Computational Geophysics Adjustment Models in 3D Geomatics and Computational Geophysics

Computational Geophysics Adjustment Models in 3D Geomatics and Computational Geophysics
اسم المؤلف
Bashar Alsadik
التاريخ
4 مايو 2024
المشاهدات
77
التقييم
(لا توجد تقييمات)
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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

  1. Statistical Introduction
  2. Propagation of Errors
  3. Least Squares Adjustment Procedures
  4. Common Observation Models and Their Adjustment in Geomatics
  5. Adjustment Using General Observation Model
  6. Adjustment with Constraints
  7. Unified Approach of Least Squares
  8. Fitting Geometric Primitives with Least Squares
  9. 3D Transformation and Co-Registration
  10. Kalman Filter
  11. Introduction to Adjustment with Levenberg-Marquardt Method
  12. 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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