Understanding Least Squares Estimation and Geomatics Data Analysis

John Olusegun Ogundare

• Publisher: Wiley
• Year: 2018
• Print ISBN: 9781119501398
• eBook ISBN: 9781119501442
• Edition: 1
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

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.

Table of contents

• Cover
• Table of Contents
• Preface
• 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
• 6 Parametric Least Squares Adjustment
• 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
• 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 Mode Filtering and Prediction
• 16 Introduction to Least Squares Collocation and the Kriging Methods
• Appendix A: Extracts from Baarda’s Nomogram
• Appendix B: Standard Statistical Distribution Tables
• Appendix C: Tau Critical Values Table for Significance Level α
• Appendix D: General Partial Differentials of Typical Survey Observables
• Appendix E: Some Important Matrix Operations and Identities
• Appendix F: Commonly Used Abbreviations
• References
• Index
• End User License Agreement