Understanding least squares estimation and geomatics data analysis. (2018)

• Record Type: Book
• Further Information: Note: John Olusegun Ogundare.
• Authors: Ogundare, John Olusegun
• Contents: Preface xiii Acknowledgments xvii About the Author xix About the Companion Website xxi 1 Introduction 1 1.1 Observables and Observations 2 1.2 Significant Digits of Observations 2 1.3 Concepts of Observation Model 4 1.4 Concepts of Stochastic Model 6 1.4.1 Random Error Properties of Observations 6 1.4.2 Standard Deviation of Observations 8 1.4.3 Mean of Weighted Observations 9 1.4.4 Precision of Observations 10 1.4.5 Accuracy of Observations 11 1.5 Needs for Adjustment 12 1.6 Introductory Matrices 16 1.6.1 Sums and Products of Matrices 18 1.6.2 Vector Representation 20 1.6.3 Basic Matrix Operations 21 1.7 Covariance, Cofactor, and Weight Matrices 22 1.7.1 Covariance and Cofactor Matrices 26 1.7.2 Weight Matrices 27 Problems 34 2 Analysis and Error Propagation of Survey Observations 39 2.1 Introduction 39 2.2 Model Equations Formulations 40 2.3 Taylor Series Expansion of Model Equations 44 2.3.1 Using MATLAB to Determine Jacobian Matrix 52 2.4 Propagation of Systematic and Gross Errors 55 2.5 Variance–Covariance Propagation 58 2.6 Error Propagation Based on Equipment Specifications 67 2.6.1 Propagation for Distance Based on Accuracy Specification 67 2.6.2 Propagation for Direction (Angle) Based on Accuracy Specification 69 2.6.3 Propagation for Height Difference Based on Accuracy Specification 69 2.7 Heuristic Rule for Covariance Propagation 72 Problems 76 3 Statistical Distributions and Hypothesis Tests 81 3.1 Introduction 82 3.2 Probability Functions 83 3.2.1 Normal Probability Distributions and Density Functions 84 3.3 Sampling Distribution 92 3.3.1 Student’s t-Distribution 93 3.3.2 Chi-square and Fisher’s F-distributions 95 3.4 Joint Probability Function 97 3.5 Concepts of Statistical Hypothesis Tests 98 3.6 Tests of Statistical Hypotheses 100 3.6.1 Test of Hypothesis on a Single Population Mean 102 3.6.2 Test of Hypothesis on Difference of Two Population Means 106 3.6.3 Test of Measurements Against the Means 109 3.6.4 Test of Hypothesis on a Population Variance 111 3.6.5 Test of Hypothesis on Two Population Variances 114 Problems 117 4 Adjustment Methods and Concepts 119 4.1 Introduction 120 4.2 Traditional Adjustment Methods 120 4.2.1 Transit Rule Method of Adjustment 122 4.2.2 Compass (Bowditch) Rule Method 125 4.2.3 Crandall’s Rule Method 126 4.3 The Method of Least Squares 127 4.3.1 Least Squares Criterion 129 4.4 Least Squares Adjustment Model Types 132 4.5 Least Squares Adjustment Steps 134 4.6 Network Datum Definition and Adjustments 136 4.6.1 Datum Defect and Configuration Defect 138 4.7 Constraints in Adjustment 139 4.7.1 Minimal Constraint Adjustments 140 4.7.2 Overconstrained and Weight-Constrained Adjustments 141 4.7.3 Adjustment Constraints Examples 143 4.8 Comparison of Different Adjustment Methods 146 4.8.1 General Discussions 158 Problems 160 5 Parametric Least Squares Adjustment: Model Formulation 163 5.1 Parametric Model Equation Formulation 164 5.1.1 Distance Observable 165 5.1.2 Azimuth and Horizontal (Total Station) Direction Observables 165 5.1.3 Horizontal Angle Observable 168 5.1.4 Zenith Angle Observable 169 5.1.5 Coordinate Difference Observable 169 5.1.6 Elevation Difference Observable 169 5.2 Typical Parametric Model Equations 170 5.3 Basic Adjustment Model Formulation 179 5.4 Linearization of Parametric Model Equations 180 5.4.1 Linearization of Parametric Model Without Nuisance Parameter 180 5.4.2 Linearization of Parametric Model with Nuisance Parameter 184 5.5 Derivation of Variation Function 186 5.5.1 Derivation of Variation Function Using Direct Approach 186 5.5.2 Derivation of Variation Function Using Lagrangian Approach 187 5.6 Derivation of Normal Equation System 188 5.6.1 Normal Equations Based on Direct Approach Variation Function 188 5.6.2 Normal Equations Based on Lagrangian Approach Variation Function 189 5.7 Derivation of Parametric Least Squares Solution 189 5.7.1 Least Squares Solution from Direct Approach Normal Equations 189 5.7.2 Least Squares Solution from Lagrangian Approach Normal Equations 190 5.8 Stochastic Models of Parametric Adjustment 191 5.8.1 Derivation of Cofactor Matrix of Adjusted Parameters 192 5.8.2 Derivation of Cofactor Matrix of Adjusted Observations 193 5.8.3 Derivation of Cofactor Matrix of Observation Residuals 194 5.8.4 Effects of Variance Factor Variation on Adjustments 196 5.9 Weight-constrained Adjustment Model Formulation 197 5.9.1 Stochastic Model for Weight-constrained Adjusted Parameters 200 5.9.2 Stochastic Model for Weight-constrained Adjusted Observations 201 Problems 202 6 Parametric Least Squares Adjustment: Applications 205 6.1 Introduction 206 6.2 Basic Parametric Adjustment Examples 207 6.2.1 Leveling Adjustment 207 6.2.2 Station Adjustment 215 6.2.3 Traverse Adjustment 223 6.2.4 Triangulateration Adjustment 235 6.3 Stochastic Properties of Parametric Adjustment 242 6.4 Application of Stochastic Models 243 6.5 Resection Example 249 6.6 Curve-fitting Example 254 6.7 Weight Constraint Adjustment Steps 260 6.7.1 Weight Constraint Examples 261 Problems 272 7 Confidence Region Estimation 275 7.1 Introduction 276 7.2 Mean Squared Error and Mathematical Expectation 276 7.2.1 Mean Squared Error 276 7.2.2 Mathematical Expectation 277 7.3 Population Parameter Estimation 280 7.3.1 Point Estimation of Population Mean 280 7.3.2 Interval Estimation of Population Mean 281 7.3.3 Relative Precision Estimation 285 7.3.4 Interval Estimation for Population Variance 288 7.3.5 Interval Estimation for Ratio of Two Population Variances 290 7.4 General Comments on Confidence Interval Estimation 293 7.5 Error Ellipse and Bivariate Normal Distribution 294 7.6 Error Ellipses for Bivariate Parameters 298 7.6.1 Absolute Error Ellipses 299 7.6.2 Relative Error Ellipses 305 Problems 309 8 Introduction to Network Design and Preanalysis 311 8.1 Introduction 311 8.2 Preanalysis of Survey Observations 313 8.2.1 Survey Tolerance Limits 314 8.2.2 Models for Preanalysis of Survey Observations 314 8.2.3 Trigonometric Leveling Problems 316 8.3 Network Design Model 322 8.4 Simple One-dimensional Network Design 322 8.5 Simple Two-dimensional Network Design 325 8.6 Simulation of Three-dimensional Survey Scheme 340 8.6.1 Typical Three-dimensional Micro-network 340 8.6.2 Simulation Results 342 Problems 347 9 Concepts of Three-dimensional Geodetic Network Adjustment 349 9.1 Introduction 350 9.2 Three-dimensional Coordinate Systems and Transformations 350 9.2.1 Local Astronomic Coordinate Systems and Transformations 352 9.3 Parametric Model Equations in Conventional Terrestrial System 354 9.4 Parametric Model Equations in Geodetic System 357 9.5 Parametric Model Equations in Local Astronomic System 361 9.6 General Comments on Three-dimensional Adjustment 365 9.7 Adjustment Examples 367 9.7.1 Adjustment in Cartesian Geodetic System 367 9.7.1.1 Solution Approach 369 &lt
• Edition: 1st
• Publisher Details: Hoboken, New Jersey : John Wiley & Sons, Inc
• Publication Date: 2018
• Extent: 1 online resource
• Subjects: 519.544; Estimation theory; Least squares
• Languages: English
• ISBNs: 9781119501442
• Related ISBNs: 9781119501404
• Notes: Note: Description based on CIP data; resource not viewed.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.