Course: Adjustment of Observations in Geodesy.

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Adjustment of Observations in Geodesy

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Module 1 – Fundamentals of Observation Adjustment

1. Concept of observation, error, and uncertainty
2. Types of errors: systematic, random, and gross errors
3. Statistical principles applied to observations
4. Accuracy, precision, and trueness concepts
5. Observation redundancy and degrees of freedom
6. Mean errors, standard deviation, and variance
7. Error propagation (Gauss’ Law)
8. Introduction to adjustment of observations
9. General structure of an adjustment problem

Module 2 – Statistics Applied to Geodesy

10. Normal distribution and the Gaussian curve
11. Hypothesis testing applied to observations
12. Chi-square (χ²) test for variance
13. Student’s t-test for individual residuals
14. Difference tests and quality control
15. Introduction to the variance–covariance matrix
16. Properties of variance–covariance matrices
17. Covariance and correlation between observations
18. Construction of the weight matrix (P)

Module 3 – Introduction to the Least Squares Method

19. Concept and fundamentals of Least Squares
20. Mathematical derivation of the Least Squares criterion
21. Normal equations and classical solution
22. Matrix formulation of Least Squares
23. Observability conditions and redundancy
24. Geometric interpretation of adjustment
25. Introduction to the Parametric Method
26. Application to geometric leveling
27. Complete leveling adjustment example

Module 4 – Parametric Method in Geodesy

28. Functional model of the parametric approach
29. Coordinate determination from linear observations
30. Traverse adjustment
31. Adjustment of simple planar networks
32. Adjustment of vertical networks
33. GNSS network adjustment (3D coordinates)
34. Adjustment with constraints
35. Residual analysis and quality control
36. Complete adjustment of a geodetic network

Module 5 – Conditional (Correlate) Method

37. Concept and formulation of the conditional method
38. Functional model for condition equations
39. Observation conditions and constraint equations
40. Construction of the coefficient matrix
41. Adjustment of geodetic triangles
42. Adjustment of direction sets
43. Application to height networks with fixed benchmarks
44. Comparison between parametric and conditional methods
45. Complete example using the conditional method

Module 6 – Combined Method

46. Concept and advantages of the combined method
47. General functional model formulation
48. Geometric interpretation of the combined method
49. Solution of combined normal equations
50. Application to constrained GNSS networks
51. Adjustment of integrated networks (horizontal + vertical)
52. Residual analysis in the combined method
53. Example of a 2D+1D network adjustment
54. GNSS leveling combined adjustment exercise

Module 7 – Advanced Applications

55. Adjustment of GPS pseudorange observations
56. Adjustment of carrier phase observations
57. Differential GNSS adjustment (base–rover)
58. Multi-sensor adjustment (GNSS + Total Station)
59. Adjustment of large geodetic networks
60. Adjustment of geocentric reference networks (e.g., SIRGAS)
61. Gross error detection through residual analysis
62. Global test for model consistency
63. Practical example with simulated GNSS network

Module 8 – Computational Implementation

64. Structuring adjustment problems in spreadsheets
65. Use of scientific software (MATLAB, Python, Scilab)
66. Matrix programming for Least Squares
67. Automatic assembly of normal equations
68. Solution using Cholesky decomposition
69. Solution using QR decomposition
70. Numerical stability analysis
71. Interpretation of results (variance, residuals, weights)
72. Complete computational example

Module 9 – Quality Assessment of Geodetic Networks

73. Quality control of geodetic networks
74. Internal and external reliability
75. Local and global redundancy
76. Deformation analysis between epochs
77. Displacement detection in monitoring networks
78. Time series adjustment
79. Accuracy assessment of 3D networks
80. Observation planning for geodetic surveys
81. Monitoring network adjustment example

Module 10 – Synthesis and Advanced Projects

82. Review of parametric, conditional, and combined methods
83. Comparison of adjustment methods
84. Selection of the appropriate functional model
85. Adjustment of integrated GNSS and leveling networks
86. Integration of local networks into global reference systems
87. Adjustment with heterogeneous weights
88. Uncertainty propagation to mapping products
89. Final project: complete network adjustment
90. Final project analysis and statistical evaluation