Understanding Least Squares Estimation and Geomatics Data Analysis

Description

Contents......Page 3 Preface......Page 11 Website......Page 15 Introduction......Page 16 Significant Digits of Observations......Page 17 Concepts of Observation Model......Page 19 Concepts of Stochastic Model......Page 21 Needs for Adjustment......Page 27 Introductory Matrices......Page 31 Covariance, Cofactor, and Weight Matrices......Page 37 Problems......Page 49 Introduction......Page 53 Model Equations Formulations......Page 54 Taylor Series Expansion of Model Equations......Page 58 Propagation of Systematic and Gross Errors......Page 69 Covariance Propagation......Page 72 Error Propagation Based on Equipment Specifications......Page 81 Heuristic Rule for Covariance Propagation......Page 86 Problems......Page 90 Statistical Distributions & Hypothesis Tests......Page 94 Introduction......Page 95 Probability Functions......Page 96 Sampling Distribution......Page 105 Joint Probability Function......Page 110 Concepts of Statistical Hypothesis Tests......Page 111 Tests of Statistical Hypotheses......Page 113 Problems......Page 130 Adjustment Methods & Concepts......Page 132 Traditional Adjustment Methods......Page 133 The Method of Least Squares......Page 140 Least Squares Adjustment Model Types......Page 145 Least Squares Adjustment Steps......Page 147 Network Datum Definition and Adjustments......Page 149 Constraints in Adjustment......Page 152 Comparison of Different Adjustment Methods......Page 159 Problems......Page 173 Parametric Least Squares Adjustment......Page 176 Parametric Model Equation Formulation......Page 177 Typical Parametric Model Equations......Page 183 Basic Adjustment Model Formulation......Page 192 Linearization of Parametric Model Equations......Page 193 Derivation of Variation Function......Page 199 Derivation of Normal Equation System......Page 201 Derivation of Parametric Least Squares Solution......Page 202 Stochastic Models of Parametric Adjustment......Page 204 Weight-constrained Adjustment Model Formulation......Page 210 Problems......Page 215 Parametric Least Squares Adjustment......Page 218 Introduction......Page 219 Basic Parametric Adjustment Examples......Page 220 Stochastic Properties of Parametric Adjustment......Page 255 Application of Stochastic Models......Page 256 Resection Example......Page 262 Curve-fitting Example......Page 267 Weight Constraint Adjustment Steps......Page 273 Problems......Page 285 Confidence Region Estimation......Page 288 Mean Squared Error and Mathematical Expectation......Page 289 Population Parameter Estimation......Page 293 General Comments on Confidence Interval Estimation......Page 306 Error Ellipse and Bivariate Normal Distribution......Page 307 Error Ellipses for Bivariate Parameters......Page 311 Problems......Page 322 Introduction......Page 324 Preanalysis of Survey Observations......Page 326 Simple One-dimensional Network Design......Page 335 Simple Two-dimensional Network Design......Page 338 Simulation of Three-dimensional Survey Scheme......Page 353 Problems......Page 360 Concepts of 3D Geodetic Network Adjustment......Page 362 Three-dimensional Coordinate Systems and Transformations......Page 363 Parametric Model Equations in Conventional Terrestrial System......Page 367 Parametric Model Equations in Geodetic System......Page 370 Parametric Model Equations in Local Astronomic System......Page 374 General Comments on Three-dimensional Adjustment......Page 378 Adjustment Examples......Page 380 Nuisance Parameters......Page 389 Needs to Eliminate Nuisance Parameters......Page 390 Nuisance Parameter Elimination Model......Page 391 Sequential Least Squares Adjustment......Page 403 Sequential Least Squares Adjustment Model......Page 407 Problems......Page 427 Post-Adjustment Data Analysis & Reliability Concepts......Page 430 Introduction......Page 431 Post-adjustment Detection and Elimination of Non-stochastic Errors......Page 432 Global Tests......Page 435 Local Tests......Page 438 s Approach to Local Test......Page 439 Concepts of Redundancy Numbers......Page 441 s Data Analysis Approach......Page 444 Concepts of Reliability Measures......Page 448 Network Sensitivity......Page 452 Problems......Page 458 Least Squares Adjustment of Conditional Models......Page 461 Conditional Model Equations......Page 462 Conditional Model Adjustment Formulation......Page 469 Stochastic Model of Conditional Adjustment......Page 480 Assessment of Observations and Conditional Model......Page 483 Covariance Propagation for Derived Parameters from Conditional Adjustment......Page 484 Simple GNSS Network Adjustment Example......Page 490 Simple Traverse Network Adjustment Example......Page 494 Problems......Page 500 Least Squares Adjustment of General Models......Page 503 General Model Equation Formulation......Page 504 Linearization of General Model......Page 507 Variation Function for Linearized General Model......Page 510 Normal Equation System and the Least Squares Solution......Page 511 Steps for General Model Adjustment......Page 512 General Model Adjustment Examples......Page 513 Stochastic Properties of General Model Adjustment......Page 522 Horizontal Circular Curve Example......Page 526 Adjustment of General Model with Weight Constraints......Page 534 Problems......Page 548 Introduction......Page 552 Minimal Datum Constraint Types......Page 553 Free Network Adjustment Model......Page 554 Constraint Model for Free Network Adjustment......Page 557 Summary of Free Network Adjustment Procedure......Page 560 Datum Transformation......Page 568 Problems......Page 575 Introduction......Page 579 Static Mode Filter......Page 583 Dynamic Mode Filter......Page 586 Kalman Filtering Examples......Page 591 Kalman Filter and the Least Squares Method......Page 615 Problems......Page 618 Introduction......Page 620 Elements of Least Squares Collocation......Page 623 Collocation Procedure......Page 624 Covariance Function......Page 625 Collocation and Classical Least Squares Adjustment......Page 628 Semivariogram Model and Modeling......Page 631 Kriging Procedure......Page 634 Comparing Least Squares Collocation and Kriging......Page 639 Extracts from Baarda Nomogram......Page 641 Standard Statistical Distribution Tables......Page 644 Tau Critical Values Table for Significance Level α......Page 654 D.1 Azimuth Observable......Page 657 D.2 Total Station Direction Observable......Page 659 D.3 Horizontal Angle Observable......Page 660 D.5 Zenith Angle Observable......Page 661 D.6 Other General Rules for Partial Differentials......Page 662 E.1 Matrix Lemmas......Page 664 E.2 Generalized Inverses and Pseudo-inverses......Page 666 Abbreviations......Page 671 Refs......Page 672 Index......Page 676