اسم المؤلف
Bashar Alsadik
التاريخ
4 مايو 2024
المشاهدات
191
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Computational Geophysics Adjustment Models in 3D Geomatics and Computational Geophysics
With Matlab Examples
Volume 4
Bashar Alsadik
Faculty member at Baghdad University – College of Engineering – Iraq (1999–2014)
Research assistant at Twente University – ITC faculty – The Netherlands (2010–2014)
Member of the International Society for Photogrammetry and Remote Sensing ISPRS
Table of contents
- Statistical Introduction
- Propagation of Errors
- Least Squares Adjustment Procedures
- Common Observation Models and Their Adjustment in Geomatics
- Adjustment Using General Observation Model
- Adjustment with Constraints
- Unified Approach of Least Squares
- Fitting Geometric Primitives with Least Squares
- 3D Transformation and Co-Registration
- Kalman Filter
- Introduction to Adjustment with Levenberg-Marquardt Method
- Post Analysis in Adjustment Computations
Appendix: MATLAB Code for Generic 2D Geodetic Networks Adjustment References
Index
Note: Page numbers followed by f indicate figures, t indicate tables and b indicate boxes.
A
Accidental errors, 3, 3f
Accuracy, 4, 4f
Additional constraints, 188
Adjusted points, ellipsoid of errors, 223–224f, 229f,
238f
Adjustment, 53, 55f, 215. See also Least squares
adjustment
with condition equations method, 62, 64
with inner constraints, 198
by observation equations, 61, 63
Airplane flight simulation, 313–326, 319f, 321f
Angle observation model, 95–100
Angular 2D resection, 99, 100f
Arithmetic mean, 6
Azimuth angle
of ellipsoid of errors, 78
of laser beam, 29–30
2D observation model, 90, 110
Azimuth direction intersection, 164, 164f
Azimuth observation model, 91
B
Body waves, 143
C
Cartesian coordinates, 100
CDF. See Cumulative distribution function (CDF)
Circle parameters, 188
Collinearity equations, 124–125
Computational geophysics, 141
Condition equations, 55, 55f, 59–66
Constrained adjustment. See also Free net adjustment
additional parameters, 188–198, 194f
correction vector, 171
direct method, 171, 174
geometric/physical conditions, 169, 169f
Helmert method, 171–173
image triangulations, 177–181, 178f
inner constraints, 198–214
LaGrange multipliers, 171
normal equations, 171
over-weighting method, 172–185
perpendicularity, 182–184b, 185
unified, 233
Control points, 155–167, 157f
Coregistration
concept, 273f
of point clouds, 274f, 279f, 280, 285f
target-based, 274f
Cosine rule, 119
Cumulative distribution function (CDF), 11–13
D
Damped least-squares method, 327
Damping factor, 328–329
Data snooping, 351–363, 352–353b, 357–361b
Datum defect, 199–200
Degree of freedom, 6, 53
Detection, identification, and adaptation
(DIA) test, 349–382
Direct adjustment method, 171, 174
Direct linear transformation (DLT), 83–84
Dynamic model
for 3D state case, 302
of filtering, 320–326, 321f
E
Earthquake
hypocenter and epicenter, 144f
and least squares adjustment, 144–151
P and S waves, 143, 143f
EKF. See Extended Kalman Filter (EKF)
Ellipse of errors, 67–70, 70f
free net adjustment, 202, 203f
Ellipsoid of errors, 67, 76–83, 78f
adjusted points, 223–224f, 229f, 238f
constrained adjustment, 177, 177f
free adjustment, 208f, 212, 214f
image triangulation, 135, 135f
Lidar sensor, 31–34, 32f
vertical angle observation, 113f
Engineering construction project, 1, 2f
Error propagation. See Propagation of errors
411Errors
classification, 348
definition, 2
preanalysis of, 43–51
Extended Kalman Filter (EKF), 299
External reliability, 385
F
Fitting
circle in 3D space, 256–258
cylinder, 261f, 263–271, 264f, 266–268b, 268f
plane, 248–250
sphere, 251
2D circle, 258–263
3D line, 247f, 250–256
Forward problem, 141, 142f
Free net adjustment, 199
convergence, 213f
of 2D network, 199, 206, 206f
for 3D networks, 200
ellipse of errors, 202, 203f
ellipsoid of errors, 208f, 212, 214f
MATLAB code, 209–210
observation equations, 207
pseudoinverse matrix, 211
variance covariance matrix, 200
variance of unit weight, 200
Fundamental matrix, 83–84
G
Gaussian curve, 304
Gauss Newton (GN) method, 327–329
Geiger’s method, 144
Generalized inverse, 47–51
General least squares model
concept of, 153, 154f
covariance matrix, 155
normal equations, 155
residuals vector, 155
sphere fitting, 155–159b
3D forward intersection by angles, 163–167b
Geodetic network, 67, 67f
GN method. See Gauss Newton (GN) method
Goodness of fit test, 346–348, 347f
GPR. See Ground penetration radar (GPR)
Gradient descent, 328, 328f
Gross errors, 2
Ground penetration radar (GPR), 216
H
Helmert method, 171–173, 179, 199, 202, 207
Homogeneous least squares adjustment, 83, 245–247b
image rectification by homography, 84–88
MATLAB code, 88
singular value decomposition, 83, 87
Hypothesis testing, classification of error in, 348–349,
348t, 349f
I
ICP. See Iterative closest point (ICP)
Image pose/resection, 337–340b
Image rectification, 84
Image space resection, 125–135
Image triangulation/intersection
with constraints, 177–181, 178f
least squares adjustment, 136–141
observation equation, 134–135, 140
Image warping, 85–88
Inner constraints. See Free net adjustment
Internal reliability, 385
Inverse problem, 142, 142f
Iterative closest point (ICP), 275
J
Jacobian matrix, 25–26
Lidar sensor error estimation, 30
quadrilateral polygon area computation, 40–43
triangular polygon area computation, 35
K
Kalman filter
applications, 299–300
concepts, 299
corrections and update, 303–304, 303f
distributions, 305
efficiency of, 299
prediction, 300–303, 300–301f
structural deformation monitoring, 306–312, 307f, 312f
workflow, 305f
Keystone distortion, 85–88
Kronecker product, 44–47, 50, 291
L
LaGrange multipliers, 56, 59, 153, 170
Laser scanner, 216
Laser scanning, 29–34
Least squares, 53
Least squares adjustment, 15–17. See also Homogeneous
least squares adjustment
angle observation model, 95–100
Azimuth observation model, 91
condition equations model, 55f, 59–66
earthquake location and, 144–151
ellipse of errors, 68–70, 70f
ellipsoid of errors, 76–83, 78f
homogeneous system, 83–88
412 INDEXimage space resection, 125–135
image triangulation/intersection, 136–141
nonhomogeneous system, 85, 87
oblique angular resection, 118–124
observation equations model, 55f, 56–59
properties, 55–56
relative ellipse of errors, 70–76, 83f
seismic waves and earth’s interior, 143
2D distance observation, 90–93
3D distance observation model, 100–105
3D line intersection model, 113–118
unified approach, 215–216, 215f, 233–242
vertical angle observation model, 105–113
Levenberg-Marquardt (LM) method, 327–329
Lidar sensors, 29
Linear least squares-based techniques, 245–247b
Linear quadratic estimation (LQE), 299
LM method. See Levenberg-Marquardt (LM) method
M
MAD. See Median absolute deviation (MAD)
MATLAB code
condition and observation adjustment method, 66
constraints with additional parameters, 194–196,
198
cumulative distribution function, 11–12
earthquake location problem, 148–149, 151
ellipsoid of errors, 79–80
free net adjustment, 209–210
for general least squares, 161–162
homography matrix, 88
image resection problem, 130–136
image triangulation, 137–138
Kalman filtering, 321–325
Kronecker product, 46
Lidar sensor error estimation, 33
normal distribution curve, 10
oblique angle resection, 121, 123
perpendicularity constrained adjustment, 185–187
polygon area computation, 38
pseudoinverse/generalized inverse computation, 50
relative ellipse of errors, 73–75
robust estimation, 368
sphere fitting, 254
3D distance observation, 103–105
weighted mean, 19, 21
Matrix form, 25–28
Median absolute deviation (MAD), 13, 364–365
Minimal constraint, 199
Misfit, 329–334
Mixed adjustment model, 153
Mixed 2D observations, 97, 97f
Mixed triangulation-trilateration network, 67, 67f
Mobile mapping system (MMS), 216
Model norm, 329–334
Most probable value (MPV), 2, 5, 7
Multidata collection system, 216f
N
Newton optimization method, 328, 328f
NLLS. See Nonlinear least squares problems (NLLS)
Nonhomogeneous least squares adjustment, 85, 87
Nonlinear least squares, 327
of 3D similarity transformation, 275–277, 276f
Nonlinear least squares problems (NLLS), 327
Nonlinear observation equations, 89–90
Normal distribution curve, 7–11
Normal equation system, 56
O
Oblique angle 3D resection model, 118–124
Observation equation model
adjustments by, 54–59, 55f, 63
angle, 96–100, 96f
azimuth, 94
free net adjustment, 207
image space resection, 127
image triangulation/intersection, 134–135, 140
line intersection, 3D space, 113–118
2D distance, 90, 92–93
3D distances, 100–105
for vertical angles, 106–107
Overlapped images, of facade, 133, 140f
Over-weighting method, 172–185
P
Panoramic camera, 216
Perpendicularity constrained adjustment, 182–184b
Perspective distortion, 85–88, 86f
Plane fitting, 245f
Point coordinates, 188
Polygon area computation, 34–42
Positional constraints, 199–200
Postadjustment analysis, 349
Postanalysis techniques, 345, 345f
Preanalysis, 23
of image intersection, 48f
Kronecker product technique, 44–47
using pseudoinverse/generalized inverse, 47–51
Precision, 4, 4f
Probable error, 13–15
Propagation of errors, 23f
definition, 23
facade area measurement, 34f
in laser scanning, 29–34
law, 24–25
INDEX 413Propagation of errors (Continued)
matrices, 25–28
of parallelogram tank, 24–25, 25f
preanalysis by pseudoinverse/generalized inverse,
47–51
preanalysis using Kronecker product, 44–47
quadrilateral polygon area computation, 39–43
rectangular facade area, 42f
triangular polygon area computation,
34–35, 37f
Pseudo code, 334–344
Pseudoinverse, 47–51, 211
Q
Quadrilateral polygon area computation, 39–43
R
Racing athletes, 1, 2f
Random errors, 3, 3f
Random Sample Consensus (RANSAC) algorithm,
376–382, 377–378b, 378f
Rank defect, 199–200
RANSAC algorithm. See Random Sample Consensus
(RANSAC) algorithm
Rectangular facade area, 42f
Redundancy, 6, 54
Redundancy number, 384–385
Relative ellipse of errors, 70–76, 81, 83f
Reliability, 5, 5f
Reliability computations, 382–385
Resection, image space, 125–135
Residual error, 5
Robust estimation technique, 363–376, 365–367b
Rodrigues rotation formula, 250f, 252f, 256–257f,
259–261
Root Mean Squared Error (RMSE), 6–7
Rotational constraints, 199–200
S
Satellite navigation system (GNSS), 216
Scale constraint, 199–200
Seismic waves, 143
Seismometer, 143
Singular value decomposition (SVD), 47, 83, 85
Slope angle error estimation, 28f
Sphere equation, 155–156
Spherical trigonometry law, 118
Standard deviation, 6
Standard ellipse of errors, 69–70, 72
Standard error, 6
Surface waves, 143
SVD. See Singular value decomposition (SVD)
Systematic errors, 2, 3f
T
Target-based coregistration, 274f
Taylor series expansion, 53
Terrestrial laser scanning (TLS), 29f, 274
2D circle, fitting, 258–263
2D models
angle observation, 95–100
Azimuth observation, 94–95
distance observation, 90–93
3D circle
fit, 252f
least squares fitting of, 258f
3D intersection, by distances, 101f, 330–333b
3D similarity transformation
close form solution, 277–291, 279–285b
to coregister the point clouds, 279f, 280, 285f
nonlinear least squares solution, 275–277, 276f
3D space
fitting circle in, 256–258
polygon area computing, 100
3D transformations, 273f, 274
computations, 273
planes to planes transformation, 296–298, 297–298b
points to points transformation, 275–291
point to plane transformation, 291–296, 293–296b
propagation of errors in, 289–291b
3D line
best fit, 247–248f
intersection model, 113–118
3D models
distance observation, 100–105
line intersection, 113–118
oblique angular resection, 118–124
Travel time, seismic waves, 143
Triangular polygon area computation, 34–35, 37f
Tri-angulation network, 67, 67f
Trilateration 2D geodetic network, 93, 93f, 98f
Trilateration network, 67, 67f
Tylor’s theorem, 24–25
U
Uncertainty, 3
Unified adjustment, 217–232, 218–222b, 224–229b
Unified approach
of least squares adjustment, 215–216, 215f
of least squares with constraints, 233–242, 235–236b
V
Variance, 6
Variance-covariance matrix, 24, 26, 28
ellipse of errors, 68
for ellipsoid of errors, 82–83
free net adjustment, 200
414 INDEXrelative ellipse of errors, 71
triangular polygon area computation, 35
Variance of unit weight, 57
Variation of coordinates method, 89
Vectors cross product, 35f
Velodyne scanning, 30
Vertical angle observation model, 105–113
W
Weighted mean, 17–22
Weight matrix, 56, 157, 164
Z
Zenith angle, 105
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