Understanding Least Squares Estimation and Geomatics Data Analysis

This book begins with an explanation of survey observables, observations and their stochastic properties. It also contains a review of matrix structure and construction and an explanation of the needs for adjustment. Next, Chapter 2 discusses analysis and error propagation of survey observations, including the application of heuristic rule for covariance propagation. In Chapter 3, the important elements of statistical distributions commonly used in geomatics are discussed. Chapter 4 contains an explanation of the concepts of datum definitions. Chapter 5 presents the formulation and linearization of parametric model equations involving typical geomatics observables, and the derivation of basic parametric least squares adjustment models, variation functions, normal equations and solution equations. In Chapter 6, the concepts of parametric least squares adjustment are applied to various geomatics problems. Chapter 7 discusses the confidence region estimation, which includes the construction of confidence intervals for population means, variances, and ratio of variances. The problems of network design and pre-analysis are discussed in Chapter 8. The concepts of three-dimensional geodetic network adjustment are introduced in Chapter 9. Chapter 10 presents, with examples, the concepts of and the needs for, nuisance parameter elimination and the sequential least squares adjustment. The steps involved in post-adjustment data analysis and the concepts of reliability are discussed in Chapter 11. Next, the least squares adjustments of conditional models and general models are discussed, respectively, in Chapters 12 and 13. Chapter 14 explains the problems of datum and an approach for performing free network adjustment. Chapter 15 concludes this book with an introduction to mathematical filtering and prediction, where simple filtering equations are constructed and solved.