Applied State Estimation and Association
ISBN: 9780262364140 | Copyright 2016
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| Contents (pg. vii) | |
| Preface (pg. xvii) | |
| About the Authors (pg. xix) | |
| Acknowledgments (pg. xxi) | |
| Introduction (pg. xxiii) | |
| 1 Parameter Estimation (pg. 1) | |
| 1.1 Introduction (pg. 1) | |
| 1.2 Problem Defi nition (pg. 2) | |
| 1.3 Defi nition of Estimators (pg. 2) | |
| 1.4 Estimator Derivation: Linear and Gaussian, Constant Parameter (pg. 13) | |
| 1.5 Estimator Derivation: Linear and Gaussian, Random Parameter (pg. 21) | |
| 1.6 Nonlinear Measurement with Jointly Gaussian Distributed Noiseand Random Parameter (pg. 28) | |
| 1.7 Cramer–Rao Bound (pg. 32) | |
| 1.8 Numerical Example (pg. 34) | |
| Appendix 1.A Simulating Correlated Random Vectors with a Given Covariance Matrix (pg. 38) | |
| Appendix 1.B More Properties of Least Squares Estimators (pg. 41) | |
| Homework Problems (pg. 45) | |
| References (pg. 48) | |
| 2 State Estimation for Linear Systems (pg. 51) | |
| 2.1 Introduction (pg. 51) | |
| 2.2 State and Measurement Equations (pg. 52) | |
| 2.3 Defi nition of State Estimators (pg. 57) | |
| 2.4 Bayesian Approach for State Estimation (pg. 60) | |
| 2.5 Kalman Filter for State Estimation (pg. 62) | |
| 2.6 Kalman Filter Derivation: An Extension of Weighted Least Squares Estimator for Parameter Estimation (pg. 63) | |
| 2.7 Kalman Filter Derivation: Using the Recursive Bayes’ Rule (pg. 65) | |
| 2.8 Review of Certain Estimator Properties in the Kalman Filter Original Paper (pg. 68) | |
| 2.9 Smoother (pg. 71) | |
| 2.10 The Cramer–Rao Bound for State Estimation (pg. 78) | |
| 2.11 A Kalman Filter Example (pg. 83) | |
| Appendix 2.A Stochastic Processes (pg. 89) | |
| Homework Problems (pg. 93) | |
| References (pg. 96) | |
| 3 State Estimation for Nonlinear Systems (pg. 99) | |
| 3.1 Introduction (pg. 99) | |
| 3.2 Problem Definition (pg. 100) | |
| 3.3 Bayesian Approach for State Estimation (pg. 101) | |
| 3.4 Extended Kalman Filter Derivation: As a Weighted Least Squares Estimator (pg. 102) | |
| 3.5 Extended Kalman Filter with Single Stage Iteration (pg. 106) | |
| 3.6 Derivation of Extended Kalman Filter with Bayesian Approach (pg. 107) | |
| 3.7 Nonlinear Filter Equation with Second Order Taylor Series Expansion Retained (pg. 109) | |
| 3.8 The Case with Nonlinear but Deterministic Dynamics (pg. 117) | |
| 3.9 Cramer–Rao Bound (pg. 120) | |
| 3.10 A Space Trajectory Estimation Problem with Angle Only Measurement and Comparison of Estimation Covariancewith Cramer–Rao Bound (pg. 129) | |
| Homework Problems (pg. 133) | |
| References (pg. 137) | |
| 4 Practical Considerations in Kalman Filter Design (pg. 141) | |
| 4.1 Model Uncertainty (pg. 141) | |
| 4.2 Filter Performance Assessment (pg. 142) | |
| 4.3 Filter Error with Model Uncertainties (pg. 147) | |
| 4.4 Filter Compensation Methods for Mismatched System Dynamics (pg. 151) | |
| 4.5 With Uncertain Measurement Noise Model (pg. 154) | |
| 4.6 Systems with Both Unknown System Inputs and MeasurementBiases (pg. 160) | |
| 4.7 Systems with Abrupt Input Changes (pg. 164) | |
| 4.8 Ill-Conditioning and False Observability (pg. 170) | |
| 4.9 Numerical Examples for Practical Filter Design (pg. 176) | |
| Homework Problems (pg. 192) | |
| References (pg. 193) | |
| 5 Multiple Model Estimation Algorithms (pg. 197) | |
| 5.1 Introduction (pg. 197) | |
| 5.2 Defi nitions and Assumptions (pg. 198) | |
| 5.3 Constant Model Case (pg. 199) | |
| 5.4 Switching Model Case (pg. 203) | |
| 5.5 Finite Memory Switching Model Case (pg. 208) | |
| 5.6 Interacting Multiple Model Algorithm (pg. 214) | |
| 5.7 Numerical Examples (pg. 216) | |
| Homework Problems (pg. 223) | |
| References (pg. 225) | |
| 6 Sampling Techniques for State Estimation (pg. 227) | |
| 6.1 Introduction (pg. 227) | |
| 6.2 Conditional Expectation and Its Approximations (pg. 228) | |
| 6.3 Bayesian Approach to Nonlinear State Estimation (pg. 237) | |
| 6.4 Unscented Kalman Filter (pg. 239) | |
| 6.5 The Point-Mass Filter (pg. 242) | |
| 6.6 Particle Filtering Methods (pg. 245) | |
| 6.7 Summary (pg. 265) | |
| Homework Problems (pg. 266) | |
| References (pg. 267) | |
| 7 State Estimation with Multiple Sensor Systems (pg. 271) | |
| 7.1 Introduction (pg. 271) | |
| 7.2 Problem Defi nition (pg. 273) | |
| 7.3 Measurement Fusion (pg. 274) | |
| 7.4 State Fusion (pg. 285) | |
| 7.5 Cramer–Rao Bound (pg. 293) | |
| 7.6 A Numerical Example (pg. 293) | |
| Appendix 7.A Estimation with Transformed Measurements (pg. 295) | |
| Homework Problems (pg. 300) | |
| References (pg. 301) | |
| 8 Estimation and Association with Uncertain Measurement Origin (pg. 303) | |
| 8.1 Introduction (pg. 303) | |
| 8.2 Illustration of the Multiple Target Tracking Problem (pg. 306) | |
| 8.3 A Taxonomy of Multiple Target Tracking Approaches (pg. 309) | |
| 8.4 Track Split (pg. 313) | |
| 8.5 The Nearest Neighbor and Global Nearest Neighbor AssignmentAlgorithms (pg. 314) | |
| 8.6 The Probabilistic Data Association Filter and the Joint ProbabilisticData Association Filter (pg. 317) | |
| 8.7 A Practical Set of Algorithms (pg. 325) | |
| 8.8 Numerical Examples (pg. 340) | |
| Appendix 8.A Example Track Initiation Equations (pg. 346) | |
| Homework Problems (pg. 354) | |
| References (pg. 354) | |
| 9 Multiple Hypothesis Tracking Algorithm (pg. 357) | |
| 9.1 Introduction (pg. 357) | |
| 9.2 Multiple Hypothesis Tracking Illustrations (pg. 359) | |
| 9.3 Track and Hypothesis Scoring and Pruning (pg. 379) | |
| 9.4 Multiple Hypothesis Tracker Implementation UsingNassi–Shneiderman Chart (pg. 384) | |
| 9.5 Extending It to Multiple Sensors with Measurement Fusion (pg. 387) | |
| 9.6 Concluding Remarks (pg. 387) | |
| Homework Problems (pg. 388) | |
| References (pg. 388) | |
| 10 Multiple Sensor Correlation and Fusion with Biased Measurements (pg. 391) | |
| 10.1 Introduction (pg. 391) | |
| 10.2 Bias Estimation Directly with Sensor Measurements (pg. 392) | |
| 10.3 State-to-State Correlation and Bias Estimation (pg. 398) | |
| Homework Problems (pg. 409) | |
| References (pg. 410) | |
| Concluding Remarks (pg. 413) | |
| Appendix A: Matric Inversion Lemma (pg. 417) | |
| Appendix B: Notation and Variables (pg. 419) | |
| Appendix C: Definition of Terminology Used in Tracking (pg. 425) | |
| Index (pg. 431) | |
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