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

Format:

Book

Author/Creator:

Ogundare, John Olusegen, author.

Language:

English

Subjects (All):

Estimation theory.

Least squares.

Physical Description:

1 online resource (721 pages)

Edition:

1st ed.

Place of Publication:

Hoboken, NJ : Wiley, 2019.

Summary:

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.

Contents:

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 Operations

1.7 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 Specification

2.6.3 Propagation for Height Difference Based on Accuracy Specification

2.7 Heuristic Rule for Covariance Propagation

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 Student´s t-Distribution

3.3.2 Chi-square and Fisher´s 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 Mean

3.6.2 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

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 Crandall´s 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 Steps

4.6 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

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

5.1.3 Horizontal Angle Observable

5.1.4 Zenith Angle Observable

5.1.5 Coordinate Difference Observable

5.1.6 Elevation Difference Observable

5.2 Typical Parametric Model Equations

5.3 Basic Adjustment Model Formulation

5.4 Linearization of Parametric Model Equations

5.4.1 Linearization of Parametric Model Without Nuisance Parameter

5.4.2 Linearization of Parametric Model with Nuisance Parameter

5.5 Derivation of Variation Function

5.5.1 Derivation of Variation Function Using Direct Approachvariation functiondirect approach.

5.5.2 Derivation of Variation Function Using Lagrangian Approachvariation functiondirect approach

5.6 Derivation of Normal Equation System

5.6.1 Normal Equations Based on normal equation systemDirect Approachvariation functiondirect approach Variation Function

5.6.2 Normal Equations Based on normal equation systemLagrangian Approach Variation Functionvariation functiondirect approach

5.7 Derivation of Parametric Least Squares Solution

5.7.1 Least Squares Solutionleast squares solution from Direct Approachvariation functionLagrangian approachdirect approach...

5.7.2 Least Squares Solutionleast squares solution from Lagrangian Approach Normal Equationsvariation functionLagrangian ap...

5.8 Stochastic Models of Parametric Adjustment

5.8.1 Derivation of Cofactor Matrix of Adjusted Parametersadjusted parameters

5.8.2 Derivation of Cofactor Matrix of Adjusted Observationsadjusted observations

5.8.3 Derivation of Cofactor Matrix of Observation Residuals

5.8.4 Effects of Variance Factor Variation on Adjustments

5.9 Weight-constrained Adjustment Model Formulation

5.9.1 Stochastic Model for Weight-constrained Adjusted Parameters

5.9.2 Stochastic Model for Weight-constrained Adjusted Observations

Chapter 6 Parametric Least Squares Adjustment: Applications

6.1 Introduction

6.2 Basic Parametric Adjustment Examples

6.2.1 Leveling Adjustment

6.2.2 Station Adjustment

6.2.3 Traverse Adjustment

6.2.4 Triangulateration Adjustment

6.3 Stochastic Properties of Parametric Adjustment

6.4 Application of Stochastic Models

6.5 Resection Example

6.6 Curve-fitting Example

6.7 Weight Constraint Adjustment Steps

6.7.1 Weight Constraint Examples

Chapter 7 Confidence Region Estimation

7.1 Introduction

7.2 Mean Squared Error and Mathematical Expectation.

7.2.1 Mean Squared Error

7.2.2 Mathematical Expectation

7.3 Population Parameter Estimation

7.3.1 Point Estimation of Population Mean

7.3.2 Interval Estimation of Population Mean

7.3.3 Relative Precision Estimation

7.3.4 Interval Estimation for Population Variance

7.3.5 Interval Estimation for Ratio of Two Population Variances

7.4 General Comments on Confidence Interval Estimation

7.5 Error Ellipse and Bivariate Normal Distribution

7.6 Error Ellipses for Bivariate Parameters

7.6.1 Absolute Error Ellipses

7.6.2 Relative Error Ellipses

Chapter 8 Introduction to Network Design and Preanalysis

8.1 Introduction

8.2 Preanalysis of Survey Observations

8.2.1 Survey Tolerance Limits

8.2.2 Models for Preanalysis of Survey Observations

8.2.3 Trigonometric Leveling Problems

8.3 Network Design Model

8.4 Simple One-dimensional Network Design

8.5 Simple Two-dimensional Network Design

8.6 Simulation of Three-dimensional Survey Scheme

8.6.1 Typical Three-dimensional Micro-network

8.6.2 Simulation Results

Chapter 9 Concepts of Three-dimensional Geodetic Network Adjustment

9.1 Introduction

9.2 Three-dimensional Coordinate Systems and Transformations

9.2.1 Local Astronomic Coordinate Systems and Transformations

9.3 Parametric Model Equations in Conventional Terrestrial System

9.4 Parametric Model Equations in Geodetic System

9.5 Parametric Model Equations in Local Astronomic System

9.6 General Comments on Three-dimensional Adjustment

9.7 Adjustment Examples

9.7.1 Adjustment in Cartesian Geodetic System

9.7.1.1 Solution Approach

9.7.2 Adjustment in Curvilinear Geodetic System

9.7.3 Adjustment in Local System

Chapter 10 Nuisance Parameter Elimination and Sequential Adjustment

10.1 Nuisance Parameters.

10.2 Needs to Eliminate Nuisance Parameters

10.3 Nuisance Parameter Elimination Model

10.3.1 Nuisance Parameter Elimination Summary

10.3.2 Nuisance Parameter Elimination Example

10.4 Sequential Least Squares Adjustment

10.4.1 Sequential Adjustment in Simple Form

10.5 Sequential Least Squares Adjustment Model

10.5.1 Summary of Sequential Least Squares Adjustment Steps

10.5.2 Sequential Least Squares Adjustment Example

Chapter 11 Post-adjustment Data Analysis and Reliability ConceptsSensitivity

11.1 Introduction

11.2 Post-adjustment Detection and Elimination of Non-stochastic Errors

11.3 Global Tests

11.3.1 Standard Global Test

11.3.2 Global Test by Baarda

11.4 Local Tests

11.5 Pope´s Approach to Local Test

11.6 Concepts of Redundancy Numbers

11.7 Baarda´s Data Analysis Approach

11.7.1 BaardaBaarda´s Approach to Local Test

11.8 Concepts of Reliability Measures

11.8.1 Internal Reliability Measures

11.8.2 External Reliability Measures

11.9 Network Sensitivity

Chapter 12 Least Squares Adjustment of Conditional Models

12.1 Introduction

12.2 Conditional Model Equations

12.2.1 Examples of Model Equations

12.3 Conditional Model Adjustment Formulation

12.3.1 Conditional Model Adjustment Steps

12.4 Stochastic Model of Conditional Adjustment

12.4.1 Derivation of Cofactor Matrix of Adjusted Observationsadjusted observations

12.4.2 Derivation of Cofactor Matrix of Observation Residuals

12.4.3 Covariance Matrices of Adjusted Observations and Residuals

12.5 Assessment of Observations and Conditional Model

12.6 Variance-Covariance Propagation for Derived Parameters from Conditional Adjustment

12.7 Simple GNSS Network Adjustment Example

12.8 Simple Traverse Network Adjustment Example

Problems.

Chapter 13 Least Squares Adjustment of General Models.

Notes:

Description based on print version record.

ISBN:

9781119501459

1119501458

9781119501404

1119501407

9781119501442

111950144X

OCLC:

1051777067