Ogundare J. Understanding Least Squares Estimation and Geomatics Data Analysis

Wiley, 2019. — 702 p. — ISBN: 978-1-119-50144-2.Provides a modern approach to least squares estimation and data analysis for undergraduate land surveying and geomatics programsRich 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.True PDFWebsiteSignificant Digits of Observations
Concepts of Observation Model
Concepts of Stochastic Model
Needs for Adjustment
Introductory Matrices
Covariance, Cofactor, and Weight Matrices
ProblemsModel Equations Formulations
Taylor Series Expansion of Model Equations
Propagation of Systematic and Gross Errors
Covariance Propagation
Error Propagation Based on Equipment Specifications
Heuristic Rule for Covariance Propagation
Problems
Statistical Distributions & Hypothesis TestsProbability Functions
Sampling Distribution
Joint Probability Function
Concepts of Statistical Hypothesis Tests
Tests of Statistical Hypotheses
Problems
Adjustment Methods & Concepts
Traditional Adjustment Methods
The Method of Least Squares
Least Squares Adjustment Model Types
Least Squares Adjustment Steps
Network Datum Definition and Adjustments
Constraints in Adjustment
Comparison of Different Adjustment Methods
Problems
Parametric Least Squares Adjustment
Parametric Model Equation Formulation
Typical Parametric Model Equations
Basic Adjustment Model Formulation
Linearization of Parametric Model Equations
Derivation of Variation Function
Derivation of Normal Equation System
Derivation of Parametric Least Squares Solution
Stochastic Models of Parametric Adjustment
Weight-constrained Adjustment Model Formulation
Problems
Parametric Least Squares AdjustmentBasic Parametric Adjustment Examples
Stochastic Properties of Parametric Adjustment
Application of Stochastic Models
Resection Example
Curve-fitting Example
Weight Constraint Adjustment Steps
Problems
Confidence Region Estimation
Mean Squared Error and Mathematical Expectation
Population Parameter Estimation
General Comments on Confidence Interval Estimation
Error Ellipse and Bivariate Normal Distribution
Error Ellipses for Bivariate Parameters
ProblemsPreanalysis of Survey Observations
Simple One-dimensional Network Design
Simple Two-dimensional Network Design
Simulation of Three-dimensional Survey Scheme
Problems
Concepts of D Geodetic Network Adjustment
Three-dimensional Coordinate Systems and Transformations
Parametric Model Equations in Conventional Terrestrial System
Parametric Model Equations in Geodetic System
Parametric Model Equations in Local Astronomic System
General Comments on Three-dimensional Adjustment
Adjustment Examples
Nuisance Parameters
Needs to Eliminate Nuisance Parameters
Nuisance Parameter Elimination Model
Sequential Least Squares Adjustment
Sequential Least Squares Adjustment Model
Problems
Post-Adjustment Data Analysis & Reliability ConceptsPost-adjustment Detection and Elimination of Non-stochastic Errors
Global Tests
Local Tests
s Approach to Local Test
Concepts of Redundancy Numbers
s Data Analysis Approach
Concepts of Reliability Measures
Network Sensitivity
Problems
Least Squares Adjustment of Conditional Models
Conditional Model Equations
Conditional Model Adjustment Formulation
Stochastic Model of Conditional Adjustment
Assessment of Observations and Conditional Model
Covariance Propagation for Derived Parameters from Conditional Adjustment
Simple GNSS Network Adjustment Example
Simple Traverse Network Adjustment Example
Problems
Least Squares Adjustment of General Models
General Model Equation Formulation
Linearization of General Model
Variation Function for Linearized General Model
Normal Equation System and the Least Squares Solution
Steps for General Model Adjustment
General Model Adjustment Examples
Stochastic Properties of General Model Adjustment
Horizontal Circular Curve Example
Adjustment of General Model with Weight Constraints
ProblemsMinimal Datum Constraint Types
Free Network Adjustment Model
Constraint Model for Free Network Adjustment
Summary of Free Network Adjustment Procedure
Datum Transformation
ProblemsStatic Mode Filter
Dynamic Mode Filter
Kalman Filtering Examples
Kalman Filter and the Least Squares Method
ProblemsElements of Least Squares Collocation
Collocation Procedure
Covariance Function
Collocation and Classical Least Squares Adjustment
Semivariogram Model and Modeling
Kriging Procedure
Comparing Least Squares Collocation and Kriging
Extracts from Baarda Nomogram
Standard Statistical Distribution Tables
Tau Critical Values Table for Significance Level α
Azimuth Observable
Total Station Direction Observable
Horizontal Angle Observable
Zenith Angle Observable
Other General Rules for Partial Differentials
Matrix Lemmas
Generalized Inverses and Pseudo-inverses
Abbreviations
Refs