Tightly Integrated Sensor-based Terrestrial LiDAR Georeferencing

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Title:
Tightly Integrated Sensor-based Terrestrial LiDAR Georeferencing
Physical Description:
1 online resource (188 p.)
Language:
english
Creator:
Wilkinson,Benjamin E
Publisher:
University of Florida
Place of Publication:
Gainesville, Fla.
Publication Date:

Thesis/Dissertation Information

Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Forest Resources and Conservation
Committee Chair:
Dewitt, Bon A
Committee Co-Chair:
Mohamed, Ahmed Hassan
Committee Members:
Smith, Scot E
Hochmair, Hartwig Henry
Peters, Jorg

Subjects

Subjects / Keywords:
accuracy -- adjustment -- autonomous -- calibration -- direct -- geomatics -- georeferencing -- gps -- imagery -- integrated -- laser -- least -- lidar -- photogrammetry -- precision -- registration -- scan -- scanning -- sensor -- simultaneous -- survey -- technique -- terrestrial
Forest Resources and Conservation -- Dissertations, Academic -- UF
Genre:
Forest Resources and Conservation thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract:
Georeferencing of terrestrial LiDAR scanning data is typically performed by using scanner target points occupying control points in the project area. This necessitates intensive field labor and extra, often cumbersome equipment. A method for georeferencing scan data using two GPS antennas firmly mounted on the optical head of a LiDAR scanner has been developed. By adding a dual GPS antenna apparatus to the scanner setup, thereby supplanting the use of multiple ground control points scattered throughout the project, we mitigate not only the problems associated with georeferencing but also induce a more efficient set up procedure while maintaining a practical level of precision. This study is an extension of the dual GPS antenna method by creating a process for a simultaneous network adjustment of multiple scanner stations. By exploiting additional sensor information from a scanner-mounted camera and point cloud matching techniques, an integrated adjustment of observations from this sensor suite is developed. Further, the technique is tested on two distinct data sets. The testing consists of comparison with conventional techniques and different combinations of the novel, more autonomous methods. Analysis includes the investigation of precision, accuracy, efficiency, and conditioning under different configurations of the system. The test results indicate that centimeter-level accuracy at a scanner-point distance of 40 meters can be achieved using only imagery and scanner-mounted GPS data, and that under certain circumstances, the autonomous methods were able to approach the same level of precision as the conventional data-driven method.
General Note:
In the series University of Florida Digital Collections.
General Note:
Includes vita.
Bibliography:
Includes bibliographical references.
Source of Description:
Description based on online resource; title from PDF title page.
Source of Description:
This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility:
by Benjamin E Wilkinson.
Thesis:
Thesis (Ph.D.)--University of Florida, 2011.
Local:
Adviser: Dewitt, Bon A.
Local:
Co-adviser: Mohamed, Ahmed Hassan.

Record Information

Source Institution:
UFRGP
Rights Management:
Applicable rights reserved.
Classification:
lcc - LD1780 2011
System ID:
UFE0043237:00001


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1 TIGHTLY INTEGRATED SENSOR BASED TERRESTRIAL LIDAR GEOREFERENCING By BENJAMIN E. WILKINSON 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 201 1

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2 201 1 Benjamin E. Wilkinson

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3 To my family and friends

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4 ACKNOWLEDGMENTS I thank Zhao, my parents, her parents, and the rest of my family for their unending support. I also thank my commi ttee, specifically my chair, Bon Dewitt and my c o chair, Ahmed Mohamed for their guidance, knowledge and patience. I could not have done it without you all.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 9 LIST OF FIGURES ................................ ................................ ................................ ........ 13 LIST OF ABBREVIATIONS ................................ ................................ ........................... 17 ABSTRACT ................................ ................................ ................................ ................... 18 CHAPTER 1 INTRODUCTION AND LITERATURE REVIEW ................................ ..................... 20 Background ................................ ................................ ................................ ............. 20 Georeferencing ................................ ................................ ................................ ....... 20 Current Methods ................................ ................................ ............................... 21 The Du al Antenna System (DAS) Method ................................ ........................ 23 Close Range Photogrammetry ................................ ................................ ................ 26 Motivation ................................ ................................ ................................ ............... 28 Hypothesis/Objectives ................................ ................................ ............................ 29 2 METHODS ................................ ................................ ................................ .............. 31 Opening Remarks on Methods ................................ ................................ ............... 31 Sensor Model ................................ ................................ ................................ .......... 31 Scanner Observations ................................ ................................ ...................... 31 Scanner tiepoints ................................ ................................ ....................... 31 Point cloud matching ................................ ................................ .................. 32 Image Observations ................................ ................................ ......................... 33 Collinearity condition ................................ ................................ .................. 33 Coplanarity condition ................................ ................................ ................. 34 Camera boresight and lever arm ................................ ............................... 36 Camera calibration (interior) ................................ ................................ ....... 37 DAS Georeferencing Para meters Observations ................................ ............... 38 Control Point Observations ................................ ................................ ............... 39 System Solution ................................ ................................ ................................ ...... 39 Scanner Solution ................................ ................................ .............................. 39 Tiepoints ................................ ................................ ................................ .... 39 Point cloud matching ................................ ................................ .................. 40 Ima ge Solution ................................ ................................ ................................ 41 Collinearity condition ................................ ................................ .................. 41 Coplanarity condition ................................ ................................ ................. 42 DAS ................................ ................................ ................................ .................. 44

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6 Control Points ................................ ................................ ................................ ... 44 Simultaneous Solution ................................ ................................ ...................... 45 Formulation ................................ ................................ ................................ 45 Simultaneous vs. Sequential Solution ................................ ........................ 48 3 DATA COLLECTION ................................ ................................ .............................. 53 Corry Village ................................ ................................ ................................ ........... 53 Site ................................ ................................ ................................ ................... 53 Laser Scan Data ................................ ................................ ............................... 53 DAS Data ................................ ................................ ................................ ......... 54 Imagery ................................ ................................ ................................ ............ 54 Orlando ................................ ................................ ................................ ................... 55 Site ................................ ................................ ................................ ................... 55 Laser Scan Data ................................ ................................ ............................... 55 DAS Data ................................ ................................ ................................ ......... 55 Imagery ................................ ................................ ................................ ............ 56 4 PROCESSING ................................ ................................ ................................ ........ 63 Scan Data ................................ ................................ ................................ ............... 63 Multistation Adjustment ................................ ................................ .................... 63 Point Cloud Matching ................................ ................................ ....................... 64 Imagery ................................ ................................ ................................ ................... 66 Image Point Acquisition ................................ ................................ .................... 66 Initial Bundle Adjustments ................................ ................................ ................ 69 DAS ................................ ................................ ................................ ........................ 73 Orientation ................................ ................................ ................................ ........ 73 Stops ................................ ................................ ................................ .......... 73 Tilt using all observations method ................................ .............................. 76 Position ................................ ................................ ................................ ............. 77 5 RESULTS AND ANALYSIS ................................ ................................ .................... 98 Opening Remarks on Results and Analysis ................................ ............................ 98 Corry Village Exterior Orientation ( EOP ) Estimation ................................ ............. 100 Configurations with Scanner Targe ts ................................ ............................. 100 Relative performance of different methods using arbitrary scanner targets ................................ ................................ ................................ ... 102 Relative performance of different methods using control scanner targets 103 Performance of methods using control scanner targets compared to methods using arbitrary scanner targets ................................ ............... 103 Configurations without Scanner Targets ................................ ......................... 104 Relative perfor mance of different methods ................................ .............. 104 Comparison of the performance of methods using sca nner targets and methods without using scanner targets ................................ ................ 106 Orlando EOP Estimation ................................ ................................ ....................... 106

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7 Configurations with Scanner Targets ................................ ............................. 107 Relative performance of different methods using arbitrary scanner targets ................................ ................................ ................................ ... 107 Relative performance of different methods using control scanner targets 108 Configurations without Scanner Targets ................................ ......................... 109 Relative performance of different methods ................................ .............. 110 Performance of methods using scanner targets compared to methods without using scanner targets ................................ ............................... 113 Sum mary Analysis of Results ................................ ................................ ............... 113 Boresight and Leverarm Experimentation and Analysis ................................ ....... 115 6 S UMMARY AND CONCLUSIONS ................................ ................................ ........ 129 7 FUTURE RECOMMENDATIONS ................................ ................................ ......... 132 Boresight and Leveram Parameters ................................ ................................ ..... 132 Coplanarity Solutions ................................ ................................ ............................ 132 Iterative Closest Point Algorithm ................................ ................................ ........... 133 Integration of More Sensors ................................ ................................ .................. 133 Mobile Mapping ................................ ................................ ................................ .... 133 Modification of the DAS Apparatus and Implementation ................................ ....... 133 Optimization of Implementation ................................ ................................ ............ 134 APPENDIX A THE PARTIAL DERIVATIVES OF THE COLLINEARITY EQUATIONS WITH BORESIGHT AND LEVER ARM CALIBRATION PARAMETERS ........................ 135 Definitions ................................ ................................ ................................ ............. 135 Other Helpful Substitutions ................................ ................................ ................... 136 The Partial Derivatives ................................ ................................ .......................... 136 B THE PARTIAL DERIVATIVES OF TH E COPLANARITY EQUATIONS WITH BORESIGHT AND LEVER ARM CALIBRATION PARAMETERS ........................ 141 Definitions ................................ ................................ ................................ ............. 141 The Partial Derivatives ................................ ................................ .......................... 142 C SCHEMATIC DRAWING OF THE DUAL ANTENNA SYSTEM MOUNTING BAR 152 D A POSTERIORI STANDARD DEVIATIONS OF INDIVIDUAL STATIONS UNDER DIFFERENT CONFIGURATIONS OF THE INTEGRATED SIMULTANEOUS ADJUSTMENT ................................ ................................ ........ 153 E F STATISTICS FOR DIFFERENT INTEGRATED METHODS ............................. 167 F COPLA NARITY VERSUS COLLINEARITY ................................ .......................... 178

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8 G DAS C O LLECTION WORKFLOW ................................ ................................ ........ 184 LIST OF REFERENCES ................................ ................................ ............................. 186 BIOGRAPHICAL SKETCH ................................ ................................ .......................... 188

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9 LIST OF TABLES Table page 2 1 Root mean square va lues of points using different methods of adjustment ........ 52 4 1 Corry village multistation adjustment solution ................................ ..................... 94 4 2 Orlando multistat ion adjustment solution ................................ ............................ 94 4 3 Error in Iterative Closest Point (ICP) solutions with respect to the relative Exterior Orientation Parameter s (EOPs) between stations ................................ 94 4 4 Camera calibration parameters in pixels ................................ ............................ 94 4 5 Initial boresight and lever arm calibration parameters ................................ ........ 94 4 6 Correlation matrix for Boresight and Leverarm Parameters (BLPs) .................... 94 4 7 Correlation matrix for BLPs and EOPs of station 1 of the Orlando data set (indicative of correla tion for all stations) ................................ ............................. 95 4 8 Average post bundle adjustment standard deviations of station EOPs for different initial boresight and lever arm circumstances ................................ ....... 95 4 9 Dual Antenna System (DAS) vector calibration parameters ............................... 95 4 10 Corry Village DAS solution for angular EOPs ................................ ..................... 96 4 11 Orlando DAS solution for angular EOPs ................................ ............................. 96 4 12 Root Mean Square Errors ( RMSEs ) for tilt components of station EOPs for the Orlando data set ................................ ................................ ........................... 96 4 13 DAS position calibration parameters ................................ ................................ .. 96 4 14 DAS position solution for Corry Village ................................ ............................... 96 4 15 DAS position solution for Orlando ................................ ................................ ....... 97 5 1 Average post adjustment standard deviations of EOPs for the Corry Village data set using scanner targets ................................ ................................ .......... 126 5 2 Average post adjustment standard deviations of EOPs for the Corry Village data set without using scanner targets ................................ ............................. 126 5 3 RMSEs for the scanner target positions from Corry Village data set configurations without using scanner targets ................................ .................... 126

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10 5 4 Average post adjustment standard deviations of EOPs for the Orland o data set using scanner targets ................................ ................................ ................. 127 5 5 Average post adjustment standard deviations of EOPs for the Orland o data set without using scanner targets ................................ ................................ ..... 127 5 6 RMSEs for method s without using scanner targets ................................ .......... 128 5 7 Reduced BLP adjustment average standard deviations for EOPs .................... 128 5 8 RMSEs from reduced B LP adjustments ................................ ........................... 128 D 1 EOP solution for ( Control Scan Target (CST) ) configuration for the Corry data set ................................ ................................ ................................ ..................... 153 D 2 EOP solution fo r ( High Level DAS (HLDAS) ) configuration for the Corry data set ................................ ................................ ................................ ..................... 153 D 3 EOP solution for (CST, Collinearity (CL) ) configuration for the Corry data set 153 D 4 EOP solution for (CST, Coplanarity (CP) ) configuration for the Corry data set 153 D 5 EOP solution for ( Arbitrary Scan Target (AST) HLDAS) configuration for the Corry data set ................................ ................................ ................................ ... 154 D 6 EOP solution for (AST, Medium Level DAS (MLDAS) ) configuration for the Corry data set ................................ ................................ ................................ ... 154 D 7 EOP soluti on for (AST, Position Only DAS (PODAS) ) configuration for the Corry data set ................................ ................................ ................................ ... 154 D 8 EOP solution for (AST, CL, HLDAS) configuration for the Corry data set ......... 154 D 9 EOP solution for (AST, CP, HLDAS) configuration for the Corry data set ........ 154 D 10 EOP solution for (AST, CL, PODAS) configuration for the Corry data set ........ 155 D 11 EOP solution for (AST, CP, PODAS) configuration for the Corry data set ........ 155 D 12 EOP solution for (AST, CL, MLDAS) configuration for the Corry data set ........ 155 D 13 EOP solution for (AST, CP, MLDAS) configuration for the Corry data set ........ 155 D 14 EOP solution for ( Single Control Target (SCT) CL, HLDAS) configuration for the Corry data set ................................ ................................ ............................. 155 D 15 EOP solution for (SCT, CP, HLDAS) configuration for the Corry data set ........ 156 D 16 EOP solution for (SCT, CL, MLDAS) configuration for the Corry data set ........ 156

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11 D 17 EOP solution for (SCT, CP, MLDAS) configuration for the Corry data set ........ 156 D 18 EOP solution for (SCT, CL, PODAS) configuration for the Corry data set ........ 156 D 19 EOP solution for (SCT, CP, PODAS) configuratio n for the Corry data set ....... 156 D 20 EOP solution for (CL, HLDAS) configuration for the Corry data set .................. 157 D 21 EOP solution for (CP, HLDAS) configuration for the Corry data set ................. 157 D 22 EOP solution for (CL, MLDAS) configuration for the Corry data set ................. 157 D 23 E OP solution for (CP, MLDAS) configuration for the Corry data set ................. 157 D 24 EOP solution for (CL, PODAS) configuration for the Corry data set ................. 157 D 25 EOP solution for (CP, PODAS) configuration for the Corry data set ................. 158 D 26 EOP solution for (CST) configuration for the Orlando data set ......................... 158 D 27 EOP solution for (HLDAS) configuration for the Orlando data set .................... 158 D 28 EOP solution for (CST, CL) configuration for the Orlando data set .................. 158 D 29 EOP solution for (CST, CP) configuration for the Orlando data set .................. 159 D 30 EOP solution for (AST, HLDAS) configuration for the Orlando data set ........... 159 D 31 EOP solution for (AST, MLDAS) configuration for the Orlando data set ........... 159 D 32 EOP solution for (AST, PODAS) configura tion for the Orlando data set ........... 159 D 33 EOP solution for (AST, CL, HLDAS) configuration for the Orlando data set ..... 160 D 34 EOP solut ion for (AST, CP, HLDAS) configuration for the Orlando data set .... 160 D 35 EOP solution for (AST, CL, MLDAS) configuration for the Orlando data set .... 160 D 36 EOP solution for (AST, CL, MLDAS) configuration for the Orlando data set .... 160 D 37 EOP solution for (AST, CL, PODAS) configuration for the Orlando data set .... 161 D 38 EOP solution for (AST, CP, PODAS) configuration for the Orlando data set .... 161 D 39 EOP solution for (SCT, CL, MLDAS) configuration for the Orlando data set .... 161 D 40 EOP solution for (SCT, CP, MLDAS) configuration for the Orlando data set .... 161 D 41 EOP solution for ( SCT, CL, PODAS) configuration for the Orlando data set .... 162

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12 D 42 EOP solution for (SCT, CP, PODAS) configuration for the Orlando data set ... 162 D 43 EOP solution for (SCT, CL, HLDAS) configuration for the Orlando data set .... 162 D 44 EOP solution for (SCT, CP, HLDAS) configuration for the Orlando data set .... 162 D 45 EOP solution for (CL, HLDAS) configuration for the Orlando data set .............. 163 D 46 EOP solution for (CP, HLDAS) configuration for the Orlando data se t ............. 163 D 47 EOP solution for (CL, MLDAS) configuration for the Orlando data set ............. 163 D 48 EOP solution for (CP, MLDAS) configuration for the Orlando data set ............. 163 D 49 EOP solution for (CL, PODAS) configuration for the Orlando data set ............. 164 D 50 EOP solution for ( CP, PODAS) configuration for the Orlando data set ............. 164 D 51 EOP solution for (CL, ICP, HLDAS) configuration for the Orlando data set ...... 164 D 52 EOP solution for (CP, ICP, HLDAS) configuration for the Orlando data set ..... 164 D 53 EOP solution for (CL, ICP, PODAS) configuration for the Orlando data set ..... 165 D 54 EOP solution for (CP, ICP, PODAS) configuration for the Orlando data set ..... 165 D 55 EOP solution for (CL, ICP, MLDAS) configuration for the Orlando da ta set ..... 165 D 56 EOP solution for (CP, ICP, MLDAS) configuration for the Orlando data set ..... 165 D 57 EOP solution for (ICP, HLDAS) co nfiguration for the Orlando data set ............ 165 D 58 EOP solution for (ICP, MLDAS) configuration for the Orlando data set ............ 166 F 1 Number of i terations and c omputation t ime for d ifferent m ethods using c oplanarity and c ollinearity ................................ ................................ ............... 182

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13 LIST OF FIGURES Figure page 1 1 Schematic illustrati on for the Z390i mounted Global Positioning System (GPS) bar ................................ ................................ ................................ ........... 24 1 2 The first prototype of the Dual A ntenna S ystem (DAS) ................................ ...... 25 2 1 Re lationship between Global Coordinate System (GLCS) ( G ), Own Coordinate System (SOCS) ( S ), and Camera Coordinate System (CACS) ( C ) ................................ ................................ ................................ ......... 36 2 2 Scanner observation design matrix ................................ ................................ .... 50 2 3 Image observation design matrix ................................ ................................ ........ 51 2 4 Simultaneous vs. sequential experiment configuration ................................ ....... 52 3 1 The eastern entrance (left) and interior (right) of Corry Village on the UF campus. ................................ ................................ ................................ .............. 57 3 2 Corry Village at the University of Florida. DAS data were collected at fou r stations along the western most road (Source: Google Earth). .......................... 58 3 3 Scan data from Station 1 of the Corry Village data set ................................ ....... 59 3 4 The DAS 2.0 mounted on a Riegl z390i ................................ ............................. 60 3 5 The Riegl USA office building ................................ ................................ ............. 61 3 6 Scan data from Station 2 of the Orlando data se t showing the location of the scanner in SOCS ................................ ................................ ................................ 62 3 7 The DAS 3.0 mounted on a Riegl vz400 ................................ ............................ 62 4 1 Multistation adjustment design ma trix ................................ ................................ 78 4 2 Corry Village scan station and target network. Units are in meters. .................. 79 4 3 Orlando scan stations and target network. Units are in meters. ........................ 80 4 4 Segmented areas of scan data used for Iterative Closest Point (ICP) analysis .. 81 4 5 The relative posit ion of segmented point clouds for Station 3 (blue) and Station 2 (magenta) in their respective SOCSs ................................ .................. 82 4 6 Individual segmented point clouds from Station 3 and Station 2 prior to applying the ICP solution ................................ ................................ .................... 82

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14 4 7 Individual segmented point clouds from Station 3 and Station 2 after applying the transformation from the ICP solution ................................ ............................ 83 4 8 Individual segmented point clouds from Station 3 and Station 2 after applying the ICP solution with the view rotated to illustrate misalignment in the ICP derived transformation ................................ ................................ ........................ 84 4 9 Overlay of image point locations (on the images) for the Corry Village data set in pixel coordinates ................................ ................................ ....................... 85 4 10 Overlay of image point locations (on the images) for the Orlando data set in pixel coordinates ................................ ................................ ................................ 86 4 11 Example of image point distribution in a single photo from the Orlando data set (image is clipped and rotated) ................................ ................................ ....... 87 4 12 Horizontal distribution of image points in GLCS for Corry Village. Units are in meters. ................................ ................................ ................................ ............... 88 4 13 Horizontal distribution of image points in GLCS for Orlando. Units are in meters ................................ ................................ ................................ ................ 89 4 14 Design matrix for the initial bundle adjustments ................................ ................. 90 4 15 Changes in Boresight Leverarm Parameters needed to represent the same camera pose as Exterior Orientation Parameter (EOP) changes .................... 90 4 16 Illustration of the calibration parameters for the DAS system ............................. 91 4 17 Raw DAS GPS vectors for a typical Corry V illage station ................................ ... 92 4 18 Raw DAS GPS vectors for a typical Orlando station ................................ .......... 92 4 19 Averaged stop vectors for a typical Orlando stati on ................................ ........... 93 4 20 Standard deviation of DAS derived EOPs vs. number of stops .......................... 93 5 1 Average post adjustment standard deviations for angul ar EOPs for the Corry Village data set using scanner targets ................................ .............................. 117 5 2 Average post adjustment standard deviations for positional EOPs for the Corry Village data set using scanner targets ................................ .................... 117 5 3 Error in georeferenced point position with respect to error in angular scanner EOP at varying scanner to point distances ................................ ...................... 118 5 4 Average post adjustment standard deviations for angular EOPs for the Corry Village data set without using scanner targets ................................ ................. 118

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15 5 5 Average post adjustment standard deviations for positional EOPs for the Corry Village data set without using scanner targets ................................ ........ 119 5 6 Average post adjustment standard deviations for angular EOPs for Arbitrary Scan Target ( AST ) and Position Only DAS ( PODAS ) methods and without scanner target High Level DAS (HLDAS) and Medium Level DAS (MLDAS) methods for the Corry Village data set ................................ ............................. 119 5 7 Error in the estimated value of tilt in degrees ................................ ................... 120 5 8 Average post adjustment standard deviations for angular EOPs for the Orlando data set using scanner targets ................................ ............................ 121 5 9 Average post adju stment standard deviations for positional EOPs for the Orlando data set using scanner targets ................................ ............................ 121 5 10 Average post adjustment standard deviations for tilt for the Orlando Data set using scanne r targets ................................ ................................ ....................... 122 5 11 Average post adjustment standard deviations for angular EOPs for the Orlando Data set without using scanner targets ................................ ............... 123 5 12 Average post adjustment standard deviations for positional EOPs for the Orlando data set without using scanner targets ................................ ................ 123 5 13 Average post adjustment standard deviations of tilt for the Orlando data set without using scanner targets ................................ ................................ ........... 124 5 14 Root Mean Square Errors ( RMSEs ) of horizontal distance, d, for the Orlando data set without using scanner targets ................................ ............................. 124 5 15 RMSEs of the Z coordinate for the Orlando Data set without using scanner targets (truncated) ................................ ................................ ............................ 125 E 1 Alpha values for F tests on varian ces of from using different methods of georeferencing the Corry Village data set ................................ ........................ 168 E 2 Alpha values for F tests on variances of from using different methods of georeferencing the Orlando data set ................................ ................................ 171 E 3 Alpha values for F tests on variances of from using different methods of georeferencing the Orlando data set ................................ ................................ 175 E 4 Alpha values for F tests on Mnea Square Error (MSE) of from using different methods of Georeferencing the Orlando data set ............................... 176 E 5 Alpha values for F tests on ( MSE ) of from using differ ent methods of georeferencing the Orlando data set ................................ ................................ 177

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16 F 1 Standard error of unit weight for ( Coplanarity ( CP ) PODAS) iterations on the C orry Village data set ................................ ................................ ....................... 179 F 2 Estimated for oscillating iterations using (CP, PODAS) (blue), estimated from converged ( Collinearity ( CL ) PODAS) (red), and bounding standard deviations for converged (CL, PODAS) ................................ ......................... 179 F 3 Stand ard error of unit weight for (CP, PODAS) iterations on the Corry Village data set using Levenberg Marquardt Algorithm ( LMA ) ................................ ..... 181

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17 LIST OF ABBREVIATION S AST Arbitrary Scan Targets BLP Boresight and Lever arm Parameter CACS Camera Coordinate System CL Collinearity CP Coplanarity CRP Close Range Photogrammetry CST Control Scan Targets DAS Dual Antenna System EOP Exterior Orientation Parameter GLCS Global Coordinate System HLDAS High Level DAS ICP Iterative Closest Point MLDAS Medium Level DAS MSE Mean Square Error PODAS Position Only DAS RMSE Root Mean Square Error SCT Single Control Target SOCS SVD Singular Value Decomposition TLG Terrestrial LiDAR Georeferencing

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18 Abstract of Dissertation Prese nted to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy TIGHTLY INTEGRATED SENSOR BASED TERRESTRIAL LIDAR GEOREFERENCING By Benjamin E. Wilkinson August 20 1 1 Chair: Bon Dewitt Co chair : Ahmed Mohamed Major: Forest Resources and Conservation Georeferencing of terrestrial LiDAR scanning data is typically performed by using scanner target points occupying control points in the project area This necessitates intensive field labor and extra, often cumbersome equipment. A method for georeferencing scan data using two GPS antennas firmly mounted on the optical head of a LiDAR scanner has been developed. By adding a dual GPS antenna apparatus to the scanner setu p, thereby supplanting the use of multiple ground control points scattered throughout the project, we mitigate not only the problems associated with georeferencing but also induce a more efficient set up procedure while maintaining a practical level of pr ecision. This study is an extension of the dual GPS antenna method by creating a process for a simultaneous network adjustment of multiple scanner stations. By exploiting additional sensor information from a scanner mounted camera and point cloud matchi ng techniques, an integrated adjustment of observations from this sensor suite is developed. Further, the technique is tested on two distinct data sets. The testing consists of comparison with conventional techniques and different combinations of the

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19 nov el, more autonomous methods. Analysis includes the investigation of precision, accuracy, efficiency, and conditioning under different configurations of the system. The test r esults indicate that centimeter level accuracy at a scanner point distance of 4 0 meters c an be achieved using only imagery and scanner mounted GPS data and that under certain circumstances, the autonomous methods were able to approach the same level of precision as the conventional data driven method

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20 CHAPTER 1 INTRODUCTION AND LIT ERATURE REVIEW Background Commercially available airborne laser scanning (ALS) systems emerged in the early 1990s following advances in laser and GPS technology that made rapid, accurate collection of topographical data feasible (Ackerman, 1999) Soon thereafter, ground based systems became available and provided a solution for obtaining data that were previously elusive due to the limited perspective of aerial collection. There are currently a small number of comme rcially manufactured terrestrial laser scanning (TLS) systems. The number of practical applications for these systems seems limitless if one considers the multitude of ways that precise 3D data can be used. Although the size s and shape s of objects can be determined using TLS with relative ease, many applications require precise positioning of TLS point clouds in world or mapping coordinates. Thus, additional methods beyond data collection must be performed to georeference the data. Georeferencing The geo referencing problem can be defined as finding the values that determine the spatial relationship of sensor data with respect to a mapping coordinate system commonly referred to as exterior orientation parameters, or EOPs In practice, EOPs provide a tran sformation from an arbitrary coordinate system to a control coordinate system. Raw sensor data usually exist in an arbitrary system defined by the sensor itself. For instance, raw digital image data are represented by the coordinates of some imaged objec t in a coordinate system defined by the pixels of the image (rows and columns). By georeferencing the imagery, a transformation from the image coordinate system to some mapping coordinate system defined by the image EOPs is found

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21 and can be applied to eac h pixel in the image. Although technically the reverse is done by defining a grid of groundels and using the transformation to retrieve digital numbers from the image. Similarly, raw TLS data are in the form of a point cloud with represented using 3D Cartesian coordinates with a standard basis and the mapping system, or global coordinate system (GLCS), is also represented in this format, the georeferencing parameters consist of the 3D conformal coordinate transformation parameters, scale, rotations, and translations, that transform the scanned points from SOCS to GLCS. Current Methods The current methods for georeferencing TLS data can be divided into two classes, sensor dri ven and data driven. The data driven approach is the more popular of the two due to its precise results and intuitive foundational concept. The most common version of this approach is to scan reflective targets within the object scene and with known GLCS coordinates (Pesci and Teza, 2008) Since the point coordinates are known in both the SOCS and GLCS, a solution for the EOPs can be found via a least squares (LS) process that minimizes the sum of the squares of the 3D point coordinate residuals. It should be mentioned that when multiple scans are used to measure a single object, the point clouds from each scan must be registered in order to produce a single point cloud. Registration can be defined as the determinati on of the relative orientation (in the form of a coordinate transformation) between point clouds. The most common methods for automatic registration (without using scanner targets) are based on the Iterative Closest Point Method (ICP) (Besl and McKay, 1992) a rigorous point cloud

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22 matching algorithm that uses overlapping point cloud area s H owever, relative orientation can be achieved with as few as three common TLS points. Although there is some inconsistency in the literature, in this study absolute orientation of point clouds (scan to ground). Sensor driven techniques involve the integrat ion of observations from extra instruments These techniques can be divided into two sub categories, direct and indirect solutions. Direct solutions involve the measurement of all EOPs from extra sensors attached to the scanner, and indirect solutions in volve the use of extra sensors attached to scanner that provide only some information about the EOPs, and therefore must be combined with external information in order to resolve the full set of EOPs. An example of direct sensor driven georeferencing is t o measure the position of a scan station using GPS (providing translation) while simultaneously measuring angular orientation via a tilt sensor and a compass (Schuhmacher and Bohm, 2005) A common indirect sen sor driven technique is to rigidly mount a single GPS antenna on the laser scanner. If at least three stations are included in the survey, the GPS observations (with known SOCS and GLCS coordinates) can be used to georeference the registered point cloud. An important consideration when using this technique is the configuration of the scan stations with respect to each other. Poor geometry can adversely affect the precision of the solution (for example scan stations configured in a line). A technique cal led back sighting may also be used, where a single control poi nt is scanned. Back sighting can be considered a hybrid of sensor driven and data driven techniques. For instance, a tilt sensor and scanner mounted GPS can be used in

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23 addition to a single back sighted control target to resolve the scanner EOPs ( Reshetyuk 2009) Data driven techniques rely on extra and often cumbersome equipment. They are also sometimes not feasible or are dangerous due to extreme terrain or other safety considerations, and e xtreme terrains tend to be prominent subjects for TLS (e.g. (Bates et al ., 2008; Hunter et al. 2003; Rosser et al 2005; Rowlands et al 2003) ) On the other hand, s ensor driven techniques result in relatively low precision results due to poor geometry a nd redundancy of observations. The D u al Antenna System (DAS) Method In order to address the problems associated with current methods for TLS georeferencing, a direct s ensor driven technique was developed using a dual GPS antenna system dubbed the DAS. It was shown to resolve precise and comprehensive georeferencing parameters for TLS data without using any external control (Wilkinson et al ., 2010) The DAS method was designed for and implemented on both the R ie gl Z390i and vz400 laser scanner s Both scanners are composed of two main parts: the optical head that rotates during scanning a utomatically or by user command; and the base which is t he physical basis for the S OCS. In the case of the Z390i, a n aluminum bar is fixed using a telescopic mount on the scanner head with two GPS antennas on each end. See Figure 1 1 for a schematic illustration. In Figure 1 1, components labeled (1) and (2) are GPS antenna s that colle ct data through a r eceiver w hich stores the observations. Component (3) is an aluminum bar on which the antennas are mounted parallel to the SOCS y axis when the optical head is not rotated (the figure shows the c onfiguration at a 90 rotation), and (4) is a telescopic mount that connects the bar to the optical head of the scan ner. Component (5) is the

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24 optical head of the scanner that rotates during scan acquisition or by user command, and (6) is the scanner base that dictates the direction of the SOCS. S imilar GPS bar apparatuses were developed for both the Z390i and the vz400 using the same basic design except that they were mounted above (Z390i) and around (vz400) the camera mount to enable simultaneous image acquisition during DAS and scanner data coll ection. Figure 1 1. Schematic illustration for the Z390i mounted GPS bar For a more in depth description of the DAS method, please see (Wilkinson et al ., 2010) The fundamental idea of the DAS method is to use short baseline differential GPS from the scanner mounted antennas to observe vectors (from one antenna to the other) in the GLCS. These data and the ir corresponding SOCS vectors can be used to solve Equation 1 1 for ( 1 1 )

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25 In Equation 1 1 is the antenna to antenna vector in the GLCS, is the same vector in the SOCS, and is the rotation matrix from the scanner frame to the ground frame. During acquisition, t he head of the scanner (item 5 in Figure 1) and the attached antenna apparatus (items 1 4 in Figure 1) are rotated by the scanner operator to several rotational stops A t each stop the vector between antenna phase centers is known in the SOCS assuming acc urate calibration, thus its components can be used as and the GPS observations can be used as in Equation 1 1 Each stop contributes three observation equations towards solving for the angular components of the EOPs Although, since the rank of the rotation matrix is two, a minimum of two stops needed for an explicit solution The solution may be found via iterative nonlinear LS, although a linearized solution can be used and is reported in (Wilkinson et al ., 2010) Figure 1 2. The first prototype of the Dual antenna system

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26 After thorough simulation, the DAS method exhibited the capability of achieving precision of <1mrad for the three Euler angles with a practical number of stops. This was made possible due to th e high precision of short baseline differential GPS vectors. Further the DAS method was tested by comparing field results (Figure 1 2 is a picture of the scanner and DAS apparatus at the tim e of the field procedures ) against conventional data driv en meth It was found to have an RMS E of less than 1mrad for the total rotation of the SOCS with respect to the GLCS, confirming t he results of the simulations. A method for finding the positional EOPs has been developed for the DAS sinc e these experiments and is reported in this study. Recently, Paffenholz and Kutterer ( 2008) developed a similar dual antenna method. However, their method involves the direct georeferencing of individual scan lines based on the trajectory of scanner moun ted antennas, and was developed to only provide the azimuth of the scan direction, whereas the DAS provides the full set of georeferencing parameters of the entire point cloud. Close Range Photogrammetry Photogrammetry began with ground based imagery (Wol f and Dewitt, 2000), modern formulation was developed in the 1950s through early 1970s mainly by Duane Brown and J.F. Kenefick (Brown, 1971; Kenefick et al 1972) and the practice of close ra nge photogrammetry (CRP) came to fruition in the early 1990s (Fraser, 1998) Through innovations in digital camera self calibration, low cost cameras can be used for precise photogrammetric measurements (Fraser 1997) Advantages of CRP mirror those of TLS : these ground based images allow for observation of objects that cannot be seen from an aerial perspective.

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27 The close range bundle adjustment is the most rigorous and p erhaps most common method of solving for the EOPs for multiple camera stations and for reproducing 3D object scenes. The bundle adjustment is a batch process solution for all EOPs that minimize s the sum of the squares of the weighted residuals of image an d control observations. In other words, it provides the optimal (i.e. most probable) solution for the camera positions and orientations with respect to each other and the mapping coordinate system (simultaneous optimal registration and georeferencing). Similar to aerial LiDAR and aerial photography, CRP and TLS data are often collected simultaneously to provide the 3D size and shape, as well as the spectral information of objects. Typically, as in aerial integration, the images are merely the TLS derived su rfaces providing texture Surprisingly, the image information is normally not used to aid in georeferencing. This, despite the fact that imagery provides a huge number of precise tie points between scan stations that are relatively eas y to identify compared to tie points derived from TLS point clouds. There has been some recent research on integrating the CRP data with TLS data for georeferencing, although it has been geared mainly towards registering the point clouds. For example Al Manasir and Fraser ( 2006) presented a method for registering TLS data automatically using CRP By firmly mounting a camera on the scanner head (with known boresight and lever arm parameter (BLP) calibration), the method uses the photogrammetric relative orientation procedure to register the point clouds. Further research used the relative orientation solution to aid in finding tie points in the scan data. In other words, they used imagery to fi nd conjugate scan points towards registration as a more precise alternative to ICP. It is worthwhile to note that the

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28 aforementioned processes use a separate space resection procedure to resolve the BLP s In contrast Schneider and Maas ( 2007) showed the potential for TLS integrated imagery to aid in calibrating both the scanner and the camera with respect to adaptively weighting data observations and quantifying mechanical anomalies. An integrated bundle adjustm ent approach for registrat ion was also presented Their method is considered a registration technique, although it could be used for georeferencing if external control points (in the form of targets with known da tum coordinates) are introduced. A single adjustment solution is found for scan stations, camera stations, and 3D coordinates of object points. The observations are the spherical scan coordinates and image coordinates of coinciding object points (they used several reflective targets). All solved parameters are in the coordinate system of one of the scan stations thus it is a registration It should be mentioned that their method relies on external scanner references in the form of target points. Furthermore, their method did not account for th e camera being mounted to the scanner, and in some of their observations, the camera was not fixed to the scanner during image acquisition. Motivation The DAS approach has shown that a level of practical precision for TLS georeferencing parameters can b e obtained autonomously using direct sensor driven techniques However, there are benefits to improving the precision while maintaining its autonomy there by broadening the scope of applications for which it can be used while preserving its advanta ges over conventional methods Further, the DAS method was designed and tested for a single station setup (nullifying the impact of image measurement integration). This was the case because multiple stations allow for

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29 a simpler autonomous solution via th e single antenna sensor driven approach. This raises the following questions: How would a multiple station configuration be implemented using the DAS ? What improvement, if any, can be achieved as far as the precision of the georeferencing solution using t he DAS at multiple stations over the conventional single antenna sensor driven approach? How can image observations be integrated into a multiple station DAS georeferencing solution? How would image observations affect t he precision? Can image tie points s upplant scanner tie points while maintaining a practical level of precision? How would the addition of ICP observations affect the solution? Hypothesis/Objectives The literature indicated that t here is a mostly unexplored niche for autonomously georeferen ced TLS data. Typically, users are constrained to scenes that accommodate external control in the form of target points with known GLCS coordinates if precise georeferencing of point clouds is necessary Although the DAS method can provide a practical le vel of precision for many applications, it is hypothesized that integration of close range imagery with the scan data from multiple stations can significantly improve the precision of the DAS solution (and possibly best the conventional method for indirect sensor driven TLS georeferencing), thus increas ing the number of applications for which it can be used. In this study, the objectives were to develop a general model that exploits scan and image observations and integrate them with t he DAS method with t he goal of improving the DAS derived EOP precision while maintaining autonomy as much as possible. Since more precise scanner EOPs yield more precise point clouds, the obtaining more precise data from less intensive fieldwork

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30 The sp ecific objective s in this study are to analyze the performance of the designed integrated method under different circu mstances and levels of autonomy in order to quantify the contribution of different observations with respect to the precision of resolved scanner EOPs. The different configurations tested include adjustments with varying combinations of included observations: With and without reflective scanner targets o Scanner targets with known GLCS coordinates o Scanner targets without known GLCS coordinates o Backsighting a single scanner target with known GLCS With and without image observations o Image observations in the form of collinearity equations o Image observations in the form of coplanarity equations With and without ICP observations Different levels of DAS integration o High level DAS integration (EOPs serve as the observations) o Medium level DAS integration (individual stop vectors serve as observations) The different configurations are compared with each other using estimated standard deviations of r esolved EOPs and, when available, RMSEs of scanned points. In order to establish the significance of different estimated standard deviations, F tests are used to obtain confidence levels for difference of variance.

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31 CHAPTER 2 METHODS O pening Remarks on Methods This section describes the designed general mode l for integrating the sensor suite (scanner, DAS, and camera) data and the method used for performing simultaneous adjustment of the data towards resolving the scanner EOPs. Also included here are brief deri vations based on the physical relationships between the sensor data and associated objects Sensor Model Scanner Observations Scanner t iepoints Each scanned point measured at the th setup in the SOCS, has the form: If the rotation matrix from the GLCS to the SOCS at the th setup is the translation or position of the th setup of the scanner in the GLCS is and the position of the scanned point in the GLCS is we have the relationship shown in Equation 2 1 (assuming relative scale is unity between the SOCS and GLCS):

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32 (2 1) Similarly, if the same point is scanned from a separate scan station with we have Equation 2 2 : (2 2) Note that Equation 2 1 is composed of 3 observation equations (Eq uations 2 3, 2 4, and 2 5). (2 3) (2 4) (2 5) where: Point c loud m atching The relative orientation of scanner data may be obtained by matching of two or more point cloud datasets from different scan positions. The matching observation s are the difference of rotation (rotation from scanner system to scanner system and translation, (translation from station to station in scanner system The relationship between the observations is shown in Equation 2 6. (2 6) Equation 2 6 can be rewritten as the condition equation shown in Equation 2 7. (2 7 )

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33 Similar to the scanner point observations, Equations 2 3, 2 4 and 2 5, can be divided into three equations and Image Observations Collinearity c ondition Each imaged point measured at the th setup in the camera coordinate system (CACS) has the form If the rotation matrix from the GLCS to the CACS is the translation/position of the camera at the th setup is and the position of point in GLCS is We have the relationship in Equation 2 6 : ( 2 8 ) where is the focal length of the camera and is a scale factor. Since each side of E quation 2 8 can considered homogeneous co ordinates of a 2D point and perspective projected 3D point respectively, it can be reduced to 2 equations by dividing both sides by their respective third components. This cancels out the scale factor, and multiplying both sides by leads to the collin earity conditions

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34 shown in Equations 2 9 and 2 10. ( 2 9 ) ( 2 10 ) Coplanarity c ondition The coplanarity condition may supplant the collinearity equations and provide s some advantages, at the cost of some disadvantages, over the collinearity condition. Consider the position of the camera at two stations and Then the base displacement of the perspective centers of the camera is A point imaged at both stations will have the ray vectors (from perspective ce nter to point) and for stations and respectively. If and are coplanar then their triple scalar product is zer o (Equation 2 11 a ). (2 11 a ) Note that GLCS coordinates of imaged points are not used in Equation 2 11 a Therefore, initial approximations of these coordinates need not be obtained prior to

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35 nonlinear least squares adj ustment as when using collinearity, and t he coplanarity condition should not be used for points t hat are both scanned and imaged, or if the point has observed GLCS coordinates. In other words, in the case of imaged control points or any scanned point col linearity should be used. In cases where imaged points appear on more than two images, the sum of the absolute value of triple scalar products for each image pair should be used as in E quation 2 11b. (2 11 b ) where n is the number of images on which the point appears. Using E quation 2 11b instead of forming multiple instances of Equation 2 11 a avoids the dependency that arises from having multiple equations containing the same observations. For example, if a point is imaged at three stations one could form three instances of E quation 2 11 a However, any one of the equations could be removed and all stations involved could be adjusted mea ning there would be a trivial equation. It is worthwhile to note that the calculation of triple scalar products, or determinants, can lead to very large numbers and can affect the conditioning of the problem. This, among other inconvenient properties, h as led researchers to avoid the coplanarity condition. In terms of the linearized least squares adjustment, the ill conditioning can lead to seemingly oscillating solutions due to round off errors. However, if the a posteriori standard deviation of unit weight is not diverging, one can consider these periodic, oscillating solutions adequate although one must accept that a global minimum of the sum of the squared residuals has not been found

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36 Camera b oresight and l ever arm The boresight rotation matrix is defined as s uch that for all stations at all stops Note that multiple images may be used from a single station at different rotation angles of the scanner head. The matrix represents the orientat ion change of the scanner head due to stop rotation ( rotation about SOCS z). Thus the boresight alignment represents the rotation from the (rotated) scanner head system to the camera coordinate system (see Figure 2 1). Figure 2 1. Relationshi p between GLCS ( G ), SOCS ( S ), and CACS ( C ) The lever arm vector is defined as

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37 Thus represents the offset of the camera origin with respect to the scanner origin in th e CACS using GLCS units also known as the lever arm or lever arm offset These values along with their precisions, can be estimated using boresight and leverarm parameter ( BLP ) calibration techniques. They may then be included as unknowns in the adjus tment and as weighted a priori observations or can be held fixed based on calibration results Camera c alibration (interior) Equations 2 9 2 10 and 2 11 should use image coordinates corrected for radial and tangential lens distortion The distortion equ ations used in this research are based on the OpenCV camera distortion model shown in Equations 2 12 and 2 1 3 where : are the radial distortion coefficients ; and are the tangential distortion coefficients ; and are the non projected undistorted image coordinates ; and are the non projected distorted image coordinates ; and (2 1 2 ) (2 1 3 ) I f and are the (measured) projected image coordinates, the non projected distorted image coo rdinates can be calculated using Equations 2 1 4 and 2 1 5 ( and are the principal point offsets) (2 1 4 ) (2 1 5 ) An iterative solution for and can be found using E quations 2 12 and 2 1 3 Further description of th is procedure can be found in Chapter 4 By re projecting the undistorted coordinates as shown in E quations 2 1 6 and 2 1 7 and in these

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38 equations can be used as the image coordinates in observ ation E quations 2 9, 2 10, and 2 11 (2 1 6 ) (2 1 7 ) Note that there are two focal length values, and in order to compensate for possible scaling difference in pixel size in the x and y direction of the image. DAS Georeferencing Parameters Observations An essential characteristic of the DAS approach is the use of GPS observations. R elative positioning using kinematic carrier phase methods were used to obtain vectors between antennas F or absolute positionin g, kinematic carrier phase post processing was performed using the nearest corresponding CORS base station The datum of these CORS sites was NAD83 (CORS), Epoch 2002.00. The inclusion of DAS observations may be approached in differe nt ways. They can be included as simply the DAS derived solutions for and at each station (high level integration HLDAS ) the weighted average of vectors at each stop at each station (medium level integration ML DAS ) or th e individually measured vectors for each GPS epoch at each stop at each station (low level integration LLDAS ) Using high level integration, the observation equations are those shown in Equation 2 1 8 DAS derived values The variables and are sequential rotation angles about the X, Y, and Z axes, respectively.

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39 (2 1 8 ) Medium level integration use s observation equation s as shown in Equation 1 1 for each stop. Similarly, low level integration uses the same equations as medium level, except with multiple equations per stop (one per GPS epoch). Due to the cumbersome nature of using low level DAS integration, it is not explored in this study The large number of observations would greatly hinder the integrated adjustment, and since LLDAS measurements are highly correla ted, a complex approach would need to be developed to handle them properly. In order to establish position from the DAS the individual GPS antenna observations must be used as opp osed to the vector between them. Control Point Observations Control point observations have the formation shown in Equation 2 19 Similar to the DAS observations, the superscript directly measured values. (2 19 ) Sy stem Solution Since the some of the observation equations are nonlinear, the least squares solution is iterative and based on first Scanner Solution Tiepoints The linearized scanner tiepoint observation equations have the form shown in Equation 2 20

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40 ( 2 20 ) where is the Jacobian matrix for scanned point at s tation , and are Equations 2 3, 2 4, and 2 5 and , and are the values of , and computed using the initial/current approximations for the unknowns. is the solut ion vector and contains the update values to be applied at each iteration. is the residual vector. Point c loud m atching The linearized scanner point cloud matching observation equations have the form shown in Equation 2 2 1 ( 2 2 1 ) W here

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41 = is the Jacobian matrix for scan stations and is Equation 2 7, and , are the components of computed using the initial/current approximations of the unknowns. is the solution vector and contains the update values to be applied at each iteration. is th e relative EOP residual vector Note that Equation 2 21 is formulated as a general least squares equation due to multiple observations in Equation 2 7, thus represents a linear transformation of observati on residuals to residuals of Equation 2 7 Image Solution Collinearity c ondition The linearized collinearity condition image observation equations have the form shown in Equation 2 22 :

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42 ( 2 22 ) where is the Jacobian matrix for image point a nd are Equations 2 9 and 2 10 and and are the values of and computed using the initial/current approximat ions for the unknowns. is the solution vector and contains the update values to be applied at each iteration. is the residual vector. Note that updates to BLPs are included in the solution vector. The solution may be solved via ge neral least squares if the imaged point has measured ground coordinates. The equations for the elements of including BLPs are given in Appendix A. In certain cases, the lens calibration parameters are included as unknowns in the adjustment. Coplanarity c ondition The linearized coplanarity condition image observation equations have the form shown in Equation 2 23 :

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43 ( 2 23 ) w here Similar to the point cloud matching equations, a general least squares solu tion is used for the coplanarity contributions is the Jacobian matrix of partial derivatives of with respect to the EOPs of stations and is the Jacobian matrix of partial

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44 derivatives of with respect to the co ordinates of image point is Equation 2 1 1 a and is computed using the initial/current approximations for the unknowns. is the solution vector and contains the update values to be applied at each iteration. is t he residual vector. Recall that for points imaged on more than two stations E quation 2 11b is used. In this case, includes the partial derivatives of Equation 2 11b for the additional station(s) and includes the partial deriv atives for the addit ional image point coordinates. The equations for the elements of and as well as the partial derivatives with respect to the boresight and leveram parameters are given in Appendix B. DAS The linearized control observation equations from the DAS solution have the form shown in Equation 2 24 ( 2 24 ) where The superscript contains the residuals. Control Points The linearized control point observation equations have the form shown in Equation 2 25

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45 ( 2 25 ) where Simultaneous Solution Formulation The simultaneous adjustment of all measurements is performed using the matrices presented in this section The matrices were split into two pieces to facilitate viewing, however, they should be consider ed one larger matrix with one stacked on the other. The design matrix for scanner observations is Figure 2 2. The design m atrix for image observations is Figure 2 3. For these figures, t he number of scan points is t he number of image points is a nd t he number of stations is Note that the control design matrix for control point and DAS observations, is an Identity Matrix and is also stacked with the other two design matrices. It is important to note that i n Figures 2 2 and 2 3 the same symb ols contain different values depending on the row they are in. For example, the submatrix that is in the row with has different values than the one in the row that contains Certain submatrices will be all zeros (f or example if point does not appear on images at station ) and in the case that a row contains all zero s it is omitted. Also note that there may be overlap in columns that is not illustrated in the figures. For example, a scanned p oint may have image points associated with it In that case, the

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46 submatrix associated with that point will be in the same column as the associated with that point. The combined design matrix, along with the combined solut ion vector, and combined observation vectors, is used to solve the entire system via nonlinear least squares. Weights for observations are assigned as the inverse of the covariance matrix for all observations except the coplanarity condition equat ions and the relative scan (point cloud matching) condition equations, which, since they must be solved via a general least squares solution, are weighted based on the general law of propagation of variances. Equation 2 26 is the formula for the coplanari ty condition weight submatrix of the combined weight matrix for point where is the covariance matrix for image point measurements Similarly, Equation 2 27 is the sub weight matrix for the relative scan condition equations for scan stations and where is the covariance matrix for observed relati ve rotation angles and translation components ( 2 26 ) ( 2 27 ) The full, combined linearized system is shown in Equation 2 28. This system can be solved using the normal equations method, Equation 2 29 ( 2 28 ) ( 2 29 ) The vector contains the corrections to the current estimations of the unknown param eters which are updated, and a new Equation 2 29 is formed. The process is continued iteratively until convergence, when the corrections are negligible. This is often called the Gauss Newton method. In Equation 2 29, is the

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47 pseudoinverse of However, if is ill conditio ned, it is recommended that the normal equations not be formed directly because you are effectively squaring the ill conditioning. A better approach is forming the pseudoinverse using singular value decomposition (SVD). The process of SVD consists of decomposing a matrix (square or rectangular) such that there is the relationship in Equation 2 30. ( 2 30 ) In Equation 2 30, is a diagonal matrix, and and are h ave orthonormal columns, meaning they satisfy the equality shown in Equation 2 31. ( 2 31 ) The properties of these component matrices allow one to form the pseudoinverse of a matrix without squaring it and compounding any ill condit ioning. The pseudoinverse of a matrix , is shown in Equation 2 32 using SVD. ( 2 32 ) Thus, the SVD derived pseudoinverse can be multiplied by to find The a posteriori standard deviat ions of estimated values can be obtained from the covariance matrix shown in Equation 2 33. ( 2 33 ) where, if is the number of redundancies and is the residual vector The designed least squares adjustments in this study were implemented using C. With the exception of the ICP algorithm, which was implemented using Matlab, all computational processing steps were also implemented in C.

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48 Simultaneous vs. Sequential Solution The design and implementation of the simultaneous solution of these types of systems tend to be relatively complicated. This leads to the temptation to use a sequential solution. However, solving simultaneously for EOPs increases the accuracy of the sol ution by avoiding the accumulation of errors from each successive step. The following is a short experiment to illustrate this point with data used later in this study. A scanner was set up at five different stations and collected laser data at each, incl uding seven common target points with the configuration shown in Figure 2 4 where all units are in meters. Three of these points served as control points. An orientation solution for all of the scanner stations was performed using three different method s: 1. Sequential solution 2. Simultaneous solution without multiple overlap of tie points (i.e. tie points were not associated with more than two scans) 3. Simultaneous solution with multiple overlap (i.e. tie points can be associated with more than two scans) The sequential solution consisted of sequentially finding the relative orientation between stations and applying the solved transformation to each subsequent scanner point coordinates until all tie points were transformed to a common arbitrary scanner coordina te system. These points were then transformed to the control coordinate system using the three target control points. Although most of the scan points were observed from more than two scan stations, the first simultaneous approach assumed that tie points were never in more than two scans. This was done to show that even if the simultaneous solution did not account for tie points being observed at more than two stations, as the sequential approach did not, it would still yield a better solution. In other words, it creates a fairer

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49 calculated coordinates are based on observations from two stations, as with the sequential approach. In addition, to avoid bias in the comparison, th e first simultaneous approach used the same control points from the same scan stations as the sequential approach. Finally, the second simultaneous approach allowed for tie points, including control points, to appear on more than two scans. The results o f the experiment, shown in Table 2 1, consist of the RMSE values of five points with known ground coordinates not used as control points in the adjustments. This experiment shows that the simultaneous solution yields more accurate results than the sequen tial method. In fact, the first simultaneous method had nearly twice the accuracy as the sequential approach when using the same control points and assuming that tiepoints appeared on less than three scans. The second simultaneous approach was superior t o both of the other methods, especially in the Z component, which is due to the higher redundancy in point observations. A scheme for allowing multiple tie point instances in a sequential solution may be implemented, granted it would approach the complexi ty of design of the simultaneous approach, and would probably net more accurate results than the sequential approach presented here, the simultaneous solution would most likely still be more accurate.

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50 Figure 2 2 Scanner o bservation d esign m atrix

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51 Figure 2 3 Image o bservation d esign m atrix

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52 Figure 2 4 Simultaneous vs. s equential e xperiment c onfiguration Table 2 1. Root mean square values of points using different method s of adjustment Method RMSE X (m) RMSE Y (m) RMSE Z (m) Sequential Approach 0.006 0.00 7 0.05 4 Simultaneous Approach 1 0.00 3 0.00 4 0.03 1 Simultaneous Approach 2 0.002 0.00 3 0.0 06 457025 457050 457075 457100 457125 155275 155300 155325 155350 155375 155400 Simulataneity Experiment Configuration Target Points Scanner Stations Target Control Points

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53 CHAPTER 3 DATA COLLECTION Two data sets were used to test th e integrated method. The project sites, the sensors used, and the scanner configurations were different for each data set. This chapter provides a description of the data collection procedures implemented for both sites, and highlights the differences be tween each to supplement the comparison of the subsequent adjustment results. Corry Village Site Corry village is located on the University of Florida campus. A large scale laser scan survey was undertaken with DAS data collected at preselected stations i n July of 2009 Corry Village is characterized by large oak and pine trees within and surrounding the site (see Figure s 3 1 and 3 2 ) This le d to poor GPS data and therefore relatively low precision in both the establishment of target control points and DAS data Laser Scan Data TLS data were collected at 32 stations in and around Corry Village using two Riegl z390 i s. Prior to scanning, 17 control points were established in the project area using GPS with average accuracy of about 1 cm horizontal and 2 c m vertical. Reflective t argets were set up on these control points and were scanned in addition to 34 reflective tiepoint targets with arbitrary coordinates. The scans were collected with a 24.1 kHz pulse rate, and a scan angle of 80 degrees for a full 360 degree panorama sweep. Each scan consists of between three and ten million points depending on the environmental surroundings at each station.

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54 DAS Data Of the 32 scan stations, DAS data were collected at four along the western most road (see Figure 3 2). The western most road was selected because it facilitated the collection of common tiepoints, both from scans and images, for several stations and because it had the most open view of the sky. Of the 17 total control points, six were viewable by the DAS station scans in addition to four arbitrary coordinate tie points. At each DAS station, the scanner head was rotated at 15 degree increments and stopped for 30 seconds at each stop. The GPS receivers collected data during and after scan acquisition a s well. In preliminary testing of the system (Wilkinson, et al., 2010) the first DAS bar prototype was attached directly on the scanner using the camera mount (shown in Figure 1 2). In order to al low for simultaneous acquisition of imagery during DAS collection, the second prototype of the DAS bar system was used at the Corry Village site. The bar consisted of a light aluminum L bar mounted above the camera (DAS 2.0), shown in Figure 3 4. A detai led description of the DAS collection procedure can be found in Appendix G. Imagery Ten digital pictures were taken at every DAS station using a Nikon D300. The images were taken at 36 degree rotation intervals of the scanner head, and have about ten perc ent overlap. Mounting and interior orientation calibrations were performed prior to data collection. Exemplary of typical photography in this data set, the images in Figure 3 1 were taken from the scanner mounted camera.

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55 Orlando Site In May of 2010, the second data collection mission was carried out at the Riegl USA offices in Orlando, Florida. In contrast with the Corry Village site, this site has very few trees and a large field next to the office buildings (see Figure 3 5). In addition, there are se veral high precision ground control points in the surrounding parking lot and field that serve as a calibration/test network for their stable of scanners. Laser Scan Data The smaller, more portable vz400 laser scanner was used in Orlando. Five station pos itions were selected based on view of the sky, tie point availability, and geometric strength. The TLS data were collected with a scan angle of 80 degrees for a full 360 degree panorama sweep. Each scan consists of between three and ten million points ba sed on the surroundings at each station. An example single station point cloud is shown in Figure 3 6. Seven points in a control point network were occupied with scanner targets. The average accuracy of these control points was <1.0cm horizontal and abo ut 1.0 cm vertical. In addition to these, two arbitrary coordinate tiepoint targets were placed in the project area. DAS Data DAS data were collected at each of the five stations in Orlando. The layout of the site allowed for good to excellent views of t he sky at each station, and to use a setup configuration with increased geometric strength compared to the Corry Village pattern. Also in contrast with the Corry Village set, the lack of trees also enabled scanning large areas of building corners, thus al lowing for viable point cloud matching patches to be extracted from the data. At each DAS station, the scanner head was rotated at 15

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56 increments and paused for one minute at each stop. The GPS receivers collected data during, before, and after scan acqu isition as well. For the Orlando data collection mission, a third DAS bar prototype (DAS 3.0) was designed and fabricated for use with the vz400. Figure 3 7 shows the DAS 3.0 during acquisition in Orlando. A schematic drawing of the bar is included as A ppendix C. The DAS 3.0 bar was much sturdier than prior iterations of the design. It consists of two aluminum box beams fixed to the top of the scanner close to the origin of the SOCS increasing the precision of the DAS derived position (discussed in det ail in Chapter 4). Imagery Seven digital pictures were taken at every DAS station using a Nikon D700 mounted to the top of the scanner. The images were taken at ~15 rotation intervals of the scanner head with about ten percent overlap between contiguous frames. As with the Corry Village data set, mounting and interior orientation calibrations were performed prior to data collection.

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57 Figure 3 1. The e astern entrance (left) and interior (right) of Corry Village on the UF campus. Both image s were taken from the scanner mounted camera.

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58 Figure 3 2 Corry Village at the University of Florida DAS data were collected at four stations along the western most road (Source: Google Earth)

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59 Figure 3 3. Scan data from Station 1 of the Corry Village data set. Points in this image are shaded based on intensity of return.

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60 Figure 3 4. The DAS 2.0 mounted on a Riegl z390i

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61 Figure 3 5 T he Riegl USA office building

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62 Figure 3 6. Scan data from Station 2 of the Orlando data set showing the locati on of the scanner in SOCS Figure 3 7 The DAS 3.0 mounted on a Riegl vz400

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63 CHAPTER 4 PROCESSING Several processing steps were applied to the scan data, imagery, and DAS data prior to including them in the simultaneous integrated georeferencing metho d. This chapter describes these steps in detail. Also included are their results and some analysis of them with respect to the overall method. Scan Data Multistation Adjustment Mutistation adjustments of the TLS data were performed for both datasets. Si nce this method on its own results in very precise results for scan station EOPs, it was used to benchmark some of the results of the other methods. Simply, multistation adjustment is a simultaneous solution of scan station EOPs and GLCS coordinates of re flective targets acquired during scanning requiring a minimum of three common targets per station and three control targets over the entire project area The design matrix for the adjustment is shown in Figure 4 1. Note that the Orlando data set resulte d in more precise standard deviations than Corry Village for the multistation adjustments average standard deviations, most notably for This was likely due to the superior geometric configuration in Orlando and better GPS reception, due to fewer obstr uctions, leading to more precise control points. Notice in Figure 4 2, a plot of scan stations and targets for the Corry Village project, that the stations and targets are distributed mostly in the North South direction with exception of only one control target located well to the east. This configuration explains the weak resolution of rotation about the (once rotated) y axis, relative to the other angular EOPs. The plot of scan stations and targets for the Orlando project shown in

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64 Figure 4 3 displays much stronger geometry with well distributed targets throughout the project area The results of the multistation adjustment for Corry Village and Orlando are shown in Tables 4 1 and 4 2, respectively. Point Cloud Matching ICP was used to find the relative orientation between stations in the Orlando data set. Several common building co rners and facades were selected as the objects of comparison between scans. Due to occlusion of these suitable objects by trees and other buildings, only adjacent scans were processed. That is, Station 1 was compared with Station 2, Station 2 was compare d with Station 3, and so on. The first step involved segmenting the point clouds to include only the areas to be compared. Examples, from Stations 1 and 2 of segmented point clouds, are shown in Figure 4 4. Notice that the tree shadows are dissimilar i n each set due to the differing perspectives from each station. In preliminary testing, areas without any occlusion were segmented and processed, such as the corner of the building in Figure 4 4, the same building in the center of the image in Figure 4 3. However, using larger sets, regardless of gaps due to occlusion, was found to yield better results. There are many variants of the ICP algorithm. The one used in this research can be summarized in the following steps where the input is two point clouds (Cloud 1 and Cloud 2), and the output is the (3D conformal) transformation parameters that align Cloud 2 with Cloud 1 : 1. The point clouds are initialized by translating Cloud 2 so that its average point coordinates are equal to those of Cloud 1 2. For each poin t in Cloud 2, the nearest neighboring point is found in Cloud 1

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65 3. Using each pair of points generated in Step 2, a least squares solution for the transformation parameters is found that minimizes the sum of the squared distances between point pairs 4. The trans formation found in Step 3 is applied to Cloud 2 5. Step 2 through 4 are repeated until the solution converges or a maximum amount of iterations is reached Note that Cloud 1 should have more points than Cloud 2. Thus when comparing point clouds, the more dens e of the two was always selected as Cloud 1. Figures 4 5 through 4 8 illustrate an example of the ICP algorithm results. Figure 4 5 shows the relative position of segmented point clouds for Stations 2 and 3 prior to transformation. Figure 4 6 shows the i ndividual segmented point clouds used for the ICP algorithm. Figure 4 7 shows the segmented points clouds after transforming them using the results from the ICP algorithm. Figure 4 8 is a rotated view of Figure 4 7 showing the offset from misalignment in the ICP solution. Observation of Figure 4 8 shows that significant error exists in the ICP solution. In order to evaluate how well the algorithm worked, the results of ICP matching were compared with the solution obtained from the multistation adjustment. The parameters error. Table 4 3 shows the calculated errors in the ICP solutions. Inspection of Table 4 3 shows that results for the station pairs (1,2) and (2,3) we re more accurate than station pairs (4,3) and (5,4). A probable explanation for this is the position of the matched objects with respect to the scan stations. In the case of Stations 1, 2, and 3, they have very similar perspectives of the object used for matching between them (the building in Figure 3 4 and 4 3). Thus, gaps caused by occlusions (from not only trees, but also square faade details) are very similar for these stations. However, stations pairs (3,4)

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66 and (4,5) have more dissimilar perspecti ves of the building, and therefore more significant differences in the data gaps caused by occlusion. This reveals a dilemma with ICP for relative orientation of scans: the object used for ICP must have sufficient texture and unique shape so that a definit ive match can be found, and at the same time, the scans being compared should have many points representing the same areas (specifically critical areas such as corners). The difference in perspective between scans can lead to shadowing, and therefore thes e two conditions can preclude each other. Another issue with ICP, is that when estimating the precision of matching results, it is assumed that conjugate scan points are the same point in object space, which is not the case. Thus, an empirical method for estimating the standard deviations of relative orientations of scans should be used, which is not a trivial task when faced with multiple combinations of diverse point clouds. However, regardless of these difficulties, under ideal circumstances and illu strated in the results in Table 4 3, ICP can yield some practical results. The angular orientation parameters for station pairs (1,2) and (2,3) had errors that were less than one standard deviation of the precision expected from the DAS. Thus, relative or ientation via ICP matching has the potential to increase the precision of EOP resolution when included as an observation in the adjustment. Imagery Image Point Acquisition Image tiepoints were measured manually using CAD software for images from both sites The points were measured manually in order to optimize their spatial distribution and avoid other problems associated with automated methods for terrestrial image matching on images with large amounts perspective difference. The Corry

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67 Village imagery y ielded 308 individually measured image points from 47 unique object space points, while the Orlando imagery had 320 individually measured image points from 73 unique object points. The reason for the higher number of object points in the Orlando data was that the stations were located on sometimes opposite sides of buildings or trees preventing the appearance of common tiepoints. The environmental characteristics of the sites, use of different cameras and different mounts also influenced how the points we re distributed in the images. Notice in Figures 4 9 and 4 10, plots of all image point locations for Corry Village and Orlando respectively, that the points from images are evenly distributed along the y axis and tend toward the center of the image along the x axis (note that the cameras were mounted in portrait orientation, so the horizon appears parallel to the y axis). This is because most suitable features were located in these areas of the images (see Figure 4 11 for illustration). In addition, the localization is more pronounced in the Orlando imagery due to the camera having a shorter focal length, and imaged objects farther from the scan stations. The best case scenario would be to have evenly distributed points across the format of the image i n order to create strong geometry of the network, leading to better resolution of the unknown parameters, EOPs, BLPs, and camera calibration. Figures 4 12 and 4 13 show the distribution of image points in GLCS for Corry Village and Orlando, respectively. include two image tiepoints located very far from the other points in order to make it easier to see the majority of the points. The omitted points were located at Easting and Northing coordinates ( 1 93.291, 610.415) and (22.572, 188.981). Comparison of

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68 Figures 4 12 and 4 13 shows that the Orlando project area had a much wider object space distribution of imaged points, whereas the Corry Village data had image points located within only a 50m wide Nor th South corridor. After the points were measured on the images, the camera calibration parameters provided by Riegl USA were applied to all of them in the manner shown in Equations 2 12 and 2 13. As mentioned in Chapter 2, this process is iterative, and is described here: First, the undistorted, non projected image coordinates, ( are initialized using the measured image coordinates by: Next, th e following steps are repeated until the solution converges (corrections become negligible): { } After convergence, the undistorted coordinates are reprojected using Equations 2 16 and 2 17. The calibration parameters used in this study are shown in Table 4 4.

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69 The aver age linear displacement from lens distortion was calculated as 11.23 pixels in the Corry Village imagery and 14.46 pixels in the Orlando imagery with maximum displacements of 49 and 75 pixels for each respectively. Initial Bundle Adjustments In order to check for blunders and to validate the camera calibration parameters, bundle adjustments were performed on both data sets. Initially, tiepoints from different images taken from the same station were included, however, these led to instability of the adju stment when the points did not occur on images taken from different stations and were therefore removed. In order to solve for the scanner stations as opposed the camera stations, was used where was initialized b ased on previous observations of boresight and leveram (see Table 4 5) and the scanner head orientation angle, at the time of exposure. In order to validate (or improve) the camera calibration parameters, focal lengths, and principal point offsets were included as unknowns. At first, radial lens distortion coefficient was included as an unknown; however, due to lack of redundancy, poor orientation diversity, and limited image point distribution, adjustments including this parameter diverged. Th e control for this modified bundle adjustment included only targets with known object space coordinates. The bundle adjustments for each location, both Corry Village and Orlando, consisted of seven imaged control points. The design matrix used in these b undle adjustments is shown in Figure 4 14. Initial approximations for pass point coordinates were found using space intersection based on estimated EOPs for each image. By observing image coordinate residuals for the first few attempts at adjustment, a ha ndful of blundered image point observations were found and removed. Final bundle

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70 adjustment results indicated standard deviations of image coordinate measurements to be about 1.0 and 0.6 pixels for the Corry Village and Orlando data sets, respectively. Scanner EOP resolution and boresight and leveram constraint Analysis of the bundle adjustments indicated a very strong correlation between some of the boresight and leveram calibration parameters and the EOPs of the stations. Tables 4 6 and 4 7 show the correlation matrices for the BLPs with themselves, and with station EOPs, respectively for the Orlando data bundle adjustment, where: Because of the intuitive geometrical explanation, the first pair of correla ted parameters to consider is BLP and station EOP This dependency exists because all scanner stations are oriented nearly vertical, thus, a constant change in for all stations can be nearly compensated for by equal change in (recalling that images were taken in portrait orientation, resulting in camera and scanner being nearly parallel) Similarly, the correlation between and is due to the slight angle from horizontal of the camera with respect to SOCS when mounted on the vz400 resulting in a compensating change in as changes, and vice versa Since is correlated with and is correlated with is necessarily correlated with This high correlation does not exist in the Corry Village data set beca use the z390 camera mount results in a very nearly horizontal camera pose with respect to SOCS Less intuitively, boresight angles and are highly correlated with station EOP ( is too, although to a lesser degree) Figure 4 15 shows the cha nge in BLPs needed to represent the same camera pose as changes illustrating the correlation This plot was created by first developing the matrix assuming

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71 and using the calibrated BLPs shown in Table 4 5. Change in to be applied to the rotation of the system can be considered rotation about the non rotated SOCS Z axis, or negative azimuth, of the tilt swing azimuth system of rotation (Wolf and Dewitt, 2000). The value of was increased successively in small increments of 0.1 and the corresponding rotation matrix was formed. Derived from this rotation matrix, the new values of the BLPs were differenced from the previous values providing the change in each parameter needed to compensate for change in An other way to understand t he and correlation is to consider that the twice rotated z axis is nearly aligned with the non rotated x axis under the configurations for both the Corry Village and Orlando data sets (Table 4 5). The correlation between t he BLPs themselves can simply be explained by the fact that if two parameters are correlated with another parameter, they are necessarily correlated with each other. Interestingly, even when relaxing the calibration parameters in the adjustment (including them as unknowns in the adjustment and as observations with very small weights a priori standard deviations of 90 for the angles and 10 m for the leveram distances), the bundle adjustment converged on relatively precise solutions for the GLCS coordinates of imaged pass points. The median a posteriori standard deviations were 2cm horizontal and less than 1cm vertical for the imaged pass points. The standard deviations of image point residuals were 0.40 pixels and 0.25 pixels for x and y coordinates, respec tively, in the Orlando data set. The results, in value and precision, were found to be the same for adjustments with loose and constrained boresight and leveram calibration parameters. This can be attributed to the compensation in the resolved scan stati on EOPs for non constrained BLPs. In other words, the EOPs of the

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72 camera can be found regardless of precise knowledge of where the camera is relative to the scanner. resolution of s can station EOPs, and therefore the absolute accuracy of scanned point cloud locations. In order to observe how constraining boresight and leveram values affect the a posteriori standard deviation of scanner station EOPs, several adjustments of the Orland o data set were executed with different handling of BLPs, the results of which are shown in Table 4 8. Observation of Cases (2) and (3) in Table 4 8 shows that regardless of a priori estimation/weighting of the boresight leveram parameters, the resulting standard deviation of scan station EOPs and are the same as in Case (1). Thus, tilt of the scanner (the combination of and ) can be resolved using CRP with very limited knowledge of BLPs. However, due to the aforementioned correlation loosely constrained (given relatively high esti mated a priori standard deviations) boresight and leveram parameters resulted in much higher standard deviations for and in Cases (2) and (3). This is because the scanner stations are oriented nearly vertical, that is, the component of SOCS is nea rly aligned with the component of GLCS. In (Wilkinson et al. 2010) it was shown that, due to the geometry of the system, and (essentially scanner tilt) had significantly higher standard d eviations than (essentially scanner azimuth) for DAS solutions. Thus, even without knowledge of the boresight leveram parameters, CRP can make a positive contribution to the resolution of the EOPs that are most weakly resolved from the DAS. Also note Table 4 8 shows that constraining either or and no other parameters (Cases (4) and (5) respectively), leads to improved precision of albeit not

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73 quite as precise as when constraining all parameters. Although, constraining improves prec ision as in Case (6), it is still an order of magnitude less precise than when constraining either of the other two boresight angles. Case (7) shows that constraining (or because of correlation) and all leveram parameters leads to station EOP pre cision of solution nearly identical to the results of full boresight and leveram knowledge. Case (8) shows that constraining and leads to precision nearly the same as that of Case (7). Since is not highly correlated with any EOPs, the relati vely high standard deviations in Case (9) are as expected. Finally, Case (10) had results similar to Case (8) except for the resolution of The higher standard deviation of this EOP is explained by the lower correlation coefficient for and comp ared to that of and (see again Table 4 7). These observations lead to the simplification of BLP calibration. With as few as two measured values (in the case of the Orlando data set, and ), station EOP post adjustment precision of bundle adj ustments is comparable to when using full a priori calibration. Further analysis of BLP calibration can be found in the Chapter 5. DAS Orientation The major advantage of the DAS is its ability to find the angular orientation in addition to the position of the platform using GPS. The basic processing scheme of the system data is given in (Wilkinson, et al., 2010) Further description of the scheme including refinement of the procedure since that pub lication is described here. Stops Processing DAS using the stops method involves 4 steps: 1. Calibration (pre mission)

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74 2. Segmentation of the raw GPS data into stops corresponding to scanner head rotation angle 3. Blunder detection 4. Solution Calibration of the DAS involves finding three constants (illustrated in Figure 4 16): the difference in height of the antennas in the SOCS, which should remain constant for all stops due to the assumption of rotatio n about the z axis of the SOCS. the radi us of the horizontal circle (in SOCS) traced by each DAS vector the stop bias, which is the angle between the y axis of the SOCS projected onto the horizontal circle and the horizontal component of the vector at the zeroth stop ( = 0) With these parameters, the vector for each stop can be calculated, an d thus Equation 1 1 can be formed for each stop of the scanner head. T he calibration parameters can be found by first finding for several stops, then appl y ing a transformation from the GLCS to the SOCS This transformation can be found via the convential method ( scanned target points with know n GLCS coordinates). The vertical component of the resulting vectors can be averaged to find the horizontal components can be used to solve for and the average angular offset for each stop can be used to find Note that is shown in Figure 4 16. This parameter is not used in orientation calibration, but is used when calibrati ng for position determination from the DAS. It is described in the Position section. The calibration results for both data sets are reported in Table 4 9. Since the GPS data are collected continuously at each station, the vectors must be segmented into st ops. Figures 4 17 and 4 18 show the raw DAS GPS data for stations at Corry and Orlando respectively. Segmentation was done by grouping vectors with close coordinates (<0.01m) and assigning values based on the time they

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75 were recorded in comparison with the field log. Stops with very poor vector precision due to loss of satellite reception from trees or other obstructions were removed. give a single vector per stop (Figure 4 19). ( 4 1 ) ( 4 2 ) ( 4 3 ) The DAS solution of the angular components of the scanner EOPs using the method from (Wilkinson, et al., 2010) are reported in Tables 4 10 and 4 11. Figure 4 20 illustrates the asymptotic relationship betw een numbers of stops and solution standard deviation also described in (Wilkinson, et al., 2010) Examination of Tables 4 10 and 4 11 shows that the Orlando data had more precise DAS results than the Corry Village data. This is most likely due to the Orla ndo site having less obstructions of the sky leading to better satellite signal reception and more useable vectors. Comparison of Figures 4 17 and 4 18 shows that the raw Orlando DAS data have much less noise than the Corry Village DAS data. This, and th e Corry Village stops were 30 seconds long whereas at Orlando, the stops lasted one minute. Also, note that as previously mentioned the values were more precise than the tilt components in both data sets.

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76 Tilt using all observations method The weakness of the tilt components, and of the DAS solution led to the development of a method for isolating them. Starting with the original DAS equation, Equation 4 1, we can isolate the z component of the SOCS vector, Equation 4 2. Expanding this relations hip by using the definition of the rotation matrix, we can form Equation 4 3. The advantage of using this observation equation is that there need not be any knowledge of and to find a solution for and This means that the stop angle, is also unnecessary. Instead of segmenting the data into stops at each station, we can use any valid DAS vector observation occurring during the occupation of the station, greatly increasing the number of observations, and thus the precision of the so lution. However, the post adjustment standard deviations for this method proved to be very optimistic after comparison with more precise conventional TLS georeferenced data. This is most likely due to correlation between GPS measurements. In the adjustm ent, this is not taken into account, and thus the redundancy number is calculated higher than it is in reality. In order to validate the improvement of the tilt isolation method over the stops method, RMSE of the stops method and the tilt isolation method are compared and shown in Table 4 12. A multistation adjustment of the Orlando data set using the conventional method (scanned targets) is treated as truth in these RMSE calculations. The standard deviations of the multistation adjustment were on the ord er of 0.010 and 0.015 for and respectively. Inspection of Table 4 12 shows a marked improvement in overall RMSE by using the tilt isolation method versus the stops method. Calculated F statistics for and were F (4,4) = 1.467, p < 0.36 and

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77 F (4,4) = 3.754 p < 0.11 respe ctively. Due to the small sample size, it can be said the variance of using the tilt isolation method is significantly smaller than that for the stops method with only a 7 4 % confidence level. However, the variance of using the tilt isolation method is significantly smaller than for the stops method with 89 % confidence. It is expected that a larger sample size would yield a higher confidence level of the improvement of the tilt isolation method, but unfortunately the Corry Village multistation adjust ment solution yielded tilt component standard deviations too high to be treated as truth towards calculating RMSE (0.038 and 0.156 for and respectively). Position Obtaining position from the DAS requires known positions of each antenna in the SOCS. Since the DAS apparatus rotates about the Z axis of the SOCS, a method is used to simplify the calibration. Only a single calibratio n parameter is needed: the balanced stops stops with angles 180 opposite of one another. This parameter is illustrated in Figure 4 16. Balanced stops are used in case one antenna has a different horizontal distance from the SOCS origin than the other. Taking the average of balanced stops will cancel out this bias. The calibration parameter can be found by using the conventional method to find the transformation from GLCS to SOCS a nd applying it to the position of the antennas obtained by GPS. By taking the average of the antenna positions measured by GPS at balanced stops , the position of the scanner, can be found by adding the rotated SOCS height offset as shown in Equation 4 4. ( 4 4 )

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78 Note that in Equation 4 4 the precision of position depends on the resolu tion of the angular orientation, and the distance So, for example, a 1 error of tilt in the Corry Village configuration (Riegl z390i, DAS 2.0), leads to a 0.014m error in position, whereas the same angular error in the Orlando configur ation (Riegl vz400, DAS 3.0), leads to 0.002m error in precision. Table 4 13 shows the DAS position calibration parameters, and Tables 4 14 and 4 15 show the solution for position from the DAS for the Corry Village and Orlando data sets respectively. Als o included are the RMSEs based on the conventional approach solutions. Note that the X component of position in the Corry Village position solution is less precise than the Y component. This is most likely due to the poor resolution of DAS derived (compared to ) combined with the relatively large value. Figure 4 1. Multistation a djustment d esign m atrix

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79 Figure 4 2 Corry Village s can s tation and t arget n etwork Units are in mete rs.

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80 Figure 4 3. Orlando s can s tation s and t arget n etwork. Units are in meters.

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81 Figure 4 4 Segmented areas of scan data used for ICP analysis. The top image is from Station 1, the bottom image is the same area from Station 2.

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82 Figure 4 5. The relative position of segmented point clouds for Station 3 (blue) and Station 2 (magenta) in their respective SOCSs Figure 4 6. Individual segmented point clouds from Station 3 and Station 2 prior to applying the ICP solution

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83 Figure 4 7. Individu al segmented point clouds from Station 3 and Station 2 after applying the transformation from the ICP solution

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84 Figure 4 8. Individual segmented point clouds from Station 3 and Station 2 after applying the ICP solution with the view rotated to il lustrate misalignment in the ICP derived transformation

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85 Figure 4 9 Overlay of image point locations (on the images) for the Corry Village data set in pixel coordinates 0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2000 2500 3000 3500 4000

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86 Figure 4 10 Overlay of image point locations (on the images) for the Orlando data set in pixel coordinates 0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2000 2500 3000

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87 Figure 4 11 Example of image point distribution in a single photo from the Orlando data set (image is clipped and rotated)

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88 Figure 4 12 Horizontal d istribution of i mage p oints in GLCS for Corry Village. Units are in meters. 100 50 0 50 100 150 200 250 100 50 0 Scanner Stations Tie Points Control Points

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89 Figure 4 13 Horizontal d istribution of i mage p oints in GLCS for Orlando. Units are in meters. 100 50 0 50 100 150 200 250 150 200 250 300 350 400 Scanner Stations Tie Points Control Points

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90 Figure 4 1 4 Design matrix for the initial bundle adjustments Figure 4 15. Changes in BLPs needed to r epresent the same camera pose as EOP changes 6.0000 4.0000 2.0000 0.0000 2.0000 4.0000 6.0000 0.0 0.2 0.4 0.6 0.8 1.0 Change in BLP ( ) Change in

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91 Figure 4 1 6 Illustration of the calibration parameters for the DAS system

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92 Figure 4 1 7 Raw DAS GPS vectors for a typical Corry Village station Figure 4 1 8 Raw DAS GPS vectors for a typical O rlando station

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93 Figure 4 1 9 Averaged stop vectors for a typical Orlando station Figure 4 20 Standard d eviation of DAS derived EOPs vs. n umber of s tops 0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 5 10 15 20 25 30 Standard Deviation ( ) Number of Stops Omega Phi Kappa

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94 Table 4 1. Corry v illage m ultistation a djustment s olution Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) ( m ) ( m ) ( m ) 1 1.154 1.308 178.746 78.003 150.113 32.845 0.016 0.084 0.009 0.009 0.008 0.027 2 0.122 1.660 91.193 70.359 117.351 31.933 0.015 0.084 0.007 0.008 0.008 0.020 3 0.149 0.404 82.911 73.408 92.446 30.837 0.018 0.021 0.007 0.009 0.008 0.021 4 0.226 0.267 81.712 74.031 39.930 29.412 0.014 0.076 0.006 0.008 0.007 0.021 0.016 0.066 0.007 0.008 0.008 0.022 Table 4 2. Orlando multistation adjustment solution ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) ( m ) ( m ) ( m ) 1 0.092 0.209 99.839 296.899 39.908 31.592 0.007 0.018 0.006 0.005 0.004 0.009 2 0.333 0.033 94.004 279.706 67.467 31.815 0.007 0.018 0.006 0.003 0.005 0.013 3 0.060 1.547 147.343 306.619 100.615 31.889 0.007 0.008 0.005 0.003 0.003 0.005 4 0.398 0.560 140.059 360.454 104.444 32.317 0.013 0.010 0.006 0.003 0.003 0.005 5 0.972 0.062 45.074 363.290 40.199 32.301 0.012 0.012 0.005 0.004 0.003 0.008 0.009 0.013 0.005 0.004 0.004 0.008 Table 4 3. Error in ICP s olutions with respect to the r elative EOPs between stations Stations ( ) ( ) ( ) X (m) Y (m) Z (m) d (m) 1,2 0.03 9 0.01 4 0.021 0.008 0.018 0.05 5 0.058 2,3 0.01 7 0.019 0.007 0.004 0.01 2 0.006 0.014 4,3 0.081 0.236 0.37 6 0.168 0.21 3 0.04 6 0.27 5 5,4 0.8 50 0.03 1 0.111 0.13 1 0.202 0.57 8 0.62 6 Table 4 4. Camera c alibration p arameters in pi xels. Corry 3692.88 3693.8 9 2165.29 1455.04 0.1148 0.1020 0.0053 0.0002 0.0004 Orlan do 2410.48 2413.02 2126.65 1427.19 0.1060 0.3734 0.9230 0.0006 0.0005 Table 4 5. Initial b oresight and l ever arm c alibration parameters ( ) ( ) ( ) (m) (m) (m) Corry 82. 14 88.60 98.06 0.262 0.005 0.034 Orlando 6.81 79.51 173.047 0.160 0. 003 0.022 Table 4 6. Correlation m atrix for BLPs 1 0.99511 1.00000 0.00000 0.00001 0.00000 0.99511 1 0.99511 0.00001 0.01678 0.00036 1.00000 0.99511 1 0.00000 0.00002 0.00000 0.00000 0.00001 0.00000 1 0.40600 0.99993 0.00001 0.01678 0.00002 0.40600 1 0.40281 0.00000 0.00036 0.00000 0.99993 0.40281 1

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95 Table 4 7. Correlation m atrix for BLPs and EOPs of s tation 1 of the O rlando d ata s et (indicative of correlation for all stations) 0.00000 0.00001 0.99998 0.00000 0.00000 0.00000 0.01720 0.00492 0.99515 0.01797 0.00085 0.00001 0.00001 0.00001 0.99998 0.00000 0.00000 0.00000 0.0001 0 0.00001 0.00000 0.92880 0.78600 1.00000 0.21837 0.02886 0.00069 0.38257 0.05638 0.40585 0.00287 0.00033 0.00002 0.93054 0.78820 0.99993 Table 4 8. Average p ost b undle a djustment s tandard d eviations of s tation EOPs for d ifferent i nitial b oresight and l ever arm c ircumstances Case Initial/Input Boresight and Leveram Conditions ( ) ( ) ( ) (m) (m) (m) 1 All parameters correct and constrained 0.012 0.015 0.063 0.017 0.013 0.009 2 All parameters corr ect and loose 0.012 0.015 12.072 0.092 0.068 10.299 3 All parameters perturbed and loose 0.012 0.015 12.823 0.092 0.068 10.305 4 correct and constrained; all others perturbed and loose 0.012 0.015 0.070 0.092 0.068 10.302 5 correct and constrain ed; all others perturbed and loose 0.012 0.015 0.070 0.092 0.068 10.302 6 correct and constrained; all others perturbed and loose 0.012 0.015 0.960 0.092 0.068 10.300 7 and correct and constrained; all others perturbed and loose 0. 012 0.015 0.063 0.018 0.014 0.009 8 and correct and constrained; all others perturbed and loose 0.012 0.015 0.070 0.019 0.015 0.011 9 and correct and constrained; all others perturbed and loose 0.012 0.015 0.070 0.085 0.062 9.335 10 and correct and constrained; all others perturbed and loose 0.012 0.015 0.070 0.019 0.015 0.121 Table 4 9. DAS v ector c alibration p arameters Site (Instrument, DAS) (m) ( m) ( ) Corry Village (Riegl z390i, DAS 2.0) 0.006 0.867 90.54 Orlando (Riegl vz400, DAS 3.0) 0.003 1.002 90.79

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96 Table 4 10 Corry Village DAS s olution for a ngular EOPs Station ( ) ( ) ( ) ( ) ( ) ( ) Station 1 0.374 1.003 178.905 0.393 0.619 0.155 Station 2 0.244 1.457 90.99 7 0.165 0.160 0.082 Station 3 0.265 0.064 83.014 0.250 0.277 0.085 Station 4 0.001 0.590 81.701 0.235 0.256 0.086 Table 4 11. Orlando DAS solution for angular EOPs ( ) ( ) ( ) ( ) ( ) ( ) Station 1 0.018 0.075 260.181 0. 069 0.064 0.024 Station 2 0.354 0.094 266.006 0.054 0.052 0.019 Station 3 0.067 1.362 212.622 0.084 0.084 0.030 Station 4 0.280 0.490 140.072 0.086 0.087 0.031 Station 5 1.072 0.515 45.055 0.124 0.173 0.048 Table 4 12 RMSEs for t ilt c omponent s of s tation EOPs for the Orlando d ata s et Stops Method Tilt Isolation Method Station ( ) ( ) ( ) ( ) Station 1 0.110 0.129 0.140 0.08 2 Station 2 0.021 0.05 7 0.03 3 0.00 1 Station 3 0.00 8 0.183 0.009 0.22 1 Station 4 0.11 8 0.06 8 0.06 5 0.020 Station 5 0.10 2 0.576 0.00 1 0.21 8 RMSE 0.08 6 0.279 0.07 1 0.14 4 Table 4 13 DAS p osition c alibration p arameters Site (Instrument, DAS) (m) Corry Village (Riegl z390i, DAS 2.0) 0.832 Orlando (Riegl vz400, DAS 3.0) 0.136 Table 4 1 4 DAS p osition s olution for Corry Village Station (m) (m) (m) Station 1 78.017 150.1 07 32.826 Station 2 70.376 117.349 31.929 Station 3 73.374 92.434 30.912 Station 4 74.021 39.933 29.464 RMSE 0.020 0.008 0.048

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97 Table 4 1 5 DAS p osition s olution for Orlando Station (m) (m) (m) Station 1 296.902 39.908 31.594 Station 2 279 .711 67.462 31.814 Station 3 306.623 100.612 31.887 Station 4 360.445 104.439 32.318 Station 5 363.281 40.209 32.293 RMSE 0.008 0.005 0.004

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98 CHAPTER 5 RESULTS AND ANALYSIS O pening Remarks on Results and Analysis This chapter presents the resul ts for different configurations of the integrated simultaneous adjustment solution. In order to analyze how different integrated methods perform relative to each other, t he configuration results and analysis for each data set are divided into two main sec tions: with scan targets and without scan targets Under each section are cases representing adjustments with di fferent included observations. In all there were 2 5 different combinations tested for the Corry Village data set and 33 for the Orlando data set. The following abbreviations are used for brevity where the results are reported (reprinted for convenience from the ABBREVIATIONS section) : CST Control Scan Targets AST Arbitrary Scan Targets SCT Single Control Target CL Collinearity CP Copla narity PODAS Position Only from DAS HLDAS High Level DAS MLDAS Medium Level DAS ICP Iterative Closest Point For clarity, adjustment methods are denoted by parentheses. The first value inside the parentheses describes the use of scanner targets, the s econd is how image observations are included, and the third is the level of DAS integration. For example, the configuration (AST, CP, PODAS) represents an adjustment where scanner observations of targets without known GLCS coordinates image observations in the form of coplanarity condition equation s and the position component from the DAS was used. When referring to multiple methods that include different combinations of

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9 9 observations with a common observation, the common observation abbreviation is used (e.g.: CST methods include (CST), (CST, CL), and (CST, CP)). As for the SCT configuration s in the Corry Village data set the western most control point was used (refer to Figure 4 2), in the Orlando data set, the control point used was the one located at approximately horizontal coordinates (330, 96) (refer to Figure 4 3). In the SCT configuration, all other scan targets were included with non control coordinates. When the CP design was used while using CST, AST or SCT configurations, image observations of scan target points were included via the collinearity condition equations since object space coordinates are available, all other image observations in these adjustments were included using the coplanarity equation Precision e stimates of im a g e and sca n ner coordinate measurements were determined by refining the estimated standard deviations from initial bundle adjustments and manufacturer technical specifications for said observations, respectively. This was achieved by defining the a priori standard d eviation of unit weight for the adjustment as unity, The estimated standard deviation s and therefore the weights of the observations, were altered until the a posteriori standard error of unit weight was approximately equal to one, As a check on the validity of the estimated standard deviations, an adjustment containing only scanner observations was used to first refine the scanner measurement standard deviations based on the criterion. Next, an adjustment with the same standard deviations for scanner measurements was augmen ted with image coordinate measurements. The standard deviations for image coordinate measurements were refined until the standard error of unit weight was again equal to one. The scanner measurements were found to have an approximate

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100 precision of 5.0mm an d 3.5mm for Corry Village (Riegl z390i) and Orlando (Riegl vz400 ) data, respectively. The resulting estimated image coordinate standard deviations were the same as those reported in the Initial Bundle Adjustment section further validating the estimates Since the coplanarity equations did not account for different values of focal length, and an average of these w as used Due to this, the image coordinate standard deviations when using coplanarity had to be increased by 0.15 pixels for b oth data sets to meet the criterion. Corry Village Exterior Orientation ( EOP ) Estimation The Corry Village data set represents sub optimal conditions, to say the least, as far as network geometry and precision of control for georeferencing TLS data. However, it provi des an opportunity to explore the efficacy of different methods of georeferencing under difficult circumstances at varying levels of o bservation autonomy. Certainly there are numerous TLS projects where it is impossible to position the sensor at m ost favo rable locations and include robust control towards determining precise georeferencing parameters. This data set is exemplary of these situations. The individual station solutions are included in Appendix D. Figure E 1 shows the full results for all F tes ts on Corry Village EOP data that are referred to in this section. Configurations with Scanner Targets The average standard deviations for configurations with scanner targets for the Corry Village data set are shown in Table 5 1 and illustrated in Figure s 5 1 and 5 2 Notice that the parameter rotation about the once rotated axis, is the most weakly resolved angular EOP. This was due to two main factors that are well illustrated by Figure 4 2 The first being that the stations themselves were positioned within the project area such

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101 that there is very little distance between them in the east west direction ( axis of the GLCS). This creates poor geometry for resolving when using the AST configurations, when the control for the adjustment is connected to the scanner itself (sensor dri ven techniques) Similarly, with the exception of one control point, the scanner targets were also distributed along a relatively narrow east west corridor creating poor geometry for resolving even when u sing CST and SCT configurations, although to a lesser degree As for the positional EOPS, there is a smaller discrepancy between configuration solution precisions with a maximum difference in standard deviation of 0.004 m for both the horizontal and vertical components. The component was the wea kest resolved coordinate, averaging nearly three times higher standard deviations than the horizontal components. The positioning of the scanners and targets their lack of diversity in height leading to weak vertical geometry as well as the lower accuracy of GPS vertical relative to horizontal measurements can explain this There are small but significant differences among the different methods precision of position. However, error in EOP position is directly related to error in scanned point position (e.g. for a level scanner, a 0.015 m error in scanner height creates a 0.015 m error in georeferenced point height). The error in EOP angular attitude affects the error in georeferenced point position based on how far the point is from the scanner. Figur e 5 3 illustrates this concept. For instance, a 0.05 attitude leads to georeferenced scanned point error of approximately 0.02 m for points 25 m away, 0.04 m for points 50 m away, 0.07 m for points 75 m away, and 0. 09 m for points 100 m away. Most of the georeferenced scan point position error stems from error in EOP in the Corry Village data set since the area of interest is located east of

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102 the scanner positions (in the GLCS x direction) and the best measure of how the different methods compare with each is quantified by how well they resolve Thus, the analysis of the methods used on this data set focus es on the relative precision s of Relative p erformance of different methods using arbitrary scanner tar gets Inspection of Figure 5 1 suggests that the different methods can be grouped into different levels of precision for F tests were carried out for each method relative to the other and indicated th e following shown in Figure E 1 (note that signific ance was tested at 90% confidence although the minimum confidence level of significant difference was 93% and the majority of results were well above 99% confidence ): (AST, CL, PODAS), (AST, CP, PODAS), and (AST, PODAS) did not have significantly different variances for relative to each other (AST, CL, HLDAS), (AST, CP, HLDAS), and (AST, HLDAS) did not have significantly different variances for relative to each other (AST, CL, MLDAS), (AST, CP, MLDAS), and (AST, MLDAS) did not have significantly different variance s for relative to each other However, each AST method with MLDAS observations had significantly lower variances for than all AST methods using H LDAS. Similarly, the three AST HLDAS configurations had significantly lower variances than the AST metho ds using PODAS. Note that the configuration (AST, PODAS) represents the typical sensor driven method for georeferencing TLS. This shows that the HL DAS and MLDAS method s are superior to the conventional method for the Corry Village data set. It can also be said that the more deeply integrated MLDAS method is significantly superior to the HLDAS method towards resolving the scanner EOPs. B ased on these results i mage observations did not have a significant effect on the results

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103 Relative perfo rmance of different methods using control scanner targets By examining Figure 5 1, notice that there is less of a distinction among methods that use control targets than among those using arbitrary targets with the exception of the (CST) method, the only m (CST) method had significantly higher variances in than the methods using CST and image observations and methods using SCT with image observations in combination with HLDAS, MLDAS, or PODAS with confidence levels of at least 99%. This indicates that when using control scan targets, the inclusion of im age observations significantly improved the solution. By c omparing the methods using control targets, CST and SCT augmented methods, in addition to im age measurements, the following were found : (SCT, CP, HLDAS), (SCT, CP, PODAS), (SCT, CP, MLDAS), and (CS T, CP) did not have significantly different variances for relative to each other. (SCT, CL, HLDAS), (SCT, CL, PODAS), (SCT, CL, MLDAS), and (CST, CL) did not have significantly different variances for relative to each other. However, the group of methods using CL, collinearity observation equations, all had significantly lower variances than the methods using CP, coplanarity observation equations although the standard deviations were different by only 0.01 Performance of methods using control scanner targets compared to methods using arbitrary scanner t argets Figure E 1 shows that all the CST and SCT methods had lower variances than the methods that did not use control scanner targets at confidence levels of greater than 99%. In other words, concerning precision, using scanner control targets (data base d georeferencing) resulted in superior results than using arbitrary scanner targets (sensor based georeferencing). The highest standard deviation for using scanner control targets was the (CST) method with a value of 0.0 53 whereas the best method wit hout

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104 using scanner control targets was (AST, CL, MLDAS) which had a standard deviation of 0.103 Configurations without Scanner Targets The average standard deviations for methods that do not use scanner target points are shown in Table 5 2 and illus trated in Figures 5 4 and 5 5. Again, was the most weakly resolved EOP, and its precision will therefore be used to quantify how well each adjustment method performed. The positional EOP post adjustment standard deviations were within 2 mm of each oth er in the horizontal components and within 6 mm of each other in the vertical component. Relative performance of different methods As expected, the (HLDAS) method had significantly higher variances for than all other methods. As for DAS configuration s with image observations the following can be seen in Figures 5 4 and E 1: The HLDAS methods had significantly lower variances than the PODAS methods The MLDAS methods had significantly lower variances than the HLDAS methods Th e s e result s are expected b ased on the results when using the similar AST methods. Contrary to the AST results, however, w ithin each method group PODAS, HLDAS, and MLDAS those using CL had slightly but significantly lower variances than those using CP, each with a confidence level o f at least 90% with the exception of PODAS where the confidence level was 83%. The fact that AST methods were not significantly different when using CP or CL, is due to the use of collinearity for the scanner point image observations, thus stabilizing the solution. The reason for better results when using collinearity for methods not using scanner targets probably stems from two factors. Firstly, the coplanarity condition observation equations did not account for

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105 different values of focal length, and More importantly, however, is the instability of the coplanarity equations under certain circumstances For more on this, see the section Appendix F Since the (CST, CL) method produced target point coordinates with a much higher lev el of precision than the without scan targets methods due to redundant observations on individual points from both the scanner and camera, they could be used to obtain RMSE error of target point coordinates The GLCS coordinates of scanner targets points were found using the adjusted scanner EOPs from the without scan targets methods. Since some were observed from different scan stations, there were targets with multiple sets of coordinates. In all, there were 19 sets of coordinates for each configuratio n towards calculating RMSEs which are shown in Table 5 3. I n Table 5 3, d represents the RMSE of horizontal distance. Significance at high confidence levels could not be established for the difference in RMSE values of the points, except for the (HLDAS) configuration, which had much higher values than all the other configurations. It is expected, however, that if targets points were included in RMSE computation with fart h er distances from the scanner in GLCS X, that the methods with better precision in would yield much better RMSEs for the Z components of the scanner targets. Regardless, inspection of Table 5 3 shows that, in general, the HLDAS and MLDAS methods with image observations had lower RMSEs than the PODAS methods. Interestingly, CP method s had better results than CL methods. Although, again, they could not be differentiated using statistical tests, and therefore the apparent superiority of CP methods can be attributed to random chance.

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106 Comparison of the p erformance of methods using sca nner targets and methods without using scanner targets Figure E 1 shows that all the CST and SCT methods had lower variances for than all the methods that did not use scanner targets at confidence levels greater than 99%. However, all of the HLDAS and MLDAS configurations without using targets had signifi cantly lower variances than all of the AST and PODAS methods at the 99.99% confidence level! Since the AST and PODAS methods represent the standard sensor based method for georeferencing, this shows that significantly better results were achieved using the DAS even without using scanner targets. Figure 5 6 is a combined chart i llustrating this superiority. Orlando EOP Estimation If the Corry Village data set represents sub optimal conditions, then the Orlando data set represents a near optimal configuration. The individual station solutions are included in Appendix D. Figure E 2 shows the full results for all F tests on Orlando tilt ( ) data which are referred to in this section. Whenever a significance level is not mentioned with respect to F test results, at least 90% confidence can be assumed. Unlike the Corry data set, t he precision of and are very similar for the Orlando data set adjustment results. Thus, it is appropriate to analyze their combined precision in the form of tilt. Equation 5 1 is the equation for tilt, the magnitude of the angle from vertical the condition where Z components of the SOCS and GLCS axes are aligned. ( 5 1 ) To simplify computations, tilt can be approximated at small angles using Equation 5 2. ( 5 2 )

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107 The approximation shown in Equ ation 5 2 is suitable for the Orlando data set since and are never greater than 2 Figure 5 7 validates this by showing the error, (shown in Equation 5 3) between true and approximated values for The error in the approximated value of ne ver exceeds 0.0003 when the absolute values of and are less than 2 ( 5 3 ) Using the law of propagation of errors and assuming no correlation between and the approximate standard deviation of can be found using Equation 5 4. ( 5 4 ) Configurations with Scanner Targets The average standard deviations for configurations with scanner targets for the Orlando data set are shown in Table 5 4, and illustrated in Figures 5 8, 5 9, and 5 10 Note that although there was some variation in the resolved positional EOP precisions (a maximum of 3 mm difference in standard deviation between each compon ent) similar to the Corry Village data set, analysis will focus on the angular EOPs as they most likely have a more substantial impact on the precision of georeferenced point clouds. Relative performance of different methods using arbitrary scanner target s As Figure 5 10 illustrates, there was very little difference in precision for estimating tilt among the methods using scanner target points. The largest difference in precision was about 0.005 An error in angular attitude of 0.1 mrad at 100 m distanc e translates to about a centimeter of positional error However, although the differences were small,

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108 an estimated significance of difference can be obtained using F tests allowing for relative evaluation of performance (refer to Figure E 2) As with the Corry Village data, the methods using AST can be grouped as follows: (AS T, HLDAS), (AST, MLDAS), and (AST, PODAS) did not have significantly different variances for (AST, CP, HLDAS), (AST, CP, PODAS), (AST, CL, HLDAS), and (AST, CL, PODAS) did not have significantly different variances for (AST, CP, MLDAS) and (AST, CL, MLDAS) did not have significantly different variances for AST methods that used CL image observations had significantly lower variances for than all AST methods without image ob servations. The ( AST, CP, HLDAS) and (AST, CP, PODAS) methods had significantly lower variances than the (AST, HLDAS) and (AST, MLDAS) methods at the 90% confidence level, however, their variances for were only significantly lower than the (AST, PODAS) method at the 79% and 84% confidence level, respectively. Finally, the (AST, CP, MLDAS) and (AST, CL, MLDAS) methods had significantly lower variances than all other AST methods. Thus, the methods using AST with image observations were superior to thos e without them Also, the methods using AST and images in combination with MLDAS integration were superior to those using HLDAS or PODAS. Examination of Figure E 2, shows that the CP methods were not significantly different than the ir CL method counterpa rts using arbitrary scanner targets in concurrence with results from the Corry Village data set for AST configurations Relative performance of different methods using control scanner targets The (CST, CL) and (CST, CP) methods did not have significantly d ifferent variances from each other for A lthough a 90% level of confidence could not be

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109 reached for the comparison of (SCT, CL, MLDAS) with the other two SCT and CL methods, it did have significantly lower var iances than the HLDAS and PODAS variant s at the 89% and 82% confidence level, resp ectively Similarly, the (SCT, CP, MLDAS) method had lower variances than the (SCT, CP, HLDAS) at the 92% confidence level and lower variances than the (SCT, CP, PODAS) method at the 85% confidence level. The SCT methods using CL were not significantly different from the ones using CP at more than 81% significance regardless of their level of DAS integration. This is in contrast with the results for the Corry Village data for these methods. It bears repeating that although the difference in the Corry V illage precision for these methods was found to be significant, there was only a slight difference between them. It is likely that the weaker geometry of the Corry Village data set compounded the instability in the resolution of an gular EOPs. The (CST, CL) and (CST, CP) methods resulted in significantly lower variances than all other methods. While t he (CST) method had significantly higher variances than the (CST, CL) and (CST, CP) methods, no significant difference could be estab lished between (CST) and any of the other control point methods. Configurations without Scanner Targets The average standard deviations for methods that d id not use scanner target points are shown in Table 5 5 and illustrated in Figures 5 11 5 12 and 5 1 3 T hese methods include variations with ICP observations. Only ICP observations between Stations 1 and 2, and 2 and 3 were used due to the low precision of all other solutions. In this study, methods that used ICP in concert with image observations inc lude adjustments of all stations. When no image observation were used with ICP observations, only Stations 1, 2, and 3 were included in the adjustments.

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110 Relative performance of different methods Inspection of Figure E 2 shows that methods (ICP, MLDAS) and (ICP, HLDAS) did not have significantly different variances for from each other but both had lower variances than (HLDAS). All three of these methods were less precise in tilt than the rest of the methods without scan targets. As for the methods that used image observations, all CP methods were not significantly different from each other regardless of their level of DAS integration or if they used ICP. Similarly, the same can be said for the CL methods. However, the CL methods for the most part had significantly lower variances for tilt than did the CP methods. The fact that HLDAS and MLDAS methods did not have more precise solutions compared to the PODAS methods, contrary to the findings in the Corry Village data set, is a testament to the better designed configuration of the stations and targets towards resolv ing tilt N otice in Table 5 4 and Figure 5 11 that there is more variation of precision in than either or and that the magnitude of the standard deviations are higher for than the tilt parameters as well Thus, a nalysis of variances in we re carried out in the form of F tests of variances for methods not using scanner targets, illustrated in Figure E 3. As with (HLDAS) had significantly higher variances for than all other methods and the methods using CL had lower variances than th ose using CP However, as opposed to the findings for tilt variances, methods using CP had significantly increased precision for when augmented with ICP observations. This may stem from the fact that ICP solution s were more precise in the component of than relative tilt (refer to the first two rows of Table 4 3 ) There was no significant improvement when using ICP for the CL methods. Another distinction from the variances of is that the level of DAS

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111 integration affected the precisi on of across the board when using CP For instance, (CP, ICP, HLDAS) had significantly lower variances for than (CP, ICP, PODAS), and (CP, ICP, MLDAS) had significantly lower variances than (CP, ICP, HLDAS). This can also be observed in the CL met hods, granted not for all of them (CL, MLDAS) and (CL, ICP, MLDAS) had significantly lower variances than their counterparts using HLDAS However, the CL methods using HLDAS were not significantly different than those using PODAS. The RMSEs for the vario us without target methods are shown in Table 5 6 and are illustrated in Figure s 5 14 and 5 15 Note that Figure 5 15 is truncated for easier viewing. For the actual values of (HLDAS), (ICP, HLDAS), and (ICP, MLDAS), refer to T able 5 6 The RMSEs were ca lculated by using the difference between coordinates of scanner targets transformed using the adjusted EOPs of stations and those found using the (CST, CL) method treated F tests were performed on the MSE results for each component of the poin ts The points numbered 24 for methods using image observations and 14 for those using only ICP and the DAS. The X and Y components were combined to obtain an RMSE value for horizontal distance, d F tests for variances of the points are shown in Figure s E 4 and E 5 for the horizontal and vertical components respectively As for the horizontal RMSEs : All methods using image points and MLDAS did not have significantly different MSEs for d All methods using HLDAS with ICP and/or image observations did not have significantly different MSEs for d (CP, PODAS) and (CP, ICP, PODAS) did not have significantly different MSEs from each other

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112 (CL, PODAS) and (CL, ICP, PODAS) did not have significantly different MSEs from each other All the methods using MLDAS a nd image points had lower MSEs for d than all methods using PODAS with at least 90% confidence. (CP, MLDAS) and (CP, ICP, MLDAS) had significantly lower MSEs than all HLDAS methods as well at the 90% confidence level The other MLDAS methods, had lower M SEs than all HLDAS methods as well, but significance levels greater than 90% could not be established for most of them. The HLDAS methods using image observations had lower MSEs for d than all methods using PODAS with at least 81% confidence, although the majority of them were lower with at least 90% confidence. Methods using CL did not have significant differences in d MSE than their CP counterpart with the exception of (CL, PODAS), which had a significantly lower MSE than (CP, PODAS). The higher precis ion in d for methods using lower level DAS integration is consistent with the results for estimated precision. However, an increase in precision for d was not found when augmenting CP methods with ICP contrary to the results found from F tests of the estimated variance of The following were found for F tests on the MSEs of the Z component of th e scanner target points: All methods using CL did not have significantly different MSEs for Z All methods using CP did not have significantly different MSEs for Z (ICP, MLDAS) and (ICP, HLDAS) did not have significantly different MSEs for Z All CL method s had lower MSEs for Z than their CP counterparts with at least 90% confidence except for (CL, HLDAS), which had a lower MSE than (CP, HLDAS) at the 89% confidence level, and (CL, ICP, HLDAS), which had a lower MSE than (CP, ICP, HLDAS) at the 88% confiden ce level. These results validate the findings for F tests on

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113 the variance of The level of DAS integration did not affect the precision of Z component MSE, and CL methods had higher precisions for Z than CP methods. Performance of methods using scanne r targets compared to methods without using scanner targets With the exception of (AST, PODAS) (the conventional methods for sensor based georeferencing) and (AST, HLDAS), the methods that did not use targets had significantly higher variances for tilt tha n all methods using targets. The best performing method that did not use scanner targets, ( CL, ICP, MLDAS), had significantly lower variances for than the AST methods that did not use image observations with at least 80% confidence. However, was resolved more precis ely using the AST methods. Summary Analysis of Results When using arbitrary scan targets, inclusion of the angular observations f rom the DAS, in the form of HLDAS or MLDAS significantly improved the solution for both data sets. This is a noteworthy finding, because it implies that the DAS method can generate better results than the conventional method for sensor driven TLS georefer encing (using only the position observations of the stations and arbitrary scanner targets). However, when using scanner targets with known GLCS coordinates, the addition of angular observations from DAS typically did not improve the solution significantl y. The addition of image observations when using either type of scanner targets generated a significantly more precise solution in the Orlando data set The precision was improved when including image observations in the Corry Village data set, but 90% s ignificance levels could not be achieved. When no scanner targets were used, the level of DAS integration played a significant role in the precision of solutions. However, while the tilt of the scanner was

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114 more precisely resolved using MLDAS and HLDAS in the Corry Village data, there was no difference in the precision of tilt when using these as opposed to PODAS for the Orlando data. Although, the resolution of in the Orlando set adjustments was significantly affected by using MLDAS and HLDAS as oppose d to PODAS suggesting that the angular EOPs provided by the DAS can have a positive impact on TLS sensor driven georeferencing in both poorly and well configured TLS station configurations when using only image observations. An interesting finding was th e superiority of medium level integration over high level integration of the DAS. This can be considered analogous to sequential versus simultaneous adjustment. By including the fundamental observations as opposed to prior solutions obtained from these o bservations, a more rigorous solution is obtained allowing for the correlation between vectors from different stations to be accounted for in the integrated adjustment. The inclusion of ICP observations significantly increased the precision of compared to (HLDAS). H owever, there was little increase in precision of This is most likely due to the shape of available features in the project area and is an indication of one of the major shortcomings of using ICP for precise TLS georeferencing. The best performing, most autonomous methods were (CL, M LDAS) and (CP, MLDAS) which yielded RMSEs of 2 cm for both the horizontal and vertical components in the Corry Village data set at an average point distance of 54 m and 1 cm for both horizontal and vertical in the Orlando data set at an average point distance of 40 m Admittedly, the Z component RMSE values for the Corry Village data set are misleading in that the targets were not distributed evenly throughout the project area. A better

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115 measure of the auton omous method precision s is the resolved angular EOP precision with respect to the relationships shown in Figure 5 3. Boresight and Leverarm Experimentation and Analysis In Chapter 4, a method for reducing the BLP calibration procedure was proposed. This parameters. The experiment consists of including only two calibration parameters as known s in the adjustment and comparing the resulting precisions and RMSEs with adjustme nts constraining the full set of BLPs. The method (CL, MLDAS) was tested for both the Corry Village and Orlando data sets with reduced BLP input In the Corry Village data, the constrained BLPs were and As for the Orlando data set, and were constrained. The remaining four BLPs were given a priori standard deviations of 90 for the angles and 100 m for the positions, essentially giving them negligible observational weight in the adjustment and therefore are treated as almost purely u nknown Table 5 7 shows the average standard deviations of these adjustments with reduced BLP calibration. Comparing Table 5 7 with precision results for adjustments with fully constrained BLPs in Tables 5 2 and 5 5, shows that for both data sets, the re sults of using a reduced BLP calibration yields nearly identical results to using the full calibrated set. Table 5 8 shows the RMSEs for the same adjustments. Again, comparing these results to those from fully constrained BLP adjustments, in Tables 5 3 a nd 5 6, shows that the difference between using fully constrained BLPs and reduced BLPs is very small (on the order of about two millimeters)

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116 These results suggest that calibration can be simplified to directly measuring the essential BLPs directly. For example, the component is very nearly the height of the camera above the SOCS origin. The angular components are slightly more complicated. As for the Corry (z390i) essential angular BLP it is nearly the direction that the camera is pointing with respect to the SOCS. In contrast, the Orlando (vz400) BLP is the third rotation of the camera with respect to the SOCS. In other words, it is the rotation about the twice rotated Z axis, the rotation about the rotated optical axis of the camera. Besides creati ng the possibility for direct measurement of BLPs, the reduced scheme presented can also serve as a guide towards the development of camera mounts designed for specific cameras that either facilitate direct measurement of the essential BLPs or are precisel y machined such that fixing the essential BLPs is prioritized.

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117 Figure 5 1. Average p ost adjustment s tandard d eviations for a ngular EOPs for the Corry Village d ata s et u sing s canner t argets Figure 5 2. Average p ost adjustment s tandard d eviatio ns for p ositional EOPs for the Corry Village d ata s et u sing s canner t argets 0.000 0.050 0.100 0.150 0.200 0.250 Average Standard Deviation ( ) 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018 0.020 Average Standard Deviations ( m) X Y Z

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118 Figure 5 3. Error in g eoreferenced p oint p osition with r espect to e rror in a ngular s canner EOP at v arying s canner to point d istances Figure 5 4. Average p ost adjustment st and ard d eviations for a ngular EOPs for the Corry Village d ata s et w ithout u sing s canner t argets 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.00 0.05 0.10 0.15 0.20 Approximate Error in Georeferenced Scanned Point Position (m) Angular Scanner EOP Error ( ) 25m 50m 75m 100m 0.000 0.050 0.100 0.150 0.200 0.250 0.300 0.350 0.400 HLDAS CP, PODAS CL, PODAS CP, HLDAS CL, HLDAS CP, MLDAS CL, MLDAS Average Standard Deviation ( )

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119 Figure 5 5. Average p ost adjustment s tandard d eviations for p ositional EOPs for the Corry Village d ata s et w ithout u sing s canner t argets Figure 5 6. Averag e p ost adjustment s tandard d eviations for a ngular EOPs for AST and PODAS m ethods and w ithout s canner t arget HLDAS and MLDAS m ethods for the Corry Village d ata s et 0.000 0.005 0.010 0.015 0.020 0.025 HLDAS CP, PODAS CL, PODAS CP, HLDAS CL, HLDAS CP, MLDAS CL, MLDAS Average Standard Deviation (m) X Y Z 0.000 0.050 0.100 0.150 0.200 0.250 AST, CL, PODAS AST, CP, PODAS AST, PODAS CP, HLDAS CL, HLDAS CP, MLDAS CL, MLDAS Average Standard Deviation ( ) Method

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120 Figure 5 7. Error in the e stimated v alue of t ilt in d egrees

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121 Figure 5 8 Average p o st adjustment s tandard d eviations for a ngular EOPs for the Orlando d ata s et u sing s canner t argets Figure 5 9. Average p ost adjustment s tandard d eviations for p ositional EOPs for the Orlando d ata s et u sing s canner t argets 0.004 0.006 0.008 0.010 0.012 0.014 0.016 Average Standard Deviation ( ) 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.010 Average Standard Deviation (m) X Y Z

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122 Figure 5 10. Average p ost adj ustment s tandard d eviations for t ilt for the Orlando Data s et u sing s canner t argets 0.008 0.009 0.010 0.011 0.012 0.013 0.014 0.015 Average Standard Deviation ( )

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123 Figure 5 11. Average p ost adjustment s tandard d eviations for a ngular EOPs for the Orlando Data s et w ithout u sing s canner t argets Figure 5 12. Average p ost adjustm ent s tandard d eviations for p ositional EOPs for the Orlando d ata s et w ithout u sing s canner t argets 0.000 0.020 0.040 0.060 0.080 0.100 0.120 0.140 0.160 0.180 Average Standard Deviation ( ) 0.006 0.007 0.008 0.009 0.010 0.011 0.012 Average Standard Deviation (m) X Y Z

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124 Figure 5 13. Average p ost adjustment s tandard d eviations of t ilt for the Orlando d ata s et w ithout u sing s canner t argets Figure 5 14. RMSEs of horizonta l distance, d, for the Orlando d ata s et without u sing s canner t argets 0.000 0.020 0.040 0.060 0.080 0.100 0.120 0.140 Average Standard Deviation ( ) 0.000 0.005 0.010 0.015 0.020 0.025 0.030 RMSE (m)

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125 Figure 5 15. RMSEs of the Z coordinate for the Orlando Data s et without u sing s canner t argets (truncated) 0.000 0.002 0.005 0.007 0.010 0.013 0.015 0.018 0.020

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126 Table 5 1 Average p ost adjustment s tandard d eviations of EOPs for the Corry Village d ata s et u sing s canner t argets Method ( ) ( ) ( ) ( m ) ( m ) ( m ) CST 0.012 0.053 0.007 0.009 0.008 0.016 CST, CL 0.009 0.021 0.005 0.007 0.006 0.013 CST, CP 0.010 0.031 0.006 0.007 0.007 0.014 AST, CL, HLDAS 0.016 0.139 0.009 0.006 0.005 0.0 16 AST, CL, MLDAS 0.015 0.103 0.008 0.006 0.005 0.015 AST, CL, PODAS 0.016 0.225 0.011 0.006 0.005 0.017 AST, CP, HLDAS 0.016 0.144 0.009 0.006 0.005 0.016 AST, CP, MLDAS 0.016 0.106 0.008 0.006 0.005 0.016 AST, CP, PODAS 0.016 0.225 0.011 0.006 0.005 0.017 AST, HLDAS 0.018 0.155 0.010 0.007 0.005 0.017 AST, MLDAS 0.016 0.113 0.009 0.007 0.005 0.016 AST, PODAS 0.015 0.206 0.010 0.006 0.004 0.016 SCT, CL, HLDAS 0.016 0.021 0.005 0.005 0.005 0.015 SCT, CL, MLDAS 0.016 0.020 0.005 0.005 0.005 0.015 SCT, CL, PODAS 0.015 0.020 0.005 0.005 0.005 0.015 SCT, CP, HLDAS 0.017 0.033 0.006 0.006 0.005 0.016 SCT, CP, MLDAS 0.016 0.030 0.006 0.006 0.005 0.015 SCT, CP, PODAS 0.016 0.031 0.006 0.006 0.005 0.015 Table 5 2 Average p ost adjustment s tandard d e viations of EOPs for the Corry Village d ata s et w ithout u sing s canner t argets Method ( ) ( ) ( ) ( m ) ( m ) ( m ) CL, HLDAS 0.016 0.127 0.022 0.006 0.007 0.014 CP, HLDAS 0.021 0.160 0.022 0.008 0.009 0.018 CL, MLDAS 0.017 0.099 0.023 0.006 0.007 0.015 CP, MLDAS 0.019 0.113 0.021 0.008 0.00 9 0.016 CL, PODAS 0.015 0.202 0.024 0.005 0.007 0.015 CP, PODAS 0.018 0.226 0.021 0.007 0.008 0.016 HLDAS 0.311 0.350 0.102 0.008 0.008 0.020 Table 5 3 RMSEs for the s canner t arget p ositions from Corry Village d ata s et c onfigurations without u sing s canner t argets Method X (m) Y (m) Z (m) d (m) CP, HLDAS 0.020 0.006 0.023 0.021 CP, MLDAS 0.020 0.006 0.024 0.021 CL, MLDAS 0.025 0.005 0.026 0.026 CL, HLDAS 0.025 0.005 0.027 0.025 CP, PODAS 0.025 0.006 0.029 0.026 CL, PODAS 0.025 0.006 0.030 0.026 HLDAS 0.095 0.021 1.432 0.097

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127 Table 5 4 Average p ost adjustment s tandard d eviations of EOPs for the Orland d ata s et u sing s canner t argets Method ( ) ( ) ( ) ( ) ( m ) ( m ) ( m ) CST 0.009 0.013 0.005 0.011 0.004 0.004 0.008 CST, CL 0.008 0.010 0.006 0.009 0.004 0.004 0.007 CST, CP 0.008 0.010 0.006 0.009 0.004 0.004 0.007 AST, HLDAS 0.015 0.015 0.007 0.014 0.006 0.006 0.009 AST, MLDAS 0.013 0.014 0.006 0.013 0.005 0.006 0.009 AST, PODAS 0.0 13 0.014 0.006 0.013 0.005 0.005 0.008 AST, CL, HLDAS 0.011 0.011 0.007 0.011 0.006 0.006 0.009 AST, CP, HLDAS 0.012 0.012 0.007 0.012 0.006 0.006 0.009 AST, CL, MLDAS 0.010 0.010 0.006 0.010 0.005 0.005 0.007 AST, CP, MLDAS 0.011 0.011 0.006 0.011 0.0 05 0.006 0.008 AST, CL, PODAS 0.011 0.011 0.007 0.011 0.006 0.006 0.008 AST, CP, PODAS 0.012 0.012 0.007 0.011 0.006 0.006 0.009 SCT, CL, MLDAS 0.010 0.010 0.006 0.010 0.005 0.005 0.007 SCT, CP, MLDAS 0.010 0.011 0.006 0.010 0.005 0.005 0.007 SCT, CL, PODAS 0.010 0.011 0.006 0.010 0.005 0.005 0.008 SCT, CP, PODAS 0.011 0.012 0.007 0.011 0.005 0.005 0.008 SCT, CL, HLDAS 0.010 0.011 0.006 0.011 0.005 0.005 0.008 SCT, CP, HLDAS 0.011 0.012 0.007 0.011 0.005 0.005 0.008 Table 5 5 Average p ost adjust ment s tandard d eviations of EOPs for the Orland d ata s et w ithout u sing s canner t argets Method ( ) ( ) ( ) ( ) ( m ) ( m ) ( m ) HLDAS 0.082 0.180 0.050 0.134 0.010 0.010 0.010 ICP, MLDAS 0.053 0.04 1 0.023 0.045 0.011 0.011 0.011 ICP, HLDAS 0.052 0.040 0.030 0.044 0.010 0.010 0.010 CP, MLDAS 0.014 0.017 0.023 0.015 0.009 0.009 0.009 CP, ICP, MLDAS 0.014 0.017 0.018 0.014 0.009 0.009 0.009 CP, ICP, HLDAS 0.014 0.017 0.021 0.014 0.009 0.009 0.008 CP, ICP, PODAS 0.014 0.016 0.025 0.014 0.009 0.009 0.009 CP, HLDAS 0.014 0.017 0.026 0.014 0.009 0.009 0.008 CP, PODAS 0.013 0.015 0.030 0.013 0.008 0.008 0.008 CL, ICP, HLDAS 0.012 0.013 0.016 0.013 0.009 0.009 0.009 CL, HLDAS 0.012 0.013 0.016 0.012 0.009 0.009 0.008 CL, ICP, PODAS 0.012 0.013 0.016 0.012 0.009 0.008 0.008 CL, ICP, MLDAS 0.012 0.013 0.014 0.012 0.008 0.008 0.008 CL, MLDAS 0.012 0.013 0.014 0.012 0.009 0.008 0.008 CL, PODAS 0.011 0.012 0.016 0.012 0.008 0.008 0.008

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128 Table 5 6 RM SEs for methods without using scanner targets Method X (m) Y (m) Z (m) d (m) CP, ICP, MLDAS 0.007 0.005 0.015 0.009 CP, MLDAS 0.007 0.005 0.015 0.009 CL, MLDAS 0.009 0.005 0.011 0.010 CL, ICP, MLDAS 0.010 0.006 0.011 0.011 CL, HLDAS 0.011 0.006 0.013 0.012 CP, HLDAS 0.009 0.008 0.017 0.012 CP, ICP, HLDAS 0.010 0.008 0.016 0.013 CL, ICP, HLDAS 0.012 0.007 0.013 0.014 ICP, HLDAS 0.012 0.009 0.094 0.015 ICP, MLDAS 0.012 0.009 0.098 0.015 CL, PODAS 0.014 0.008 0.013 0.016 HLDAS 0.014 0.009 0.146 0.0 17 CL, ICP, PODAS 0.015 0.009 0.013 0.018 CP, ICP, PODAS 0.017 0.014 0.018 0.022 CP, PODAS 0.017 0.019 0.017 0.025 Table 5 7 Reduced BLP a djustment a verage s tandard d eviations for EOPs Method/Site ( ) ( ) ( ) (m) (m) (m) (CL, MLDAS) Orlando 0.014 0.015 0.017 0.008 0.008 0.008 (CL, MLDAS) Corry Village 0.017 0.099 0.023 0.006 0.007 0.015 Table 5 8 RMSEs from r educed BLP a djustments Method X (m ) Y (m) Z (m) d (m) (CL, MLDAS) Orlando 0.010 0.006 0.014 0.012 (CL, MLDAS) Corry Village 0.025 0.005 0.028 0.025

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129 CHAPTER 6 SUMMARY AND CONCLUSIONS Terrestrial laser scanning has become a viable method for obtaining precise 3D information for many different applications from archaeology and paleontology to industrial as built surveys and building deformation modeling. New systems continue to emerge that are smaller, faster, and more precise than their predecessors. In addition, a host of different sensors is being integrated into these systems. Nowadays, TLS systems are typically equipped with a camera, and GPS antenna mounts with tilt sensors becoming a standard feature on the units as well As the technology evolves, the need for meth ods to georeference the data remains a large part of development. The conventional method for georeferencing the TLS data is to use scan targets with known coordinates. This requires a separate field survey that can cost a large amount of time and money. Consider that each target point must be surveyed in prior to scanning, which depending on the project can take days before the area is actually scanned. Also during scan acquisition, targets must be moved, typically in a leap frog fashion, as each new s canner station is introduced taking up valuable time In the case of some projects, the placing of the targets can be dangerous in addition to exhausting. Consider mapping landslide areas, glaciers, toxic waste dumps etc. Sensor driven techniques have been developed that can circumvent the need for scanner targets, at sometimes a great cost, however, of lost precision. A method was developed using dual GPS antennas that allowed for direct sensor based georeferencing of a single station with results suf ficient enough for many applications. This study presented a method for using the DAS system at multiple stations, and with the aid of a scanner mounted camera, that ties together scanner EOPs increasing their

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130 precision and therefore the precision of res ulting point clouds. In addition, a nearly comprehensive study was undertaken to compare different methods at different levels of autonomy. The idea was to determine the level of self containment that could be achieved with respect to observations toward s resolving EOPs while maintaining precision. The study could also be looked at as a guide to determining the level of precision one could expect given certain observations and configuration characteristics. In order to do this, a general model/method was designed and implemented allowing observations from scanner target points, point cloud matching, the dual antenna system at different levels of integration, and imagery in the form of either collinearity or coplanarity conditions. The results from s evera l experimental adjustments showed that, as expected the conven tional data driven approach was superior to all other methods, but could be significantly improved when augmented with image observations. The addition of angular components from using the DAS showed to significantly improve the precision of the conventional method for indirect sensor based georeferencing for both poorly configured (Corry Village) and well configured (Orlando) scanner station networks. Although ICP did show some promising res ults, the inclusion of them did not significantly improve solutions using image observations. Counter to the objective of generality, ICP should be consigned to projects that have sufficiently shaped objects to match. This, not to mention the need to pre serve the details of matched objects from different perspectives stemming from different scanner stations. Perhaps the most promising results were those from using high and medium level DAS integration and image observations, the most autonomous of the m ethods. The

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131 (CL, MLDAS) and (CP, MLDAS) methods were significantly superior to the indirect sensor based method (AST, PODAS) in the Corry village data set. Thus, without using scanner points, we were able to get more precise results than the conventional method that does use scanner points. This only extends to the Corry Village data set, and its nearly linear configuration of scanner stations. Although, as with Corry Village, some situations require confinement to a linear configuration of s tations. A s for the Orlando data set, representing the more optimally configured of the two, (CL, MLDAS) and (CP, MLDAS) had results comparable to those obtained by (AST, PODAS), and could be considered a more autonomous alternative to the conventional without a gre at loss of precision. The (CL, MLDAS) and (CP, MLDAS) yielded RMSEs of 1 cm for both horizontal and vertical components of check points for the Orlando data and 2 cm for both the horizontal and vertical components of the Corry Village data at an average c heck point distance of 40 and 50 m, respectively. Thus, at a very high level of autonomy ( essentially never having to enter proje ct area at all) we achieved centimeter level prec ision for point clouds, certainly a useable level of precision for many applic ations.

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132 CHAPTER 7 FUTURE RECOMMENDATIO NS The methods developed in this study can be used immediately to yield practical results for terrestrial laser scan georeferencing. In addition, t he results of this study open the door for many different areas of research to follow. A few suggested directions for further research include the following. Boresight and Leveram Parameters A method for simplifying the BLPs of the camera with respect to the camera was reported in this study. However, more detailed experimentation of methods to simplify the resolution of the BLPs (in the spirit of autonomy) should be pursued. As mentioned, machining of camera mounts that exploit the existence of essential and non essential BLPs could be explored. Similarly, methods of directly obtaining the BLPs should be tested with respect to precision versus analytical calibration methods and the overall adjustment precision. Coplanarity Solutions Coplanarity equations were an effective method of improving the adjustment results using image observations. However, it was show n that they tend to be unstable under certain circumstances. After a thorough literature review not much was found in the way of settling this issue. There is the possibility of using the scale restraint eq uation (Mikhail, Bethel, and McGlone, 2001). This should be explored as an alternative to c oplanarity as it has the same advantage of non necessity of object space coordinates of imaged points. However, the scale restraint equations also include the com putation of determinants which may lead to similar numerical instability.

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133 Another alternative could be to use an extended precision programming library to reduce the round off error that creates the instability. Iterative Closest Point Algorithm The result s of the ICP were disappointing in t his study. Experiments should be made under better conditions for ICP in concert with DAS observations to see if a more precise solution can be achieved than what was found in Orlando. Perhaps a good place to start wou ld be places with big rocks and no trees (the opposite of Corry Village and Orlando sites). Integration of More Sensors Although tilt sensors have become very popular in TLS lately the y were not explored in this study. Similarly, inertial sensor s could pr ovide significant precise observations that could contribute to better solutions of the integrated solution of angular EOPs These should be explored in future experiments with the system. Mobile Mapping This leads directly from the addition of inertial s ensors. Including video observations of dynamic scenes could serve as the image observations towards more precise point clouds from mobile ground based scanners. Also, how could the DAS system be i mplemented on a moving platform? Perhaps if the DAS was fixed to the vehicle platform itself, in a long baseline quad antenna system, QAS, a viable precision could be obtained without the need for rotating stops of the scanner head Modification of the DAS Apparatus and Implementation The length of the current DAS bar was chosen because it was the longest baseline that was easy to carry and was stable when mounted on top of the scanner head However, an even shorter bar could yield useable precisions if the stops were made

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134 longer. Also, the idea of low level D AS was introduced in this study, but was not implemented. Experimentation with the raw vectors for each GPS measurement epoch could be included in the integrated adjustment, although characterization of the high correlation between contiguous vectors woul d need to be accounted for. Optimization of Implementation Table F 1 gives an example of the execution time for the adjustment solution. Consider the fact that the data sets used in this study were relatively small. Optimizing the algorithm, and subseque nt code for speed, would make the presented method much more attractive for larger surveys.

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135 APPENDIX A THE PARTIAL DERIVATI VES OF THE COLLINEAR ITY EQUATIONS WITH BORESIGHT AND LEVER ARM CALIBRATION PARA METERS Definitions Boresight Calibration Matrix: Rotation Matrix for the scanner at the th setup : Rotation Matrix for the camera at the th setup : It should be noted that in actual implementation includes the rotation of the scanner head such that However, these terms are exclud ed for simplification and more general utility of this appendix. Position of the scanner in ground coordinates at the th setup : Position of imaged point in ground coordinates :

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136 L ever arm offset for the camera with respect to the scanner (in the camera coordinate system) : Other H elpful S ubstitutions The P artial D erivatives

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137

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141 APPENDIX B THE PARTIAL DERIVATI VES OF THE COPLANARI TY EQUATIONS WITH BORESIGHT AND LEVER ARM CALIBRATION PARA METERS Definitions The same definitions as in Appendix A are used in addition to the following: A point imaged at stations and will have the ray vectors (from perspective center to point) : The coplanarity condition can be considered the triple scalar product o r determinant: The partial derivative of determinant with respect to some parameter is the following sum (note that if any row or column of a matrix is all zeros, the determinant is zero) :

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142 The P artial D erivatives w here

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143 w here

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144 w here

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145 where

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146 where

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147 where

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148

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149

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150 where where

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151 where where

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152 APPENDIX C SCHEMATIC DRAWING OF THE DUAL ANTENNA SYS TEM MOUNTING BAR

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153 APPENDIX D A POSTERIORI STANDAR D DEVIATIONS OF INDI VIDUAL STATIONS UNDE R DIFFERENT CONFIGURAT IONS OF THE INTEGRAT ED SIMULTANEOUS ADJUSTMENT Table D 1 EO P solution for (CST) configuration for the Corry data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 1.154 1.308 178.746 78.003 150.113 32.845 0.016 0.084 0.009 0.009 0.008 0.027 2 0.12 2 1.660 91.193 70.359 117.351 31.933 0.015 0.084 0.007 0.008 0.008 0.020 3 0.149 0.404 82.911 73.408 92.446 30.837 0.018 0.021 0.007 0.009 0.008 0.021 4 0.226 0.267 81.712 74.031 39.930 29.412 0.014 0.076 0.006 0.008 0.007 0.021 Avg. 0.016 0.0 66 0.007 0.008 0.008 0.022 Table D 2 EOP solution for (HLDAS) configuration for the Corry data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 0.374 1.003 178.905 78.017 150.107 32.826 0.593 0.500 0.155 0.008 0.008 0.020 2 0.244 1.457 90.997 70.376 117.349 31.930 0.165 0.300 0.082 0.008 0 .008 0.020 3 0.265 0.064 83.014 73.374 92.434 30.912 0.250 0.300 0.085 0.008 0.008 0.020 4 0.001 0.590 81.701 74.021 39.933 29.464 0.235 0.300 0.086 0.008 0.008 0.020 Avg. 0.311 0.350 0.102 0.008 0.008 0.020 Table D 3 EOP solution for (CST CL) configuration for the Corry data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 1.146 1.460 178.751 77.998 150.112 32.840 0.010 0.025 0.006 0.008 0.007 0.017 2 0.121 1.584 91.184 70.360 117.348 31.946 0.009 0.020 0.005 0.006 0 .006 0.013 3 0.145 0.407 82.919 73.402 92.443 30.842 0.009 0.012 0.005 0.006 0.007 0.012 4 0.232 0.248 81.709 74.032 39.928 29.416 0.009 0.027 0.004 0.007 0.006 0.012 Avg. 0.009 0.021 0.005 0.007 0.006 0.013 Table D 4 EOP solution for (CST, CP) configuration for the Corry data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 1.140 1.453 178.742 78.001 150.114 32.840 0.010 0.035 0.007 0.008 0.007 0.018 2 0.123 1.588 91.189 70.361 117.349 31.943 0.010 0.036 0.006 0.007 0 .007 0.014 3 0.147 0.411 82.915 73.404 92.444 30.847 0.011 0.013 0.006 0.007 0.007 0.013 4 0.233 0.207 81.710 74.031 39.929 29.411 0.009 0.039 0.005 0.007 0.006 0.013 Avg. 0.010 0.031 0.006 0.007 0.007 0.014

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154 Table D 5 EOP solution for ( AST, HLDAS) configuration for the Corry data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 1.192 1.387 178.760 78.017 150.109 32.831 0.018 0.152 0.012 0.007 0.005 0.020 2 0.084 1.576 91.206 70.366 117.348 31.950 0.017 0.152 0.009 0.006 0 .005 0.016 3 0.193 0.379 82.951 73.386 92.441 30.874 0.019 0.159 0.012 0.007 0.005 0.013 4 0.187 0.171 81.724 74.018 39.924 29.476 0.017 0.157 0.008 0.008 0.005 0.021 Avg. 0.018 0.155 0.010 0.007 0.005 0.017 Table D 6 EOP solution for (AST, MLDAS) configuration for the Corry data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 1.191 1.445 178.757 78.017 150.109 32.828 0.016 0.111 0.010 0.007 0.005 0.018 2 0.085 1.517 91.204 70.366 117.348 31.954 0.016 0.106 0.008 0.005 0 .005 0.014 3 0.192 0.315 82.949 73.386 92.441 30.875 0.018 0.118 0.011 0.006 0.005 0.012 4 0.189 0.121 81.723 74.018 39.924 29.475 0.016 0.116 0.007 0.008 0.005 0.019 Avg. 0.016 0.113 0.009 0.007 0.005 0.016 Table D 7 EOP solution for (AST, PODAS) configuration for the Corry data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 1.193 1.364 178.762 78.018 150.109 32.832 0.014 0.201 0.013 0.006 0.004 0.018 2 0.083 1.604 91.208 70.366 117.349 31.948 0.014 0.203 0.009 0.004 0 .004 0.017 3 0.195 0.419 82.953 73.386 92.441 30.875 0.016 0.210 0.011 0.005 0.004 0.011 4 0.186 0.187 81.726 74.017 39.924 29.477 0.014 0.209 0.008 0.007 0.004 0.017 Avg. 0.015 0.206 0.010 0.006 0.004 0.016 Table D 8 EOP solution for (AST, CL, HLDAS) configuration for the Corry data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 1.182 1.466 178.771 78.014 150.109 32.829 0.016 0.139 0.010 0.007 0.005 0.018 2 0.083 1.578 91.204 70.365 117.348 31.957 0.016 0.139 0.008 0.005 0 .005 0.015 3 0.182 0.411 82.945 73.394 92.442 30.869 0.016 0.139 0.009 0.005 0.005 0.011 4 0.194 0.232 81.727 74.014 39.924 29.477 0.015 0.140 0.007 0.008 0.005 0.019 Avg. 0.016 0.139 0.009 0.006 0.005 0.016 Table D 9 EOP solution for (AST, CP, HLDAS) configuration for the Corry data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 1.175 1.455 178.765 78.015 150.110 32.829 0.016 0.144 0.011 0.007 0.005 0.019 2 0.086 1.585 91.206 70.366 117.348 31.954 0.016 0.143 0.009 0.005 0 .005 0.015 3 0.181 0.447 82.948 73.391 92.441 30.873 0.017 0.145 0.010 0.006 0.005 0.011 4 0.194 0.186 81.726 74.016 39.924 29.475 0.016 0.146 0.007 0.008 0.005 0.020 Avg. 0.016 0.144 0.009 0.006 0.005 0.016

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155 Table D 10 EOP solution for (A ST, CL, PODAS) configuration for the Corry data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 1.184 1.404 178.775 78.015 150.109 32.832 0.016 0.225 0.014 0.007 0.005 0.020 2 0.081 1.640 91.207 70.365 117.348 31.952 0.016 0.225 0.009 0.005 0 .005 0.019 3 0.184 0.474 82.948 73.394 92.442 30.869 0.016 0.226 0.011 0.005 0.005 0.011 4 0.192 0.292 81.729 74.013 39.924 29.479 0.015 0.226 0.009 0.007 0.005 0.019 Avg. 0.016 0.225 0.011 0.006 0.005 0.017 Table D 11 EOP solution for (AST CP, PODAS) configuration for the Corry data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 1.177 1.392 178.768 78.016 150.110 32.831 0.016 0.224 0.014 0.007 0.005 0.020 2 0.083 1.649 91.209 70.366 117.348 31.950 0.016 0.224 0.010 0.005 0 .005 0.019 3 0.183 0.510 82.951 73.392 92.441 30.873 0.016 0.225 0.011 0.005 0.005 0.011 4 0.191 0.248 81.728 74.015 39.924 29.477 0.015 0.226 0.009 0.007 0.005 0.019 Avg. 0.016 0.225 0.011 0.006 0.005 0.017 Table D 12 EOP solution for (AST CL, MLDAS) configuration for the Corry data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 1.180 1.532 178.767 78.014 150.110 32.826 0.016 0.103 0.009 0.007 0.005 0.018 2 0.085 1.512 91.202 70.365 117.348 31.961 0.015 0.102 0.008 0.005 0 .005 0.014 3 0.180 0.345 82.943 73.394 92.442 30.870 0.015 0.103 0.008 0.005 0.005 0.011 4 0.196 0.167 81.725 74.014 39.924 29.475 0.015 0.104 0.007 0.008 0.005 0.019 Avg. 0.015 0.103 0.008 0.006 0.005 0.015 Table D 13 EOP solution for (AST CP, MLDAS) configuration for the Corry data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 1.174 1.523 178.761 78.015 150.110 32.825 0.016 0.105 0.010 0.007 0.005 0.018 2 0.087 1.517 91.203 70.366 117.348 31.959 0.016 0.104 0.008 0.005 0 .005 0.014 3 0.180 0.377 82.946 73.391 92.441 30.874 0.016 0.106 0.009 0.006 0.005 0.011 4 0.195 0.122 81.724 74.016 39.924 29.474 0.015 0.108 0.007 0.008 0.005 0.019 Avg. 0.016 0.106 0.008 0.006 0.005 0.016 Table D 14 EOP solution for (SCT CL, HLDAS) configuration for the Corry data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 1.183 1.465 178.753 78.001 150.107 32.828 0.016 0.024 0.006 0.006 0.005 0.018 2 0.083 1.580 91.186 70.362 117.343 31.956 0.016 0.020 0.006 0.005 0 .005 0.012 3 0.182 0.412 82.921 73.400 92.437 30.869 0.016 0.012 0.005 0.005 0.005 0.011 4 0.194 0.234 81.711 74.030 39.921 29.476 0.016 0.028 0.005 0.007 0.005 0.020 Avg. 0.016 0.021 0.005 0.005 0.005 0.015

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156 Table D 15 EOP solution for (S CT, CP, HLDAS) configuration for the Corry data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 1.176 1.477 178.747 78.003 150.108 32.826 0.017 0.035 0.008 0.006 0.005 0.019 2 0.086 1.566 91.190 70.362 117.344 31.955 0.017 0.036 0.007 0.005 0 .005 0.012 3 0.184 0.414 82.920 73.401 92.437 30.874 0.017 0.012 0.005 0.005 0.005 0.012 4 0.194 0.176 81.712 74.028 39.921 29.473 0.016 0.049 0.006 0.008 0.005 0.021 Avg. 0.017 0.033 0.006 0.006 0.005 0.016 Table D 16 EOP solution for (SC T, CL, MLDAS) configuration for the Corry data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 1.183 1.466 178.752 78.001 150.107 32.828 0.016 0.023 0.006 0.006 0.005 0.017 2 0.083 1.578 91.186 70.362 117.343 31.956 0.015 0.019 0.005 0.004 0 .005 0.011 3 0.183 0.411 82.921 73.400 92.437 30.868 0.016 0.012 0.005 0.004 0.005 0.011 4 0.194 0.234 81.710 74.030 39.921 29.476 0.015 0.028 0.005 0.007 0.005 0.019 Avg. 0.016 0.020 0.005 0.005 0.005 0.015 Table D 17 EOP solution for (SCT CP, MLDAS) configuration for the Corry data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 1.176 1.479 178.747 78.003 150.108 32.826 0.016 0.033 0.007 0.006 0.005 0.018 2 0.086 1.563 91.189 70.362 117.344 31.955 0.016 0.033 0.006 0.005 0 .005 0.012 3 0.184 0.414 82.920 73.401 92.437 30.874 0.016 0.012 0.005 0.005 0.005 0.012 4 0.194 0.178 81.711 74.028 39.921 29.473 0.016 0.043 0.005 0.007 0.005 0.020 Avg. 0.016 0.030 0.006 0.006 0.005 0.015 Table D 18 EOP solution for (SCT CL, PODAS) configuration for the Corry data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 1.183 1.465 178.753 78.001 150.107 32.828 0.016 0.023 0.006 0.006 0.005 0.017 2 0.083 1.580 91.186 70.362 117.343 31.956 0.015 0.019 0.005 0.004 0 .005 0.011 3 0.183 0.412 82.922 73.400 92.437 30.869 0.015 0.012 0.005 0.004 0.005 0.011 4 0.193 0.232 81.711 74.030 39.921 29.477 0.015 0.027 0.005 0.007 0.005 0.019 Avg. 0.015 0.020 0.005 0.005 0.005 0.015 Table D 19 EOP solution for (SCT CP, PODAS) configuration for the Corry data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 1.176 1.485 178.747 78.003 150.108 32.826 0.016 0.033 0.007 0.006 0.005 0.018 2 0.086 1.559 91.190 70.362 117.344 31.956 0.016 0.034 0.006 0.005 0 .005 0.012 3 0.183 0.414 82.919 73.401 92.437 30.874 0.016 0.012 0.005 0.005 0.005 0.011 4 0.193 0.155 81.712 74.027 39.921 29.474 0.016 0.044 0.005 0.007 0.005 0.020 Avg. 0.016 0.031 0.006 0.006 0.005 0.015

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157 Table D 20 EOP solution for (CL HLDAS) configuration for the Corry data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 1.178 1.486 178.783 78.018 150.107 32.829 0.018 0.127 0.022 0.007 0.007 0.017 2 0.081 1.567 91.200 70.362 117.346 31.956 0.015 0.126 0.021 0.005 0 .006 0.014 3 0.185 0.403 82.940 73.391 92.437 30.868 0.014 0.126 0.022 0.005 0.007 0.010 4 0.203 0.268 81.702 74.017 39.933 29.478 0.016 0.127 0.022 0.007 0.008 0.017 Avg. 0.016 0.127 0.022 0.006 0.007 0.014 Table D 21 EOP solution for (CP, HLDAS) configuration for the Corry data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 1.161 1.490 178.784 78.018 150.106 32.829 0.021 0.159 0.020 0.009 0.009 0.020 2 0.091 1.556 91.189 70.369 117.350 31.953 0.019 0.154 0.020 0.007 0 .009 0.017 3 0.169 0.431 82.962 73.379 92.434 30.873 0.022 0.162 0.027 0.009 0.009 0.014 4 0.207 0.266 81.720 74.021 39.933 29.477 0.022 0.163 0.023 0.009 0.009 0.021 Avg. 0.021 0.160 0.022 0.008 0.009 0.018 Table D 22 EOP solution for (CL, MLDAS) configuration for the Corry data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 1.175 1.551 178.778 78.018 150.107 32.826 0.019 0.100 0.023 0.007 0.008 0.017 2 0.083 1.503 91.196 70.362 117.346 31.960 0.016 0.098 0.022 0.005 0 .007 0.013 3 0.183 0.339 82.936 73.391 92.437 30.868 0.015 0.099 0.023 0.005 0.007 0.011 4 0.204 0.206 81.698 74.017 39.933 29.477 0.017 0.101 0.023 0.007 0.008 0.018 Avg. 0.017 0.099 0.023 0.006 0.007 0.015 Table D 23 EOP solution for (CP, MLDAS) configuration for the Corry data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 1.158 1.570 178.771 78.018 150.106 32.827 0.019 0.112 0.018 0.008 0.008 0.018 2 0.093 1.494 91.189 70.370 117.350 31.956 0.017 0.105 0.018 0.007 0 .008 0.014 3 0.163 0.361 82.968 73.379 92.434 30.873 0.021 0.115 0.026 0.008 0.009 0.012 4 0.209 0.189 81.722 74.021 39.933 29.476 0.020 0.119 0.021 0.008 0.009 0.019 Avg. 0.019 0.113 0.021 0.008 0.009 0.016 Table D 24 EOP solution for (CL PODAS) configuration for the Corry data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 1.182 1.417 178.796 78.019 150.107 32.831 0.017 0.201 0.025 0.006 0.007 0.018 2 0.078 1.638 91.212 70.362 117.346 31.951 0.015 0.201 0.023 0.004 0 .006 0.017 3 0.187 0.474 82.952 73.391 92.437 30.868 0.014 0.202 0.024 0.005 0.007 0.010 4 0.202 0.335 81.713 74.016 39.932 29.481 0.015 0.202 0.024 0.007 0.007 0.017 Avg. 0.015 0.202 0.024 0.005 0.007 0.015

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158 Table D 25 EOP solution for (CP PODAS) configuration for the Corry data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 1.166 1.376 178.780 78.018 150.106 32.833 0.018 0.227 0.018 0.007 0.008 0.019 2 0.086 1.666 91.194 70.371 117.349 31.947 0.016 0.218 0.017 0.006 0 .008 0.018 3 0.187 0.540 82.929 73.379 92.434 30.871 0.019 0.231 0.025 0.007 0.008 0.011 4 0.196 0.363 81.701 74.020 39.933 29.480 0.018 0.228 0.023 0.007 0.008 0.018 Avg. 0.018 0.226 0.021 0.007 0.008 0.016 Table D 26 EOP solution for (CS T) configuration for the Orlando data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 0.092 0.209 99.839 296.899 39.908 31.592 0.007 0.018 0.006 0.005 0.004 0.009 2 0.333 0.033 94.004 279.706 67.467 31.815 0.007 0.018 0.006 0.003 0. 005 0.013 3 0.060 1.547 147.343 306.619 100.615 31.889 0.007 0.008 0.005 0.003 0.003 0.005 4 0.398 0.560 140.059 360.454 104.444 32.317 0.013 0.010 0.006 0.003 0.003 0.005 5 0.972 0.062 45.074 363.290 40.199 32.301 0.012 0.012 0.005 0.004 0.003 0 .008 Avg. 0.009 0.013 0.005 0.004 0.004 0.008 Table D 27 EOP solution for (HLDAS) configuration for the Orlando data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 0.018 0.075 260.181 296.902 39.906 31.589 0.100 0.150 0.050 0.010 0.010 0.010 2 0.354 0.094 266.006 279.699 67.462 31.811 0.070 0.150 0.050 0.010 0.0 10 0.010 3 0.067 1.362 212.622 306.619 100.615 31.889 0.070 0.150 0.050 0.010 0.010 0.010 4 0.280 0.490 140.072 360.454 104.443 32.317 0.070 0.150 0.050 0.010 0.010 0.010 5 1.072 0.515 45.055 363.289 40.200 32.300 0.100 0.300 0.050 0.010 0.010 0.01 0 Avg. 0.082 0.180 0.050 0.010 0.010 0.010 Table D 28 EOP solution for (CST, CL) configuration for the Orlando data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 0.086 0.235 99.837 296.899 39.907 31.600 0.007 0.011 0.006 0.005 0.004 0.007 2 0.332 0.006 94.007 279.707 67.468 31.835 0.007 0.012 0.006 0.003 0. 006 0.010 3 0.060 1.541 147.343 306.618 100.614 31.886 0.007 0.008 0.005 0.003 0.004 0.005 4 0.400 0.565 140.059 360.454 104.444 32.316 0.010 0.008 0.006 0.004 0.003 0.005 5 0.978 0.071 45.075 363.290 40.198 32.303 0.010 0.009 0.005 0.004 0.003 0 .007 Avg. 0.008 0.010 0.006 0.004 0.004 0.007

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159 Table D 29 EOP solution for (CST, CP) configuration for the Orlando data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 0.081 0.222 99.840 296.898 39.908 31.591 0.007 0.011 0.006 0.005 0.004 0.007 2 0.329 0.023 94.004 279.706 67.467 31.824 0.007 0.015 0.006 0.003 0. 006 0.012 3 0.057 1.541 147.344 306.619 100.614 31.888 0.007 0.008 0.005 0.003 0.003 0.005 4 0.417 0.553 140.059 360.454 104.445 32.310 0.009 0.007 0.006 0.004 0.003 0.004 5 0.971 0.071 45.075 363.290 40.198 32.303 0.010 0.009 0.005 0.004 0.003 0 .007 Avg. 0.008 0.010 0.006 0.004 0.004 0.007 Table D 30 EOP solution for (AST, HLDAS) configuration for the Orlando data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 0.086 0.215 99.839 296.898 39.905 31.586 0.014 0.017 0.007 0.006 0.006 0.009 2 0.339 0.030 94.005 279.705 67.465 31.813 0.015 0.014 0.007 0.005 0. 007 0.00 9 3 0.053 1.546 147.342 306.617 100.613 31.888 0.015 0.011 0.006 0.006 0.005 0.00 9 4 0.392 0.570 140.063 360.453 104.444 32.319 0.016 0.015 0.007 0.006 0.006 0.0 10 5 0.971 0.071 45.071 363.291 40.200 32.299 0.013 0.019 0.007 0.006 0.007 0 .010 Avg. 0.015 0.015 0.007 0.006 0.006 0.009 Table D 31 EOP solution for (AST, MLDAS) configuration for the Orlando data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 0.094 0.204 99.839 296.898 39.905 31.590 0.013 0.016 0.006 0.006 0.005 0.009 2 0.330 0.037 94.005 279.705 67.465 31.812 0.014 0.012 0.006 0.005 0. 006 0.00 8 3 0.062 1.543 147.342 306.617 100.613 31.886 0.013 0.010 0.006 0.005 0.00 5 0.008 4 0.387 0.570 140.064 360.453 104.444 32.321 0.015 0.014 0.007 0.006 0.00 6 0.009 5 0.968 0.058 45.071 363.291 40.200 32.298 0.012 0.018 0.006 0.005 0. 00 6 0.009 Avg. 0.013 0.014 0.006 0.005 0.006 0.009 Table D 32 EOP solution for (AST, PODAS) configuration for the Orlando data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 0.085 0.218 99.840 296.898 39.905 31.586 0.013 0.015 0.006 0.005 0.005 0.008 2 0.340 0.028 94.005 279.705 67.465 31.813 0.014 0.012 0.006 0.004 0. 00 6 0.007 3 0.052 1.548 147.342 306.617 100.613 31.888 0.014 0.010 0.006 0.005 0.00 5 0.00 8 4 0.398 0.568 140.063 360.453 104.444 32.317 0.014 0.013 0.006 0.005 0.00 6 0.00 9 5 0.975 0.076 45.072 363.291 40.199 32.301 0.011 0.017 0.006 0.005 0 .00 6 0.00 9 Avg. 0.013 0.014 0.006 0.005 0.005 0.008

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160 Table D 33 EOP solution for (AST, CL, HLDAS) configuration for the Orlando data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 0.075 0.229 99.838 296.898 39.905 31.582 0.011 0.012 0.007 0.006 0.006 0.008 2 0.346 0.015 94.006 279.705 67.465 31.818 0.011 0.011 0.007 0.005 0. 007 0.008 3 0.047 1.539 147.341 306.617 100.613 31.884 0.011 0.010 0.007 0.006 0.005 0.008 4 0.393 0.576 140.063 360.453 104.445 32.320 0.011 0.011 0.007 0.006 0.006 0.009 5 0.972 0.086 45.072 363.291 40.199 32.301 0.011 0.012 0.007 0.006 0.007 0 .010 Avg. 0.011 0.011 0.007 0.006 0.006 0.009 Table D 34 EOP solution for (AST, CP, HLDAS) configuration for the Orlando data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 0.06 6 0.223 99.840 296.897 39.905 31.578 0.012 0.013 0.007 0.006 0.006 0.009 2 0.349 0.025 94.005 279.705 67.464 31.816 0.012 0.013 0.007 0.005 0.007 0.009 3 0.040 1.543 147.342 306.617 100.612 31.893 0.011 0.011 0.007 0.006 0.005 0.008 4 0.420 0.554 140.063 360.453 104.445 32.313 0.012 0.012 0.008 0.006 0.007 0.009 5 0.971 0.092 45.072 363.291 40.199 32.306 0.012 0.013 0.007 0.006 0.007 0.010 Avg. 0.012 0.012 0.007 0.006 0.006 0.009 Table D 35 EOP solution for (AST, CL, MLDAS) configur ation for the Orlando data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 0.073 0.225 99.837 296.899 39.906 31.584 0.009 0.011 0.006 0.005 0.005 0.008 2 0.347 0.020 94.005 279.705 67.4 67 31.819 0.010 0.010 0.006 0.004 0.006 0.007 3 0.046 1.537 147.341 306.617 100.614 31.888 0.009 0.009 0.006 0.004 0.004 0.006 4 0.390 0.574 140.063 360.453 104.446 32.325 0.010 0.010 0.006 0.004 0.005 0.007 5 0.968 0.083 45.072 363.291 40.201 32 .301 0.009 0.011 0.006 0.005 0.005 0.009 Avg. 0.010 0.010 0.006 0.005 0.005 0.007 Table D 36 EOP solution for (AST, CL, MLDAS) configuration for the Orlando data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 0.069 0.219 99.840 296.898 39.905 31.579 0.011 0.012 0.006 0.006 0.005 0.008 2 0.345 0.029 94.005 279.705 67.464 31.815 0.011 0.011 0.006 0.005 0.006 0.008 3 0.044 1.542 147.342 306.617 100.612 31.893 0.011 0.010 0.00 6 0.006 0.005 0.008 4 0.420 0.553 140.063 360.453 104.445 32.313 0.011 0.011 0.007 0.006 0.006 0.009 5 0.971 0.088 45.072 363.291 40.200 32.306 0.011 0.012 0.006 0.006 0.006 0.009 Avg. 0.011 0.011 0.006 0.005 0.006 0.008

PAGE 161

161 Table D 37 EOP solution for (AST, CL, PODAS) configuration for the Orlando data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 0.076 0.230 99.838 296.898 39.905 31.583 0.011 0.011 0.007 0.006 0.006 0.0 08 2 0.345 0.014 94.006 279.705 67.465 31.819 0.011 0.011 0.007 0.005 0.007 0.008 3 0.048 1.540 147.341 306.617 100.613 31.883 0.011 0.010 0.007 0.006 0.005 0.008 4 0.396 0.575 140.063 360.453 104.444 32.319 0.011 0.011 0.007 0.006 0.006 0.009 5 0.974 0.087 45.072 363.291 40.199 32.301 0.011 0.012 0.007 0.006 0.007 0.009 Avg. 0.011 0.011 0.007 0.006 0.006 0.008 Table D 38 EOP solution for (AST, CP, PODAS) configuration for the Orlando data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 0.067 0.224 99.840 296.897 39.905 31.579 0.012 0.012 0.007 0.006 0.006 0.008 2 0.348 0.024 94.005 279.705 67.465 31.816 0.012 0.012 0.007 0.005 0.007 0.008 3 0.041 1.544 147.343 306.617 100.612 31.893 0.011 0.010 0.007 0.006 0.005 0.008 4 0.423 0.554 140.063 360.453 104.445 32.311 0.011 0.011 0.007 0.006 0.006 0.009 5 0.973 0.093 45.073 363.291 40.199 32.307 0.011 0.013 0.007 0.006 0.007 0.010 Avg. 0.012 0.012 0.007 0.006 0.006 0.009 Table D 39 EOP solution for (SCT, CL, MLDAS) configuration for the Orlando data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 0.073 0.225 99.837 296.899 39.906 31.5 84 0.009 0.011 0.006 0.005 0.005 0.008 2 0.347 0.020 94.005 279.705 67.467 31.819 0.010 0.010 0.006 0.004 0.006 0.007 3 0.046 1.537 147.341 306.617 100.614 31.888 0.009 0.009 0.006 0.004 0.004 0.006 4 0.390 0.574 140.063 360.453 104.446 32.325 0.0 10 0.010 0.006 0.004 0.005 0.007 5 0.968 0.083 45.072 363.291 40.201 32.301 0.009 0.011 0.006 0.005 0.005 0.009 Avg. 0.010 0.010 0.006 0.005 0.005 0.007 Table D 40 EOP solution for (SCT, CP, MLDAS) configuration for the Orlando data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 0.068 0.219 99.839 296.898 39.907 31.579 0.010 0.011 0.006 0.005 0.005 0.008 2 0.346 0.029 94.004 279.705 67.466 31.815 0.010 0.011 0.006 0.004 0 .006 0.008 3 0.043 1.542 147.342 306.617 100.614 31.893 0.010 0.009 0.006 0.004 0.004 0.006 4 0.420 0.553 140.063 360.453 104.447 32.313 0.010 0.010 0.006 0.004 0.005 0.007 5 0.970 0.088 45.072 363.291 40.201 32.306 0.010 0.012 0.006 0.005 0.005 0.009 Avg. 0.010 0.011 0.006 0.005 0.005 0.007

PAGE 162

162 Table D 41 EOP solution for (SCT, CL, PODAS) configuration for the Orlando data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 0.071 0.229 99.838 296.898 39.907 31.583 0.010 0.011 0.006 0.006 0.005 0.008 2 0.350 0.017 94.006 279.705 67.467 31.820 0.010 0.011 0.006 0.004 0.006 0.008 3 0.043 1.539 147.341 306.617 100.614 31.889 0.010 0.010 0.006 0.004 0.004 0.006 4 0.392 0.574 140.063 360.453 104.446 32.325 0.011 0.011 0.007 0.005 0.005 0.007 5 0.969 0.087 45.072 363.291 40.201 32.302 0.010 0.012 0.006 0.006 0.005 0.009 Avg. 0.010 0.011 0.006 0.005 0.005 0.008 Table D 42 EOP solution for (SCT, CP, PODAS) con figuration for the Orlando data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 0.065 0.224 99.839 296.898 39.907 31.578 0.010 0.012 0.007 0.006 0.005 0.008 2 0.349 0.025 94.005 279.705 67.466 31.817 0.011 0.012 0.007 0.004 0.006 0.008 3 0.040 1.544 147.342 306.617 100.614 31.894 0.011 0.010 0.006 0.004 0.004 0.006 4 0.422 0.553 140.063 360.453 104.447 32.312 0.011 0.011 0.007 0.005 0.005 0.007 5 0.972 0.093 45.073 363.291 40.2 01 32.307 0.010 0.013 0.007 0.006 0.005 0.010 Avg. 0.011 0.012 0.007 0.005 0.005 0.008 Table D 43 EOP solution for (SCT, CL, HLDAS) configuration for the Orlando data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 0.070 0.228 99.837 296.898 39.906 31.582 0.010 0.012 0.006 0.006 0.005 0.008 2 0.350 0.018 94.006 279.705 67.467 31.820 0.010 0.011 0.006 0.004 0.006 0.008 3 0.043 1.538 147.341 306.617 100.614 31.889 0.010 0.010 0.006 0.004 0.004 0.006 4 0.390 0.575 140.063 360.453 104.446 32.325 0.011 0.011 0.007 0.005 0.005 0.007 5 0.968 0.086 45.072 363.291 40.201 32.301 0.010 0.012 0.006 0.006 0.005 0.010 Avg. 0.010 0.011 0.006 0.005 0.005 0.008 Table D 44 E OP solution for (SCT, CP, HLDAS) configuration for the Orlando data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 0.065 0.223 99.839 296.898 39.907 31.578 0.011 0.013 0.007 0.006 0.005 0 .009 2 0.349 0.026 94.004 279.705 67.466 31.816 0.011 0.012 0.007 0.004 0.006 0.009 3 0.040 1.543 147.342 306.617 100.614 31.894 0.011 0.010 0.006 0.004 0.004 0.006 4 0.419 0.554 140.063 360.453 104.447 32.313 0.011 0.012 0.007 0.005 0.005 0.008 5 0.971 0.092 45.072 363.291 40.201 32.306 0.011 0.013 0.007 0.006 0.006 0.010 Avg. 0.011 0.012 0.007 0.005 0.005 0.008

PAGE 163

163 Table D 45 EOP solution for (CL, HLDAS) configuration for the Orlando data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 0.069 0.200 99.831 296.906 39.904 31.589 0.014 0.015 0.026 0.009 0.009 0.008 2 0.329 0.055 94.011 279.700 67.463 31.814 0.015 0.016 0.031 0.009 0.009 0.008 3 0.064 1.516 147.346 306.614 100.617 31.883 0.014 0.013 0.015 0.009 0.008 0.008 4 0.409 0.565 140.035 360.454 104.442 32.324 0.011 0.015 0.027 0.009 0.008 0.008 5 0.951 0.101 45.097 363.289 40.200 32.296 0.013 0.024 0.031 0.009 0.009 0.009 Avg. 0.014 0.017 0.026 0.009 0.009 0.008 Table D 46 EOP solution for (CP, HLDAS) configuration for the Orlando data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 0.069 0.200 99.831 296.906 39.904 31.589 0. 014 0.015 0.026 0.009 0.009 0.008 2 0.329 0.055 94.011 279.700 67.463 31.814 0.015 0.016 0.031 0.009 0.009 0.008 3 0.064 1.516 147.346 306.614 100.617 31.883 0.014 0.013 0.015 0.009 0.008 0.008 4 0.409 0.565 140.035 360.454 104.442 32.324 0.011 0. 015 0.027 0.009 0.008 0.008 5 0.951 0.101 45.097 363.289 40.200 32.296 0.013 0.024 0.031 0.009 0.009 0.009 Avg. 0.014 0.017 0.026 0.009 0.009 0.008 Table D 47 EOP solution for (CL, MLDAS) configuration for the Orlando data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 0.063 0.216 99.825 296.897 39.903 31.587 0.012 0.012 0.011 0.008 0.009 0.008 2 0.344 0.027 94.003 279.710 67.463 31.818 0.012 0.012 0.011 0.008 0.008 0.008 3 0.051 1.518 147.333 306.614 100.616 31.878 0.011 0.011 0.010 0.008 0.008 0.007 4 0.387 0.566 140.036 360.454 104.446 32.324 0.011 0.012 0.020 0.009 0.008 0.008 5 0.969 0.086 45.078 363.288 40.198 32.297 0.012 0.015 0.019 0.009 0.009 0.009 Avg 0.012 0.013 0.014 0.009 0.008 0.008 Table D 48 EOP solution for (CP, MLDAS) configuration for the Orlando data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 0.066 0.198 99.84 0 296.904 39.905 31.592 0.014 0.015 0.020 0.009 0.009 0.009 2 0.327 0.060 93.990 279.700 67.463 31.812 0.016 0.016 0.026 0.009 0.009 0.009 3 0.064 1.514 147.345 306.616 100.615 31.884 0.014 0.014 0.015 0.009 0.008 0.008 4 0.411 0.552 140.047 360.4 55 104.444 32.322 0.012 0.015 0.024 0.009 0.009 0.009 5 0.951 0.070 45.084 363.288 40.200 32.296 0.013 0.024 0.029 0.009 0.009 0.009 Avg. 0.014 0.017 0.023 0.009 0.009 0.009

PAGE 164

164 Table D 49 EOP solution for (CL, PODAS) configuration for the Or lando data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 0.062 0.223 99.821 296.899 39.903 31.586 0.012 0.012 0.012 0.008 0.008 0.008 2 0.346 0.020 93.998 279.710 67.464 31.819 0.012 0.012 0.012 0.008 0.008 0.008 3 0.049 1.522 147.328 306.612 100.617 31.879 0.011 0.011 0.011 0.008 0.008 0.007 4 0.392 0.570 140.012 360.455 104.445 32.323 0.011 0.012 0.025 0.009 0.008 0.008 5 0.972 0.100 45.085 363.287 40.198 32.298 0.012 0.015 0.021 0.009 0.009 0.009 Avg. 0.011 0.012 0.016 0.008 0.008 0.008 Table D 50 EOP solution for (CP, PODAS) configuration for the Orlando data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 0.071 0.203 99.840 296.905 39.904 31.592 0.013 0.014 0.023 0.008 0.008 0.008 2 0.327 0.047 94.044 279.701 67.463 31.812 0.015 0.015 0.041 0.008 0.008 0.00768 3 0.069 1.521 147.338 306.615 100.617 31.883 0.013 0.013 0.015 0.008 0.008 0.007 36 4 0.415 0.566 140.013 360.456 104.442 32.322 0.011 0.014 0.031 0.008 0.008 0.00768 5 0.957 0.113 45.123 363.287 40.200 32.297 0.013 0.022 0.039 0.008 0.008 0.00789 Avg. 0.013 0.015 0.030 0.008 0.008 0.008 Table D 51 EOP solution for (C L, ICP, HLDAS) configuration for the Orlando data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 0.061 0.220 99.816 296.900 39.899 31.586 0.012 0.013 0.012 0.008 0.009 0.008 2 0.348 0.0 23 93.998 279.705 67.463 31.818 0.013 0.013 0.011 0.008 0.008 0.008 3 0.048 1.522 147.337 306.616 100.621 31.880 0.012 0.012 0.011 0.009 0.008 0.008 4 0.388 0.569 140.025 360.454 104.446 32.324 0.012 0.013 0.024 0.010 0.009 0.009 5 0.970 0.096 4 5.080 363.288 40.198 32.297 0.013 0.016 0.021 0.010 0.010 0.009 Avg. 0.012 0.013 0.016 0.009 0.009 0.009 Table D 52 EOP solution for (CP, ICP, HLDAS) configuration for the Orlando data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 0.066 0.200 99.818 296.906 39.904 31.590 0.014 0.015 0.016 0.009 0.009 0.008 2 0.333 0.051 94.003 279.698 67.462 31.812 0.015 0.015 0.015 0.009 0.009 0.008 3 0.066 1.519 147.345 306.617 100.617 31.884 0.013 0.014 0.013 0.009 0.008 0.008 4 0.410 0.563 140.034 360.455 104.443 32.323 0.012 0.015 0.028 0.009 0.008 0.009 5 0.952 0.099 45.097 363.288 40.200 32.296 0.013 0.024 0.032 0.009 0.009 0.009 Avg. 0.014 0.017 0.021 0.009 0.009 0.00 8

PAGE 165

165 Table D 53 EOP solution for (CL, ICP, PODAS) configuration for the Orlando data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 0.062 0.222 99.814 296.901 39.899 31.586 0.012 0.01 3 0.012 0.008 0.008 0.008 2 0.347 0.022 93.995 279.705 67.463 31.819 0.012 0.012 0.012 0.008 0.007 0.008 3 0.049 1.523 147.334 306.615 100.622 31.879 0.012 0.011 0.011 0.008 0.008 0.008 4 0.392 0.570 140.009 360.455 104.445 32.323 0.011 0.012 0.02 6 0.009 0.009 0.009 5 0.972 0.099 45.084 363.287 40.198 32.298 0.012 0.015 0.021 0.009 0.009 0.009 Avg. 0.012 0.013 0.016 0.009 0.008 0.008 Table D 54 EOP solution for (CP, ICP, PODAS) configuration for the Orlando data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 0.070 0.201 99.813 296.906 39.904 31.592 0.013 0.014 0.018 0.008 0.008 0.008 2 0.329 0.050 93.998 279.698 67.462 31.812 0.015 0.014 0.016 0.008 0.008 0.008 3 0.070 1.521 147.339 306.617 100.618 31.884 0.013 0.013 0.014 0.008 0.008 0.007 4 0.416 0.566 140.012 360.456 104.442 32.322 0.011 0.014 0.032 0.008 0.008 0.008 5 0.957 0.113 45.123 363.287 40.200 32.297 0.013 0.023 0.040 0.008 0.008 0.008 Avg. 0.013 0.015 0.024 0.008 0.008 0.008 Table D 55 EOP solution for (CL, ICP, MLDAS) configuration for the Orlando data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 0.064 0.215 99. 818 296.899 39.899 31.588 0.012 0.012 0.010 0.008 0.008 0.008 2 0.345 0.028 94.000 279.706 67.463 31.818 0.012 0.012 0.010 0.008 0.007 0.008 3 0.051 1.518 147.339 306.617 100.621 31.879 0.011 0.011 0.009 0.008 0.007 0.007 4 0.388 0.566 140.034 360 .454 104.446 32.324 0.011 0.012 0.020 0.009 0.008 0.009 5 0.969 0.085 45.077 363.288 40.198 32.297 0.012 0.015 0.019 0.009 0.009 0.009 Avg. 0.012 0.013 0.014 0.008 0.008 0.008 Table D 56 EOP solution for (CP, ICP, MLDAS) configuration for th e Orlando data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 0.066 0.198 99.840 296.904 39.905 31.592 0.014 0.015 0.020 0.009 0.009 0.009 2 0.327 0.060 93.990 279.700 67.463 31.812 0. 016 0.016 0.026 0.009 0.009 0.00 9 3 0.064 1.514 147.345 306.616 100.615 31.884 0.014 0.014 0.015 0.009 0.008 0.008 4 0.411 0.552 140.047 360.455 104.444 32.322 0.012 0.015 0.024 0.009 0.009 0.00 9 5 0.951 0.070 45.084 363.288 40.200 32.296 0.013 0 .024 0.029 0.009 0.009 0.00 9 Avg. 0.014 0.017 0.023 0.009 0.009 0.009 Table D 57 EOP solution for (ICP, HLDAS) configuration for the Orlando data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 Sta1 0.018 0.075 99.816 296.902 39.906 31.589 0.051 0.041 0.031 0.010 0.010 2 Sta2 0.367 0.138 94.008 279.699 67.463 31.810 0.051 0.038 0.029 0.010 0.010 3 Sta3 0.088 1.411 147.363 306.619 100.615 31.889 0.055 0.040 0.030 0.010 0.010 Avg. 0.052 0.040 0.030 0.010 0.010

PAGE 166

166 Table D 58 EOP solution for (ICP, MLDAS) configuration for the Orlando data set Sta. ( ) ( ) ( ) (m) (m) (m) ( ) ( ) ( ) (m) (m) (m) 1 0.012 0.053 99.817 296.902 39.906 31.589 0.053 0.041 0.023 0.011 0.011 0.011 2 0.371 0.147 94.008 279.699 67.463 31.810 0.053 0.039 0.022 0.01 1 0.01 1 0.01 1 3 0.084 1.403 147.364 306.619 100.614 31.889 0.052 0.042 0.023 0.01 1 0.01 1 0.01 1 Avg. 0.053 0.041 0.023 0. 011 0.011 0.011

PAGE 167

167 APPENDIX E F STATISTICS FOR DIFFERENT INTEGR ATED METHODS Each figure in this section show s the values for F tests on the difference in estimated variances and MSEs from experiments in Chapter 5 Ea ch row shows the method, the estimated standard deviation or RMSE and the values for F tests on the corresponding column. For example, in Figure E 1 the value for the F statistic of (AST, HLDAS) versus (AST, PODAS) is 0.046237, indicating the varianc e of (AST, HLDAS) was significantly less than the variance of (AST, PODAS), with a confidence level of 95.3763%. Values less than 0.10 are highlighted in green with green text indicating the row method had significantly lower variance than the column meth od with at least a 90% confidence. Similarly, the cells highlighted in red with red text indicate the row method had a significantly higher variance than the column method at 90% confidence. Standard deviation cells highlighted green indicate scanner tar gets were used, orange indicates no scanner targets were used in the corresponding methods. The chart s are split into parts for easy viewing.

PAGE 168

168 Figure E 1. Alpha v alues for F tests on v ariances of from using d ifferent m ethods of g eoreferencing the Cor ry Village d ata s et

PAGE 169

169 Figure E 1. Continued

PAGE 170

170 Figure E 1. Continued

PAGE 171

171 Figure E 2. Alpha v alues for F tests on v ariances of from using d ifferent m ethods of g eoreferencing the Orlando d ata s et

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172 Figure E 2. Continued

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173 Figure E 2. Continued

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174 F igure E 2. Continued

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175 Figure E 3. Alpha v alues for F tests on v ariances of from using d ifferent m ethods of g eoreferencing the Orlando d ata s et Figure E 3. Continued

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176 Figure E 4 Alpha v alues for F tests on MSE of from using d ifferent m ethod s of Georeferencing the Orlando d ata s et Figure E 4 Continued

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177 Figure E 5 Alpha v alues for F tests on MSE of from using d ifferent m ethods of g eoreferencing the Orlando d ata s et Figure E 5 Continued

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178 APPENDIX F COPLANARITY VERSUS C OLLINEARITY Results from the experiments in this study showed that there were small, but noteworthy increases in precision when using collinearity as opposed to coplanarity. In practical photogrammetry, the coplanarity condition equations are typically relegated to f inding the relative orientation of image pairs. This is due to the characteristic instability found when using coplanarity to solve for the EOPs of multiple images simultaneously (Mikhail, et al. 2001). The numerical instability is caused by the use of determinants in Equation 2 11b. This leads to very large numbers in the design matrix. For instance, in the Corry Village data set, a point observed on six images yielded for Station 1, where is Equation 2 11b. The condit ion numbers for and in Equation 2 28 are approximately and respectively for the method (CP, PODAS) of the Corry Village data set. The poor conditioning of these matrices leads to round off error in the adjust ment computations that manifest as oscillations about the minimum of the squared residuals. Figure F 1 shows the standard error of unit weight for the first few iterations of the (CP, PODAS) method for the Corry Village data set. Note that after the 16 th iteration, the standard error of unit weight oscillates between four values. The solution vector, corrections to be applied to previous iteration estimations of EOPs, exhibits the same trend where the sum of four sequential corrections is equal to zero l eading to continuous oscillation. The estimated solutions for during the oscillating phase is shown in Figure F 2 Note that the solution for and the associated estimated standard deviations (above and below)

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179 found via (CL, PODAS) are included in the plot for comparison. Note that the oscillating solutions from (CP, PODAS) are well within a single standard deviation of estimated from the converged (CL, PODAS) solution. Figure F 1. Standard e rror of u nit w eight for (CP, PODAS) it erations on t he Corry Village d ata s et Figure F 2 Estimated for o scillating it erations using (CP, PODAS) (blue), estimated from converged (CL, PODAS) (red), and bounding standard deviations for converged (CL, PODAS) Although the oscillating solution can be considered as converged, there are methods of finding a single convergent value for poorly behaving functions. The most hailed of these is the Levenberg Marquardt Algorith m (LMA) (Press et al ., 1992). The 1 1.05 1.1 1.15 1.2 1.25 1.3 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 Standard Error of Unit Weight Iteration 1.8 1.7 1.6 1.5 1.4 1.3 1.2 1.1 1 ( )

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180 LMA can be considered a hybrid method of typical nonlinear least squares approach (Gauss Newton Method), and Gradient Descent. Gradient Descent is an iterative algorithm where, in the case of nonlinear least squares, one takes steps in the direction of the negative gradient of a function to be minimize d, in our case the squares of the residuals until a minimum is reached and therefore the gradient is zero. If is the step size, then the Gradient Descent Algorithm is described by Equation F 1 ( F 1 ) The matrix is the n egative gradient of the square of the residuals, and is the solution vector to be added to the current approximation of the unknowns The Levenberg Marquardt algorithm is described by Equation F 2 ( F 2 ) Note that Equation F 2 is the normal equations with a dampening value, Also note that the dampening values are scaled by the diagonal elements of thus steps are larger for lower magnitude gradients of the function and convergence time is respect to starting conditions and choices at each iteration. The recommendation for the LMA given in (Press et al ., 1992) is the following (a dapted): 1. Start with a small value for ( is suggested) 2. Solve Equation F 2 3. If the standard error of unit weight increased or stayed the same, increase by a factor of 10 and go back to 2. 4. If the If the standard error of unit weight decreased, ap ply the corrections, decrease by a factor of 10, and go back to 2.

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181 The process is continued until corrections are negligible or is larger than a selected threshold The main idea behind the LMA is that if the Gauss Newton component is not working, mor e weight is applied to the Gradient Descent component. The downsides to the LMA include convergence on local minima and the sometimes large number of iterations required. The LMA was used to adjust the (CP, PODAS) Corry Village data with the resulting st andard errors of unit weight for each iteration shown in Figure F 3 Figure F 3 Standard e rror of u nit w eight for (CP, PODAS) i terations on the Corry Village d ata s et u sing LMA Comparison of Figure 5 3 with Figure F 1 shows that using LMA increased the precision of the overall solution (exhibited by the lower standard error of unit weight), although much more iterations were necessary to reach convergence and as stated before, the algorithm converges only on a local minimum In many of the experiments in this study, collinearity was shown to yield significantly more precise results than coplanarity. this study refers to the probability that any difference between m ethods was not due to random chance not that any practical improvement exists The superiority of the 0.99 0.995 1 1.005 1.01 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 Standard Error of Unit Weight Iteration

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182 collinearity method was most likely due to the numerical instability of the coplanarity equations and the fact that camera calibration parameter estimate s and were averaged to obtain a single focal length value used for CP methods. Coplanarity provides many advantages over collinearity, not the least of which is speed. Since the collinearity equations necessitate the inclusion of object s pace coordinates for imaged points, the adjustments using CL involve much larger adjustments than those using CP, and therefore more time is need for each iteration. That said, CL methods converged in much fewer iterations than did CP methods. Table F 1 shows the number of iterations and time per iteration for (CP, PODAS) and (CL, PODAS) adjustments of the Corry Village data set and is indicative of results for CP versus CL methods in each data set. Note that the same initial approximations were used for each method, and that although the implementation was not optimized for speed, the values reported here are valid for comparing computation time. Table F 1 indicates that even when using LMA, the methods using coplanarity were much faster than the ones us ing CL. Table F 1 Number of i terations and c omputation t ime for d ifferent m ethods using c oplanarity and c ollinearity Iterations Time per Iteration (ms) Total Time (ms) (CL, PODAS) 3 1638 4914 (CP, PODAS) 17 33 561 (CP, PODAS) LMA 37 34 1258 As a fi nal note, the instability of the coplanarity condition equations may be defeated by using extended precision arithmetic libraries, thus decreasing the probability of experiencing round off errors. Another suggestion is the use of a hybrid method that firs t finds a solution using coplanarity, then uses that solution to obtain initial approximations for object space points via space intersection, and finally solves

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183 for the unknowns using the collinearity equations. Granted this would not be a great choice for applications with time constraints.

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184 APPENDIX G DAS COLLECTION WORKF LOW The first thing to consider prior to scanning when using the DAS system is the location of the scanner stations The stations should be located where they have the clearest view of the sky as possible and should be well distributed relative to each other in the project area. K eep the stations as far from linearly aligned as possible. The GPS receivers sh ould collect data continuously when scanning and when mov ing from station to station. Collecting the DAS stops after scanning minimizes the effects of the scanner settling into soft ground and causing errors in the DAS derived EOPs Once scanning is complete at a station the DAS stops are collected. T he head of the scanner is rotated, using controlling software, to orientations at 15 increments. Thus, f or full coverage, 24 stops are needed. At each of these stops, the angle is recorded from output in the scanner software since the angle measured by the enc oders may be slightly different from the orientation angle to which the scanner was instructed to move The GPS time should be recorded when a stop begins and ends. Certain receivers allow users to flag events in the GPS file, which is useful in processi ng for finding the stops in the data. The stops should last from one to two minutes. Once the DAS stops are collected, images are taken such that full 360 panoramic coverage is obtained The overall process after mission planning, is summarized in the following list. 1. Begin recording GPS observations. 2. Set up the scanner and scan the area of interest including fine scan of targets if needed 3. After scanning, record 24 DAS stops at 15 increments. a. Orient the scanner head

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185 b. Record the GPS time and measured sc anner head angle c. Collect data for one to two minutes d. Record GPS time e. Repeat 4. Obtain images for 360 panoramic coverage 5. Move to the next station and repeat.

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186 LIST OF REFERENCES Ackerman, F. 1999 Airborne laser scanning present status and future expectation. ISPRS Journal of Photogrammetry and Remote Sensing, 54: 65 67. Al Manasir, K., and C. S. Fraser, 2006 Registration of terrestrial l aser scanner data using imagery, The Photogrammetric Record, 21 : 255 268. Bates, K. T., F. Rarity, P. L Manning, D. Hodgetts, B. Vila, O. Oms, A. Galobart, and R. Gawthorpe 2008 High resolution LiDAR and photogrammetric survey of the fumanya dinosaur tracksites (catalonia): Implications for the conservation and interpretati on of geological heritage sites Journal of the Geological Society, 165 : 115 127. Besl, P. J., and H. D. McKay, 1992 A method for registration of 3 D shapes. Pattern Analysis and Machine Intelligence, IEEE Transactions on, 14 : 239 256. Brown, D. C., 1971 Close range camera calibration Photogrammetric Engineering, 37 : 855 866. Fraser, C. S., 1998 Some thoughts on the emergence of dig ital close range photogrammetry, Photogrammetric Record, 16 : 37 50. Fraser, C. S., 1997 Di gital camera self calibration, ISPRS Journal of Photogrammetry and Remote Sensing, 52 : 149 159. Hunter, G., H. Pinkerton, R. Airey and S. Calvari, 2003 The application of a long range laser scanner for monitoring volcanic activity on mount etna. Journal of Volcanology and Geothermal Research, 123 : 203 210. Kenefick, J. F., M. S. Gyer and B. F. Harp, 1972 Close range camera calibration, Photogrammetric Engineering, 38 : 1117 1126. Mikhail, E., J.S. Bethel, and J.C. McGlone, 2001. Introduction to Modern Photogrammetry John Wiley and Sons, Inc., New York 479 p. Paffe nholz J A., H. Kutterer 20 08. Direct Georeferencing of Static Terrestrial Laser Scans. Proceedings of FIG Working Week 14 19 June Stockholm, Sweden pp. 2776 2790 Pesci, A., and G. Teza, 2008 Terrestrial laser scanner and retro reflective targets: An experiment for anomalous effects investigation. Int ernational Journal of Remote Sensing 29 : 5749 5765. Press, W.H., S.A. Teukolsky, W. T. Vetterling, and B.P. Flannery, 1992. Numerical Recipes in C: The Art of Scientific Computing Cambridge University Press, Cambridge, United Kingdom, 1002 p.

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187 Reshetyuk, Y., 2009. Self Calibration and Direct Georeferencing in Terrestrial Laser Scanning Doctoral thesis, Royal Institute of Technology, Stockholm, Sweden, 174p. Rosser, N. J., D. N. Petley, M. Lim, S. A. Du nning and R. J. Allison, 2005 Terrestrial laser scanning for monitoring the process of hard rock coastal cliff erosion, Quarterly Journal of Engineering Geology and Hydrogeology, 38 : 363 375. Rowlands, K. A., L. D. Jones and M. Whitworth, 2003 Landslid e laser scannin g: A new look at an old problem, Quarterly Journal of Engineering Geology and Hydrogeology 36 : 155 157. Schneider, D., and H. D. Maas, 2007 Integrated bundle adjustment with variance component estimation fusion of terrestrial laser scanner data, panoramic and central perspective image data, International Archives on Photogrammetry and Remote Sensing, 37 : 373 378. Schuhmacher, S., and J. Bohm 2005 Georeferencing of terrestrial laserscanner data for applica tions in architectural modeling, P roceedings of the ISPRS Working Group V/4 Workshop 3D ARCH, 22 24 August, Venice, Italy, unpaginated. Wilkinson, B., A. Mohamed B. Dewitt, and G. Seedahmed, 2010 A novel approach to t errestrial LiDAR georeferencing, Photogrammetric Engineering and Remote Sensing, 76: 6. Wolf, P.R., and B.A. Dewitt, 2000. Elements of Photogrammetry (with Applications in GIS) McGraw Hill, Inc., New York 624 p.

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188 BIOGRAPHICAL SKETCH Ben Wilkinson was born in Gainesville when his father was attending the University of Florida. He grew up in Wadesboro, Florida, just east of Tallahassee. After meeting with David Gibson following a couple of years of undecided and liberal arts majors, he decided to and enroll in the g eomatics program at UF He received his Bachelor of Science and Master of Science degrees in 2004 and 2007, respectively. Ben married his high school sweetheart, Zhao, in 2007. In his free time, Ben enjoys composing music and playing guitar. He has two dogs and three cats.