AAHbR)]TJ/F3 7.97 Tf 6.59 0 TD[(1=2)=2max(AHbR)]TJ/F3 7.97 Tf 6.58 0 TD[(1A): Therefore,foranyxeda,thesolution^2to( 4{39 )isgivenby: ^2=1 Notefrom( 4{23 )that^2=1=41.Using( 4{42 ),theoptimizationproblem( 4{39 )reducesto minamax(AHbR)]TJ/F3 7.97 Tf 6.58 0 TD[(1A)subjecttoka)]TJ/F1 11.95 Tf 12.29 0.17 TD[(ak2:(4{43) Viarelativelysimplealgebraicmanipulations,wecanreformulate( 4{43 )asaSemi-DeniteProgramming(SDP)problem[ 71 ]: minsubjecttomax(AHbR)]TJ/F3 7.97 Tf 6.58 0 TD[(1A)jja)]TJ/F1 11.95 Tf 12.29 0.16 TD[(ajj2; whichisequivalentto minsubjecttoI)]TJ/F1 11.95 Tf 11.95 0 TD[((A)]TJ/F3 7.97 Tf 18.23 4.93 TD[(1=2)HbR)]TJ/F3 7.97 Tf 6.58 0 TD[(1(A)]TJ/F3 7.97 Tf 18.23 4.93 TD[(1=2)0jja)]TJ/F1 11.95 Tf 12.29 0.17 TD[(ajj2; andhenceequivalentto minsubjectto264I(A)]TJ/F3 7.97 Tf 18.23 4.33 TD[(1=2)H(A)]TJ/F3 7.97 Tf 18.23 4.33 TD[(1=2)bR3750264(a)]TJ/F1 11.95 Tf 12.29 0.17 TD[(a)H(a)]TJ/F1 11.95 Tf 12.29 0.17 TD[(a)I3750: However,theso-obtainedSDPproblemhaslargedimensions,andthereforeitscom-putationalcomplexityisveryhigh[ 71 ].

PAGE 59

InordertousethecomputationallyconvenientLagrangiansolverin[ 74 70 ]toobtaina,wemodify( 4{43 )asfollows.First,notethat wheretr()denotesthetraceofamatrix,andwehaveusedthefactthatmax(~A~B)max(~A)max(~B)foranypositivesemi-denitematrices~Aand~B(e.g.,LemmaA.6.20in[ 83 ]).Forsimplicity,weconsiderminimizingtheupperboundin( 4{47 )inlieuof( 4{43 ),thatis, minatr(AHbR)]TJ/F3 7.97 Tf 6.59 0 TD[(1A)subjecttoka)]TJ/F1 11.95 Tf 12.29 0.16 TD[(ak2:(4{48) LeteRldenotethelthblockmatrixofsizeMMontheblockdiagonalofbR)]TJ/F3 7.97 Tf 6.59 0 TD[(1.Then( 4{48 )canberewrittenas minaaH LXl=1eRl!asubjecttoka)]TJ/F1 11.95 Tf 12.29 0.16 TD[(ak2;(4{49) whichhaspreciselytheformoftheRCBproblemsolvedin[ 70 ];thereforetheLa-grangiansolverintroducedin[ 70 ]canbedirectlyusedtoobtainthesolutionof( 4{49 ). Next,weconsiderrobustifyingbhSCB1in( 4{22 ),thatmaximizestheSINR.Whenaisuncertain,inthesensethatweonlyknowka)]TJ/F1 11.95 Tf 12.59 0.16 TD[(ak2,withwhatvalueofashouldweusehSCB1?Wemaythinkofusingamaxmaxapproach: maxa2CmaxhSINR;(4{50) whereC=fajka)]TJ/F1 11.95 Tf 13.23 0.16 TD[(ak2g.Let~adenotethesolutionto( 4{50 );thenh(~a)obtainedfrom( 4{50 )willhaveasmallgainatanya6=~a,owingtoitsmaxmaxSINRderivation.Hence,inthelikelyeventthatatrue6=~a,thesolutionof( 4{50 )willhavepoorrobustness.Withtheabovefactinmind,aminmaxSINRapproach

PAGE 60

ismoresound: mina2CmaxhSINR:(4{51) From( 4{23 ),wecanseethat( 4{51 )isequivalentto( 4{43 ),whichisthedesigncriterionbasedonthecovariancettingapproach.Let^abethesolutionto( 4{51 );thenh(^a)mayhaveareasonablegainforainthevicinityof^a,soitwillberobust.Ofcourse,therobustsolutionbaseon( 4{51 )willhavepoorerresolutionthan( 4{50 ).Evidently,onecannotachieverobustnessandhighresolutionsimultaneously;onecanonlycompromisebetweenthem.Inparticular,notethatminimizinganupperboundontheSINR,inlieuoftheSINRitself,likein( 4{49 ),willgiveasolutionthatislessrobustthan( 4{51 )buthasahigherresolution.NotethatbydecreasinginRCBwealsoincreasetheresolutionattheexpenseofrobustness.However,thereappearstobeadierencebetweencompromisingresolutionversusrobustnessbyminimizinganupperSINRboundandbydecreasing.Whenwedecrease,RCBwillbefocusingona=amoreandmore,whereaswhenweminimizeanupperboundtheRCBbasedmethodwillbefocusingontheathatminimizestheupperbound.Thelattermaybebetterthantheformerwheneveraisreallyuncertainandhencewecannotdecreaseinajustiedmanner. RegardingtherobusticationofhSCB2,weusethefactthat(see( A{3 )and( 4{47 )) andhenceobtainanestimateofaforbhSCB2alsobyminimizingtheupperboundin( 4{48 ).EstimatesoftheltershRCB1andhRCB2oftheRCBbasedmethodsareobtainedbyinsertingtheestimatedainto( 4{22 )and( 4{29 ),respectively,andthecorrespondingapproachesarereferredtoasRCB1andRCB2.

PAGE 61

4{51 )),wenowderiveageneralizedrobustAPESbeamformingapproach,referredtoasGRAPES.NotethattheoutputSINRcorre-spondingtohAPES1isproportionalto: SINRAPES1=max()]TJ/F1 11.95 Tf 8.08 0 TD[() Basedon( 4{51 ),theoptimizationproblemoftheGRAPESmethodisthereforeasfollows minamax()]TJ/F1 11.95 Tf 8.08 0 TD[() or,equivalently, maxahHAPES1bRhAPES1subjecttoka)]TJ/F1 11.95 Tf 12.3 0.17 TD[(ak2: InsertinghAPES1of( 4{36 )into( 4{55 )weobtain: Notethat[ 83 ] tr(AHeQ)]TJ/F3 7.97 Tf 6.58 0 TD[(1A):

PAGE 62

Replacing44byitslowerboundin( 4{57 ),wecanobtainanestimateofabysolvingthefollowingoptimizationproblem minatrAHeQ)]TJ/F3 7.97 Tf 6.59 0 TD[(1Asubjecttoka)]TJ/F1 11.95 Tf 12.3 0.17 TD[(ak2:(4{58) ThisisthesameproblemasfortheRCBbasedmethods,butwitheQreplacedbybR(see( 4{48 )).TheestimateofthelterhRGAPESisobtainedbyinsertingtheestimatedaobtainedfrom( 4{58 )into( 4{36 ). 4{13 )directlyforexplosivedetectiondoesnotyieldaconstantfalsealarmrate(CFAR)detector[ 18 ].Insteadwemightthinkofusingthefollowingdetectionvariable: cvar(^); wherecvar(^)isanapproximatevarianceof^.Inpracticalapplications,toobtainalowfalsealarmrate,thedetectionthresholdshouldbestrictlygreaterthanzero.Hence,wecanusethefollowingequivalentdetectionvariableinlieuof( 4{59 ): ~zd,Re(~) cvar[Re(~)]: Thecvar[Re(~)]aboveisobtainedas(seeAppendix B fordetails) 2hHQh whereQisanestimateofQobtainedbyusingthe^in( 4{13 )toreplacethein( 4{2 ): Q=1 whichisguaranteedtobenon-negativedenite.

PAGE 63

Inserting( 4{14 )and( 4{61 )in( 4{60 )yields ~zd=p q Substituting(9)into( 4{63 )gives ~zd=p q Underthenullhypothesis=0(i.e.,noexplosiveispresent),wecanapprox-imatethedistributionof~zdasN(0;1)(seeAppendix C ).ThisleadsdirectlytoadetectionrulethathasaCFARpropertysincethestatisticalpropertiesof~zdareindependentoftheinterferenceandnoisescenario. 4.3 and 4.4 areasfollows: 4{2 ); 4.3.1.1 4.3.1.2 4.3.1.3 ,RCB1andRCB2inSubsection 4.3.2.1 ,andGRAPESinSubsection 4.3.2.2 ); 4{11 ); 4{14 ); 4{62 ); 4{60 ).

PAGE 64

Figure4{1. QRsignalvs.samplenumber(obtainedbyscanningaTNTmineinalownoiseandRFI-freeexperiment). 4{1 ,whichisobtainedfromanexperimentalmeasurementfreeofRFIandataveryhighSINR[ 18 ].Weassumethattheinterfer-enceplusnoiseterme(n)in( 4{1 )isbothspatiallyandtemporallycolored.InourMonte-Carlosimulations,manysetsofindependentreal-worldmeasuredbackgrounddataarescaledandthenusedtosimulatetheinterferenceplusnoiserealizations.TheQRsignalisaddedtothescaledbackgrounddatasettogettheQRmeasurementsinvariousMonte-Carlotrials,withthescalingfactordeterminedbytheinputSINR.WechoosethesnapshotnumbertobeN=50,thetemporallterordertobeL=3.

PAGE 65

TheinputSINRisdenedas SINR=10log10Ps where denotestheaverageQRsignalpower,and denotestheinterferenceplusnoisepower.Tosimulatesteeringvectorerrors,eachelementofthesteeringvectoraisperturbedwitharandomnoise,andthenscaled,sothatka)]TJ/F1 11.95 Tf 12.29 0.16 TD[(ak20:1. Figure 4{2 showsanexampleofthemainantennaoutputwithaninputofSINRequalto-10dB;specicallyFigures 4{2 (a)and 4{2 (b)showthereal-partofthemainchanneloutputinthetimedomainandthemodulusoftheoutputspectrum.TwostronginterferencepeaksareobservedinFigure 4{2 (b)andoneofthemisaroundthezero-frequency,whichisthespectrumlocationofthedesiredQRsignal.ThisgureshowsthechallengeoftheQRsignaldetectioninthepresenceofstrongRFIs.ItalsomotivatestheexploitationofthetemporalcorrelationoftheRFIsforimprovedQRsignaldetection. Nowweturntoevaluatingthedetectionperformancesofourapproachesintermsofreceiveroperatingcharacteristics(ROC)(probabilityofdetection(Pd)versusprobabilityoffalsealarm(Pf)).Anensembleofdataconsistingof270separatebackgroundmeasurementsetsisusedinthisexample.Tosimulatethedatasamplesinthepresenceoftheexplosive,weaddtheQRsignaltotherst135backgroundmeasurementsets.Theremainder135measurementsetsareusedasthedatasampleswithouttheexplosive.Thenweapplyoursixnewapproachestoallthe270setstoestimatethesignalamplitudeandcalculatethecorrespondingPdandPf.ROC

PAGE 66

(a) (b) Figure4{2. Anexampleofthemainchanneloutput:(a)thereal-partoftheoutputinthetimedomain,and(b)themodulusofthespectrumoftheoutput.

PAGE 67

curvesforthecaseswithandwithoutsteeringvectorerrorsareplottedinFigure 4{3 .ROCcurvesforSCB1andRCB1areshowninFigure 4{3 (a).WenotefromFigure 4{3 (a)that,whensteeringvectorerrorsexist,theperformanceofSCB1issignicantlydegradedwithrespecttothecasewithoutsteeringvectorerrors;butforRCB1thedegradationissmaller.Also,RCB1performsdistinctlybetterthanSCB1inthepresenceofsteeringvectorerrors.TheseresultsindicatethatRCB1ismorerobustthanSCB1.Figure 4{3 (b)showsROCcurvesforSCB2andRCB2inthecaseswithandwithoutsteeringvectorerrors.ItcanbeobservedthatSCB2andRCB2havesimilarperformancesinbothcases;atverylowPfrange(<0.025),SCB2showsalargerdierencethanRCB2betweenthecaseswithandwithoutthesteeringvectorerrors.Figure 4{3 (c)presentsROCcurvesforAPES1andGRAPES,fromwhichweobservethatbothapproachesperformquitesimilarly,whichisduetotherobustnessofAPESbasedmethods. Figure 4{3 (d)presentsacomparisonbetweenSCB1andSCB2,usingthecorre-spondingROCcurvesfromFigures 4{3 (a)and 4{3 (b).Thesecurvesshowthat,whenthereisnosteeringvectorerror,SCB1hasabetterperformancethanSCB2;however,inthepresenceofsteeringvectorerrors,theperformanceofSCB1isdegradedmorethanthatofSCB2.TherobustnessofSCB2withrespecttoSCB1isthusveried. Toillustratehowthechoiceoftheuserparameteraectstheperformancesofthethreerobustapproaches,Figures 4{4 (a), 4{4 (b),and 4{4 (c)showtheROCcurvesofRCB1,RCB2,andGRAPES,respectively,fordierentvalues,namely,0.05,0.1,and0.2.TheseROCcurvessuggestthatthethreeapproachesallperformsimilarlyforvariousvaluesandhencetheyarenotsensitivetothevaluechosenfor. Toillustratehowthetemporallterorderaectsthedetectionperformance,Figures 4{5 (a)4{5 (f)showtheROCcurvesofthesixnewapproacheswithvarioustemporallterorderL(namely,L=1to5)inthepresenceofsteeringvectorerrors,respectively.Wenotethatforallmethods,theperformanceisthepoorestwhen

PAGE 68

(a) (b) Figure4{3. Detectionperformance(ROC)comparisonsbetweenthecaseswithandwithoutsteeringvectorerrorsfor(a)SCB1andRCB1,(b)SCB2andRCB2,(c)APES1andGRAPES,and(d)SCB1andSCB2.

PAGE 69

(c) (d) Figure4{3. Continued.

PAGE 70

(a) (b) (c) Figure4{4. Detectionperformance(ROC)withdierentvaluesfor(a)RCB1,(b)RCB2,and(c)GRAPES.

PAGE 71

4{5 (a)and 4{5 (b),wenotethatforSCB1andRCB1,whenL=2orL=3,theyyieldsimilargoodperformances.However,fortheSCB1method,whenPf>0:05,L=3yieldsbetterperformancethanthatofL=2;whenPf<0:05,L=2yieldsbetterperformancethanthatofL=3.ButfortheRCB1method,thereisonlyaslightlydierentbetweenL=2andL=3.ThisshowsthatRCB1ismorerobustthanSCB1forthechoiceofthelterorderL.WhenL>3theperformancesofSCB1andRCB1degradesignicantly. FromFigures 4{5 (c)and 4{5 (d),wenotethatSCB2andRCB2yieldthebestperformancewhenL=3,andtheirperformancesalsodegradewhenL>3.WealsonotethatwhenL>3,RCB2outperformsSCB2.ThisveriestherobustnessofRCB2.FromFigures 4{5 (e)and 4{5 (f),wenotethatwhenL>2,boththeAPRES1andGRAPESmethodsachievesimilargoodperformances.FortheAPESbasedmethodstheycanachieveagoodperformanceinawiderangeofchoiceofL.FromtheresultsobtainedinFigure 4{5 ,wecanconcludethattheAPESbasedmethodsaremorerobustthantheCaponbasedmethods. Figure 4{6 showstheROCcurvesofthesixproposedmethodsinthepresenceofsteeringvectorerrors.APES1andGRAPESarethebestamongthesixapproacheswhicharefollowedbyRCB1andRCB2. Finally,137real-worldmeasuredQRdatasetswitheNc=4,whichwerecollectedbytheQuantumMagnetics,Inc.,areusedtocompareournewapproacheswiththreeexistingmethods,viz.M3Lmethod[ 17 ],ALS[ 17 ]andamulti-stagecombinedmethod[ 18 ].Amongthem,thereare77measuredlandminedatasetsand60measuredbackgrounddatasets.Inthisreal-worldexample,thesixnewmethodsprovidesimilarROCcurves,andtherobustmethodsperformslightlybetterthantheirnon-robustiedcounterparts.WeuseGRAPESasarepresentativeofthenewmethodstocomparewiththepreviousmethods.FromFigure 4{7 ,wecanseethatGRAPES

PAGE 72

(a) (b) Figure4{5. Detectionperformance(ROC)withvarioustemporallterorderLinthepresenceofsteeringvectorerrorsfor(a)SCB1,(b)RCB1,(c)SCB2,(d)RCB2,(e)APES1,and(f)GRAPES.

PAGE 73

(c) (d) Figure4{5. Continued.

PAGE 74

(e) (f) Figure4{5. Continued.

PAGE 75

Figure4{6. Detectionperformance(ROC)comparisonamongthenewmethodsinthepresenceofsteeringvectorerrors. outperformsthecombinedapproachwhenPf<0:2,whichistheregionofinterest,andhasamuchbetterperformancethanthatoftheM3L,andALSmethods.

PAGE 76

Figure4{7. Detectionperformance(ROC)comparisonofM3L,ALS,combinedap-proachandGRAPESforthereal-worldexample.

PAGE 77

ThespectralstructureoftheQRsignalofthe14NinRDXissomewhatmorecomplicatedthanthatinTNT.Theformermaycontainupto18possibletransitions[ 1 ].ThesimplestRDXdetectoristodetectonlyoneRDXQRfrequencyataround3.41MHzbecausethisfrequencyhastheweakesttemperaturedependenceofabout60Hz/C.Atthe3.41MHzfrequency,theRDXsignaldoesnotsuerfromtheRFIcausedbytheAMradiobroadcasting.However,itsuersfromsomeunknownimpulsiveRFIs. Therefore,todetecttheveryweakQRsignalduetoeitherTNTorRDX,theRFImitigationisessentialandarobustRFImitigationmethodisnecessaryforthesuccessfuldetectionoflandmines.Inthepastfewyears,manyeortshavebeendevotedtoimprovetheQRexplosivedetectionperformancebyeitherreningtheQRsensordesign[ 1 ]ordevelopingsignalprocessingmethods[ 17 29 ],[ 44 ]-[ 46 ].Mostexistinginvestigationsfocusondetectingasingletypeofexplosive,i.e.,eitherTNTorRDX.SinceasingleminecancontainonlyTNT,onlyRDX,oracompoundof 67

PAGE 78

TNTandRDXexplosives,adetectordesignedtodetectonlyonetypeofexplosivemaynotprovidethebestperformance. Inthischapter,wewillfocusonthejointdetectionofTNTandRDXexplosivesforthelandminedetectionviatheQRsensorsothattheoveralllandminedetec-tionabilityisimprovedandthedetectorperformanceistheoreticallypredictable.TomitigatetheunavoidableRFIsassociatedwiththeQRmeasurements,weapplyGRAPESmethodintroducedinChapter 4 ,toexploitthetemporalandspatialcor-relationsofRFIsviatheadaptiveltering.BasedontheoutputofGRAPES,wedeviseageneralizedlikelihoodratiotest(GLRT)forthejointTNT/RDXdetection,whichisreferredtoastheGRAPES-GLRTdetector.GRAPES-GLRTissimpleandhastheconstantfalsealarmrate(CFAR)property,whichmeansthatthefalsealarmrateofthedetectorisindependentoftheinterferenceandnoisepower.CFARisade-siredpropertyinalmostalltargetdetectionapplicationssincethedetectionthresholdcanbepre-determinedandxedforadesiredfalsealarmrate.TheeectivenessoftheproposedGRAPES-GLRTdetectorisdemonstratedwiththeexperimentaldatacollectedbyQuantumMagnetics(QM),Inc. Theremainderofthischapterisorganizedasfollows.InSection 5.2 ,weintroducethedatamodelandformulatetheproblemofinterest.InSection 5.3 ,weconsiderusingGRAPESforRFImitigationbyexploitingthetemporalandspatialcorrelationsofRFIs.Section 5.4 presentsourGRAPES-GLRTdetectorforthejointTNT/RDXdetectionanditsperformanceanalysis.ExperimentalexamplesarepresentedinSection 5.5 toillustratetheexcellentperformanceoftheproposeddetector.Finally,Section 5.6 containsoursummary.

PAGE 79

bothRFIsandtheQRsignalandthereferenceantennasreceiveonlytheRFIs.TheQRsignalisdemodulatedtothedirectcurrent(DC)(i.e.,zerofrequency)upondigitalizationinthereceiver. TodetecttheQRresponseoftheTNTexplosive(similarforRDX),aphasecycledpulsesequenceisusedintheQRsystem.TheexperimentisdesignedtoproducethemaximumamountofsignalperunittimefromtheTNT14NnucleiandtovarythephaseoftheQRsignalinapredictablemannersoastoseparateitfromotherartifacts(e.g.,magneto-acousticringing,piezo-electricringingandpulsering-down). Onepulsesequenceconsistsoftwosubsequences:positiveandnegative,eachofwhichcontainsasequenceofNsechoescalledanechotrain.EachechoissampledtoobtainNffast-timesamplesduringtheacquisitionwindowandthecorrespondingsamplingintervalisreferredtoasthefast-timesamplinginterval(inanalogytotheradarterminology[ 84 ]).ThecorrespondingsamplesfromoneechotoanotherformtheNsslow-timesamples.Thefast-timeandslow-timesamplesformanNfNsmatrix.Theamplitude~(ns)ofthensthechodecaysexponentiallywithatimeconstantT2: ~(ns)=e)]TJ/F5 7.97 Tf 6.59 0 TD[(nsTs=T2;ns=0;;Ns)]TJ/F1 11.95 Tf 11.96 0 TD[(1;(5{1) whereTsisthetimeintervalbetweentwoadjacentechoesortheslow-timesamplinginterval. Apairofadjacentpositiveandnegativeisreferredtoasaloop.Theloopisthenrepeatedmultipletimes(sayNptimes),i.e.,thedataacquisitionprocessisrepeatedNptimes,witheachprocessobtainingthesameQRsignal.Theentiredatacollectionprocessintheserepeatedloopsiscalledascan.HenceeachscanobtainsNpdatamatricesofdimensionNfNs.Thedatacollectedfromthenegativesubsequenceissubtractedoutfromthoseinthepositivesubsequence.Thisprocessisreferredtoas

PAGE 80

deringing,whichcancelsoutanyringingfromtheconstantphaserefocusingpulsesandaddsuptheQRsignals. SincethespeciedQRsignalfrequencyisdown-convertedtozerofrequencyupondigitalizationinthereceiver,itisconvenienttocomeupwithadatamodelinthefrequencydomainbyperformingtheone-dimensional(1-D)Fouriertransform(FT)alongthefast-timedimensionforthedatasetsfromeachantennaandthenpickinguptheproperfrequencybinsaroundthedown-convertedQRsignalfrequency.Todoso,awindowedFT(WFT)isusuallyusedtoreducethesidelobes,andthezerofrequencybinispickedforthemainantennaoutputwhilemultiplefrequencybins(sayNb)aroundthezerofrequencybinarecollectedfromthereferenceantennaoutputs.Letk=1denoteTNTprobingandk=2denoteRDXinterrogation.Fortheprobingofthekthtypeofexplosive,(1+NcNb)spatialsamplesareobtainedforeachechofromonemainandNcreferenceantennas.EachchannelhasNp;kslow-timesamplesequences,eachwithNs;ksamples.Henceafterpickingfrequencybins,wehave2-Dcomplex-valueddatamatricesofdimension(1+NcNb)Np;kNs;k;k=1;2,whichisshowninFigure 5{1 Ourfast-frequency-domaindatamodelregardingthedatavectorxk(n)forthenthslow-timesampleandthekthexplosiveisexpressedas wherekistheunknownsignalamplitude,a0isavectoroflength(1+NcNb)withtherstelementbeing1andtheremainingonesbeingzero,duetothefactthatthemainantennareceivesboththeQRsignalandRFIswhilethereferencesantennasreceiveonlyRFIs,s1(n)isthesignalwaveformforTNTgivenbys1(n)=~(mod[n)]TJ/F1 11.95 Tf 10.81 0 TD[(1;Ns;1])(withmod[n)]TJ/F1 11.95 Tf 12.3 0 TD[(1;Ns;1]denotingthemoduleofn)]TJ/F1 11.95 Tf 12.31 0 TD[(1overNs;1),thecounterpartforRDXiss2(n)=1foralln's,ek(n)isavectorcontainingtheRFIsandnoise.Werefertoa0asthesteeringvectorandNk=Np;kNs;k;k=1;2;asthetotalsnapshotnumber.

PAGE 81

Figure5{1. DatacubefromQRdatacollection BecausetheTNTandRDXexplosivesareprobedwithdierentfrequencies,theRFIplusnoisesequencesfe1(n)gN1n=1andfe2(n)gN2n=1areassumedtobeindependentofeachother. Inpractice,itisusuallynecessarytoperformaphasecorrectiontocompensateoutthephaseerrorduetofactorssuchassystemdelayandinitialphaseofthetransmittedsignal.Thiscanbedoneonthedatasamplesxk(n).Afterthephasecorrection,thesignalamplitudekbecomesreal-valuedandnon-negative(i.e.,k0fork=1;2).Fornotationalconvenience,westillusexk(n)todenotexk(n)ejk,whereejkaccountsforthephasecorrectionandkisknown. TheproblemofinteresthereinistomitigatetheRFIs,estimatetheTNTandRDXsignalamplitudes,andperformjointTNT/RDXdetection.Figure 5{2 outlinestheowchartofthesignalprocessingsteps.

PAGE 82

Figure5{2. SignalprocessingowchartforjointTNT/RDXdetection. ~xk(n)=ask(n)+vk(n);n=1;;eNk: where ~xk(n)=[xTk(n)xTk(n+L)]TJ/F1 11.95 Tf 11.95 0 TD[(1)]T;(5{4) 4.3.2.2 forthedetailsoftheGRAPESmethod).Althoughthefollowingjointdetectionscheme

PAGE 83

isderivedbasedontheoutputofGRAPESmethod,itcanbeappliedtotheoutputsofanyofaformentionedadaptivemethodsinChapter 3 andChapter 4 Let^hkdenotetheestimatedGRAPESlterforthekthtypeofexplosive,whichisgivenby, ^hk=eQ)]TJ/F3 7.97 Tf 6.58 0 TD[(1k^Ak(^AHkeQ)]TJ/F3 7.97 Tf 6.59 0 TD[(1k^Ak))]TJ/F3 7.97 Tf 6.59 0 TD[(1k;(5{7) whereeQkandkaredenedin( 4{34 )and( 4{25 ),respectively,forthekthtypeofexplosive,and ^Ak,266666664^ak000^ak0............00^ak3777777752C~NcLL;(5{8) with^akdenotingtheestimatedaobtainedfrom( 4{58 ). Passingthedatasequencef~xk(n)gNkn=1;k=1;2,throughthelter^hkyieldsascalarsequence where ~sk(n)=LXl=1l;ksk(n+l)]TJ/F1 11.95 Tf 11.95 0 TD[(1);n=1;;eNk; and

PAGE 84

5.4.1Detection WeassumethattheTNTandRDXmeasurementsareindependentofeachotherandthat"k(n)isazero-meancircularlysymmetriccomplexGaussianrandomprocesswithanunknownvariance2k;k=1;2:Thejointprobabilitydensityfunction(PDF)ofthelteredsequencefyk(n)geNkn=1underH1is (2k)eNkexp()]TJ/F8 11.95 Tf 13.46 11.11 TD[(eNkc1;k(k) where with and ThejointPDFofthespatiallylteredsequencefyk(n)geNkn=1underH0is (2k)eNkexp()]TJ/F8 11.95 Tf 13.46 11.1 TD[(eNkc0;k where

PAGE 85

From( 5{14 ),thenegativelog-likelihoodfunctionunderH1forthekthexplosiveisproportionalto whereln()denotesthenaturallogarithmoperation.MinimizingV1;k(2k;k)in( 5{20 )withrespectto2kunderH1resultsin^2k=c1;k(k).Similarly,wecanobtain^2k=c0;kunderH0. Byusingtheestimate^2kunderH1in( 5{20 ),minimizingthecostfunctionin( 5{20 )withrespecttokbecomesminimizing where and yk=1 Consideringtheconditionk0,itisclearthattheminimizationofV2;k(k)in( 5{21 )withrespecttokgives ^k=tru(Re(yk)) where tru(x)=8><>:x;x00;x<0;(5{25)

PAGE 86

andyr;kistherealpartofyk.Then,theresidualofthecostfunctionV2;k(k)is WeobtaintheGLRTforthejointTNT/RDXdetectionas Q2k=1f0;kfyk(n)geNkn=1;^2kH0H1><>:c1;k(^k)underH1c0;kunderH0:(5{28) Bytakingthelogarithmofbothsidesof( 5{27 ),theGLRTformulationcanbesimpliedas where,2ln0and,2ln0.Using( 5{26 )in( 5{29 )gives Dene ~k,s

PAGE 87

andlet Thenwerewrite( 5{30 )inacompactformat wherethefunctionk(k)isgivenby 2eNk2k):(5{34) Thedetectorin( 5{33 )addsuptheoutputsoftheindividualTNTandRDXdetectors.InAppendix D ,weshowthatthejointGLRTstatisticin( 5{33 )isindependentoftheinterferenceandnoisescenariounderH0andthusitisaCFARtest. 5{33 )isaCFARtest,thedetectionthresholdcanbedeterminedaccordingtothedesiredPFA.ThisrequiresthedeterminationofthePDFofthedetectionvariable. ItisshowninAppendix E thatthePDFofthevariable~zk,~2kisgivenby whereFgk(2eNk)]TJ/F1 11.95 Tf 12.33 0 TD[(1;1)istheF-distributionwithapairofparameters(2eNk)]TJ/F1 11.95 Tf 12.32 0 TD[(1;1).Let~k,k(~k),whichisobtainedbyreplacingkin( 5{34 )with~k.ThePDFof~kcanbedirectlyderivedfrom( 5{35 )byavariablereplacement.Thatis

PAGE 88

Since~1and~2areindependentofeachother,andunderH0,theyeachcanbeex-pressedasaratioofaGaussiandistributed(N(0;1))variableanda-distributedvariable(seeAppendix D ),eachofthemhasanequalprobability(0.5)tobenegativeandnon-negative.Therefore,underH0eachofthevariables1and2hasaproba-bilityof0.5tobezero.Asforthedetectionvariable,itwilltakevaluesfromfourpossiblesubsets,eachofwhichoccurswith0.25,accordingtothesignsof~1and~2.Thatis Consequently,thePDFofthedetectionvariableunderH0canbeexpressedasamixtureformation, where()istheDiracDeltafunction,andthesymboldenotestheconvolution.Notethat,eventhoughthePDFofin( 5{38 )isonlythefunctionofN1andN2,noexplicitclosedformisavailableforit,andthecomputationofthedetectorthresholdforagivenPFAissomewhatcomplicated.Tosimplifytheproblem,weconductanasymptoticanalysisinAppendix F andshowthatforlargeeNkthefunctionk(k)in( 5{34 )canbesimplyapproximatedas: andthedetectorissimplied

PAGE 89

Figure5{3. PDFof~z2kand~kforvariousdatalengthN Sinceyk(n)N(0;2k)underH0,itisstraightforwardtoshowthat~kN(0;1),whichresultsin ~zk=~2k2(1)(5{42) Here2(n)denotesthe2-distributionwithndegreesoffreedom[ 85 ].Toshowtheeectivenessofusingapproximationin( 5{41 ),Figure 5{3 plotsthePDFcurvesof2(1)andf~k(~k)(see( 5{36 ))foreNk=5;10;50;100.WenotefromFigure 5{3 thatforeNk>50,theapproximatePDFof~zkisveryclosetotheaccurateexpression.WeremarkthattheconditioneNk>50iseasilysatisedintheQRexperiments. Again,since~1and~2areindependentofeachother,thevariable~z=~21+~22willbe2(2)distributed.Itisinterestingtonotethat,ifweonlyconsiderthereal-valuedsignalamplitudeforeachtypeofexplosive,thisresultagreeswiththerelevantconclusionin[ 86 ]thatforrathergeneralmodels,theasymptoticdistributionofthe

PAGE 90

GLRTquantityis2distributedwithdegreesoffreedomequaltothedierencebetweenthenumberoffreeparametersunderH1andH0. Similartothedetectionvariable,thesimplieddetectorztakesvaluesfromthecorrespondingfourpossiblesubsets,eachofwhichoccurswith0.25,accordingtothesignsof~1and~2: Accordingly,wedeploya2-mixturedistributiontomodelthedetectionvariablezunderH0.ThecorrespondingPDFpz(z)isgivenas wherepn(),n=1,2,isthePDFforthe2(n)distribution.LetFz(z)denotethecumulativedensityfunction(CDF)ofzunderH0andFn()denotetheCDFforthe2(n)distribution.Thenwehave Thus,foradesiredPFA(sayPf),wecandeterminethecorrespondingdetectionthresholdbysolving

PAGE 91

Figure5{4. Probabilityoffalsealarmversusdetectionthresholdforthe2-mixturedistributionforthejointTNT/RDXdetectionaswellasindividualTNTorRDXdetection. Inthecasethatweconcentrateondetectingonlyonetypeofexplosive,thedetectionthresholdcanbesimilarlydeterminedbysolving Figure( 5{4 )showsthecurvesofPf(solid-line)andPf;1(dashed-line)versus.ForaPFAof0:05,forexample,simplieddetectorthresholdsare=4.23and2.71forthejointTNT/RDXandindividualTNTorRDXdetections,respectively. 5{46 ); 5{3 );

PAGE 92

4.3.2.2 ; 5{9 ),andcalculatethesequencef~sk(n)g~Nkn=1using( 5{10 ); 5{32 )withPs;k,^k,andc0;kcalculatedbyusing( 5{22 ),( 5{24 )and( 5{19 ),respectively; 5{40 ). Foreachscan,weusedatasamplesfrom4antennas(1mainantennaandNc=3referenceantennas).Afterthederinging,weweighthefast-timedatasamplesoftheTNTprobingwithanon-symmetricHanningwindow(seethedashedlineinFigure 5{5 )separatelyforeachantennaoutput.Usingthenon-symmetricHanningwindowismotivatedbymatchingthewindowtothemeasuredTNTfast-timewaveform(seethesolidlineinFigure 5{5 )obtainedbyscanningaTNTmineinahighSNRandRFI-freeexperiment.ThecurvesinFigure 5{5 indicatethattheTNTfast-timewaveform

PAGE 93

Figure5{5. TNTfast-timewaveform(obtainedbyscanningaTNTmineinahighSNRandRFI-freeexperiment)andnon-symmetricHanningwindow. canbewellapproximatedasanon-symmetricHanningwindow.Withthisweightingscheme,weareapplyingamatchedltertothefast-timeTNTmeasurements.NowindowisappliedtothederingeddatasamplesoftheRDXinterrogationbecausetheRDXsignalwaveformisaconstantinbothfast-andslow-timedimensions. BecausebothoftheTNTandRDXmeasuredsignalsaredown-convertedtozerofrequencyupondigitalizationatthereceiver,wechoosetouseonlythezerofrequencybin(i.e.,Nb=1)fromeachantennaoutputtoformthedatasequencesfx1(n)gN1n=1andfx2(n)gN2n=1forTNTandRDX,respectively.Anecientwaytodosoistosumupallthefast-timesamples(afterproperderingingandwindowing)ofeachechoineachspatialchannel.Wehavealsotestedusingmultiplefrequencybinsfromthereferencechannels,butnoimprovementonthedetectionperformanceisfoundforthisdataset.Wehaveused1=2=0:1. Now,weevaluatetheperformanceofthedetectorintermsofthereceiveroper-atingcharacteristic(ROC),i.e.,probabilityofdetection(Pd)versusPf.Allthe260mine-freescansand330minescansareusedinthisexperiment.TheROCcurvesof

PAGE 94

thedetectorwhenappliedtoindividualTNT,RDXandjointTNT/RDXdetectionsareshowninFigures 5{6 .ItisclearthatthefusionoftheindividualTNTandRDXdetectionviaGLRThasimprovedthedetectionperformance. Figure5{6. ROCcurvesfortheGRAPES-GLRTdetector.

PAGE 95

Forthesingleantennabasedapplication,wehaveinvestigatedthesignalampli-tudeestimationwithanarbitraryknownwaveforminthepresenceofstronginterfer-enceandnoise.Wehavepresentedthreeadaptivenite-impulseresponse(FIR)lterbasedmethodstosuppressthestronginterferences.WerstextendedthegeneralizedCapon(GC)estimatortothesignalamplitudeestimationproblem.Undertheframe-workofRCB,bothrobustGCandapproximaterobustRGCweredevisedtomitigatethesmallsnapshotproblemsbyallowinganuncertaintysetforthesignalcovariancematrix.Numericalexampleshaveshownthatthesethreeadaptiveapproachescanperformmuchbetterthanthenon-adaptiveleast-squares(LS)method,andthattherobustiedestimatorsoutperformtheirnon-robusitiedcounterpart. Fortheantennaarraybasedapplication,wehaveproposedseveralnewadaptivebeamformingmethodstomitigatetheRFIsbyexploitingtheirspatialandtemporalcorrelations.Twocases,withexactanduncertainsteeringvector,havebeencon-sideredinthiswork.Whenthesteeringvectorispreciselyknown,wedevisedtwoSCB-basedadaptiveapproaches(SCB1andSCB2)andoneAPES-basedapproach(APES1).SCB1maximizesSINRandgiveshighresolution,butitissensitivetothemodelingerrorslikeSCB.SCB2isamodiedversionofSCB1obtainedbymeansofasub-optimaldesign.SCB2giveslowerresolutionthanSCB1butismorerobust. 85

PAGE 96

APES1wasderivedusingtheAPESprinciple,andhasbeenshowntobemorerobustthanbothSCB1andSCB2.Whenthesteeringvectoruncertaintyexists,whichmaybecausedbysmallnumberofsnapshotsornon-stationaryRFIsandnoiseintheQRapplication,wehavedevelopedtworobustapproaches(RCB1andRCB2)basedontheRCBprinciple.RCB1andRCB2wereobtainedbyrobustifyingSCB1andSCB2,respectively.WehavealsodevisedageneralizedrobustAPESbeamforming(GRAPES)methodusingtheAPESprinciplebuttakingintoaccountthesteeringvectoruncertaintyinmuchthesamefashionasinthederivationofRCB.Wehavealsoanalyzedthetrade-obetweenresolutionandrobustnessforvariousmethods.Bothsimulationandexperimentalresultshaveshownthattherobustiedapproaches(RCB1,RCB2,andGRAPES)aremorerobustagainststeeringvectorerrorsthantheirnon-robustiedcounterparts.Thereal-worldexampleforTNTlandminedetec-tionhasdemonstratedthatournewmethodscanachievebetterperformancethantheexistingM3L,ALS,andcombinedmethodsintheQRapplication. Forthedetectionofcompoundexplosives,wehaveproposedajointGLRTde-tectorandderivedthecorrespondingdetectionstatisticbasedontheoutputofRFImitigationforindividualQRexplosiveprobings.ThetheoreticalanalysishasshownthatthisjointdetectorhasaCFARproperty.ItseectivenesshasbeendemonstratedwiththeexperimentaldatacollectedbyQM.ThejointGLRTdetectorhassigni-cantlyimprovedtheoveralldetectionperformanceoftheQRsensorascomparedtotheindividualsingletypeexplosivedetectors.Finally,weremarkthateventhoughourjointGLRTdetectorisderivedforthejointdetectionoftwotypesofexplosives,itcanbereadilyextendedtothejointdetectionofmoretypesofexplosives.

PAGE 98

4.3.1.2 By( 4{23 ),wehave wherethespectraldecompositionofasymmetricmatrixandtheorthogonalityofeigenvectorsofamatrixhavebeenusedtoobtainthesecondequalityin( A{1 )[ 87 ]. Alsonotethat 1=jjjj4=H(AHbR)]TJ/F3 7.97 Tf 6.58 0 TD[(1A))]TJ/F3 7.97 Tf 6.59 0 TD[(1=2(AHbR)]TJ/F3 7.97 Tf 6.59 0 TD[(1A)1=22[H(AHbR)]TJ/F3 7.97 Tf 6.58 0 TD[(1A))]TJ/F3 7.97 Tf 6.58 0 TD[(1][H(AHbR)]TJ/F3 7.97 Tf 6.59 0 TD[(1A)]; wheretheCauchy-Schwartzinequalityhasbeenusedtoobtaintheinequalityin( A{2 ).Using( A{1 )and( A{2 ),wehave Thisconcludestheproof. 88

PAGE 99

4{61 ) Inthisappendix,wecalculatethevarianceofthesignalamplitudeestimate~.Tosimplifytheanalysisofthestatisticalpropertiesof~,wemakethefollowingassumptions: Inserting( 4{10 )into( 4{14 )yields ~=+PeNn=1hHv(n)sF(n) Thereforethevarianceof~isgivenby var(~)=E[j~)]TJ/F4 11.95 Tf 11.95 0 TD[(j2]=E24PeNn=1hHv(n)sF(n) whereE[]denotesstatisticalexpectation. ByAssumptionA1,( B{2 )canbeapproximatedas var(~)hHEhPeNn=1PeNn0=1v(n)sF(n)sF(n0)vH(n0)ih 89

PAGE 100

ByAssumptionA2,( B{3 )canbefurthersimpliedas var(~)hHPeNn=1jsF(n)j2Ev(n)vH(n)h where UsingthestatisticalpropertyofcircularlysymmetriccomplexGaussiannoise,wehave var[Re(~)]=1 2var(~)=1 2hHQh

PAGE 101

4{63 ) UnderthenullhypothesisH0,that=0,andunderAssumptionA2,wehave ~x(n)CN(0;Q);(C{1) whereCN(0;Q)denotesthecircularlysymmetriccomplexGaussiandistributionwithzero-meanandcovariancematrixQ.FromA2and( C{1 )wecandirectlyverifythat Furthermore,wehave Normalizing( C{3 )weobtain Bytakingtherealpartof( C{4 )andnormalizingit,wenallyhave q whereN(0;1)denotestheGaussiandistributionwithzero-meanandvariance1. NotethatwheneN>>1,QisapproximatelyequaltoQ,whichmeansthateN>>1, ~zd=p q 91

PAGE 102

Sincethedistributionof~zd,underH0,isindependentofthenoiseandinterferencescenario,thestatisticaltestin( 4{64 )isaCFARtest.

PAGE 103

5{33 ) WenowshowthatthejointGLRTstatisticdenedin( 5{33 )isindependentofthenoiseandinterferencescenariounderH0andthusitisaCFARtest. UnderH0,yk(n)N(0;2k),andastraightforwardcalculationshowsthatykin( 5{23 )satises ykN(0;kskk2 whichnaturallyleadsto Furthermore,denethenormalizedquantities ~yk(n)=yk(n) andlet ~yk=[~yk(1)~yk(Nk)]T:(D{4) Thenwehave and 2k~yr;kk2,k2(Nk);k=1;2;(D{6) where~yr;kdenotestherealpartof~yk,and2(n)denotesthe2distributionwithndegreesoffreedom.From( 5{31 )weknowthat ~k=p 93

PAGE 104

Itisclearfrom( D{5 )and( D{6 )that~kdoesnotdependentontheinterferenceandnoisecovariance,andnordokin( 5{32 )andk(k)in( 5{34 ).ThusthejointGLRTdetectionstatisticin( 5{33 )isaCFARtest.

PAGE 105

5{35 ) Letskbethenormalizedversionofsk;k=1;2,(i.e.sk=sk=kskk)suchthatkskk=1anddenoteyi;kastheimaginarypartofyk.Then,fromthesecondequalityof( 5{31 ),wehave ~zk=~2k=2Nk)]TJ/F1 11.95 Tf 5.21 -9.52 TD[(sTkyr;k2 Considerthenormalizedquantities~yk(n)in( D{3 ).Wecanrewrite( E{1 )as ~zk=2Nk)]TJ/F1 11.95 Tf 5.21 -9.51 TD[(sTk~yr;k2 Notethattherandomvector~ykisinvarianttoaunitarytransformation.WecandesignaunitarymatrixeUk(withrstcolumnbeingskandtheothercolumnsorthonormaltothesk)suchthat where0Nk)]TJ/F3 7.97 Tf 6.58 0 TD[(1isanall-zerovectoroflengthNk)]TJ/F1 11.95 Tf 11.95 0 TD[(1.Thus( E{2 )canbesimpliedto ~zk=2Nkt2r;k(1) wheretr;k=eUTk~yr;k,ti;k=eUTk~yi;kandtr;k(1)istherstelementoftr;k. Dividingboththenumeratoranddenominatoroftherightsideof( E{4 )byt2r;k(1),weget ~zk=2Nk where 95

PAGE 106

withtkbeingthesubvectoroftr;kconsistingofalltheelementsoftr;kexceptfortr;k(1).Sincealltheelementsoftr;kandti;kareindependentlyandidenticallydistributedGaussianvariableswithzero-meanandvariance1 2,gkobeysanF-distribution[ 85 ]withapairofparameters(2Nk)]TJ/F1 11.95 Tf 11.22 0 TD[(1,1),whichisdenotedasFgk(2Nk)]TJ/F1 11.95 Tf 11.21 0 TD[(1;1).ThenthePDFof~zkisgivenby Thisconcludestheproof.

PAGE 107

5{39 ) WeprovebelowthatforlargeNk;k=1;2; k(k)=)]TJ/F1 11.95 Tf 9.3 0 TD[(2Nkln1)]TJ/F1 11.95 Tf 20.39 8.09 TD[(1 2Nk2k2k:(F{1) Fromtheequalityin( F{1 ),weobtain 1)]TJ/F4 11.95 Tf 11.95 0 TD[(e)]TJ/F13 5.98 Tf 7.78 4.62 TD[(k(k) 2Nk=1 2Nk2k(F{2) Since 2Nk1)]TJ/F4 11.95 Tf 13.15 8.09 TD[(k(k) 2Nk;(F{3) forlargeNk,itisclearthat( F{2 )canbeapproximatedas 97

PAGE 108

[1] A.N.Garroway,M.L.Buess,J.B.Miller,B.H.Suits,A.D.Hibbs,G.A.Bar-rall,R.Matthews,andL.J.Burnett,\Remotesensingbynuclearquadrupoleresonance,"IEEETransactionsonGeoscienceandRemoteSensing,vol.39,pp.1108{1118,June2001. [2] J.Barras,M.J.Gaskell,N.Hunt,R.I.Jenkinson,K.R.Mann,D.A.G.Pedder,G.N.Shilstone,andJ.A.S.Smith,\Detectionofammoniumnitrateinsidevehi-clesbynuclearquadrupoleresonance,"AppliedofMagneticResonance,vol.25,no.3-4,pp.411{437,2004. [3] A.J.Blauch,ModelingandControlDesigninNuclearQuadrupoleResonance:ApplicationtoMineDetectionandInterrogation.Ph.D.Dissertation,Pennsyla-vaniaStateUniversity,May2000. [4] V.S.Grechishkin,\NQRdevicefordetectingplasticexplosives,mines,anddrugs,"AppliedPhysics.A,SolidsSurf,vol.A55,pp.505{507,December1992. [5] A.HudsonandT.Rayner,NarcoticsDetectionBasedonQuadrupoleResonance(QR).www.maths.dur.ac.uk/dma0ped/EM/2004-5/NarcoticsDetectionBasedonQuadrupoleResonance.pdf,October2003. [6] E.Rao,\Applicationofanexplosivedetectiondevicebasedonquadrupoleres-onance(QR)technologyinaviationsecurity,"SecurityTechnology,2001IEEE35thInternationalCarnahanConferenceon,pp.282{288,16-19October2001. [7] T.N.Rudakov,A.V.Belyakov,andV.T.Mikhaltsevich,\Alow-frequencyinstrumentforremotenuclearquadrupoleresonanceexperiments,"MeasurementScienceandTechnology,vol.8,pp.444{448,April1997. [8] T.N.Rudakov,V.T.Mikhaltsevich,andO.P.Selchikhin,\Theuseofmulti-pulsenuclearquadrupoleresonancetechniquesforthedetectionofexplosivescontainingRDX,"JournalofPhysicsD:AppliedPhysics,vol.30,pp.1377{1382,May1997. [9] J.Stegenga,Humanitariande-mining:DetectionalgorithmsforNQRsignals.M.S.Thesis,UniversityofTwente(Netherland),January2004. [10] B.D.Nordwall,\Airportsecurityspursnewinterestinsensors,"AviationWeek&SpaceTechnology,pp.48{50,January2002. [11] QuantumMagneticsInc.Webpage.www.qm.com,August2003. 98

PAGE 109

[12] [13] C.BruschiniandB.Gros,\Asurveyofcurrentsensortechnologyresearchforthedetectionoflandmines,"theInternationalWorkshoponSustainableHuman-itarianDemining,29September-1October,Zagreb,Croatia1997. [14] A.Jakobsson,M.Mossberg,M.D.Rowe,andJ.A.S.Smith,\Exploitingtem-peraturedependencyinthedetectionofNQRsignals,"IEEETransactionsonSignalProcessing,2005(toappear). [15] A.Jakobsson,M.Mossberg,M.D.Rowe,andJ.A.S.Smith,\Exploitingtem-peraturedependencyinthedetectionofNQRsignals,"ICASSP,Detection,Es-timation,ClassicationTheoryandApplicationsI,pp.653{656,2005. [16] S.D.Somasundaram,J.A.S.Smith,K.Althoefer,andL.D.Seneviratne,\De-tectionoflandminesusingnuclearquadrupoleresonance(NQR):Anoverview,"2004. [17] Y.Jiang,P.Stoica,andJ.Li,\Arraysignalprocessingintheknownwave-formandsteeringvectorcase,"IEEETransactionsonSignalProcessing,vol.52,pp.23{35,January2004. [18] G.Liu,Y.Jiang,H.Xiong,J.Li,andG.A.Barrall,\Radiofrequencyinterfer-encesuppressionforlandminedetectionbyquadrupoleresonance,"EURASIPJournalonAppliedSignalProcessing:SpecialIssueonRadarSpace-TimeAdap-tiveProcessing,Inpress. [19] P.Stoica,H.Xiong,L.Xu,andJ.Li,\Adaptivebeamformingforquadrupoleresonance,"DigitalSignalProcessing,Inpress. [20] J.LiandP.Stoica,\AnadaptivelteringapproachtospectralestimationandSARimaging,"IEEETransactionsonSignalProcessing,vol.44,pp.1469{1484,June1996. [21] P.Stoica,H.Li,andJ.Li,\Amplitudeestimationofsinusoidalsignals:Sur-vey,newresults,andanapplication,"IEEETransactionsonSignalProcessing,vol.48,pp.338{352,February2000. [22] P.StoicaandR.L.Moses,IntroductiontoSpectralAnalysis.EnglewoodClis,NJ:Prentice-Hall,1997. [23] J.Capon,\Highresolutionfrequency-wavenumberspectrumanalysis,"Proceed-ingsoftheIEEE,vol.57,pp.1408{1418,August1969. [24] D.D.FeldmanandL.J.Griths,\Aprojectionapproachforrobustadaptivebeamforming,"IEEETransactionsonSignalProcessing,vol.42,pp.867{876,April1994.

PAGE 110

[25] P.StoicaandR.Moses,SpectralAnalysisofSignals.EnglewoodClis,NJ:Prentice-Hall,2005. [26] Y.Wang,J.Li,andP.Stoica,\Rank-decientrobustCaponlterbankap-proachtocomplexspectralestimation,"IEEETransactionsonSignalProcess-ing,vol.53,pp.2713{2726,August2005. [27] A.Jakobsson,M.Mossberg,M.D.Rowe,andJ.A.S.Smith,\Frequencyselec-tivedetectionofnuclearquadrupoleresonancesignals,"IEEETransactionsonGeoscienceandRemoteSensing,2005(toappear). [28] H.KrimandM.Viberg,\Twodecadesofarraysignalprocessingresearch:Theparametricapproach,"IEEESignalProcessingMagazine,vol.13,no.4,pp.67{94,July1996. [29] Y.Tan,S.L.Tantum,andL.M.Collins,\Landminedetectionwithnuclearquadrupoleresonance,"inProc.IGARSS'02,pp.1575{1578,2002. [30] H.Xiong,J.Li,andG.A.Barrall,\JointTNTandRDXdetectionviaQuadrupoleResonance,"IEEETransactionsonAerospaceandElectronicSys-tems,submitted2004. [31] J.H.Michels,P.Varshney,andD.D.Weiner,\Synthesisofcorrelatedmulti-channelrandomprocesses,"IEEETransactionsonSignalProcessing,vol.42,pp.362{375,February1994. [32] A.L.SwindlehurstandP.Stoica,\Maximumlikelihoodmethodsinradararraysignalprocessing,"ProceedingsoftheIEEE,vol.86,pp.421{441,February1998. [33] S.L.Tantum,L.M.Collins,L.Carin,I.Gorodnitsky,A.D.Hibbs,D.O.Walsh,G.A.Barrall,D.M.Gregory,R.Matthews,andS.A.Vierkotter,\Signalpro-cessingforNQRdiscriminationofburiedlandmines,"inProc.SPIE,vol.3710,pp.474{482,1999. [34] T.R.Witten,\Presentstate-of-the-artingroundpenetratingradarsforminedetection,"inDetectionandRemediationTechnologiesforMinesandMinelikeTargetIII,vol.3392ofProc.SPIE,pp.576{585,1998. [35] M.Bradley,T.Witten,R.McCummins,andM.Duncan,\Minedetectionwithgroundpenetratingsyntheticapertureradar,"inDetectionandRemedi-ationTechnologiesforMinesandMinelikeTargetVII,vol.4742ofProc.SPIE,pp.248{258,2002. [36] J.Kositsky,R.Cosgrove,C.Amazeen,andP.Milanfar,\Resultsfromaforward-lookingGPRminedetectionsystem,"inDetectionandRemediationTechnologiesforMinesandMinelikeTargetVII,vol.4742ofProc.SPIE,pp.206{217,2002.

PAGE 111

[37] R.Kapoor,M.Ressler,andG.Smith,\Forward-lookingminedetectionusinganultra-widebandradar,"inDetectionandRemediationTechnologiesforMinesandMinelikeTargetV,vol.4038ofProc.SPIE,pp.1067{1076,2000. [38] T.Gozani,P.Ryge,andP.Shea,\Explosivedetectionsytembasedonthermalneutronactivation,"IEEETransactionsonAerospaceandElectronicSystemsMagazine,vol.4,pp.17{20,December1989. [39] A.JeremicandA.Nehorai,\Landminedetectionandlocalizationusingchem-icalsensorarrayprocessing,"IEEETransactionsonSignalProcessing,vol.48,pp.1295{1305,May2000. [40] J.M.SabatierandN.Xiang,\Aninvestigationofacoustic-to-seismiccouplingtodetectburiedantitanklandmines,"IEEETransactionsonGeoscienceandRemoteSensing,vol.39,pp.1146{1154,June2001. [41] S.P.Beevor,J.Sander,I.Raitt,J.D.Burrows,andK.Mann,\Non-invasiveinspectionofbaggageusingcoherentX-rayscattering,"EuropeanConventiononSecurityandDetection,pp.301{305,16-18May1995. [42] K.L.Russell,J.E.McFee,andW.Sirovyak,\Remoteperformancepredictionforinfraredimagingofburiedmines,"inDetectionandRemediationTechnologiesforMinesandMinelikeTargetII,vol.3079ofProc.SPIE,1997. [43] G.A.Clark,S.K.Sengupta,W.D.Aimonetti,F.Roeske,andJ.G.Donetti,\Multispectralimagefeatureselectionforlandminedetection,"IEEETransac-tionsonGeoscienceandRemoteSensing,vol.38,pp.304{311,January2000. [44] R.M.Deas,I.A.Burch,andD.M.Port,\DetectionofRDXandTNTmineliketargetsbynuclearquadrupoleresonance,"inProc.SPIE,vol.4742,pp.482{489,2002. [45] A.D.Hibbs,G.A.Barrall,P.V.Czipott,A.J.Drew,D.M.Gregory,D.K.Lath-rop,Y.K.Lee,E.E.Magnuson,R.Matthews,D.C.Skvoretz,S.A.Vierkotter,andD.O.Walsh,\DetectionofTNTandRDXlandminesbystand-onuclearquadrupoleresonance,"inProc.SPIE,vol.3710,pp.454{463,1999. [46] A.D.Hibbs,G.A.Barrall,P.V.Czipott,D.K.Lathrop,Y.K.Lee,E.E.Magnuson,R.Matthews,andS.A.Vierkotter,\Landminedetectionbynuclearquadrupoleresonance,"inDetectionandRemediationTechnologiesforMinesandMinelikeTargetIII,vol.3392ofProc.SPIE,pp.522{532,1998. [47] V.S.GrechishkinandN.Y.Sinyavskii,\Newtechnologies:nuclearquadrupoleresonanceanexplosiveandnarcoticdetectiontechnique,"Physics-Uspekhi,vol.40,no.4,pp.393{406,1997. [48] J.A.S.Smith,\Nuclearquadrupoleresonancespectroscopy,GeneralPrinciples,"JournalofChemistryEduction,vol.48,pp.39{49,1971.

PAGE 112

[49] J.A.S.Smith,\Nitrogen-14quadrupoleresonancedetectionofRDXandHMXbasedexplosives,"inEuropeanConventiononSecurityandDetection,vol.408,pp.288{292,16-18May1995. [50] J.A.S.Smith,\Minedetectionbynuclearquadrupoleresonance,"Proc.Conf.DeminingTechnologies,Ispra,Italy,pp.314{321,1998. [51] M.D.RoweandJ.A.S.Smith,\Minedetectionbynuclearquadrupolereso-nance,"ProceedingsoftheEURELInternationalConfernceontheDetectionofAbandonedLandmines,Edinburgh,UK,vol.431,pp.62{66,1996. [52] J.L.SchianoandM.D.Ginsberg,\ApulsedspectrometerdesignedforfeedbackNQR,"Z.Naturforsch,vol.55a,no.1-2,pp.61{66,2000. [53] J.L.Schiano,T.Routhier,A.J.Blauch,andM.D.Ginsberg,\Feedbackopti-mizationofpulsewidthintheSORCsequence,"JournalofMagneticResonance,vol.140,pp.84{90,September1999. [54] A.D.Hibbs,G.A.Barrall,P.V.Czipott,A.J.Drew,D.K.Lathrop,Y.K.Lee,E.E.Magnuson,R.Matthews,D.C.Skvoretz,andS.A.Vierkotter,\Manportableminedetectorusingnuclearquadruoleresonance-rstyearprogressandtestresults,"inDetectionofabandonedlandmines,ConferencePublication,no.458,pp.138{141,12-14October1998. [55] C.Williams,P.V.Czipott,andL.J.Burnett,\Quantummagneticstargetslandmineexplosivesusingquadrupoleresonance,"JournalofMineAction(Issue:5.2),p.http://www.maic.jmu.edu/journal/5.2/features/quantum.htm,August2001. [56] R.A.MarinoandS.A.Klainer,\Multiplespinechoesinpurequadrupolereso-nance,"JournalofChemistryPhysics,vol.67,no.7,pp.3388{3389,1977. [57] S.S.Kim,J.R.P.Jayakody,andR.A.Marino,\Experimentalinvestigationsofthestrongo-resonantcomb(SORC)pulsesequencein14NNQR,"ZeitschriftNaturforschungA:AJournalofPhysicalSciences,vol.47,no.A,pp.415{420,1992. [58] W.S.Hinshaw,\Imageformationbynuclearmagneticresonance:Thesensitive-pointmethod,"JournalofAppliedPhysics,vol.47,no.8,pp.3709{3721,1976. [59] Y.Tan,AdvancedSignalProcessinginLandmineDetectionwithQuadrupoleResonance.Ph.D.Dissertation,DukeUniversity,2004. [60] B.H.Suits,A.N.Garroway,andJ.B.Miller,\Surfaceandgradiometercoilsnearaconductingbody:Thelift-oeect,"JournalofMagneticResonance,vol.135,pp.373{379,1998. [61] B.H.SuitsandA.N.Garroway,\Optimizingsurfacecoilsandtheself-shieldedgradiometer,"JournalofAppliedPhysics,vol.94,pp.4170{4178,2003.

PAGE 113

[62] B.H.Suits,A.N.Garroway,andJ.B.Miller,\Noise-immunecoilforunshieldedmagneticresonancemeasurements,"JournalofMagneticResonance,vol.131,pp.154{158,1998. [63] B.H.Suits,A.N.Garroway,J.B.Miller,andK.L.Sauer,\14Nmagneticresonanceformaterialsdetectionintheeld,"SolidStateNuclearMageticRes-onance,vol.24,pp.123{136,2003. [64] B.VanVeenandK.Buckley,\Beamforming:Aversatileapproachtospatialltering,"IEEEASSPMagazine,vol.5,pp.4{24,April1988. [65] H.L.V.Trees,Detection,Estimation,andModulationTheory,PartIV,Opti-mumArrayProcessing.NewYork:JohnWiley&Sons,Inc.,2002. [66] Y.Tan,S.L.Tantum,andL.M.Collins,\Cramer-Raolowerboundforestimat-ingquadrupoleresonancesignalsinnon-Gaussiannoise,"IEEESignalProcessingLetters,vol.11,pp.490{493,May2004. [67] Y.Tan,S.L.Tantum,andL.M.Collins,\Kalmanlteringforenhancedland-minedetectionusingquadrupoleresonance,"IEEETransactiononGeoscienceandRemoteSensing,vol.43,pp.1507{1516,July2005. [68] Y.Jiang,J.Li,andP.Stoica,\ArraysignalprocessingforQR,"the36thAsilo-marConferenceonSignals,SystemsandComputers,pp.893{897,PacicGrove,CA,Nov2002. [69] A.Hassanien,S.Shahbazpanahi,andA.B.Gershman,\AgeneralizedCaponestimatorforlocalizationofmultiplespreadsources,"IEEETransactionsonSignalProcessing,vol.52,pp.280{283,January2004. [70] J.Li,P.Stoica,andZ.Wang,\OnrobustCaponbeamforminganddiagonalloading,"IEEETransactionsonSignalProcessing,vol.51,pp.1702{1715,July2003. [71] L.VandenbergheandS.Boyd,\Semideniteprogramming,"SIAMReview,vol.38,pp.49{95,March1996. [72] J.F.Sturm,\UsingSeDuMi1.02,aMATLABtoolboxforoptimizationoversymmetriccones,"Optim.Meth.Software,vol.11-12,pp.625{653,August1999. [73] R.Lacoss,\Dataadaptivespectralanalysismethods,"Geophysics,vol.36,no.4,pp.661{675,1971. [74] P.Stoica,Z.Wang,andJ.Li,\RobustCaponbeamforming,"IEEESignalProcessingLetters,vol.10,pp.172{175,June2003. [75] P.Stoica,H.Li,andJ.Li,\AnewderivationoftheAPESlter,"IEEESignalProcessingLetters,vol.6,pp.205{206,August1999.

PAGE 114

[76] A.B.Gershman,\Robustadaptivebeamforminginsensorarrays,"InternationalJournalofElectronicsandCommunications,vol.53,no.6,pp.305{314,1999. [77] S.A.Vorobyov,A.B.Gershman,andZ.-Q.Luo,\Robustadaptivebeamformingusingworst-caseperformanceoptimization:Asolutiontothesignalmismatchproblem,"IEEETransactionsonSignalProcessing,vol.51,pp.313{324,Febru-ary2003. [78] A.B.Gershman,\Robustadaptivebeamforming:Anoverviewofrecenttrendsandadvancesintheeld,"InternationalConferenceonAntennaTheoryandTechniques,pp.30{35,September9-12,Sevastopol,UKraine2003. [79] R.G.LorenzandS.P.Boyd,\Robustminimumvariancebeamforming,"IEEETransactionsonSignalProcessing,vol.53,pp.1684{1696,May2005. [80] E.Larsson,J.Li,andP.Stoica,\High-resolutionnonparametricspectralanaly-sis:Theoryandapplications.inhigh-resolutionandrobustsignalprocessing(Y.Hua,A.GershmanandQ.Cheng,eds.),"pp.151{251,2004. [81] A.JakobssonandP.Stoica,\CombingCaponandAPESforestimationofspec-trallines,"Circuits,Systems,andSignalProcessing,vol.19,no.2,pp.159{169,2000. [82] H.Li,J.Li,andP.Stoica,\Performanceanalysisofforward-backwardmatched-lterbankspectralestimators,"IEEETransactionsonSignalProcessing,vol.46,pp.1954{1966,July1998. [83] M.Siotani,T.Hayakawa,andY.Fujikoshi,ModernMultivariateStatisticalAnal-ysis:AGraduateCourseandHandbook.Columbus,Ohio:AmericanSciencesPress,Inc.,1985. [84] J.Ward,\Space-timeadaptiveprocessingforairborneradar,"TechnicalReport1015,MITLincolnLaboratory,December1994. [85] G.CasellaandR.L.Berger,StatisticalInference(SecondEdition).PacicGrove,CA:Duxbury/ThomsonLearning,2002. [86] T.SoderstromandP.Stoica,SystemIdentication.London,U.K.:Prentice-HallInternational,1989. [87] D.A.Harville,MatrixAlgebraFromAStatistician'sPerspective.NewYork:Springer,1997.

PAGE 115

HongXiongreceivedtheB.Sc.degreeinelectricalengineeringfromNanjingUniversityofAeronauticsandAstronautics,Nanjing,China,in1988,andtheM.Sc.degreeinelectricalengineeringfromUniversityofElectronicScienceandTechnologyofChina(UESTC),Chengdu,China,in1991.ShealsoreceivedtheM.ScdegreeinelectricalengineeringfromUniversityofFlorida,Gainesville,Florida,in2003.FromApril1991toAugust1999,shewasalecturerwiththeDepartmentofElectricalEngineeringatUESTC.SheisnowworkingtowardthePh.D.degreeinelectricalengineeringattheUniversityofFlorida.SheisamemberofPhiKappaPhi. 105


Permanent Link: http://ufdc.ufl.edu/UFE0013387/00001

Material Information

Title: Robust Adaptive Methods and Their Applications in Quadrupole Resonance
Physical Description: Mixed Material
Copyright Date: 2008

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
System ID: UFE0013387:00001

Permanent Link: http://ufdc.ufl.edu/UFE0013387/00001

Material Information

Title: Robust Adaptive Methods and Their Applications in Quadrupole Resonance
Physical Description: Mixed Material
Copyright Date: 2008

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
System ID: UFE0013387:00001


This item has the following downloads:


Full Text











ROBUST ADAPTIVE METHODS AND THEIR APPLICATIONS
IN QUADRUPOLE RESONANCE
















By

HONG XIONG


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA


2006

















To my parents, my husband, and my son.















ACKNOWLEDGMENTS

I would like to express my sincere gratitude to my advisor, Dr. Jian Li, for

her support, encouragement, inspiration, and patience in guiding this research. I am

deeply indebted to her for providing numerous insightful remarks and sl.::.-- Iri -

which fundamentally influenced the research process. My special appreciation is due

to Dr. C('!Lii..i Ai, Dr. Dapeng Wu, and Dr. Liuqing Yang for serving on my

supervisory committee and for their contribution to my graduate education at the

University of Florida. I am also grateful for their valuable discussions, comments and

S-l-. -1 i. .- on my work. I am deeply grateful to Dr. Petre Stoica for his comments

and si-- :. -1 i. .i' which influenced part of the work.

I gratefully acknowledge Mr. Luzhou Xu for his helpful discussions and valuable

comments that substantially improved this work. I wish to thank Dr. Zhisong Wang

for his help during this work. I also thank all the fellow graduate students in the SAL

group with whom I had the great pleasure of interacting.

I am deeply thankful to my parents, my husband and my son for their help,

encouragement, and support. Finally, I would like to thank all the people who helped

me during my Ph.D. study.















TABLE OF CONTENTS
page

ACKNOWLEDGMENTS ................... ...... iii

LIST OF FIGURES ................... ......... vii

ABSTRACT ....................... ........... ix

CHAPTER

1 INTRODUCTION .................... ....... 1

1.1 QR Technology for Explosive Detection ................ 1
1.2 Signal Amplitude Estimation in QR Application ........... 2
1.3 Scope of the W ork ........................... 4
1.4 Organization of the Dissertation .......... .......... 5

2 BACKGROUND ........ .............. ........ 6

2.1 Explosive Detection Technologies ................. 6
2.2 Basics of QR ................... ... 7
2.2.1 Principles of QR .................. .... 8
2.2.2 Pulse Sequences .................. .... 9
2.2.3 Observed Signals .................. .... .. 10
2.3 Advantages and ('C! 11, i ;! of QR .................. .. 11
2.4 QR Signal Processing Methods ............ .. .. 13

3 SINGLE ANTENNA BASED
SIGNAL AMPLITUDE ESTIMATION AND DETECTION ...... 16

3.1 Introduction .............. . . ...... 16
3.2 Problem Formulation and Preliminaries . . ...... 17
3.3 Adaptive FIR Filter Based Estimation Methods . .... 20
3.3.1 Generalized Capon (GC) Filter ............... .. 20
3.3.2 Robust Generalized Capon (RGC) Filter . . ... 21
3.3.3 Approximate Robust Generalized Capon (ARGC) Filter 23
3.4 Detection .................. ............. .. 25
3.5 Summary of Implementation Steps ................. .. 27
3.6 Numerical Examples .................. ....... .. 28
3.6.1 First Example .................. ..... .. .. 28
3.6.2 Second Example .................. ..... .. 34
3.7 Summary .................. ............. .. 35









4 ANTENNA ARRAY BASED SIGNAL ESTIMATION AND DETECTION 38

4.1 Introduction ................... ........ 38
4.2 Data Model and Problem Formulation ...... ........ 40
4.3 Adaptive Beamforming Methods ......... .......... 43
4.3.1 Known Array Steering Vector ................ 43
4.3.1.1 SCB Based Approach: SCB1 . . 44
4.3.1.2 SCB Based Approach: SCB2 . . 45
4.3.1.3 APES Based Approach: APES1 . .... 46
4.3.2 Uncertain Array Steering Vector .. . . . 47
4.3.2.1 RCB Based Approaches: RCB1 and RCB2 . 47
4.3.2.2 Generalized Robust APES Beamforming Approach:
GRAPES .................. .. 51
4.4 Detection .................. ............. .. 52
4.5 Summary of Implementation Steps ................ 53
4.6 Numerical Examples .................. ....... .. 54
4.7 Summary .................. ............. .. 65

5 JOINT COMPOUND EXPLOSIVE DETECTION . . 67

5.1 Introduction . . . . . . .. 67
5.2 Problem Formulation .................. ....... .. 68
5.3 RFI Mitigation by GRAPES .................. ..... 72
5.4 Joint TNT/RDX Detection .................. ..... 74
5.4.1 Detection. .................. ......... .. 74
5.4.2 Detector Threshold Determination . . ..... 77
5.4.3 Summary of the Detection Steps . . ...... 81
5.5 Experimental Results .................. ....... .. 82
5.6 Summary .................. ............. .. 84

6 SUMMARY AND FUTURE WORK ............ .. ... .. 85

6.1 Summary .................. ............. .. 85
6.2 Future W ork . . . . . . . .. 87

APPENDIX

A PROOF OF A1 > A2 USED IN SECTION 4.3.1.2 . . 88

B DERVIATION OF (4-61) .................. ....... .. 89

C STATISTICAL PROPERTIES OF Zd IN (4 63) ............. 91

D CFAR PROPERTY OF IN (5 33) .................. ... 93

E PROOF OF (5-35) ....... ........ ............. 95

F PROOF OF (5-39) ....... ........ ............. 97









REFERENCES ................................... 98

BIOGRAPHICAL SKETCH ................... ...... 105















LIST OF FIGURES
Figure page

2-1 QR Spectrum of 14N [11] ........................ 9

3-1 An example of signal waveform versus sample number. . .... 29

3-2 An example of the modulus of the received signal spectra. . ... 30

3-3 Biases and MSEs of the estimated amplitudes versus the SNR when N=
12, ISR1 = ISR2 = 20 dB, and L=4. (a) Biases, and (b) MSEs. .... 32

3-4 Biases and MSEs of the estimated amplitudes versus the SNR when
N=12, ISR1 = 40 dB, ISR2 = 20 dB, and L=4. (a) Biases, and (b) MSEs. 33

3-5 Detection performance (ROC) comparison of LS, GC, ARGC, and RGC
when N=12, ISR1 = 40 dB, ISR2 = 20 dB, SNR = 5 dB, and L=4. 34

3-6 The signal waveform versus sample number (second example). ..... 35

3-7 Biases and MSEs of the estimated amplitudes versus the SNR (second
example) when N=12, L= 4, ISR1 ISR2 20 dB. (a) Biases, and (b)
MSEs ...... ............. ................. .. 36

4-1 QR signal vs. sample number (obtained by scanning a TNT mine in a
low noise and RFI-free experiment). ............... .... 54

4-2 An example of the main channel output: (a) the real-part of the output
in the time domain, and (b) the modulus of the spectrum of the output. 56

4-3 Detection performance (ROC) comparisons between the cases with and
without steering vector errors for (a) SCB1 and RCB1, (b) SCB2 and
RCB2, (c) APES1 and GRAPES, and (d) SCB1 and SCB2. ...... ..58

4-4 Detection performance (ROC) with different c values for (a) RCB1, (b)
RCB2, and (c) GRAPES. .................. ..... 60

4-5 Detection performance (ROC) with various temporal filter order L in the
presence of steering vector errors for (a) SCB1, (b) RCB1, (c) SCB2, (d)
RCB2, (e) APES1, and (f) GRAPES. ............... 62

4-6 Detection performance (ROC) comparison among the new methods in the
presence of steering vector errors. .............. ...... 65









4-7 Detection performance (ROC) comparison of M3L, ALS, combined ap-
proach and GRAPES for the real-world example. ........... ..66

5-1 Data cube from QR data collection ................ .... 71

5-2 Signal processing flow chart for joint TNT/RDX detection . .... 72

5-3 PDF of z2 and (k for various data length N ...... . 79

5-4 Probability of false alarm versus detection threshold for the X2-mixture
distribution for the joint TNT/RDX detection as well as individual TNT
or RDX detection. .................. .. ...... 81

5-5 TNT fast-time waveform (obtained by scanning a TNT mine in a high
SNR and RFI-free experiment) and non-symmetric Hanning window. 83

5-6 ROC curves for the GRAPES-GLRT detector. .. . ..... 84















Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

ROBUST ADAPTIVE METHODS AND THEIR APPLICATIONS
IN QUADRUPOLE RESONANCE

By

Hong Xiong

Al ,v 2006

C('!, : Jian Li
Major Department: Electrical and Computer Engineering

Signal amplitude estimation and detection problems have been encountered in

many practical applications including the emerging quadrupole resonance (QR) tech-

nology for the detection of substance of interest (e.g., explosives). In the QR ap-

plication, the signal waveform is known a prior. The main challenge of applying

QR to the detection of substance of interest is that the returned QR signal is often

unavoidably corrupted by strong radio frequency interference (RFIs).

Motivated by the QR application, this dissertation investigates robust adaptive

methods for the amplitude estimation of a signal with known arbitrary waveform

in the presence of strong RFIs and noise. The main objective is to fundamentally

address the signal processing perspectives for explosive detection by QR. The focus

is to establish realistic data models, devise innovative signal processing algorithms,

and evaluate their performances.

For the single antenna based application, we consider the amplitude estimation

of a signal with arbitrary known waveform in the presence of strong interference

and noise. Three adaptive finite-impulse response filter based methods are presented

to suppress the strong interference. We first extend the generalized Capon (GC)









estimator to the problem of signal amplitude estimation. Then we devise two robust

methods to mitigate the small snapshot number problems by allowing an uncertainty

set for the signal covariance matrix.

For the antenna array based application, we propose several adaptive beamform-

ing approaches to improve the QR signal detection performance via exploiting both

the spatial and temporal correlations of RFIs. We operate in the framework of signal

amplitude estimation with known signal waveform and make use of three adaptive

beamforming approaches, viz., the standard Capon beamformer (SCB), the robust

Capon beamformer (RCB), and the amplitude and phase estimation (APES) algo-

rithm, to develop several new approaches for mitigating the spatially and temporally

correlated RFIs.

For the detection of compound explosives, we derive a joint generalized likelihood

ratio test (GLRT) detector based on the outputs of RFI mitigation filters designed

for individual QR explosive probings. We also conduct a detailed statistical analysis

on the joint GLRT detector and show that it has a constant false alarm rate property.















CHAPTER 1
INTRODUCTION

1.1 QR Technology for Explosive Detection

As early as the 1950s, researchers working in the field of nuclear magnetic reso-

nance (NMR) introduced the idea of using nuclear quadrupole resonance (QR) tech-

nology to detect explosives [1]. Since then, the QR technology has been receiving

increasing attention for many applications [1]-[9] including humanitarian defining

and homeland security because it provides a unique signature of the substance of

interest.

QR is similar to NMR since they are both magnetic resonance phenomena [1].

However they have a significant difference. Instead of using an external (static)

magnetic field, like an NMR device, a QR device makes use of the natural < i .1 1111,,

electrical field gradient within the materials [1]. Hence, it is understood that QR is

similar to NMR without a magnet [1]. As a result, QR based equipment is safer and

more reliable to use and transport than its NMR counterpart.

In recent years, the urgent demand for homeland security and the fight against

terrorism makes explosive detection a hot topic. As we know, trained dogs have been

recognized as the quickest and most reliable detectors for explosives. However, they

easily become tired and the resource of dogs that can be trained for this purpose is

very limited. Hence, the need to develop machine based detectors becomes urgent [10].

The InVision (now part of GE) '., -.-- ,.-. screener is an example which is used in many

airports for aviation security. The '. ,.-- ,.-.- screener is a shielded device built based on

the QR technology. However, when cost, size, and weight are concerned, unshielded

QR systems are preferred over their shielded counterparts, such as handheld QR









wands for screening personnel and QR shoe scanners [11]. However, radio frequency

interference (RFI) suppression is critical for unshielded QR systems [1].

Landmine detection is another important application of the QR technology. Be-

cause of the huge economic loss and severe threat to human life caused by landmines,

landmine detection has received significant attention from many governments and

humanitarian groups in recent decades [12]. It is estimated that there are more than

100 million landmines in over 70 countries around the world and that an injury or

death from landmines occurs every 20 minutes [3, 9], [12]-[14]. By using existing

technologies, it would take more than 500 years and $33 billion to clean them up

assuming no more mines would be buried [15, 16]. Hence, it is urgent to develop

efficient and robust methods to detect landmines. The unique spectral signatures of

explosives provided by QR make QR a promising method for landmine detection [1].

1.2 Signal Amplitude Estimation in QR Application

Signal amplitude estimation is a key step in applying the QR technology to

explosive detection [1], [17]-[19]. In the QR application, the signal waveform is known

a prior to within a multiplicative constant [17]. The main challenge of applying QR

to the detection of substance of interest is that the QR probing is often unavoidably

corrupted by strong RFIs that are usually spatially and temporally correlated. For

instance, the QR frequency for the trinitrotoluene (TNT) explosive is around 842

KHz at normal room temperature [1]. Since this frequency falls within the amplitude

modulation (AM) radio frequency band and cannot be changed by other means, the

AM radio signals can appear as strong RFIs that can seriously degrade the QR signal

detection performance. Hence to detect the very weak QR signal, the RFIs must

be effectively suppressed in order to attain accurate signal amplitude estimation and

achieve satisfactory detection performance. Motivated by the QR application, this

dissertation investigates robust adaptive amplitude estimation for a signal with a

known arbitrary waveform in the presence of strong RFIs and noise.









Many methods have been proposed for signal amplitude estimation ([17], [20]-

[22] and the references therein). One of them is the least-squares (LS) method [21, 22],

which is widely used for signal amplitude estimation due to its simplicity. However,

in the presence of strong colored interference and noise, the performance of LS

degrades significantly. Several adaptive nonparametric methods, including standard

Capon beamformer (SCB) [23], Amplitude and Phase Estimation (APES) [20], and

MAtched FIlter (\ AFI) [21], were proposed for estimating the complex amplitudes

of sinusoidal signals [21]. However, these methods are not directly applicable to the

QR problem due to the signal waveform being non-sinusoidal. Furthermore, in the

array based applications, these approaches assume that a precise steering vector is

available. They are not immune to the steering vector error and thus suffer from

low robustness problem. They may perform poorly when the number of snapshots

is small and/or non-stationary interference and noise exist. These two factors can

be viewed as equivalent to steering vector errors even when the array steering vector

has no error [24]-[26]. Therefore, new robust adaptive methods are needed for the QR

application under the framework of signal amplitude estimation with an arbitrary

known f
In addition to the arbitrary known .:,,,,.,l ,,.r, f.'i,,, and robustness issues, an-

other important issue that needs to be taken into account in the QR application is the

spatial and temporal correlations of RFIs [17, 18]. Reference antennas, which receive

RFIs only, can be used together with the main antenna, which receives both the QR

signal and the RFIs, for improved RFI mitigation [1, 17], [27]-[30]. By taking advan-

tage of the spatial correlation of the RFIs received by the antenna array, the RFIs

can be reduced significantly. However, the RFIs are usually colored both spatially

and temporally [31, 32], and hence exploiting only the spatial diversity of the antenna

array may not give the best performance. Although several approaches have been pro-

posed to reduce the negative effect of RFIs on landmine detection [1, 17, 18, 29, 33],









exploiting both the spatial and temporal correlations of the interference has not

been fully investigated. In this study, we will exploit both the spatial and temporal

correlations of RFIs to improve the explosive detection performance.

1.3 Scope of the Work

The main objective of this dissertation is to fundamentally address the signal

processing perspectives for the detection of substances of interest by QR. The focus

is to establish realistic data models, devise innovative signal processing algorithms,

and evaluate their performances. In particular, we develop several robust adaptive

methods for RFI mitigation, signal amplitude estimation, and signal detection for

both single antenna and array based configurations. We also devise a joint detector

for the detection of compound substance of interest.

First, we investigate the single antenna based amplitude estimation of a signal

with an arbitrary known waveform in the presence of strong interference and noise.

Three adaptive finite-impulse response (FIR) filter based methods are presented to

suppress the strong interference. We first extend the generalized Capon (GC) esti-

mator to the problem of signal amplitude estimation. Then we devise two robustified

methods to mitigate the small snapshot problems by allowing an uncertainty set for

the signal covariance matrix.

Second, we consider the antenna array based signal amplitude estimation and

detection problem. We present several adaptive beamforming approaches to improve

the QR signal detection performance via exploiting both the spatial and temporal

correlations of the RFIs. We operate in the framework of signal amplitude estimation

with known signal waveform and make use of three adaptive beamforming approaches,

viz., SCB, the robust Capon beamformer (RCB), and APES algorithm, to develop

several new approaches for mitigating the spatially and temporally correlated RFIs

effectively.






5


Third, we investigate the compound explosive detection problem. Since a single

mine can contain more than one type of explosives (e.g., TNT and Royal Demolition

eXplosive (RDX) compound), a detector designed to detect only one type of explosive

may not provide the best detection. In this aspect, we focus on the joint detection of

TNT and RDX explosives for the landmine detection via the QR sensor. We derive

a generalized likelihood ratio test (GLRT) detector for the joint compound detection

based on the outputs of RFI mitigation for individual QR explosive probing, which is

referred to as the joint GLRT detector. We also conduct a detailed statistical analysis

on the joint GLRT detector and show that our detector has a constant false alarm

rate (CFAR) property and that the detection variable obeys a X2-mixture distribution

in the mine-free scenario.

1.4 Organization of the Dissertation

The remainder of this dissertation is organized as follows. C'!i lpter 2 briefly in-

troduces the background of explosive detection via QR. In Chapter 3, three adaptive

methods are presented to deal with the single antenna based signal amplitude esti-

mation problem. In ('!i Ilter 4, several adaptive beamforming approaches and their

robustified versions are proposed to improve the QR signal detection performance,

which exploit both spatial and temporal correlations of the RFIs. C'! Ilpter 5 presents

a joint GLRT detector for the compound explosive detection and conducts a theoret-

ical analysis of the detection statistics. Finally, we summarize this work and outline

the future work in ('!C Ipter 6.















CHAPTER 2
BACKGROUND

In this chapter, we will briefly introduce the background of explosive detection

via QR. First, we will introduce the existing explosive detection technologies, espe-

cially for the landmine detection; second, we will briefly review some basics of QR,

which includes the principle of QR, some commonly used pulse sequences, and the

observation signals in QR; third, we will present an overview of the advantages and

the challenges of QR; finally, a literature review of the existing QR signal processing

methods will be given.

2.1 Explosive Detection Technologies

Tod-,- most of the civilian defining is still done by hand, for example, a prodding

method. Although prodding is a reliable and simple method, it is extremely slow,

laborious, and hazardous [3].

A conventional technology for the landmine detection is the electromagnetic

(EM) based metal detector. Because it is cheap and easy to operate, it has been

widely used in practice. The metal detector can provide a high probability of de-

tection (Pd) for anti-tank (AT) mines, which contain about 5 ~ 10 kg of explosives

and are buried within 10 cm depth [1]. However, it is hardly useful to detect the

buried anti-personnel (AP) mines, which are usually very small, contain 50 ~ 100

g of explosives, and are buried under the surface [1]. The reflected EM signal from

an AP mine is very weak compared with that from an AT mine [1]. This makes it

difficult to distinguish landmines from other metal detritus (clutter), such as shell

fragments, rusty nails, etc. [1]. As a result, metal detectors inevitably suffer from a

high false alarm rate (FAR). Usually 100-1000 false alarms for each real mine will be

produced by such kinds of metal clutter [13].









As we know, the basic requirement for the landmine detection is to achieve a

high Pd (> 9',-.) with a reasonably low FAR, and the detection systems should be

capable of operating under various environments [3]. Moreover, most of the modern

landmines are not metal-cased but plastic- or wood-cased. They contain very little or

even no metal and thus can hardly be detected by metal detectors. Hence, the metal

detector cannot satisfy these basic requirements, and developing new technologies to

detect landmine becomes very urgent.

In the past few decades, many technologies have been investigated for detecting

both metal and non-metal landmines. These include, for example, ground penetrating

radar (GPR) [34]-[37], thermal neutron activation (TNA) [38], QR sensor [1], trace

explosive detector [39], acoustic detector [40], advanced metal detector, X-ray [41],

infrared [42] and multispectral imaging [43] methods, and mine detecting dogs [13].

Among them, QR is a promising technology because a QR detector intends to detect

the content instead of the case of the landmine. Explosives (e.g., TNT and RDX)

are usually rich in 14N that is associated with highly specific QR signals at particular

frequencies [1, 29, 33], [44]-[46]. Hence, QR can be used as a confirmation sensor

assisting other sensors for FAR reduction.

2.2 Basics of QR

Since the 1950s, many researchers around the world have worked on the QR

technology. More recently, Grechishkin, at the Kaliningrad State University in Russia,

proposed an approach to determine the burial depth of the landmine by finding the

optimal frequency offset of the radio frequency (RF) pulse sequence and improve

the performance of the detection system [3, 4, 47]. Smith and his colleagues at

King's College of the University of London have been working extensively on explosive

detection since 1980 [48]-[51]. They produced commercial QR detection systems for

narcotics and explosive detection for airline ', ,.-.- -.-, inspection [3]. Schiano et al. at

Pennsylvania State University proposed a feedback optimization method to achieve









the optimal performance of the detection system [52, 53]. Their method can reach

the maximum signal-to-noise ratio (SNR) by adaptively adjusting the pulse width,

and thereby improving the detectability of landmines by QR [52].

In the recent decade, Quantum Magnetics (QM), Inc. has worked on projects re-

lated to explosive detection by QR [1, 11], [44]-[46], [54], which include non-destructive

evaluation, landmine detection, and some security applications. QM has also built

commercial QR detection systems for explosive detection used in airports [11].

2.2.1 Principles of QR

QR is a form of radio frequency spectroscopy [2]. It is similar to NMR and the

magnetic resonance imaging (l RI) technique used in the medical industry but with-

out using a magnet [1]. It provides quite special possibilities for detecting chemical

substances in solid form.

The basic detection principle by QR is simple ([1], p.1110): "applying a pulse

or series of RF pulses resonant at the appropriate QR frequency of the material of

interest and looking for the presence (or absence) of a return signal." The detection

by QR includes the following steps [55].

* A series of low-power RF pulses, referred to as exciting pulses, are generated and
emitted by a transmitter;

* Due to the stimulations of these exciting pulses, the alignment of the nuclei
within the molecules of explosive is disturbed and re-arranged;

* During the procedure of the nuclei turning back to their original state, a char-
acteristic RF signal is emitted, which is referred to as an echo;

* The QR sensor receives the echo. After proper amplification, frequency down-
conversion, and digitization, the received signal is sent to a computer based
processor;

* The computer based processor rapidly analyzes the received signal and makes a
decision, i.e., to determine whether the type of sought-after explosive's nuclei is
present in the target or not.









Since the frequency of the echo from the nuclei depends on the molecular struc-

ture of the atoms, it is unique for each type of explosive. Hence, QR can be used to

accurately detect the presence of explosive, due to its high sensitivity to the target's

chemical substance. Figure 2-1 shows the QR frequencies of some explosives and

narcotics [11].


Excitation PETN
Bandwidth TNT
5 KHz
RDX
HMX
Heroin









0 1 2 3 4 5

Signal frequency in MHz
Figure 2-1. QR Spectrum of 14N [11]


2.2.2 Pulse Sequences

The RF pulse sequence design is a key step to obtain a useful QR signal. Because

the multi-pulse technique can improve the detection capability of the QR signal, it has

been widely used in QR applications. By coherently adding the individually acquired

signals, the SNR can be improved. In particular, the pulse sequences are designed to

maximize the SNR and reject the spurious RF responses [2]. Listed below are several

commonly used multi-pulse sequences.

Spin-lock spin echo (SLSE) pulse sequence: The SLSE pulse sequence

generates decaying spin-echo sequences and the acquired signals can be coherently

added [3] to enhance the SNR. It is the first sequence that produces a series of QR









signals in a short time for coherently averaging, which was introduced in the late

1970s [3, 56].

The strong off-resonant comb (SORC) pulse sequence: "The SORC se-

quence is a series of off-resonant RF pulses separated by equal spacing that yields a

steady-state signal in the pulse repetition period" ([53], p.85). The SORC sequence

can produce the stable spin-echoes such that the received signals can be coherently

added [3]. One advantage of the SORC sequence is that the generated signal has

the comparable amplitude with that of the free induction decay signal [53]. It was

introduced in the early 1980s [57].

The phase alternated (PAPS) and non-phase alternated (NPAPS)

pulse sequences: The combination of the phase alternated and non-phase alter-

nated pulse sequences was first developed for MRI application [3, 58]. This combined

pulse sequence can be used to reduce the direct current offset and remove the system

correlated noise by varying the phase of the QR signal in a predictable manner to

separate it from other artifacts [3]. The PAPS is repeated n times, followed by n

repetitions of NPAPS. The entire sequence may be repeated m times in order to im-

prove sensitivity. Similar to SORC, this combined sequence can also produce stable

signals, which can be coherently averaged to improve the SNR [3].

2.2.3 Observed Signals

There are two commonly used observation signals for QR: free induction decays

(FIDs) and spin echoes, which are explained as follows [16], [48]-[51].

Free induction decays: "FID is a decaying signal observed immediately fol-

lowing the exciting pulse; it is generated by the interaction of the oscillating magnetic

field B1 of the applied RF with the magnetic moment of the quadrupolar nucleus"

([49], p.289). Due to the fast decaying of the FID signal and the strong ringing after
the RF pulse, FID can hardly be used for the QR signal detection.









Spin echoes: After the first pulse, QR signals from the 14N may be out of phase

[16]. However, particular pulse sequences can be used to take them back to in phase

and useful spin echoes can be obtained during a longer time than FID [16]. Therefore,

spin echoes are widely used in the practical QR applications.

2.3 Advantages and Challenges of QR

The QR technology is receiving more and more attention in applications includ-

ing explosive detection, drug traffic control, etc. This is due to the fact that QR as

a detection method has many advantages [1]-[3], which are summarized as follows.

* QR is a safe non-invasive technology;

* QR is able to detect metal or non-metallic landmines since it detects the 14N
nuclei in the explosive instead of the case of the explosive;

* QR is able to detect a target compound with a very low FAR due to its specific
frequency signature;

* Unlike NMR, QR can be used in the portable detection systems because no
external magnetic field is needed;

* QR is capable of detecting other 14N compound, such as narcotics, and can be
used in border security detection, airline '. .-.- ,.-. detection, drug detection, etc.

Despite the aforementioned advantages, several challenges need to be addressed

before QR can be used. The main restriction is that the measured SNR is low because

the returned QR signal is weak compared with the ambient noise [16], especially for

small AP landmines. Some efforts have been made to enhance the SNR of QR by

improving the hardware design including the search coil and antennas ([1] and the

references therein).

Suffering from the strong RFIs is another challenge for the practical QR applica-

tion. Since the frequency of the QR signal is low (0.5 ~ 6 MHz) [51], it is unavoidably

corrupted by RFIs located in this frequency band. For example, the frequency of the

TNT QR signal is 0.842 MHz, which is within the frequency band of AM radio. Hence









the AM radio signal can appear as strong RFIs that can seriously degrade the explo-

sive detection by QR. Therefore, to detect the very weak QR signal, it is essential to

mitigate the RFIs [1, 16, 17, 59].

The ringing produced by the search coil and associated hardware is also a prob-

lem of QR system [1, 16]. Although the exciting pulse has ended, the coil cannot

immediately obtain the useful QR signal because of the ring problem [16]. Using the

phase cycling of the pulse sequence is an efficient way to reduce the ringing problem

[1, 8, 16].
Using the signal average is another efficient method to improve SNR [1, 3]. In-

stead of transmitting one pulse, the transmitter sends out a multi-pulse sequence.

Then the obtained QR signals can be coherently averaged over the entire pulse se-

quence. In addition, the RF pulse sequences also need to be carefully designed to

maximize the SNR in a unit time [2]. For the uncorrelated noise, the SNR will be

increased by the number of the averaged QR signals [3]. However, this method is not

effective in the presence of correlated noise or interference [3].

Optimizing the search coil design is also an efficient way to increase SNR and

hence improve the QR signal detection performance [60]. In the landmine detection

application, surface coils are widely used. Suits et al. have addressed many coil

design issues and proposed several methods to improve the coil design [60]-[63].

Reducing RFIs is another way to enhance the SNR. In the hardware design both

passive and active strategies have been considered to reduce RFIs [1]. The N i.,1

Research Laboratory (NRL) designed a QR gradiometer coil [60], which is a passive

approach. It is reported that the gradiometer coil can reduce the far field magnetic

interference by 30 dB [1]. However, the acquired QR signal may also be reduced at

the same time [60]. Asymmetric gradiometers have been proposed to partly solve the

QR signal loss problem [16]. QM developed an efficient QR coil (used as the main

antenna) and a set of external remote antennas (used as reference antennas) to reduce









RFIs [1]. The main antenna is designed and placed to receive both RFIs and QR

signal while the reference antennas receive RFIs only [1]. RFIs in the main antenna

can be significantly reduced by subtracting the estimated RFIs from the reference

antennas [1]. The drawback of this active approach is that it requires high dynamic

range and accurate balance of the antennas [1].

2.4 QR Signal Processing Methods

Given the limitations of the hardware and pulse sequence designs, the develop-

ment of signal processing methods is a key issue for improving the QR signal detection

performance. Hence developing an efficient and effective signal processing algorithm

to improve the QR signal detection performance is necessary. In this section, we will

give a brief review of current QR signal processing methods.

The energy detector is the most widely used signal detection method because it

is simple and easy to implement. It works as follows: first, it transforms the collected

QR signal into the frequency domain and calculates the power of the frequency bin

of interest; then, a preset threshold is used to determine the presence of the target

of interest, such as a landmine. This approach works quite well when the signal-

to-inference-plus-noise ratio (SINR) is high [16]. However, in the practical landmine

detection, where the SINR is usually low, it is difficult to obtain a good detection

performance by using this method alone.

An adaptive noise cancellation method has been used by Tantum et al. [33] to

reduce the RFIs for QR. Their method is used in a similar fashion to the QM's active

approach for RFI reduction [1]. It is reported that by using a 1-tap least mean squares

algorithm, the adaptive noise cancellation method [64, 65] can reduce the RFIs by

more than 50 dB [33]. However, this method may amplify the white noise and it may

suffer from the signal cancellation due to minimizing the total output power [64].

An average power detector based on power spectral estimation algorithms has

been proposed by Tan et al. in [29]. The experimental results in Tan et al. [29] show









that the average power detector outperforms the non-adaptive B i- -i i,1 detector, and

can provide robust detection performance by the distinguishable features of the QR

signal and the RFI in the frequency domain [59]. However, we note that the average

power detector is preferred after the RFI mitigation. It may suffer from the low

SINR just as the conventional energy detector. By considering the RFI as a colored

non-Gaussian process, Tan et al. [66] derived a Cramer-Rao lower bound. More

recently, they proposed a two-step adaptive Kalman filter to estimate and detect the

QR signal in the post-mitigation signal [59, 67]. As shown with numerical results

in Tan et al. [67] this method can provide robust landmine detection performance.

However, to obtain the coefficient and covariance matrices [67], this method requires

training data, which may not be available in real application.

Jiang et al. [17, 68] investigated the landmine detection by QR under the frame-

work of signal amplitude estimation with known signal waveform and steering vector.

They proposed a maximum likelihood (il I) estimator and a Capon estimator and

derived closed-form expressions for the bias and mean-squared errors (\!SrI-) of both

estimators in the presence of spatially colored but temporally white interference and

noise [17]. They also showed that both estimators are .,-i-!''iilli ically statistically

efficient for large data snapshots. The ML estimator is unbiased while the Capon

estimator is biased downward. An alternative least square (ALS) method is also pro-

posed to consider a more general case, in which the interference and noise are both

temporally and spatially colored. The numerical results in Jiang et al. [17] show that

in most cases, the ALS method is superior to the model-mismatched maximum like-

lihood (i\3L) method, which ignores the temporal correlation of the interference and

noise [17]. However, ALS is slightly worse than M3L for more challenging cases, where

the desired signal and the interference are closely spaced in the temporal frequency

domain.









Stegena investigated several detection algorithms for QR signals [9], which in-

clude B li-, -i ,i method, matched filter (\Ill), and maximum entropy (M\!;) method.

It is observed that the B i-, -i i, method is the most robust method against noise;

however, it requires a priori information. The performance of MF and ME degrades

rapidly as the SNR decreases. In addition, the ME method is found to be most

computationally intensive among these three methods.

By exploiting the temperature dependency of the QR frequencies, Jakobsson et

al. developed several new methods, which include a non-linear least squares method,

an approximate maximum likelihood detector (AML), and a frequency selective AML

detector, to enhance the SNR and improve the QR signal detection performance

[14, 15, 27].

We have investigated the RFI mitigation for landmine detection by QR in Liu

et al. [18]. By exploiting both the spatial and temporal correlation of the RFIs,

we propose a combined approach to mitigate the RFIs efficiently and effectively and

improve the TNT detection performance. First we considered exploiting the spatial

correlation of the RFIs only and proposed a maximum likelihood (\llI) estimator

for signal amplitude estimation and a CFAR detector for TNT detection; second,

we adopted a multi-channel autoregressive (\!AR) model to take into account the

temporal correlation of the RFIs; third, we made use of the spatial and temporal cor-

relations by using a two-dimensional (2-D) robust RCB followed by the ML method

for improved RFI mitigation. Finally, we combined the merits of all three methods

for TNT detection. The experimental results show that the combined approach out-

performs all the three proposed methods, and its robustness has been demonstrated

as well by using data sets collected at different times and conditions.















CHAPTER 3
SINGLE ANTENNA BASED
SIGNAL AMPLITUDE ESTIMATION AND DETECTION

3.1 Introduction

Three adaptive methods are presented in this chapter to estimate the amplitude

of a signal with an known arbitrary waveform. Like the MAFI method in [21], our new

methods are designed to suppress the strong interference and noise by passing the

observed data samples through an adaptive finite impulse response (FIR) filter. Then

the signal amplitude is estimated from the FIR filter output using a simple LS method.

Three adaptive FIR filters are provided in this chapter based on the generalized Capon

principle [69]. We first extend the generalized Capon (GC) estimator in [69] to the

problem of signal amplitude estimation. Then by allowing an uncertainty set for the

signal covariance matrix, we propose a robust GC (RGC) estimator to mitigate the

small snapshot number problems. To simplify the computational complexity of the

RGC estimator, we also devise an approximate robust GC (ARGC) estimator for

signal amplitude estimation. Numerical examples show that the adaptive methods

outperform the LS method significantly and that the robustified adaptive methods

outperform their non-robustified counterpart.

The remainder of this chapter is organized as follows. In Section 3.2, we for-

mulate the problem of interest and provide some preliminary results. Section 3.3

presents the adaptive approaches. Section 3.4 provides a detection scheme. Section

3.5 summarizes the implementation steps of the proposed methods. Numerical ex-

amples are provided in Section 3.6 to demonstrate the performance and effectiveness

of the signal amplitude estimators. Finally, Section 3.7 contains the summary.









3.2 Problem Formulation and Preliminaries

Consider a data model for a signal corrupted by the interference and noise


x(n) = s(n) + e(n), n = 1, 2, N, (3-1)


where x(n) E C is the nth measured data sample, s(n) E C is the nth sample of

the known signal waveform, 3 is the unknown signal amplitude (to be estimated),

e(n) E C denotes the interference and noise term (which is assumed to be uncorrelated

with the known signal), and N is the total number of data samples. The problem of

interest herein is to estimate the signal amplitude 3 from the observed data sequence

{x(n)}7 in the presence of interference and noise.

To deal with the correlated interference and noise, we adopt the -I lii, tech-

nique used in [20, 21]. By partitioning {x(n)}1, into N overlapping subvectors,

referred to as snapshots, with length L = N N + 1, the data model in (3-1) can be

rewritten as:


x(n) = s(n)+e(n), n=1, N, (3-2)


where

x(n) A [x(n) ... x(n + L 1)]P (3-3)

s(n) A [s(n) ... s(n + L 1)], (3-4)

and

e(n)) [e(n) ... e(n + L- 1)]T, (3-5)

with (.)T denoting the transpose.

We note that when the signal waveform satisfies


s(n p) = cps(n),


(3-6)









with c, being a constant independent of n (for example, (3-6) satisfied by a complex-

valued sinusoid), Equation (3-2) reduces to the standard form in [17], i.e.,

x(n) /3as(n)+e(n), n = 1, ,N, (3-7)

with

a [co cl- .CL-1]T. (3-8)

Then the methods proposed in [17, 21] can be applied directly to estimate 3. In

this chapter, however, we consider the general case where the known signal waveform

is arbitrary, for example, like the one shown in Figure 3-1, which occurs in the

application of using QR technology for explosive detection.

Let


h =[h, h2 ... hL]T (3-9)

denote the coefficient vector of an FIR filter of length L, whose determination will be

addressed in the next section. Passing the signal x(n) through the filter h yields


y,(n) = hx(n) (3-10)

F(n) + hHe(n), n =i ,- (3 11)

where (.)H denotes the conjugate transpose and


SF(n) hHs(n). (3-12)

Applying the LS method to (3-11) gives the following estimate of 3

= 1y (n)s(n) (313)
E 1N IF(n) 12
hHXh
h h (3-14)
hHRh









where
N
x, =- Yx(n)sH(n), (315)
n=l
and

1
R, = Ys(n)sn) (3-16)

is the sample covariance matrix of the signal vector, and (.)* denotes the complex

conjugate. Note from (3-14) that a scaling factor of h does not affect 3.

When 3 is known to be real-valued, the estimate of 3 is given by


R = Re(3), (3-17)

where Re(.) denotes the real part. When 3 is known to be real-valued and non-

negative, the estimate of 3 is given by

J Re(3), if Re() > (318)

S 0, if Re(3) < 0.

The standard LS method can be viewed as a special case of (3-14)-(3-18) corre-

sponding to h being a scalar (i.e., L = 1). For complex-valued 3,

)LS = N=(n)s*(n) (3 19)
En= IS 12

The LS estimates of 3 when 3 is known to be real-valued or real-valued and non-

negative are given, respectively, by


LSR Re(LS), (3-20)

and

LS Re(), if Re(LS) > 0(321)
S 0, if Re(LS) < 0.









3.3 Adaptive FIR Filter Based Estimation Methods

We present next three data-adaptive FIR filters, which are needed in (3-14) for

the estimation of the signal amplitude 3.

3.3.1 Generalized Capon (GC) Filter

From (3-11), the average power of the FIR filter output can be expressed as

SN
P =( yp)y() (3-22)

ShHRh, (3-23)


where
N1
N
is the sample covariance matrix of {x(n)}. From (3-2), we have approximately that


R R, + Q, (3-25)


where ao = |/32, and Q denotes the sample covariance matrix of the interference and

noise term.

The GC filter is obtained by solving the following maximum signal-to-interference-

plus-noise (SINR) problem [19]

hHRh
max. (3-26)
h hHRh

Note that (3-26) is approximately equivalent to

ShHR h + hHQh hHQh
mm in m--
h hHRfh h hHRh
hHRh
max. (3-27)
h hHQh

As is well-known, the solution to the optimization problem above is given by


hGc max(R 1Rs),


(3-28)









where Pmax(-) denotes the principal eigenvector corresponding to the largest eigen-

value of a matrix. We refer to the estimator of 3 (see (3-14)) obtained by using the

filter in (3-28) as the GC estimator.

Using the hGc in (3-28) yields the following estimate of a2:


2 hHRhH --(3-29)
GC GC A.(f- I
Amax(R 1s)

where Amax(') denotes the maximum eigenvalue of a matrix.

3.3.2 Robust Generalized Capon (RGC) Filter

To mitigate the small snapshot number problems, we adopt the technique in [70]

that allows an uncertainty in the signal covariance matrix, and then derives a robust

generalized Capon (RGC) filter.

Let

R, = DoDO, (3 30)

where Do denotes a square root of Rs. We assume that the "true" square root matrix

D belongs to the uncertainty set:


|D Doll < (3-31)


where c denotes the radius of the "uncertainty sphere" and I I IF denotes the Frobenius

norm of a matrix.

Similar to the robust Capon beamformer (RCB) in [70], we adopt the covariance

fitting framework and formulate the RGC optimization problem as:


max a2 subject to R c2DDH > 0
2,D
I|D- Dol|| < (3-32)


To exclude the trivial solution D = 0, the parameter c must satisfy the following

inequality


|IDo1 1 > .


(3-33)









For any given D, the solution oa to (3-32) is readily obtained by noting following

equivalences:

R DDH > 0 I aR-DDHR- > 0 (3-34)

S1 omax(Rf- DDHR- ) > 0
2 1
Amax(DHR-1D)

Hence the maximizing estimate of a2 is given by


S(335)
S- Amx(DHR-1D) 35)

which is the same as the one in (3-29).

By using (3-35), the optimization problem in (3-32) can be simplified as:

min max(DHR-1D) subject to |D Do||0 < e. (3-36)
D

Via relatively simple algebraic manipulations, we can reformulate (3-36) as a Semi-

Definite Programming (SDP) problem [71]:


mina subject to a > Amax(DHR-1D)

e> I|D-Dol 2 (3-37)

which is equivalent to


mina subject to al DHR-D > 0

e> |ID- Do | (338)









and hence equivalent to

al DH
min i subject to > 0
D R

Se vecH(D Do) (339)
> 0, (3-39)
vec(D Do) I

where vec(.) denotes the vectorization operator (stacking the columns of a matrix on

top of each other). However, the so-obtained SDP problem has large dimensions and

therefore its computational complexity is somewhat high [71]. Using the D obtained

by solving (3-39) in (3-28), we obtain the robust generalized Capon (RGC) filter

hRGc -Pmax(R-1DDH). (3 40)

The corresponding estimator of f is referred to as the RGC estimator.

3.3.3 Approximate Robust Generalized Capon (ARGC) Filter

For simplicity, we replace Amax(DHR-1D) in (3-36) with its upper bound

tr(DHR-1D), where tr(-) denotes the trace of a matrix:

min tr(DHR-D) subject to |D Do||l < e. (3-41)
D

It is easy to check that the solution to (3-41) occurs on the boundary of the constraint

set [70]. Hence the problem in (3-41) can be simplified as follows:

mintr(DHR-1D) subject to I D Do|0 e. (3-42)
D

Using the Lagrangian multiplier methodology, we construct a function 0 as


0 = tr(DH 1D) + p(|D Do|| e),


(3-43)









where p > 0 is the Lagrange multiplier. Minimizing 0 respect to D yields

D + I Do

Do- (I + pR) -Do, (3-44)

where the matrix inversion lemma [25] has been used to obtain the second equality
in (3-44). The Lagrange multiplier p in (3-44) can be obtained as the solution of the
following constraint equation:

(p) ^ I(I +pR )- D0Do e. (3-45)

Let
R UFUH, (3 46)

where the columns of U contain the eigenvectors of R, and F is a diagonal matrix
with its diagonal elements being the corresponding eigenvalues 71 > 72 > > 7L.
Let
Z = UHDo, (3-47)

and let z4 denote the lth row of Z, then we have


o(P) = ( I+ pUFUH)-1Dol I

IU(I + pI) l-UHDo

= (1 Zp112 (3-48)
S=1 + 7)2

Hence, the constraint equation (3-45) can be written as:


II)2 = (3-49)
( 1 (t + p7l) 2

Since the first-order derivative of w(p) with respect to p is less than zero,
for any p > 0 the function w(p) is strictly monotonically decreasing function for
p > 0. Furthermore, =(0) E= 1 I zll 12 > 0, and we note also that for p / 0,









limpo w(p) = 0 < c. Hence, there is a unique solution p > 0 to (3-49). A lower
bound and an upper bound on p can be obtained as follows. Replacing 71 in (3-49)

by 71 and by 7L, respectively, yields

|F < < ZF (350)
(1 + p7)2 (1 + L)2

From (3-50), we obtain the following lower and upper bounds on p:

I< Z I< < (3-51)
71C 7LCV

From (3-49), we can also obtain another upper bound on p by (dropping the "1" in

the denominator of (3-49))


< L I 1 1/2 (3-52)

Therefore

F min 11112 F (3-53)
71 CI A C 32 7L

Equation (3-49) can be solved efficiently by using the Newton method initialized

with a value of p in the interval given by (3-53). Then the estimated D is obtained

by inserting the so-obtained p into (3-44). Using this D in (3-28), we obtain an

approximate robust GC (ARGC) filter as

hARGC Pmax(R -1D H), (354)

and the associated estimator of f is referred to as the ARGC estimator.

3.4 Detection

Using the estimate of the signal amplitude given in (3-14) directly for signal

detection does not yield a constant false alarm rate (CFAR) detector [18]. Instead








we might think of using the following detection variable (see Section 4.4 for details):

a Re(/)
Zd Re (3-55)
var[Re (s3)]

where var[Re(/)] is an approximate variance of Re(/).
Inserting (3-2) into (3-17) yields
i = hH i e(n)s(n)(
= ( + F (3-56)
Zln= 1F(n)12
Then we can calculate the variance of 3, which is given by

var(/) = E[If -01|2
Vy h ,E;i e(n)) s* (n) y:N SF
h Z 1 e( n )s() SF(nl)eH(nl)h (
= E 21 (3-57)
(zl1 IF(fl) 2) ]

Assuming h is independent of e(n) and hHe() is a white sequence, (3-57) can be
approximated as

ShH H 1 ISF(2) 12e(n)e'(n)h
var (0) E i2
(E,,n 1 IFII (M)|2)2
hHQh
h h (3 58)
n-l ISF() 12
where
Q =E[e(n)eH(n)]. (3 59)

Using the statistical property of circularly symmetric complex Gaussian noise, we
have

var[Re(/)] =-var(3)
2
1 hHQh
S, iF(3-60)
Cn-1 ISF(n)








where Q is an estimate of Q obtained by using 3 in (3-18) to replace 3 in (3-2):


N l
which is guaranteed to be non-negative definite.
Inserting (3-17) and (3-60) into (3-55) yields

v'2(Re(Efg I yp(n)s*(n)))
Zd = (3-62)
/(hH Qh) | 1s(n) 12

Substituting (3-14) into (3-62) gives

2 (Re (hH X(n) )))

C/(hHQh) |s 1,(n)12
2[Re(hHXh)] (
(3-63)
/(hHQh) (hH th)

Under the null hypothesis = 0 (i.e., no signal of interest is present), it can be
easily shown that the distribution of Zd is approximately A'(0, 1). This leads directly
to a detection rule that has a CFAR property since the statistical properties of Zd are
independent of the interference and noise scenario.
3.5 Summary of Implementation Steps
The main steps of the new approaches derived to detect the signal of interest in
this chapter are as follows:

Step 1: Use the acquired data sequence {x(n)}N to form the -, .i-li:,, snap-
shot sequence {x(n)} 1, according to (3-3) and calculate its sample covariance
matrix R using (3-24). Similarly, form {s(n)}}l, according to (3-4) and calcu-
late Rf using (3-16); then calculate X, using (3-15);

* Step 2: Estimate the FIR filter h by using one of the proposed approaches (GC
(3-28), RGC (3-40), and ARGC (3-54)) in Section 3.3;

* Step 3: Obtain the estimate 3 of the signal amplitude according to (3-17) and
(3-18);









* Step 4: Estimate the covariance matrix Q of the interference and noise using
(3-61);

* Step 5: Calculate the detection statistic Zd according to (3-63).

3.6 Numerical Examples

In this section, we present numerical examples to demonstrate the performance

of the adaptive methods desired herein. We assume that the noise term e(n) in (3-1)

contains strong narrowband interference and noise, i.e.,


e(n) io(n)+ ,,(n), n = 2 ,N, (3-64)


where vo(n) denotes the noise, and the interference term io(n) is a sum of complex

sinusoids:
No
io(n) bnoej'-- -7+ o0 (3-65)
no=1
with bno, fTo, and being the amplitude, frequency, and phase of the noth in-

terference, respectively, and No being the total number of interfering signals. The

interference-to-signal ratio (ISR) of the noth interference is defined as


ISRo 10 gloglo p no 1,... ,No, (3-66)


where P, is the average signal power defined as

Ps 1 =()12 (3-67)
n=l

3.6.1 First Example

In the first example, we consider a known signal waveform as shown in Figure

3-1, which is a typical signal waveform in the QR based TNT detection application

[18]. We assume that the signal amplitude f is known to be real-valued and non-

negative. We set the true value of the signal amplitude to be3 1, the snapshot

number to be N = 12, the filter order to be L = 4, and the number of interference

























2 4 6 8 10 12
Sample Number


Figure 3-1. An example of signal waveform versus sample number.


to be No = 2; the interference are located at fl = 0.08 Hz and f2 = 0.1 Hz with

ISRi = ISR2 = 20 dB (except when specified otherwise). We choose c = 0.01|Do112

for the uncertainty set of the signal covariance matrix for the robustified estimators

(RGC and ARGC). We use the SeDuMi software [72] to find the solution to the SDP

problem in (3-39) for the RGC estimator.

Totally 500 independent background data sets, obtained by using the real QR

measurements, are used as the colored noise realizations ,,(n) in (3-64), and the

simulated signal and interference are added to the scaled background measurements

to generate the observed data sequence {x(n)}7 in various simulation trials; the

scaling factor of the background data Ko is determined by the input SNR, which is

defined as

SNR 10logl( ), (3-68)
KO P.
where
N
=Q v(n)12 (369)
n=d
denotes the average power of the measured background data.

























0
Frequency


Figure 3-2. An example of the modulus of the received signal spectra.


Figure 3-2 shows the modulus of the simulated signal spectra when SNR = 0 dB.

In Figure 3-2, the solid line denotes the modulus of the spectrum of the simulated

signal x(n), the dots denote the modulus of spectrum of the interference plus noise,

and the dashed line denotes the modulus of the spectrum of the desired signal. From

Figure 3-2, we see that there are strong peaks around the zero frequency, and that

the frequency location of the signal of interest is also around zero.

First, we examine the performance of the LS and the three adaptive methods

(GC, RGC, and ARGC) discussed herein as the SNR varies. Figures 3-3(a) and

3 3(b) show the biases and mean-squared-errors (lS\ Sl'-) of the estimated signal am-

plitudes as functions of the SNR. It is observed from Figure 3-3(a) that the robustified

estimators, RGC and ARGC, have the similar biases that are much lower than those

of the LS and non-robustified GC estimators. From Figure 3-3(b), we note that all

new methods have much lower MSEs than that of the LS method. Although the GC

method gives a similar MSE with those of the RGC and ARGC methods when the

SNR is low (<-2 dB), when the SNR is high (> -2 dB), the RGC and ARGC meth-

ods give much lower MSEs than that of the GC method. The MSE of LS method









is very large probably due to the presence of the strong colored interference. These

results show that, by allowing an uncertainty set for the signal covariance matrix to

mitigate the small snapshot number problems, the robustified methods can be used

to improve the performance of the signal amplitude estimation.

Next, we examine the impact of the interference power on the signal amplitude

estimation performance for these methods. A similar scenario to the example in Fig-

ure 3-3 is considered, except that we increase the power of the first interference to

ISR1 = 40 dB. Figures 3-4(a) and 3-4(b) show the biases and MSEs of the esti-

mated amplitudes as functions of the SNR, respectively. The performance of the new

methods is similar to that in Figure 3-3. This shows that the adaptive methods can

effectively suppress the interference and therefore they are not seriously affected by

the interference powers. However, we note that the performance of the LS method is

severely degraded due to the increase of the interference power.

Then, we turn to evaluating the detection performances of the LS and the pro-

posed methods in terms of receiver operating characteristics (ROC) (probability of

detection (Pd) versus probability of false alarm (Pf)). In this example, we fix the SNR

= 5 dB. An ensemble of data consisting of 500 separate background measurements

is used in this example. To simulate the data samples in the presence of the target,

we add the QR signal to the first 250 background measurements. The remainder 250

measurements are used as the data samples without the target. Then we apply the

LS method and the three adaptive methods to all the 500 sets to estimate the signal

amplitude and calculate the corresponding Pd and Pf. The so-obtained ROC curves

are plotted in Figure 3-5. From Figure 3-5, we can clearly see that the three adaptive

methods outperform the LS method significantly, and that the robustified methods,

RGC and ARGC, have the similar detection performance but they outperform the

GC method, especially for Pf < 0.2.















































-2 0 2 4 6 8 10 12 14 16
SNR (dB)


10
-2 0 2 4 6 8 10 12 14 16
SNR (dB)

(b)


Figure 3-3. Biases and MSEs of the estimated amplitudes versus the SNR when N

12, ISR1 = ISR2 = 20 dB, and L 4. (a) Biases, and (b) MSEs.


- -I I I I I -













.-




-- LS
GC
+ ARGC
RGC
I I I I I I I


I


. -2


W
M
mU
U)


10-1


















































102




101


LU
U)
2 100




10-1


I I I I I I I


I I


-2 0 2 4 6 8 10 12 14 16
SNR (dB)

(a)


-2 0 2 4 6 8 10 12 14 16
SNR (dB)

(b)


Figure 3-4. Biases and MSEs of the estimated amplitudes versus the SNR when

N=12, ISR, = 40 dB, ISR2 = 20 dB, and L 4. (a) Biases, and (b)
MSEs.


- LS
GC
ARGC
RGC







:4 I + ( :* I


I I I I I I I I I
















4
-- LS
- GC
+ ARGC
RGC
,I l l l l l I


I


10~2L



























Figure 3-5. Detection performance (ROC) comparison of LS, GC, ARGC, and RGC
when N=12, ISR1 = 40 dB, ISR2 = 20 dB, SNR = 5 dB, and L 4.


Finally, we compare the computational complexity of the robustified methods. A

computational comparison between RGC and ARGC shows that the latter is compu-

tationally much more efficient than the former; in one of the trials, for example, and

without optimizing our MATLAB codes, we noticed that ARGC needs only about

0.05 seconds while RGC runs over 8.3 seconds of the CPU time of a typical SunBlade

100 workstation.

3.6.2 Second Example

In the second example, we consider a known signal waveform as shown in Fig-

ure 3-6, which is a typical binary signal waveform widely used in the code-division

multiple access (CDMA) system. The same scenario is used as in the first example

except for a different signal waveform.

Now, we examine the performance of the LS (non-adaptive) and the three adap-

tive methods (GC, RGC, and ARGC) discussed in this chapter as the SNR varies.

Figures 3-7(a) and 3-7(b) show the biases and MSEs of the estimated signal ampli-

tudes as functions of the SNR. From Figure 3-7(a), we note that all the proposed














0.
0.
0.
0.

E
-0.
-0.
-0.
-0.


2 4 6 8 10 12
Sample Number


Figure 3-6. The signal waveform versus sample number (second example).



methods significantly outperform the LS method. It is also observed from Figure

3-7(a) that the adaptive methods have similar biases when the SNR is less than -10

dB. However, when the SNR is greater than -10 dB, the biases of RGC and ARGC

methods are smaller than that of GC method while RGC and ARGC have similar

biases. From Figure 3-7(a) we note that the robustified methods ARGC and RGC

give much smaller bias than that of the non-robustified method GC.

From Figure 3-7(b), we note that the new methods give much lower MSEs than

that of the LS method. We also note that the proposed methods have similar MSEs

when the SNR is less than -10 dB. For SNR > -10 dB, the robustified methods

(RGC and ARGC) work similarly well and they both significantly outperform the

non-robustified GC method. This confirms again that by taking into account the

uncertainty of the signal covariance matrix, the robustified methods can significantly

mitigate the negative effect due to the small snapshot numbers.

3.7 Summary

In this chapter, three adaptive estimators have been presented for estimating the

amplitude of a signal with an arbitrary known waveform in the presence of strong


8-
6-
4-
2-
0
0 -- -- -- -- -- -- -- ---- -- --
2-
4-
6-
8-
1 11


)























0.7 I

0.6

0.5- --

0.4

0.3 LS
GC
0.2 ARGC
RGC
0.1 -

0

-0.1

-n 9


0 -15 -10 -5


-15 -10 -5


0
SNR (dB)


0
SNR (dB)


5 10 15


5 10 15 20


Figure 3-7. Biases and MSEs of the estimated amplitudes versus the SNR (second

example) when N=12, L = 4, ISR1 = ISR2 = 20 dB. (a) Biases, and (b)

MSEs.


uJ -.
U010
a


-- LS
-GC
ARGC
RGC






*+*+ + :


10-3
-20









interference and noise. These estimators, including the generalized Capon (GC),

the robust GC (RGC), and the approximate RGC (ARGC) estimators, are based on

the principle of generalized Capon beamforming. The robustified adaptive estima-

tors, including RGC and ARGC, can be used to mitigate the small snapshot number

problems by allowing an uncertainty set for the signal covariance matrix. Our simu-

lation results have shown that the proposed methods can effectively suppress strong

interference and achieve much better performances than the data-independent LS

method. It has also been demonstrated that the robustified methods can provide

better performance than their non-robustified counterpart. As for the two robustified

methods, RGC and ARGC, they have been shown to perform similarly but the latter

has much less computational complexity than the former.















CHAPTER 4
ANTENNA ARRAY BASED SIGNAL ESTIMATION AND DETECTION

4.1 Introduction

Quadrupole resonance (QR) is an emerging technology for landmine detection,

drug traffic control, airport and border security check, etc. For landmine detection,

for example, the QR technology can be used to probe the unique frequency signature

of explosives (e.g., TNT) contained in landmines [1, 14]. The QR frequency of TNT,

however, is located within the AM radio frequency band [1, 17, 18, 29]. Consequently

the AM radio signals appear as strong RFIs that can seriously degrade the QR signal

detection performance. An antenna array can be used to mitigate the strong RFIs

[1, 17], [27]-[29]. RFIs can be reduced significantly by taking advantage of the spatial

correlations of RFIs. However, the interference and noise are usually both spatially

and temporally colored [31, 32]. Although several approaches have been proposed to

reduce the negative effect of RFIs on landmine detection [1, 17, 18, 29, 33], exploiting

both the spatial and temporal correlations of the interference has not been fully

investigated. In this chapter, we exploit both the spatial and temporal correlations

of RFIs to improve the explosive detection performance.

The QR problem of estimating the complex amplitude of a signal with known

waveform and known steering vector was considered in [17]. Specifically, signal ampli-

tude estimation in the presence of spatially colored but temporally white interference

and noise, as well as parameter estimation in the case of both spatially and temporally

correlated interference and noise were considered. In the latter case, by modelling

the interference and noise vector as a multichannel autoregressive random process, an

alternating least squares (ALS) method was proposed in [17]. It has been shown via

simulations that in most cases, the ALS method is superior to the model-mismatched









maximum likelihood ( I3L) method, which ignores the temporal correlation of the in-

terference and noise. However, ALS is slightly worse than M3L in challenging cases,

for instance when the desired signal and the interference are closely spaced in the

temporal frequency domain.

In this chapter, we will work in the framework of signal amplitude estimation

with known signal waveform and make use of three adaptive beamforming approaches,

viz., the standard Capon beamformer (SCB) [23, 73], the robust Capon beamformer

(RCB) [70, 74], and the amplitude and phase estimation (APES) method [20, 75], to

develop several new approaches for mitigating the spatially and temporally correlated

RFIs.

SCB is a data-adaptive beamformer that has a better resolution and much better

interference rejection capability than the data independent methods, such as the

d,1 li-- ,ild-sum method, provided that the array steering vector is accurately known

[70]. However the performance of SCB degrades drastically whenever the knowledge

of the steering vector is imprecise, the snapshot number is small, or non-stationary

interference and noise exist [70].

Several methods have been proposed to improve the robustness of SCB ([24, 70,

74], [76]- [79] and the references therein). RCB is a natural extension of SCB to the
case of uncertain steering vectors, that is robust against steering vector errors and

yet it has high resolution and strong interference rejection capability [70].

APES is an effective non-parametric spectral analysis approach ( [20, 25, 75, 80]

and the references therein). Extensive empirical and analytical studies of SCB and

APES have shown that although APES yields somewhat wider spectral peaks than

SCB, its amplitude estimate is much more accurate than the SCB estimate [20, 81]:

in particular, the latter is biased downwards while the former is unbiased [82].

Straightforward extensions of SCB and APES to our problem of signal amplitude

estimation with known signal waveform, in the presence of both temporally and









spatially correlated RFIs, lead to two SCB-based approaches, referred to as SCB1

and SCB2, and one APES-based approach, referred to as APES1. Similar to SCB

and APES, all these three new approaches assume precise knowledge of the array

steering vector. SCB1 maximizes the signal-to-interference-plus-noise ratio (SINR)

and gives high resolution, but it is sensitive to the modelling errors like SCB. SCB2 is

a modified version of SCB1 obtained by means of a sub-optimal design. SCB2 gives

lower resolution than SCB1 but is more robust. APES1 is derived using the APES

principle [75], and is more robust than both SCB1 and SCB2.

Next, considering the presence of the steering vector uncertainty, we develop

two robust approaches based on the RCB principle, which we refer to as RCB1 and

RCB2. RCB1 and RCB2 are obtained by rob, -I ili.i-; SCB1 and SCB2, respectively.

They are more robust to steering vector errors than their SCB counterparts. We also

devise a generalized robust APES beamforming (GRAPES) method using the APES

principle but taking into account the steering vector uncertainty in much the same

fashion as in the derivation of RCB. The robustness of GRAPES is better than that

of APES1 at the cost of some resolution loss. The trade-off between resolution and

robustness for various methods is also discussed in this chapter.

The remainder of this chapter is organized as follows. In Section 4.2, we introduce

the data model and formulate the problem of interest. Section 4.3 presents the

new adaptive beamforming approaches. Section 4.4 provides a detection scheme.

Section 4.5 gives a summary of the implementation steps. Simulated and experimental

results are provided in Section 4.6 to demonstrate the effectiveness of the proposed

approaches. Finally, Section 4.7 contains our summary.

4.2 Data Model and Problem Formulation

Consider a QR system consisting of a main antenna and N, reference antennas.

Each of these antennas provides a spatial data acquisition channel. The main antenna

receives both RFIs and the QR signal while the reference antennas receive only the









RFIs. The QR measurements can be characterized by the following data model

[17, 18]

x(n) = pas(n) +e(n), n =1,- ,N, (4-1)

where x(n) E CN xl (with VN = Nc + 1) is the nth observed data snapshot; 3 > 0

is the unknown signal amplitude; a E CN cx is the steering vector with the first

element equal to one and the others equal to zeros (due to the fact that the main

antenna receives both the QR signal and RFIs while the reference antennas receive

only RFIs); s(n) E C is the known signal waveform; N is the number of snapshots; and

e(n) e CNcxl denotes the interference and noise. The problem of interest herein is to

estimate 3 from the observed data sequence {x(n)}1 in the presence of temporally

and spatially correlated interference and noise {e(n)}N. i

The maximum likelihood method of [17], derived under the assumption that e(n)

is temporally white, performs well when e(n) satisfies the assumption. However, it

cannot be expected to perform satisfactorily when it is applied directly to (4-1) by

ignoring the possible temporal correlation of the interference and noise. To deal with

the temporal correlation of e(n), we adopt the -i 111:, technique of [20] that is

based on the following spatial-temporal data model,


x(n) 3as(n) +v(n), n = 1, -- ,N, (4-2)

where

x(n) [xT(n) ... xT(n + L- 1)]T, (4-3)

as(n) = [aTs(n) ... aTs(n + L 1)]T, (4-4)

v(n) [eT(n) ... eT(n + L 1)T, (4-5)

N = N L + 1, (.)T denotes the transpose, and L is the so-called temporal filter

order.









We note that for some special waveforms (for example, a complex sinusoid)

satisfying the equation

s(n- p) = s(n), (4-6)

with c, being a constant that does not depend on n, (4-2) reduces to the standard

form in [17],

R(n) = 3acs(n) + v(n), n = 1, V, (4-7)

where ac = [aTco ... aTCL_ ]T. Then SCB, RCB, and APES in [17, 70, 75]

can be applied directly. However, in this chapter, we consider the general case of

an arbitrary signal waveform, which occurs in many applications including the QR

application considered herein.

Let

h [hT h T ... h ]T (4-8)

denote a finite impulse response (FIR) filter coefficient vector of dimension LNc x 1,

where hi, I 1, L, is an N x 1 vector. The determination of h will be discussed

in the next section. Here we discuss briefly how we will use h for estimating the

amplitude 3. Passing the signal x(n) through the filter h yields,


y,(n) = hH(n) (49)

S s,(n) + hHv(n), n =1,- ,N, (4-10)

where (.)H denotes the conjugate transpose,


SF(n) hHas(n)
L
S as(n + l- 1), n = 1, ,N, (4-11)
a 1
and


a hHa, 1, ... ,L.


(4-12)









From (4-10), by using the least squares (LS) method and the fact that 3 > 0, an

estimate of 3 can be obtained as

Re(t), if Re(3) > 0,
(4-13)
0, if Re) < 0,

where

Sy =p(n) S (4-14)
N1 ISF(n)'2
Here Re(-) denotes the real part of a complex scalar, and (.)* denotes the complex

conjugate.

4.3 Adaptive Beamforming Methods

We present several new approaches to design the FIR filter based on the princi-

ples of SCB, APES, and RCB. In the case that the array steering vector a is known

precisely, we devise two SCB-based approaches, referred to as SCB1 and SCB2, and

one APES-based approach, referred to as APES1. Taking into account the uncer-

tainty of the steering vector, we propose two new RCB methods, referred to as RCB1

and RCB2, and one generalized robust APES method, referred to as GRAPES.

4.3.1 Known Array Steering Vector

Given the array steering vector a and the signal waveform sequence {s(n)} ,

we define
a 0 ..* 0

0 a ... 0
AA e CNCLXL, (4-15)


0 0 .** a

and
1N
r- s()SH e CLxL, (416)
N (









with s(n) = [s(n) ... s(n + L 1)]T. We also let

1 N
RsA -2 as (n )a
n=l
= 2AFAH. (4 17)

4.3.1.1 SCB Based Approach: SCB1

By following the principle of Capon method [23], which aims at maximizing the

output SINR, the SCB1 method obtains the FIR filter by maximizing an estimated

output SINR (or just call it SINR in short) as follows:

hHRsh
max (4 18)
h hHQh

where Q is an estimate of Q, which is the covariance matrix of the interference and

noise vector v(n). From (4-2), Q can be estimated as:


Q = R Rs, (4-19)

where
1N
R= ~ (n)xH(n). (4-20)
nl
By using (4-17) and (4-19), the optimization problem in (4-18) can be rewritten as

hH (AFAH) h
max (4 21)
h hHRh

Solving the optimization problem in (4-21) yields [22],


hSCB1 max (R-1AFAH) (4 22)

where Pmax(-) is the eigenvector corresponding to the largest eigenvalue of a matrix.

The maximum value of (4-21) corresponding to (4-22) is

A1 Amax(R- AFA)

SAmax(FAHR-1A), (4-23)









where Amax(-) denotes the largest eigenvalue of a matrix.

Note that in the case of L = 1, we have A = a, and (4-22) reduces to


h = cR-a, (4-24)


with c being a constant. When h is scaled to satisfy hHa = 1, we get the SCB [17].

Note also that h can be arbitrarily scaled because a scaling of h leaves 3 in (4-14)

unchanged. Similar to SCB, SCB1 may be sensitive to modeling errors, so we may

want to relax the optimization problem in (4-21) to seek a more robust solution, as

explained in the following.

4.3.1.2 SCB Based Approach: SCB2

In this subsection, we consider a method, referred to as SCB2, which is subopti-

mal from an SINR point of view, but which turns out to be more robust than SCB1.

We replace the optimization problem in (4-21) by the following two steps:

* maximize the signal power of the filter output (the numerator of (4-21));

* use the remaining degrees of freedom in h to minimize the total power of the
filter output (the denominator of (4-21)).

Let

a= [a1 .. aOL]T, (4-25)

where ca has been defined in (4-12). Then the signal power of the filter output is

proportional to

hHArAHh aHra. (4-26)

Under the constraint that I||112 = 1, (4-26) achieves its maximum value at


a = Pmax(). (4-27)


Now the remaining problem is to solve


min hHRh subject to AHh a.
h


(4-28)









By solving the optimization problem in (4-28), the SCB2 beamformer is readily

obtained as [25]

hSB2 R-1A(AHR-1A)-la. (4-29)

The value of (4-21) achieved by hscB2 in (4-29) is

A2& Amax(4(30))
aH(AHR-1A)-la (4 30)

We note that from a maximum SINR viewpoint, hscB1 is an optimal solution

while hSCB2 is only a suboptimal one (in the sense that A2 < A1, see Appendix A for

the proof). However, SCB2 may be more robust to modeling errors than SCB1 since

the signal output power is maximized first in SCB2, which offers some protection

against the nulling of the desired signal suffered by SCB1, as we will also show via

numerical examples in Section 6.

4.3.1.3 APES Based Approach: APES1

Somewhat similar to the formulation of APES in [75], the APES1 method is

formulated as follows,

N L 2
min hH(n) -3 as(n +l 1) subject to AHh a, (4-31)
h,/3
n= 1 l 1

where a is given by (4-27). Minimizing the cost function in (4-31) with respect to

3 (assumed complex-valued for the filter design purpose) yields

hH Y 1
hZ Rx(n s(n)( (4 32)

n-MISF(n)12

and therefore the optimization problem in (4-31) reduces to


minhHQh subject to AHh a, (4-33)
h

where


c R ggH


(4-34)









and
g x(n) (4-35)
0i ~N 1/2"
Ss,(n) 2] 2
The solution to the problem in (4-33) is [25]


hAPES Q-1A(AHQ-1A)-1a (4-36)

which is similar to hscB2 in (4-29), but with R replaced by Q.

4.3.2 Uncertain Array Steering Vector

We now turn to the design of the FIR filter in the presence of inaccurate array

steering vectors. Specifically we assume that a belongs to an uncertainty sphere [70]


aI a- 11 (4 37)

where a and c are given (c is a user parameter which is used to describe the size of the

steering vector uncertainty). Although in some applications we may know a exactly,

such as a = a = [1 0 ... O]T in the QR application [1], we can still consider a

as being an uncertain vector due to the sampling errors in R [24, 25].

4.3.2.1 RCB Based Approaches: RCB1 and RCB2

We can obtain RCB based designs by using the covariance fitting approach (e.g.,

[74, 25]). To do so, observe from (4-2) that

R = 2AFAH + Q, (4 38)

where a2 32. Hence the covariance fitting problem becomes

max c2 subject to R 2AFAH > 0
a,a2
II a- a 112< (439)

We note that the first inequality in (4-39) is equivalent to


I 2R- 1/2AFAH R-1/2 > 0,


(4-40)









which yields

1 > a2 mx(R-1/2AFAH -1/2)

a22mx(AHR-1A). (4-41)

Therefore, for any fixed a, the solution a2 to (4-39) is given by:

2 = (4-42)
Amax(FAHR-1A)

Note from (4-23) that a2 = /A1. Using (4-42), the optimization problem (4-39)

reduces to

minAmax(FAHR-1A) subject to | a a 112< C. (443)
a
Via relatively simple algebraic manipulations, we can reformulate (4-43) as a Semi-

Definite Programming (SDP) problem [71]:

mina subject to a > Amax(FAH -1A)

S> Ila-a a2, (444)

which is equivalent to

mina subject to al (Ar1/2)HR-1(Ar1/2) > 0

S> Ila- a 2, (4-45)

and hence equivalent to

(A I (Ar1/2)H
minac subject to (A1H > 0
(AT1/2)

(a a)H
(a a > 0. (4-46)
(a-a) I

However, the so-obtained SDP problem has large dimensions, and therefore its com-

putational complexity is very high [71].









In order to use the computationally convenient Lagrangian solver in [74, 70] to

obtain a, we modify (4-43) as follows. First, note that


Amax(FAHfR-A) < AXmx(F)Amax(AHR-'A)

< Ax(F) tr(AHR-1A) A3, (4 47)


where tr(.) denotes the trace of a matrix, and we have used the fact that Amax(AB) <

Amax(A)Amax(B) for any positive semi-definite matrices A and B (e.g., Lemma A.6.20

in [83]). For simplicity, we consider minimizing the upper bound in (4-47) in lieu of

(4-43), that is,


mintr(AHfR-A) subject to || a aa 12< C. (448)
a

Let RI denote the lth block matrix of size M x M on the block diagonal of R-1.

Then (4-48) can be rewritten as


min a H 1 a subject to || a (4-49)
a

which has precisely the form of the RCB problem solved in [70]; therefore the La-

grangian solver introduced in [70] can be directly used to obtain the solution of (4-49).

Next, we consider rob- ifi i-; h sci in (4-22), that maximizes the SINR. When

a is uncertain, in the sense that we only know I| a a 112< c, with what value of a

should we use hscBl? We may think of using a max max approach:


max max SINR, (4-50)
aEC h

where C = {al I a- a 112< e}. Let a denote the solution to (4-50); then h(a)

obtained from (4-50) will have a small gain at any a / a, owing to its maxmax

SINR derivation. Hence, in the likely event that atrue / a, the solution of (4-50)

will have poor robustness. With the above fact in mind, a minmax SINR approach









is more sound:

min max SINR. (4-51)
aEC h

From (4-23), we can see that (4-51) is equivalent to (4-43), which is the design

criterion based on the covariance fitting approach. Let a be the solution to (4-51);

then h(a) may have a reasonable gain for a in the vicinity of a, so it will be robust.

Of course, the robust solution base on (4-51) will have poorer resolution than (4-50).

Evidently, one cannot achieve robustness and high resolution simultaneously; one can

only compromise between them. In particular, note that minimizing an upper bound

on the SINR, in lieu of the SINR itself, like in (4-49), will give a solution that is less

robust than (4-51) but has a higher resolution. Note that by decreasing c in RCB we

also increase the resolution at the expense of robustness. However, there appears to

be a difference between compromising resolution versus robustness by minimizing an

upper SINR bound and by decreasing c. When we decrease c, RCB will be focusing

on a = a more and more, whereas when we minimize an upper bound the RCB based

method will be focusing on the a that minimizes the upper bound. The latter may be

better than the former whenever a is really uncertain and hence we cannot decrease

e in a justified manner.

Regarding the robustification of hscB2, we use the fact that (see (A-3) and (4

47))

/2 < 1 A < A3, (4-52)

and hence obtain an estimate of a for hSCB2 also by minimizing the upper bound

in (4-48). Estimates of the filters hRCB1 and hRcB2 of the RCB based methods are

obtained by inserting the estimated a into (4-22) and (4-29), respectively, and the

corresponding approaches are referred to as RCB1 and RCB2.









4.3.2.2 Generalized Robust APES Beamforming Approach: GRAPES

Using the previous idea (see (4-51)), we now derive a generalized robust APES

beamforming approach, referred to as GRAPES. Note that the output SINR corre-

sponding to hAPES1 is proportional to:

SINRAPES1 m = (4-53)
hAPESIRhAPESI -max,
Based on (4-51), the optimization problem of the GRAPES method is therefore as

follows

min Amax(F) subject to I| a- a ||2< C, (4-54)
a hPESRhAPES -max()
or, equivalently,

max hAHPESiRhAPES1 subject to | a -a 112< e. (4-55)
a

Inserting hAPES1 of (4-36) into (4-55) we obtain:


A4 = hHpESI RhAPESI

SaH(AHQ-1A)- AHQ-1Q + ggH)Q-1A(AHQ -A)-l

a H(AH -lA)-a + aH(AHQ 'A)- AHQ-g 2 (4 56)

Note that [83]


A4 > aH(AHQ-1A)- c

> Amin[(AHQ-lA)-1]
1
Amax(AHQ-lA)
1
A> trA). (4-57)
tr(AHQ-'A)









Replacing A4 by its lower bound in (4-57), we can obtain an estimate of a by solving
the following optimization problem

mintr (AH 1A) subject to a aa 12< e. (4 58)
a

This is the same problem as for the RCB based methods, but with Q replaced by R

(see (4-48)). The estimate of the filter hRGAPES is obtained by inserting the estimated
a obtained from (4-58) into (4-36).
4.4 Detection

Using the estimate of the signal amplitude given in (4-13) directly for explosive

detection does not yield a constant false alarm rate (CFAR) detector [18]. Instead
we might think of using the following detection variable:

Zd (4 59)
var(s)

where var(/) is an approximate variance of 3. In practical applications, to obtain
a low false alarm rate, the detection threshold should be strictly greater than zero.
Hence, we can use the following equivalent detection variable in lieu of (4-59):

da Re (0) (460)
S. (4-60)
var[Re ( )]

The var[Re ())] above is obtained as (see Appendix B for details)

1 hHQh (461)
var [Re (0)]= (4-61)
n-1 SF(n)2

where Q is an estimate of Q obtained by using the ) in (413) to replace the 3 in

(4-2):

Q [i(n) -sas()] [xi() /as(n)] (462)
which is guaranteed to be non-negative definite.
which is guaranteed to be non-negative definite.








Inserting (4-14) and (4-61) in (4-60) yields

v2 ( ze s(E f (n))
Zd = (463)
/(hHQh) 1 s(n)12

Substituting (9) into (4-63) gives

'- (Re (hH x(n)(n)))
zd = (4-64)
/(hH h) Y 1 sp(n) 12

Under the null hypothesis f = 0 (i.e., no explosive is present), we can approx-
imate the distribution of Zd as AI(0, 1) (see Appendix C). This leads directly to a
detection rule that has a CFAR property since the statistical properties of Zd are
independent of the interference and noise scenario.
4.5 Summary of Implementation Steps
The main steps of the new approaches derived to QR signal detection in Sections
4.3 and 4.4 are as follows:

* Step 1: Use the acquired data sequence {x(n)} 1, to form the spatial-temporal
snapshot sequence {x(n)}L according to (4-2);

* Step 2: Estimate the FIR filter coefficient vector h by using one of the proposed
approaches (SCB1, SCB2 and APES1 in Subsections 4.3.1.1, 4.3.1.2, 4.3.1.3,
RCB1 and RCB2 in Subsection 4.3.2.1, and GRAPES in Subsection 4.3.2.2);

* Step 3: Pass the sequence {x(n)}j,1 through the FIR filter built in Step 2
according to (9), and calculate the sequence {s,(n)}7L1 using (4-11);

* Step 4: Obtain the estimate f of the signal amplitude as in (4-14);

* Step 5: Estimate the covariance matrix Q of the interference and noise using
(4-62);

* Step 6: Calculate the detection statistic zd according to (4-60).














0.8 -


W 0.6 -


0.4 -










low noise and RFI-free experiment).


4.6 Numerical Examples

In this section, we present several numerical examples to illustrate the perfor-

mance of the proposed methods. We consider a QR system consisting of N, = 4

antennas (one main and three reference antennas). Accordingly, the steering vector

is given by a = [1 0 0 O]T. We set the true value of the signal amplitude to be / = 1.

The signal waveform is shown in Figure 4-1, which is obtained from an experimental

measurement free of RFI and at a very high SINR [18]. We assume that the interfer-

ence plus noise term e(n) in (4-1) is both spatially and temporally colored. In our

Monte-Carlo simulations, many sets of independent real-world measured background

data are scaled and then used to simulate the interference plus noise realizations. The

QR signal is added to the scaled background data set to get the QR measurements

in various Monte-Carlo trials, with the scaling factor determined by the input SINR.

We choose the snapshot number to be N = 50, the temporal filter order to be L = 3.









The input SINR is defined as


SINR 10 llogio (4-65)


where
| N|2
P, y (l)2 (466)
n=l
denotes the average QR signal power, and


P= tr (1 ten)eHn)) (4-67)

denotes the interference plus noise power. To simulate steering vector errors, each

element of the steering vector a is perturbed with a random noise, and then scaled,

so that l|a -a|l2 m 0.1.

Figure 4-2 shows an example of the main antenna output with an input of SINR

equal to -10 dB; specifically Figures 4-2(a) and 4-2(b) show the real-part of the main

channel output in the time domain and the modulus of the output spectrum. Two

strong interference peaks are observed in Figure 4-2(b) and one of them is around the

zero-frequency, which is the spectrum location of the desired QR signal. This figure

shows the challenge of the QR signal detection in the presence of strong RFIs. It also

motivates the exploitation of the temporal correlation of the RFIs for improved QR

signal detection.

Now we turn to evaluating the detection performances of our approaches in

terms of receiver operating characteristics (ROC) (probability of detection (Pd) versus

probability of false alarm (Pf)). An ensemble of data consisting of 270 separate

background measurement sets is used in this example. To simulate the data samples

in the presence of the explosive, we add the QR signal to the first 135 background

measurement sets. The remainder 135 measurement sets are used as the data samples

without the explosive. Then we apply our six new approaches to all the 270 sets to

estimate the signal amplitude and calculate the corresponding Pd and Pf. ROC







56






























010 20 30 40 50
5-

4-
















Snapshot Number

(a)
1-

















100
0.



-1







E I III
0 10 20 30 40 50
Snapshot Number














(b)
120


100-


80-


60 6-




20




0
-0.5 0 0.5
Frequency

(b)

Figure 4-2. An example of the main channel output: (a) the real-part of the output
in the time domain, and (b) the modulus of the spectrum of the output.









curves for the cases with and without steering vector errors are plotted in Figure

4-3. ROC curves for SCB1 and RCB1 are shown in Figure 4-3(a). We note from

Figure 4 3(a) that, when steering vector errors exist, the performance of SCB1 is

significantly degraded with respect to the case without steering vector errors; but for

RCB1 the degradation is smaller. Also, RCB1 performs distinctly better than SCB1

in the presence of steering vector errors. These results indicate that RCB1 is more

robust than SCB1. Figure 4-3(b) shows ROC curves for SCB2 and RCB2 in the cases

with and without steering vector errors. It can be observed that SCB2 and RCB2

have similar performances in both cases; at very low Pf range (<0.025), SCB2 shows

a larger difference than RCB2 between the cases with and without the steering vector

errors. Figure 4-3(c) presents ROC curves for APES1 and GRAPES, from which we

observe that both approaches perform quite similarly, which is due to the robustness

of APES based methods.

Figure 4 3(d) presents a comparison between SCB1 and SCB2, using the corre-

sponding ROC curves from Figures 4-3(a) and 4-3(b). These curves show that, when

there is no steering vector error, SCB1 has a better performance than SCB2; however,

in the presence of steering vector errors, the performance of SCB1 is degraded more

than that of SCB2. The robustness of SCB2 with respect to SCB1 is thus verified.

To illustrate how the choice of the user parameter c affects the performances of

the three robust approaches, Figures 4-4(a), 4-4(b), and 4-4(c) show the ROC curves

of RCB1, RCB2, and GRAPES, respectively, for different c values, namely, 0.05, 0.1,

and 0.2. These ROC curves -i-i-, -1 that the three approaches all perform similarly

for various c values and hence they are not sensitive to the value chosen for C .

To illustrate how the temporal filter order affects the detection performance,

Figures 4-5(a) 4-5(f) show the ROC curves of the six new approaches with various

temporal filter order L (namely, L = 1 to 5) in the presence of steering vector errors,

respectively. We note that for all methods, the performance is the poorest when













































0.95

0.9

0.85-

0.8

S0.75-

0.7-

0.65

0. -SCB2 w/o error
-*- RCB2 wlo error
0.55 -e- SCB2 with error
-A- RCB2 with error


0.1 0.15


0.2 0.25


Figure 4-3. Detection performance (ROC) comparisons between the cases with and
without steering vector errors for (a) SCB1 and RCB1, (b) SCB2 and
RCB2, (c) APES1 and GRAPES, and (d) SCB1 and SCB2.

























0.85

0.

- 0.7

0.

0.6


0.95


0.9

0.85

0.8

. 0.75
0.75

0.67

0.65


0 0.05 0.1 0.15 0.2 0.;
Pf

(c)


1l ------------------ B b-- :- f l C -k >= f --- f-


0.1 0.15
Pf

(d)


0.2 0.25


Figure 4-3. Continued.


-1-








-A- APES1 w/o error
GRAPES wlo error
-- APES1 with error
-4- GRAPES with error


r -








SCB1 w/o error
SCB2 w/o error
-6- SCB1 with error
-e- SCB2 with error


I


,1








60






1i --- ^,- I ^- ------

0.95

0.9

0.85 -

0.8

S0.75

0.7

0.65

0.6-
-- = 0.05
0.55 = 0.1
=0.2
0.5
0 0.05 0.1 0.15 0.2 0.25
Pf

(a)


0.95

0.9

0.85

0.8

0.75

0.7-

0.65

0.6
-- 8 = 0.05
0.55 -- =0.1
=0.2
0.5
0 0.05 0.1 0.15 0.2 0.25
Pf

(b)


0.95-

0.9

0.85

0.8

a 0.75

0.7

0.65

0.6
-- 8 = 0.05
0.55 = 0.1
=0.2
0.5 ---,"
0 0.05 0.1 0.15 0.2 0.25
Pf


(c)


Figure 4-4. Detection performance (ROC) with different c values for (a) RCB1, (b)

RCB2, and (c) GRAPES.









L = 1. The effectiveness of taking into account the temporal correlation of RFIs via

the -1 1.11.1: technique is thus verified. From Figures 4-5(a) and 4-5 (b), we note

that for SCB1 and RCB1, when L 2 or L = 3, they yield similar good performances.

However, for the SCB1 method, when Pf > 0.05, L = 3 yields better performance

than that of L = 2; when Pf < 0.05, L = 2 yields better performance than that of

L = 3. But for the RCB1 method, there is only a slightly different between L = 2 and

L = 3. This shows that RCB1 is more robust than SCB1 for the choice of the filter

order L. When L > 3 the performances of SCB1 and RCB1 degrade significantly.

From Figures 4-5(c) and 4-5(d), we note that SCB2 and RCB2 yield the best

performance when L = 3, and their performances also degrade when L > 3. We

also note that when L > 3, RCB2 outperforms SCB2. This verifies the robustness of

RCB2. From Figures 4-5(e) and 4-5(f), we note that when L > 2, both the APRES1

and GRAPES methods achieve similar good performances. For the APES based

methods they can achieve a good performance in a wide range of choice of L. From

the results obtained in Figure 4-5, we can conclude that the APES based methods

are more robust than the Capon based methods.

Figure 4-6 shows the ROC curves of the six proposed methods in the presence of

steering vector errors. APES1 and GRAPES are the best among the six approaches

which are followed by RCB1 and RCB2.

Finally, 137 real-world measured QR data sets with Nc = 4, which were collected

by the Quantum Magnetics, Inc., are used to compare our new approaches with

three existing methods, viz. M3L method [17] ALS [17] and a multi-stage combined

method [18]. Among them, there are 77 measured landmine data sets and 60 measured

background data sets. In this real-world example, the six new methods provide

similar ROC curves, and the robust methods perform slightly better than their non-

robustified counterparts. We use GRAPES as a representative of the new methods

to compare with the previous methods. From Figure 4-7, we can see that GRAPES



























Pf
(a)


(b)


Figure 4-5. Detection performance (ROC) with various temporal filter order L in the
presence of steering vector errors for (a) SCB1, (b) RCB1, (c) SCB2, (d)
RCB2, (e) APES1, and (f) GRAPES.





























Pf
(c)


Figure 4-5. Continued.































Pf
(e)


Figure 4-5. Continued.



















n 0.7
0.7

0.6 SCB1
-e- SCB2
0. RCB1
-A- RCB2
0.5 APES1
-4- GRAPES
0.5---I-I-=
0 0.05 0.1 0.15 0.2 0.25
Pf

Figure 4-6. Detection performance (ROC) comparison among the new methods in
the presence of steering vector errors.


outperforms the combined approach when Pf < 0.2, which is the region of interest,

and has a much better performance than that of the M3L, and ALS methods.

4.7 Summary

In this chapter we have proposed several new approaches to estimate the QR

signal amplitude by exploiting the spatial and temporal correlations of the RFIs.

Our in i, -i shows that SCB1 gives higher resolution than SCB2, but it is sensitive

to steering vector errors and to the related small snapshot size problem. SCB2 gives

lower resolution than SCB1 due to its sub-optimal SINR design, but it can be more

robust than SCB1. RCB1 and RCB2 are more robust than their SCB1 and SCB2

counterparts in the presence of steering vector errors. APES based methods (APES1

and GRAPES) are more robust than the Capon based methods. Moreover, the real-

world example shows that our new methods can achieve better performance than the

existing M3L, ALS and combined methods in the QR application for TNT landmine

detection.

















































0.

0.


9 ,i'

8
I,5




6

5

4 -

3 -
M3L
2 Combined approach
GRAPES
1 .... ALS
-


0' I I I I
0 0.2 0.4 0.6 0.8 1
Pf


Figure 4-7. Detection performance (ROC) comparison of M3L, ALS, combined ap-

proach and GRAPES for the real-world example.















CHAPTER 5
JOINT COMPOUND EXPLOSIVE DETECTION

5.1 Introduction

TNT and RDX are widely used explosives in landmines, but their detection by

QR in a mine field suffers from severe RFI. The QR frequency for the 14N in TNT

is around 0.842 MHz at normal room temperature with a slight shift of 100 ~ 150

Hz/C when the surrounding temperature changes. Since this frequency is located

within the AM radio frequency band and cannot be changed in other means, the AM

radio signals can appear as strong RFIs that can seriously degrade the TNT detection

by QR in a mine field.

The spectral structure of the QR signal of the 14N in RDX is somewhat more

complicated than that in TNT. The former may contain up to 18 possible transitions

[1]. The simplest RDX detector is to detect only one RDX QR frequency at around

3.41 MHz because this frequency has the weakest temperature dependence of about

60 Hz/C. At the 3.41 MHz frequency, the RDX signal does not suffer from the

RFI caused by the AM radio broadcasting. However, it suffers from some unknown

impulsive RFIs.

Therefore, to detect the very weak QR signal due to either TNT or RDX, the

RFI mitigation is essential and a robust RFI mitigation method is necessary for the

successful detection of landmines. In the past few years, many efforts have been

devoted to improve the QR explosive detection performance by either refining the

QR sensor design [1] or developing signal processing methods [17, 29], [44]-[46]. Most

existing investigations focus on detecting a single type of explosive, i.e., either TNT

or RDX. Since a single mine can contain only TNT, only RDX, or a compound of









TNT and RDX explosives, a detector designed to detect only one type of explosive

may not provide the best performance.

In this chapter, we will focus on the joint detection of TNT and RDX explosives

for the landmine detection via the QR sensor so that the overall landmine detec-

tion ability is improved and the detector performance is theoretically predictable.

To mitigate the unavoidable RFIs associated with the QR measurements, we apply

GRAPES method introduced in C'! lpter 4, to exploit the temporal and spatial cor-

relations of RFIs via the adaptive filtering. Based on the output of GRAPES, we

devise a generalized likelihood ratio test (GLRT) for the joint TNT/RDX detection,

which is referred to as the GRAPES-GLRT detector. GRAPES-GLRT is simple and

has the constant false alarm rate (CFAR) property, which means that the false alarm

rate of the detector is independent of the interference and noise power. CFAR is a de-

sired property in almost all target detection applications since the detection threshold

can be pre-determined and fixed for a desired false alarm rate. The effectiveness of

the proposed GRAPES-GLRT detector is demonstrated with the experimental data

collected by Quantum Magnetics (QM), Inc.

The remainder of this chapter is organized as follows. In Section 5.2, we introduce

the data model and formulate the problem of interest. In Section 5.3, we consider

using GRAPES for RFI mitigation by exploiting the temporal and spatial correlations

of RFIs. Section 5.4 presents our GRAPES-GLRT detector for the joint TNT/RDX

detection and its performance analysis. Experimental examples are presented in

Section 5.5 to illustrate the excellent performance of the proposed detector. Finally,

Section 5.6 contains our summary.

5.2 Problem Formulation

Consider a QR system consisting of a main antenna and Nc reference antennas.

Each of these antennas provides a spatial data acquisition channel and the data

acquisition is done simultaneously on these channels. The main antenna receives









both RFIs and the QR signal and the reference antennas receive only the RFIs. The

QR signal is demodulated to the direct current (DC) (i.e., zero frequency) upon

digitalization in the receiver.

To detect the QR response of the TNT explosive (similar for RDX), a phase

cycled pulse sequence is used in the QR system. The experiment is designed to

produce the maximum amount of signal per unit time from the TNT 14N nuclei and

to vary the phase of the QR signal in a predictable manner so as to separate it

from other artifacts (e.g., magneto-acoustic ringing, piezo-electric ringing and pulse

ring-down).

One pulse sequence consists of two subsequences: positive and negative, each of

which contains a sequence of N, echoes called an echo train. Each echo is sampled

to obtain Nf fast-time samples during the acquisition window and the corresponding

sampling interval is referred to as the fast-time sampling interval (in analogy to the

radar terminology [84]). The corresponding samples from one echo to another form

the N, slow-time samples. The fast-time and slow-time samples form an Nf x N,

matrix. The amplitude d(ns) of the nth echo decays exponentially with a time

constant T2:

a(n) e-" T T2 = 0, Ns 1, (5-1)

where T, is the time interval between two .,i.i i:ent echoes or the slow-time sampling

interval.

A pair of .lIi i:ent positive and negative is referred to as a loop. The loop is then

repeated multiple times (Ziv Np times), i.e., the data acquisition process is repeated

Np times, with each process obtaining the same QR signal. The entire data collection

process in these repeated loops is called a scan. Hence each scan obtains N1 data

matrices of dimension N, x N, The data collected from the negative subsequence is

subtracted out from those in the positive subsequence. This process is referred to as









deringing, which cancels out any ringing from the constant phase refocusing pulses

and adds up the QR signals.

Since the specified QR signal frequency is down-converted to zero frequency upon

digitalization in the receiver, it is convenient to come up with a data model in the

frequency domain by performing the one-dimensional (1-D) Fourier transform (FT)

along the fast-time dimension for the data sets from each antenna and then picking

up the proper frequency bins around the down-converted QR signal frequency. To

do so, a windowed FT (WFT) is usually used to reduce the sidelobes, and the zero

frequency bin is picked for the main antenna output while multiple frequency bins (-v

Nb) around the zero frequency bin are collected from the reference antenna outputs.

Let k = 1 denote TNT probing and k = 2 denote RDX interrogation. For the probing

of the kth type of explosive, (1 + NNb) spatial samples are obtained for each echo

from one main and N, reference antennas. Each channel has Np,k slow-time sample

sequences, each with N,,k samples. Hence after picking frequency bins, we have 2-D

complex-valued data matrices of dimension (1 + NCNb) x Np,kNk, k = 1, 2, which is

shown in Figure 5-1 .

Our fast-frequ'- 'i --domain data model regarding the data vector xk(n) for the

nth slow-time sample and the kth explosive is expressed as


Xk(n,) 3kaoSk(n) + ek(n), n = 1, Nk, k = 1,2, (5-2)

where /k is the unknown signal amplitude, ao is a vector of length (1+ NCNb) with the

first element being 1 and the remaining ones being zero, due to the fact that the main

antenna receives both the QR signal and RFIs while the references antennas receive

only RFIs, si(n) is the signal waveform for TNT given by s (n) = a (mod[n- 1, NA,1])

(with mod[n 1, N,1] denoting the module of n 1 over N,1), the counterpart for

RDX is s2 (n) = 1 for all n's, ek (n) is a vector containing the RFIs and noise. We refer

to ao as the steering vector and Nk = Np,kN,k, k = 1, 2, as the total snapshot number.






71




1 st loop 2nd loop -th loop
SV N -th ref ch N -th refch N -th ref ch

I lst ref ch 1st ref ch I* 1st ref ch
.o main ch main ch main ch /
Slow -time 1 ... N+1 ... 2Ns (N,-1)N+1 ...
FFT along
i fast -time i
i then stack
collected
S ^~~-freq bins 1




xk(n)
1 N 2Ns NpN n

Figure 5-1. Data cube from QR data collection


Because the TNT and RDX explosives are probed with different frequencies, the RFI

plus noise sequences {ei(n))} i and {e2(n)}J21 are assumed to be independent of

each other.

In practice, it is usually necessary to perform a phase correction to compensate

out the phase error due to factors such as system delay and initial phase of the

transmitted signal. This can be done on the data samples xk(n). After the phase

correction, the signal amplitude /3k becomes real-valued and non-negative (i.e., /3k > 0

for k = 1, 2). For notational convenience, we still use xk(n) to denote xk(n)eJ where

ejC" accounts for the phase correction and ', is known.

The problem of interest herein is to mitigate the RFIs, estimate the TNT and

RDX signal amplitudes, and perform joint TNT/RDX detection. Figure 5-2 outlines

the flow chart of the signal processing steps.











Data acquisition and deringing

I
Windowed FFT in fast-time and pick
up frequency bin(s) from each channel


Phase correction


RFI mitigation via adaptive
filtering


GLRT


Making decision


Figure 5-2. Signal processing flow chart for joint TNT/RDX detection.


5.3 RFI Mitigation by GRAPES

Using the -I I !.i, technique, we have the spatial-temporal data model as:


Xk(n) -j3as,(n) + v(n), n= 1, Nk.


(5-3)


Xk () [x (n) x(n + L- )]T,

as (n) = [aTsk(n) (n + L 1)]T,

k (n) =[e(n) ... e(n + L 1)]T,


(5-4)

(5-5)

(5-6)


Nk = Nk L + 1, and L is the temporal filter order. Then we perform the adaptive

filtering for RFI mitigation by using the GRAPES method ( see Subsection 4.3.2.2 for

the details of the GRAPES method). Although the following joint detection scheme


where









is derived based on the output of GRAPES method, it can be applied to the outputs

of any of aforementioned adaptive methods in ('!C plter 3 and ('!C plter 4.

Let hk denote the estimated GRAPES filter for the kth type of explosive, which

is given by,

hk -Qk (AH-Q IAk1, (5-7)

where Qk and Ok are defined in (4-34) and (4-25), respectively, for the kth type of

explosive, and
ak 0 ... 0


Ak 0 ac '" NEC L, (5-8)


0 0 ... ak

with aik denoting the estimated a obtained from (4-58).

Passing the data sequence {xk(n,)} 1 k = 1,2, through the filter fk yields a

scalar sequence


yk(n) = hXfk(n)

S/3Sk(n)+) Ek(n), n =1, ,Nk, (5-9)

where
L
Sk(n) = a,kSk(n 1+), n -l,1 Nk, (5-10)
l 1

ak h a, 1 1,... ,L, (5 11)

and


(5-12)


,k~n) kHvk(n)-








5.4 Joint TNT/RDX Detection
5.4.1 Detection
We consider the joint TNT/RDX detection as a binary decision problem between
two hypotheses, Ho and H1; the former means that no explosive is present, while the
latter indicates the contrary:

Ho0: yk(n)= Ek(n), n = 1, ,Nk, k = 1, 2
(5-13)
HI: yk(n)= 3kSk (n)+ k (n), n 1= ,Nk, k = 1, 2

We assume that the TNT and RDX measurements are independent of each other
and that Ek(n) is a zero-mean circularly symmetric complex Gaussian random process
with an unknown variance ok, k = 1, 2. The joint probability density function (PDF)
of the filtered sequence {yk(n,)}n 1 under H1 is
fI- (7kf I)\~l1k 2 1 \ TkcClk(/3k)\
fl,k k n) k, k H = 1 exp C~ k = 2, (5-14)
(72)Ni Uk J

where

Cl,k(3k) -- I Y kSk 2, -k =1,2, (5-15)
Nk
with

yk r, (1) k(2) ... ~(k ( k)]T (5-16)

and

Sk [[k(~ ) Sk(2) ... s (Tk)]T. (5-17)

The joint PDF of the spatially filtered sequence {Jk(n))}NFk under Ho is


fo,k (k(n)k; o H) exp k 1,2, (5-18)

where

1
Co,k Yk 2l, k 1,2. (5-19)
Nk









From (5-14), the negative log-likelihood function under H1 for the kth explosive

is proportional to


V In U) Clk~ k =1,2, (5-20)

where In(.) denotes the natural logarithm operation. Minimizing V1,k(o 3k) in (5

20) with respect to oa under H1 results in -2 = cl,k(3k). Similarly, we can obtain
&2 = Co,k under Ho.

By using the estimate o2 under H1 in (5-20), minimizing the cost function in

(5-20) with respect to /3k becomes minimizing


V2,(k ) C1,k(k)

S1Yk y- OkSk 2
Nk
co,k 2/3k Re(yk) + 3PP,k

Ck + P, Re(yk) 2 Re2(yk) (5
Co,k + Ps,k (5-21)

where
1
Ps, 1 s- 2, k t1,2, (5-22)

and
1 T
Yk --Skyk, k 1,2. (5-23)
Nk
Considering the condition /3k > 0, it is clear that the minimization of V2,k(/3) in

(5-21) with respect to 3k gives

tru (Re(y))
3tru (sFy,k
tru (Sk k = 1, 2, (5-24)
II Sk 112

where
t x, x > 0
tru(x) = (5-25)
0, x < 0,









and yr,k is the real part of yk. Then, the residual of the cost function V2,k(/k) is


V3,k = C1,k () -

= CO,k Ps,k. (5-26)

We obtain the GLRT for the joint TNT/RDX detection as

n 1fl,k ({k(n)} jl k, H1 Hi
Ho = > 2ro (5-27)
nlk fo,k {yk n)} 1;= H o) o

where To is a threshold, which is to be determined according to the desired probability

of false alarm (PFA). The PDFs fl,k({yk (n)} r I HI) and fo,k({yk1(n)}J k; 21 Ho)

are given in (5-14) and (5-18), respectively, with 3k in (5-14) replaced by )3k obtained

in (5-24) and oa replaced by


12 Cl,k(ik) under H (528)
k (5-28)
CO,k under Ho.

By taking the logarithm of both sides of (5-27), the GLRT formulation can be

simplified as

S 2NTk [n(co,k) in (cl,k(k))] >1 (5-29)
k=1 Ho
where ^ 2 In o and 7 A 2 In T. Using (5-26) in (5-29) gives
2( 2 Hi
-2k In1 > T. (5-30)
k 1 Ok <
k=1 Ho

Define

k 2Nk
VP,kCO,k

Sk kYr,k k = 1,2, (5-31)
I Sk I Yk









and let


rlk = tru (yk)

S 2N ,k, k 1, 2. (5-32)
CO,k

Then we rewrite (5-30) in a compact format

2 H1
k E r( ) > 7, (5-33)
k 1 Ho

where the function fk(r1k) is given by


k(Tk) -2Nkn(l -T). (5-34)
21Nk

The detector in (5-33) adds up the outputs of the individual TNT and RDX detectors.

In Appendix D, we show that the joint GLRT statistic ( in (5-33) is independent of

the interference and noise scenario under Ho and thus it is a CFAR test.

5.4.2 Detector Threshold Determination

Since the joint GLRT statistic in (5-33) is a CFAR test, the detection threshold

can be determined according to the desired PFA. This requires the determination of

the PDF of the detection variable.

It is shown in Appendix E that the PDF of the variable Zk = k is given by


k (k) 21Vk f (2Nk 1,1) -, (5-35)
(2Nk 1)2(2Nk-1)W

where F, (2Nk 1,1) is the F-distribution with a pair of parameters (2Nk 1,).

Let k A fk('7k), which is obtained by replacing rlk in (5-34) with rk. The PDF of k

can be directly derived from (5-35) by a variable replacement. That is

2Nk Zk
f (fk) fk (fk) (5-36)
21 k z=2Nk(1-e









Since p1 and 92 are independent of each other, and under Ho, they each can be ex-

pressed as a ratio of a Gaussian distributed (V A/(0, 1)) variable and a x-distributed

variable (see Appendix D), each of them has an equal probability (0.5) to be negative

and non-negative. Therefore, under Ho each of the variables Tr1 and r/2 has a proba-

bility of 0.5 to be zero. As for the detection variable it will take values from four

possible subsets, each of which occurs with 0.25, according to the signs of r1 and 92.

That is
i1(q1) + 2(22) for r1 > 0, 2 > 0

i1(-1) for i > 0, 2 < 0 (
{ (5-37)
2(22) for 91 < 0, 2 > 0
0 for 91 < 0, 92 < 0

Consequently, the PDF of the detection variable ( under Ho can be expressed as a

mixture formation,


f () = 0.256(0) + 0.25f& () + 0.25&f () + 0.25f& () f () (5-38)

where 6(.) is the Dirac Delta function, and the symbol 0 denotes the convolution.

Note that, even though the PDF of in (5-38) is only the function of N1 and N2, no

explicit closed form is available for it, and the computation of the detector threshold

for a given PFA is somewhat complicated. To simplify the problem, we conduct an

.,-vmptotic analysis in Appendix F and show that for large Nk the function Qk(rlk) in

(5-34) can be simply approximated as:


k(rk) r Zk (5-39)

and the detector is simplified
2
Hi
Z zk z >r. (5-40)
k 1 Ho



























Figure 5-3. PDF of z2 and k for various data length N

Furthermore, under Ho, for large Nk consider


co,k O oA k 1,2. (541)

Since yk(n) ~ A(0, o ) under Ho, it is straightforward to show that Ok ~ A/(0, 1),

which results in

(k = (1) (5-42)

Here X2(n) denotes the X2-distribution with n degrees of freedom [85]. To show the

effectiveness of using approximation in (5-41), Figure 5-3 plots the PDF curves of

X2(1) and f&(k) ( see (5-36)) for Nk 5,1,0,50,100. We note from Figure 5-3 that
for Nk > 50, the approximate PDF of Zk is very close to the accurate expression. We

remark that the condition Nk > 50 is easily satisfied in the QR experiments.

Again, since p1 and r2 are independent of each other, the variable z = 12 + i

will be X2(2) distributed. It is interesting to note that, if we only consider the real-

valued signal amplitude for each type of explosive, this result agrees with the relevant

conclusion in [86] that for rather general models, the .i-,iiill. ic distribution of the









GLRT quantity is X2 distributed with degrees of freedom equal to the difference

between the number of free parameters under H1 and Ho.

Similar to the detection variable the simplified detector z takes values from

the corresponding four possible subsets, each of which occurs with 0.25, according to

the signs of r1 and 72:


+ 12 X2(2) for 7i > 0, 92 > 0

I X2(1) for r1 > 0, 72 < 0
z= (5-43)
Sf X2(1) for 1 < 0, q2 > 0
0 for r0 < 0, q2 < 0

Accordingly, we deploy a X2-mixture distribution to model the detection variable z

under Ho. The corresponding PDF pz(z) is given as

p,(z) = 0.256(z) + 0.5pi(z) + 0.25p2(z), (5-44)

where p,(-), n = 1, 2, is the PDF for the X2(n) distribution. Let Fz(z) denote the

cumulative density function (CDF) of z under Ho and F,(.) denote the CDF for the

X2(n) distribution. Then we have

F,(z) = pz(p)dp

S0.25 + 0.5Fi(z) + 0.25F2(). (5-45)

Thus, for a desired PFA (-v PF), we can determine the corresponding detection

threshold r by solving

Pf = (-)

S0.75 0.5F(7-) 0.25F2(r). (5-46)

















. 0.2

0.15

0.1


0 1 2 3 4 5 6 7
Detection threshold


Figure 5-4. Probability of false alarm versus detection threshold for the X2-mixture
distribution for the joint TNT/RDX detection as well as individual TNT
or RDX detection.


In the case that we concentrate on detecting only one type of explosive, the

detection threshold can be similarly determined by solving


Pf,i = 0.5 0.5Fi(r). (5-47)

Figure (5-4) shows the curves of Pf (solid-line) and Pfi (dashed-line) versus r.

For a PFA of 0.05, for example, simplified detector thresholds are r = 4.23 and 2.71

for the joint TNT/RDX and individual TNT or RDX detections, respectively.

5.4.3 Summary of the Detection Steps

In summary, the steps of the GRAPES-GLRT detector for the joint TNT/RDX

detection are as follows.

* Step 1: For a given Pf, determine the detection threshold r by solving (5-46);

* Step 2: Use the acquired data sequence {xk(n)}Z 1 to form the spatial-temporal
snapshot sequence {xk(n)} 1 according to (5-3);









* Step 3: Estimate the FIR filter coefficient vector hk by using GRAPES in Sub-
section 4.3.2.2;

Step 4: Pass the sequence {xk(n)} 1 through the FIR filter built in Step 3
according to (5-9), and calculate the sequence {sk(n)}1Z) using (510);

* Step 5: Obtain the detection output Zk, k 1,2, from each individual set of
QR measurements according to (5-32) with P,,k, 3k, and co,k calculated by using
(5-22), (5-24) and (5-19), respectively;

* Step 6: Compute the detection variable z and render a decision according to
(5-40).

5.5 Experimental Results

We present experimental results to illustrate the performance of the proposed

GRAPES-GLRT detector for the joint TNT/RDX detection by QR. The data we use

were collected by the QR sensor built by QM. Both TNT and RDX measurements

are obtained at each scan. Various data collection parameters are used. The number

of fast-time samples in each echo is N,1 = 50 to 380, the number of slow-time samples

N in an echo train varies from 60 to 130, and the number Np,1 of the repeated QR

pulse sequence loops varies from 1 to 4 for each scan. There are totally 590 scans

in the data set, which consists of 260 mine-free scans and 330 mine scans. The 260

mine-free scans are from two types of background, crush and run (CR) and bank run

gravel (BRG). All of the 330 mine scans are from plastic-cased mines, which include

TNT/RDX compound mines and TNT mines.

For each scan, we use data samples from 4 antennas (1 main antenna and N = 3

reference antennas). After the deringing, we weigh the fast-time data samples of the

TNT probing with a non-symmetric Hanning window (see the dashed line in Figure

5-5) separately for each antenna output. Using the non-symmetric Hanning window

is motivated by matching the window to the measured TNT fast-time waveform (see

the solid line in Figure 5-5) obtained by scanning a TNT mine in a high SNR and RFI-

free experiment. The curves in Figure 5-5 indicate that the TNT fast-time waveform

























20 30
Fast-time sample


Figure 5-5. TNT fast-time waveform (obtained by scanning a TNT mine in a high
SNR and RFI-free experiment) and non-symmetric Hanning window.


can be well approximated as a non-symmetric Hanning window. With this weighting

scheme, we are applying a matched filter to the fast-time TNT measurements. No

window is applied to the deringed data samples of the RDX interrogation because

the RDX signal waveform is a constant in both fast- and slow-time dimensions.

Because both of the TNT and RDX measured signals are down-converted to zero

frequency upon digitalization at the receiver, we choose to use only the zero frequency

bin (i.e., Nb 1) from each antenna output to form the data sequences {xi(n)}L1i

and {x2(n)}, 1 for TNT and RDX, respectively. An efficient way to do so is to sum

up all the fast-time samples (after proper deringing and windowing) of each echo in

each spatial channel. We have also tested using multiple frequency bins from the

reference channels, but no improvement on the detection performance is found for

this data set. We have used = 62 = 0.1 .

Now, we evaluate the performance of the detector in terms of the receiver oper-

ating characteristic (ROC), i.e., probability of detection (Pd) versus Pf. All the 260

mine-free scans and 330 mine scans are used in this experiment. The ROC curves of











the detector when applied to individual TNT, RDX and joint TNT/RDX detections

are shown in Figures 5-6. It is clear that the fusion of the individual TNT and RDX

detection via GLRT has improved the detection performance.

1III

0.9 .... ,
.......,

0.8 -'

0.7

0.6
II-
C 5.6- ..--'- -' -
0.5 -

0.4 -,'- "

0.3 -

0.2 Joint TNT/RDX
.-.- TNT
0.1 -- RDX
0 I I I I I
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
Pf
Figure 5-6. ROC curves for the GRAPES-GLRT detector.



5.6 Summary

In this chapter, we have proposed a GRAPES-GLRT detector for the joint

TNT/RDX detection by QR. GRAPES has been used to perform the adaptive beam-

forming to mitigate the RFIs by exploiting the spatial and temporal correlations of

the RFIs. We also derived the joint GLRT statistic based on the output of GRAPES

and shown that it has the CFAR property. By considering non-negative QR signal

amplitudes, we have also obtained a X2-mixture distribution to model the detection

variable and show how to determine the detection threshold according to the de-

sired probability of false alarm. The effectiveness of the proposed GRAPES-GLRT

detector has been demonstrated with the experimental data collected by Quantum

Magnetics (QM), Inc.















CHAPTER 6
SUMMARY AND FUTURE WORK

6.1 Summary

In this study, we have investigated developing robust adaptive methods for signal

amplitude estimation in the QR application based on both single antenna and antenna

array configurations. We have also investigated joint QR signal detection for detecting

compound explosives.

For the single antenna based application, we have investigated the signal ampli-

tude estimation with an arbitrary known waveform in the presence of strong interfer-

ence and noise. We have presented three adaptive finite-impulse response (FIR) filter

based methods to suppress the strong interference. We first extended the generalized

Capon (GC) estimator to the signal amplitude estimation problem. Under the frame-

work of RCB, both robust GC and approximate robust RGC were devised to mitigate

the small snapshot problems by allowing an uncertainty set for the signal covariance

matrix. Numerical examples have shown that these three adaptive approaches can

perform much better than the non-adaptive least-squares (LS) method, and that the

robustified estimators outperform their non-robusitified counterpart.

For the antenna array based application, we have proposed several new adaptive

beamforming methods to mitigate the RFIs by exploiting their spatial and temporal

correlations. Two cases, with exact and uncertain steering vector, have been con-

sidered in this work. When the steering vector is precisely known, we devised two

SCB-based adaptive approaches (SCB1 and SCB2) and one APES-based approach

(APES1). SCB1 maximizes SINR and gives high resolution, but it is sensitive to the

modeling errors like SCB. SCB2 is a modified version of SCB1 obtained by means of

a sub-optimal design. SCB2 gives lower resolution than SCB1 but is more robust.









APES1 was derived using the APES principle, and has been shown to be more robust

than both SCB1 and SCB2. When the steering vector uncertainty exists, which may

be caused by small number of snapshots or non-stationary RFIs and noise in the

QR application, we have developed two robust approaches (RCB1 and RCB2) based

on the RCB principle. RCB1 and RCB2 were obtained by rob-il- ik!.'-; SCB1 and

SCB2, respectively. We have also devised a generalized robust APES beamforming

(GRAPES) method using the APES principle but taking into account the steering

vector uncertainty in much the same fashion as in the derivation of RCB. We have

also analyzed the trade-off between resolution and robustness for various methods.

Both simulation and experimental results have shown that the robustified approaches

(RCB1, RCB2, and GRAPES) are more robust against steering vector errors than

their non-robustified counterparts. The real-world example for TNT landmine detec-

tion has demonstrated that our new methods can achieve better performance than

the existing M3L, ALS, and combined methods in the QR application.

For the detection of compound explosives, we have proposed a joint GLRT de-

tector and derived the corresponding detection statistic based on the output of RFI

mitigation for individual QR explosive probings. The theoretical analysis has shown

that this joint detector has a CFAR property. Its effectiveness has been demonstrated

with the experimental data collected by QM. The joint GLRT detector has signifi-

cantly improved the overall detection performance of the QR sensor as compared to

the individual single type explosive detectors. Finally, we remark that even though

our joint GLRT detector is derived for the joint detection of two types of explosives,

it can be readily extended to the joint detection of more types of explosives.









6.2 Future Work

In this dissertation, we have mainly explored robust adaptive approaches for

signal amplitude estimation with applications in QR. There are many possible ap-

proaches of further improving the performance in this topic. Followings are a couple

of directions that are closely related to our present work.

More efficient use of spatial and temporal correlations of RFIs

We may consider exploiting the spatial and temporal correlations of RFIs for

the RFI mitigation in a more efficient way. In the implementations of the proposed

approaches in this study, the numbers of both frequency bins (for spatial correlation

consideration) and temporal tap (for temporal correlation consideration) are deter-

mined based on our experience. It is worthy to investigate optimal selections for these

numbers in order to attain more efficient RFI mitigation and thus improve the QR

signal detection performance.

Tracking of QR signal frequency change

Since the QR signal frequency slightly varies according to the surrounding tem-

perature at a rate depending on the type of explosive (e.g., 100 ~ 150 Hz/ for TNT),

the down-converted QR frequency may not be exactly at the DC location. In our

previous investigations, based on the knowledge that the QR sequence was automat-

ically optimized according to the estimated mine temperature entered by the system

operator, we have assumed that the QR signal frequency is known exactly (zero-

frequency after digital down-conversion in the receiver) and fixed in all simulations

and experiments. However, possible temperature estimation error may have impact

on the signal amplitude estimation and detection performance. For this reason, we

may need to find an optimal method to track the change of the QR signal frequency

and further improve the detection performance.














APPENDIX A
PROOF OF A1 > A2 USED IN SECTION 4.3.1.2
By (4-23), we have

Amax(AHf-1A) > aH(FAHfR-A)a

H ((AxF)aaH) AHR-lA) a

Amx(F)aH(AHR-1A)a, (A-1)

where the spectral decomposition of a symmetric matrix and the orthogonality of
eigenvectors of a matrix have been used to obtain the second equality in (A-1) [87].
Also note that


|a|4 aH(AHR- A)-1/2(AHR- A)1/ 2a

< [aH(AHR-1A)-la][aH(AHR-1A)a], (A-2)

where the Cauchy-Schwartz inequality has been used to obtain the inequality in (A
2). Using (A-1) and (A-2), we have

A1 = Amax(FAH-A)

> Amax() A. (A-3)
aH(AHR-1A)-la

This concludes the proof.













APPENDIX B
DERVIATION OF (4-61)
In this appendix, we calculate the variance of the signal amplitude estimate 3.
To simplify the analysis of the statistical properties of 3, we make the following
assumptions:

* Al: h is (nearly) independent of v(n). This is not strictly true for the adaptive
methods. However, since the adaptive filter h converges to a constant vector for
a large snapshot number N, this assumption is reasonable.

* A2: hHv(n), is (nearly) a temporally white sequence; also, {v(n)} is circularly
symmetric i.i.d. Gaussian.
Inserting (4-10) into (4-14) yields

S + ZrzrlhH'v(n)s*(n) (B 1)
ln= 1s F(n)12
Therefore the variance of 3 is given by

var(3) = E[\I 12]
i 21
:n- 1 ISF(n) 1

(z 1 (f ElS ) 2) 2

where E[.] denotes statistical expectation.
By Assumption Al, (B-2) can be approximated as

hHE [Z71 ol v(un)s~(n)s,(no)vH(no0) h
var(1) SF() 12). (B-3)









By Assumption A2, (B-3) can be further simplified as


var (3)


where


Q E[v(n)vH(n)].


Using the statistical property of circularly symmetric complex Gaussian noise, we
have


var [Re (/3)1


1
-var (3)
2
1 hHQh
2 r |SF(7) |2
Zn-1 ISF^n)


(B-6)


hH 1 SF( 2E [v(n)VH()] h
(hnHi1 12 2)
hHQh
zn-I1 ISF()12


(B-4)


(B-5)