Understanding least squares estimation and geomatics data analysis

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Yazar:

Ogundare, John Olusegun, author.

ISBN:

9781119501404

9781119501459

9781119501442

Basım Bilgisi:

1st edition.

Fiziksel Tanımlama:

1 online resource

İçerik:

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.

Özet:

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

Provides a modern approach to least squares estimation and data analysis for undergraduate land surveying and geomatics programs Rich in theory and concepts, this comprehensive book on least square estimation and data analysis provides examples that are designed to help students extend their knowledge to solving more practical problems. The sample problems are accompanied by suggested solutions, and are challenging, yet easy enough to manually work through using simple computing devices, and chapter objectives provide an overview of the material contained in each section. Understanding Least Squares Estimation and Geomatics Data Analysis begins with an explanation of survey observables, observations, and their stochastic properties. It reviews matrix structure and construction and explains the needs for adjustment. Next, it discusses analysis and error propagation of survey observations, including the application of heuristic rule for covariance propagation. Then, the important elements of statistical distributions commonly used in geomatics are discussed. Main topics of the book include: concepts of datum definitions; the formulation and linearization of parametric, conditional and general model equations involving typical geomatics observables; geomatics problems; least squares adjustments of parametric, conditional and general models; confidence region estimation; problems of network design and pre-analysis; three-dimensional geodetic network adjustment; nuisance parameter elimination and the sequential least squares adjustment; post-adjustment data analysis and reliability; the problems of datum; mathematical filtering and prediction; an introduction to least squares collocation and the kriging methods; and more. ' -Contains ample concepts/theory and content, as well as practical and workable examples -Based on the author's manual, which he developed as a complete and comprehensive book for his Adjustment of Surveying Measurements and Special Topics in Adjustments courses -Provides geomatics undergraduates and geomatics professionals with required foundational knowledge -An excellent companion to Precision Surveying: The Principles and Geomatics Practice Understanding Least Squares Estimation and Geomatics Data Analysis is recommended for undergraduates studying geomatics, and will benefit many readers from a variety of geomatics backgrounds, including practicing surveyors/engineers who are interested in least squares estimation and data analysis, geomatics researchers, and software developers for geomatics.

Notlar:

John Wiley and Sons

Konu Terimleri:

Estimation theory.

Least squares.

Théorie de l'estimation.

MATHEMATICS -- Probability & Statistics -- General.

Probability & Statistics.

MATHEMATICS.

Estimation theory

Least squares

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