Understanding least squares estimation and geomatics data analysis

Understanding least squares estimation and geomatics data analysis / John Olusegun Ogundare.

Provides a modern approach to least squares estimation and data analysis for undergraduate land surveying and geomatics programs.

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Bibliographic Details
Main Author: Ogundare, John Olusegun (Author)
Format: eBook
Language:English
Published: Hoboken, NJ : John Wiley & Sons, 2018.
Edition:1st edition.
Subjects:
Estimation theory.
Least squares.
MATHEMATICS > Probability & Statistics > General.
Estimation theory
Least squares
Online Access:Click for online access
Table of Contents:
  • 1. Introduction
  • 2. Analysis and error propagation of survey observations
  • 3. Statistical distributions and hypothesis tests
  • 4. Adjustment methods and concepts
  • 5. Parametric least squares adjustment model formulation
  • 6. Parametric least squares adjust applications
  • 7. Confidence region estimation
  • 8. Introduction to network design and preanalysis
  • 9. Concepts of three-dimensional geodetic network adjustment
  • 10. Nuisance parameter elimination and sequential adjustment
  • 11. Post-adjustment data analysis and reliability concepts sensitivity
  • 12. Least squares adjustment of conditional models
  • 13. Least squares adjustment of general models
  • 14. Datum problem and free network adjustment
  • 15. Introduction to dynamic model filtering and prediction
  • 16. Introduction to least squares collocation and the kriging method
  • Appendix A. Extracts from Baarda's nomogram
  • Appendix B. Standard statistical distribution tables
  • Appendix C. Tau critical values table for significance level a (alpha)
  • Appendix D. General partial differentials of typical survey observables
  • Appendix E. some important matrix operations and identities
  • Appendix F. Commonly used abbreviations.
  • Intro; Title Page; Copyright Page; Contents; Preface; Acknowledgments; About the Author; About the Companion Website; Chapter 1 Introduction; 1.1 Observables and Observations; 1.2 Significant Digits of Observations; 1.3 Concepts of Observation Model; 1.4 Concepts of Stochastic Model; 1.4.1 Random Error Properties of Observations; 1.4.2 Standard Deviation of Observations; 1.4.3 Mean of Weighted Observations; 1.4.4 Precision of Observations; 1.4.5 Accuracy of Observations; 1.5 Needs for Adjustment; 1.6 Introductory Matrices; 1.6.1 Sums and Products of Matrices; 1.6.2 Vector Representation.
  • 1.6.3 Basic Matrix Operations1.7 Covariance, Cofactor, and Weight Matrices; 1.7.1 Covariance and Cofactor Matrices; 1.7.2 Weight Matrices; Problems; Chapter 2 Analysis and Error Propagation of Survey Observations; 2.1 Introduction; 2.2 Model Equations Formulations; 2.3 Taylor Series Expansion of Model Equations; 2.3.1 Using MATLAB to Determine Jacobian Matrix; 2.4 Propagation of Systematic and Gross Errors; 2.5 Variance-Covariance Propagation; 2.6 Error Propagation Based on Equipment Specifications; 2.6.1 Propagation for Distance Based on Accuracy Specification.
  • 2.6.2 Propagation for Direction (Angle) Based on Accuracy Specification2.6.3 Propagation for Height Difference Based on Accuracy Specification; 2.7 Heuristic Rule for Covariance Propagation; Problems; Chapter 3 Statistical Distributions and Hypothesis Tests; 3.1 Introduction; 3.2 Probability Functions; 3.2.1 Normal Probability Distributions and Density Functions; 3.3 Sampling Distribution; 3.3.1 Studentś t-Distribution; 3.3.2 Chi-square and Fisherś F-distributions; 3.4 Joint Probability Function; 3.5 Concepts of Statistical Hypothesis Tests; 3.6 Tests of Statistical Hypotheses.
  • 3.6.1 Test of Hypothesis on a Single Population Mean3.6.2 Test of Hypothesis on Difference of Two Population Means; 3.6.3 Test of Measurements Against the Means; 3.6.4 Test of Hypothesis on a Population Variance; 3.6.5 Test of Hypothesis on Two Population Variances; Problems; Chapter 4 Adjustment Methods and Concepts; 4.1 Introduction; 4.2 Traditional Adjustment Methods; 4.2.1 Transit Rule Method of Adjustment; 4.2.2 Compass (Bowditch) Rule Method; 4.2.3 Crandallś Rule Method; 4.3 The Method of Least Squares; 4.3.1 Least Squares Criterion; 4.4 Least Squares Adjustment Model Types.
  • 4.5 Least Squares Adjustment Steps4.6 Network Datum Definition and Adjustments; 4.6.1 Datum Defect and Configuration Defect; 4.7 Constraints in Adjustment; 4.7.1 Minimal Constraint Adjustments; 4.7.2 Overconstrained and Weight-Constrained Adjustments; 4.7.3 Adjustment Constraints Examples; 4.8 Comparison of Different Adjustment Methods; 4.8.1 General Discussions; Problems; Chapter 5 Parametric Least Squares Adjustment: Model Formulation; 5.1 Parametric Model Equation Formulation; 5.1.1 Distance Observable; 5.1.2 Azimuth and Horizontal (Total Station) Direction Observables.

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