## Applied State Estimation and Association

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Contents (pg. vii)
Preface (pg. xvii)
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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