Mathematics & statistics
Adjustment theory: an introduction
Peter J. G. Teunissen
TU Delft OPEN Publishing · Second edition (2024) · English · Published 2024
Least-squares adjustment, mathematical model representations and estimation from redundant observations, with a historical appendix.
- Learning stage
- Advanced college
- Prerequisites
- Linear algebra, calculus and introductory probability.
- PDF pages
- 211 in this file
- Editorial review
- 2026-10-29
Contents
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Preface
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Contents
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Introduction
1 Linear estimation theory: an introduction
1 Linear estimation theory: an introduction
1.1 Introduction
1.2 Least-squares estimation (orthogonal projection)
1.3 Weighted least-squares estimation
1.4 Weighted least-squares is also orthogonal projection
Intermezzo: Cholesky decomposition
1.5 The mean and covariance matrix of least-squares estimators
1.6 Best Linear Unbiased Estimators (BLUE’s)
1.7 The Maximum Likelihood (ML) method
1.8 Summary
Table 1.1
2 The model with observation equations
2 The model with observation equations
2.1 Introduction
2.2 Least-squares estimation
Intermezzo
2.3 The mean and covariance matrix of least-squares estimators
2.4 Best Linear Unbiased Estimation
2.5 The orthogonal projector
2.6 Summary
Best Linear Unbiased Estimation
3 The model with condition equations
3 The model with condition equations
3.1 Introduction
3.2 Best Linear Unbiased Estimation
3.3 The case B*E{y}=b^0, b^0≠0
3.4 Summary
Best Linear Unbiased Estimation
4 y^R - Variates
4 y^R - Variates
4.1 Introduction
4.2 Free variates
4.3 Derived variates
4.4 Constituent variates
5 Mixed model representations
5 Mixed model representations
5.1 Introduction
5.2 The model representation B*E{y}=Ax
5.3 The model representation E{y}=Ax , B*x=0
6 Partitioned model representations
6 Partitioned model representations
6.1 Introduction
6.2 The partitioned model E{y} = (A1 : A2)(xsub1 over xsub2)
6.3 The partitioned model (recursive estimation)
Table 6.1: Recursive estimation (A-form)
Table 6.2: Recursive estimation (B-form)
Table 6.3
6.4 The partitioned model (block estimation I)
6.5. The partitioned model (block estimation II)
Table 6.4: Block estimation
Table 6.5: Block estimation
6.6 The partitioned model (Estimation in phases)
Table 6.6: Estimation in phases
Table 6.7: Correspondence between partitioned condition equations and partitioned observation equations
7 Nonlinear models, linearization, iteration
7 Nonlinear models, linearization, iteration
7.1. The nonlinear A-model
7.2 The nonlinear B-model and its linearization
Appendix A Taylor’s theorem with remainder
Appendix B Unconstrained optimization: optimality conditions
Appendix C Linearly constrained optimization: optimality conditions
Appendix D Constrained optimization: optimality conditions
Appendix E Mean and variance of scalar random variables
Appendix F Mean and variance of vector random variables
Appendix F Mean and variance of vector random variables
Appendix G
A BRIEF ACCOUNT ON THE EARLY HISTORY OF ADJUSTING GEODETIC AND ASTRONOMICAL OBSERVATIONS0F
Literature
Index
Sources and permissions
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Author, publisher, and discovery sources
Authors: Peter J. G. Teunissen
Publisher: TU Delft OPEN Publishing
- Discovered through Open Textbook Library: Source record · Checked 2026-10-29
- Discovered through Open Textbook Library: Source record · Checked 2026-10-25
CC BY 4.0
Peter J. G. Teunissen. Adjustment theory: an introduction. TU Delft OPEN Publishing. Second edition (2024). CC BY 4.0.
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Checked 2026-10-29