Understanding least squares estimation and geomatics data analysis /
| Main Author: | |
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| Corporate Author: | |
| Format: | eBook |
| Language: | English |
| Published: |
Hoboken, NJ :
John Wiley & Sons,
2018.
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| Edition: | 1st edition. |
| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
Table of 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 Operations1.7 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 Specification2.6.3 Propagation for Height Difference Based on Accuracy Specification; 2.7 Heuristic Rule for Covariance Propagation; Problems; 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 Studentś t-Distribution; 3.3.2 Chi-square and Fisherś 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 Mean3.6.2 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; Problems; 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 Crandallś 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 Steps4.6 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; Problems; 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.