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E-raamat: Applied State Estimation and Association

(MIT Lincoln Laboratory), (MIT Lincoln Laboratory)
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Applied State Estimation and AssociationSuurem pilt
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Applied state estimation and association is an important area for practicing engineers in aerospace, electronics, and defense industries, used in such tasks as signal processing, tracking, and navigation. This book offers a rigorous introduction to both theory and application of state estimation and association. It takes a unified approach to problem formulation and solution development that helps students and junior engineers build a sound theoretical foundation for their work and develop skills and tools for practical applications.

Chapters 1 through 6 focus on solving the problem of estimation with a single sensor observing a single object, and cover such topics as parameter estimation, state estimation for linear and nonlinear systems, and multiple model estimation algorithms. Chapters 7 through 10 expand the discussion to consider multiple sensors and multiple objects. The book can be used in a first-year graduate course in control or system engineering or as a reference for professionals. Each chapter ends with problems that will help readers to develop derivation skills that can be applied to new problems and to build computer models that offer a useful set of tools for problem solving. Readers must be familiar with state-variable representation of systems and basic probability theory including random and stochastic processes.

Preface xvii
About the Authors xix
Acknowledgments xxi
Introduction xxiii
1 Parameter Estimation
1(50)
1.1 Introduction
1(1)
1.2 Problem Definition
2(1)
1.3 Definition of Estimators
2(11)
1.3.1 Constant Parameter Estimation
3(1)
1.3.2 Random Parameter Estimation
4(3)
1.3.3 Properties of Estimators
7(4)
1.3.4 Measure of Estimator Quality: Estimation Errors
11(2)
1.4 Estimator Derivation: Linear and Gaussian, Constant Parameter
13(8)
1.4.1 Least Squares Estimator
13(3)
1.4.2 Weighted Least Squares Estimator
16(4)
1.4.3 Maximum Likelihood Estimator
20(1)
1.5 Estimator Derivation: Linear and Gaussian, Random Parameter
21(7)
1.5.1 Least Squares Estimator
22(1)
1.5.2 Weighted Least Squares Estimator
23(2)
1.5.3 Maximum a Posteriori Probability Estimator
25(2)
1.5.4 Conditional Mean Estimator
27(1)
1.6 Nonlinear Measurement with Jointly Gaussian Distributed Noise and Random Parameter
28(4)
1.7 Cramer-Rao Bound
32(2)
1.8 Numerical Example
34(17)
Appendix 1.A Simulating Correlated Random Vectors with a Given Covariance Matrix
38(3)
Appendix 1.B More Properties of Least Squares Estimators
41(4)
Homework Problems
45(3)
References
48(3)
2 State Estimation for Linear Systems
51(48)
2.1 Introduction
51(1)
2.2 State and Measurement Equations
52(5)
2.3 Definition of State Estimators
57(3)
2.3.1 Observability
58(2)
2.3.2 Estimation Error
60(1)
2.4 Bayesian Approach for State Estimation
60(2)
2.5 Kalman Filter for State Estimation
62(1)
2.6 Kalman Filter Derivation: An Extension of Weighted Least Squares Estimator for Parameter Estimation
63(2)
2.7 Kalman Filter Derivation: Using the Recursive Bayes' Rule
65(3)
2.8 Review of Certain Estimator Properties in the Kalman Filter Original Paper
68(3)
2.9 Smoother
71(7)
2.9.1 Notation and Definitions
72(1)
2.9.2 Fixed Interval Smoother
73(1)
2.9.3 Fixed Point Smoother
74(1)
2.9.4 Fixed Lag Smoother
74(1)
2.9.5 FIS for Deterministic Systems with Noisy Measurements
75(2)
2.9.6 Application of FIS for Kalman Filter Initial Condition Computation
77(1)
2.10 The Cramer-Rao Bound for State Estimation
78(5)
2.10.1 For Deterministic Systems
79(3)
2.10.2 For Stochastic Linear Systems
82(1)
2.11 A Kalman Filter Example
83(16)
Appendix 2.A Stochastic Processes
89(4)
Homework Problems
93(3)
References
96(3)
3 State Estimation for Nonlinear Systems
99(42)
3.1 Introduction
99(1)
3.2 Problem Definition
100(1)
3.3 Bayesian Approach for State Estimation
101(1)
3.4 Extended Kalman Filter Derivation: As a Weighted Least Squares Estimator
102(4)
3.4.1 One-Step Prediction Equation
103(1)
3.4.2 Update Equations
103(3)
3.5 Extended Kalman Filter with Single Stage Iteration
106(1)
3.6 Derivation of Extended Kalman Filter with Bayesian Approach
107(2)
3.7 Nonlinear Filter Equation with Second Order Taylor Series Expansion Retained
109(8)
3.7.1 One-Step Prediction
110(2)
3.7.2 Update Equations
112(1)
3.7.3 A Numerical Example
113(4)
3.8 The Case with Nonlinear but Deterministic Dynamics
117(3)
3.9 Cramer-Rao Bound
120(9)
3.9.1 For Deterministic Nonlinear Systems
121(1)
3.9.2 For Stochastic Nonlinear Systems
122(7)
3.10 A Space Trajectory Estimation Problem with Angle Only Measurement and Comparison of Estimation Covariance with Cramer-Rao Bound
129(12)
Homework Problems
133(4)
References
137(4)
4 Practical Considerations in Kalman Filter Design
141(56)
4.1 Model Uncertainty
141(1)
4.2 Filter Performance Assessment
142(5)
4.2.1 Achievable Performance: Cramer-Rao Bound
142(1)
4.2.2 Residual Process
143(1)
4.2.3 Filter Computed Covariance
144(3)
4.3 Filter Error with Model Uncertainties
147(4)
4.3.1 Bias and Covariance Equations
147(1)
4.3.2 Overmodeled and Undermodeled Cases
148(3)
4.4 Filter Compensation Methods for Mismatched System Dynamics
151(3)
4.4.1 State Augmentation
151(1)
4.4.2 The Use of Process Noise
152(1)
4.4.3 The Finite Memory Filter
153(1)
4.4.4 The Fading Memory Filter
153(1)
4.5 With Uncertain Measurement Noise Model
154(6)
4.5.1 Unknown Constant Bias
154(1)
4.5.2 Residual Bias with Known a Priori Distribution
155(1)
4.5.3 Colored Measurement Noise
156(4)
4.6 Systems with Both Unknown System Inputs and Measurement Biases
160(4)
4.7 Systems with Abrupt Input Changes
164(6)
4.8 III-Conditioning and False Observability
170(6)
4.8.1 False Observability in Radar Tracking Applications
171(1)
4.8.2 Quasi-Decoupling Filter
172(4)
4.9 Numerical Examples for Practical Filter Design
176(21)
4.9.1 Sinusoidal Signal in Noise
177(12)
4.9.2 Comparison of Methods in Treating Constant Unknown Biases
189(3)
Homework Problems
192(1)
References
193(4)
5 Multiple Model Estimation Algorithms
197(30)
5.1 Introduction
197(1)
5.2 Definitions and Assumptions
198(1)
5.3 Constant Model Case
199(4)
5.4 Switching Model Case
203(5)
5.5 Finite Memory Switching Model Case
208(6)
5.5.1 One-Step Model History
208(4)
5.5.2 Two-Step Model History
212(2)
5.6 Interacting Multiple Model Algorithm
214(2)
5.7 Numerical Examples
216(11)
Homework Problems
223(2)
References
225(2)
6 Sampling Techniques for State Estimation
227(44)
6.1 Introduction
227(1)
6.2 Conditional Expectation and Its Approximations
228(9)
6.2.1 Linear and Gaussian Cases
229(1)
6.2.2 Approximated by Taylor Series Expansion
229(1)
6.2.3 Approximated by Unscented Transformation
230(2)
6.2.4 Approximated by Point Mass Integration
232(1)
6.2.5 Approximated by Monte Carlo Sampling
233(4)
6.3 Bayesian Approach to Nonlinear State Estimation
237(2)
6.4 Unscented Kalman Filter
239(3)
6.5 The Point-Mass Filter
242(3)
6.6 Particle Filtering Methods
245(20)
6.6.1 Sequential Importance Sampling Filter
249(2)
6.6.2 Sequential Importance Resampling Filter
251(4)
6.6.3 Auxiliary Sampling Importance Resampling Filter
255(1)
6.6.4 Extended Kalman Filter Auxiliary Sampling Importance Resampling Filter
256(2)
6.6.5 Sequential Importance Resampling Filter Algorithm for Multiple Model Systems
258(3)
6.6.6 Particle Filters for Smoothing
261(4)
6.7 Summary
265(6)
Homework Problems
266(1)
References
267(4)
7 State Estimation with Multiple Sensor Systems
271(32)
7.1 Introduction
271(2)
7.2 Problem Definition
273(1)
7.3 Measurement Fusion
274(11)
7.3.1 Synchronous Measurement Case
274(4)
7.3.2 Asynchronous Measurement Case
278(2)
7.3.3 Measurement Preprocessing for a Given Sensor to Reduce Data Exchange Rate
280(2)
7.3.4 Update with Out-of-Sequence Measurements
282(3)
7.4 State Fusion
285(8)
7.4.1 The Fundamental State Fusion Algorithm
286(7)
7.5 Cramer-Rao Bound
293(1)
7.6 A Numerical Example
293(10)
Appendix 7.A Estimation with Transformed Measurements
295(1)
7.A.1 Problem Definition
295(1)
7.A.2 A Fundamental Theorem
296(3)
7.A.3 Extension to Measurement Fusion versus State Fusion
299(1)
Homework Problems
300(1)
References
301(2)
8 Estimation and Association with Uncertain Measurement Origin
303(54)
8.1 Introduction
303(3)
8.1.1 Track Ambiguity Illustration
304(2)
8.1.2 Acceptance Gate
306(1)
8.2 Illustration of the Multiple Target Tracking Problem
306(3)
8.3 A Taxonomy of Multiple Target Tracking Approaches
309(4)
8.4 Track Split
313(1)
8.5 The Nearest Neighbor and Global Nearest Neighbor Assignment Algorithms
314(3)
8.6 The Probabilistic Data Association Filter and the Joint Probabilistic Data Association Filter
317(8)
8.7 A Practical Set of Algorithms
325(15)
8.7.1 Initiation Process
325(7)
8.7.2 Continuation Process
332(5)
8.7.3 Illustration of Immediate and Delayed Resolution
337(2)
8.7.4 A Joint Multiscan Estimation and Decision Process
339(1)
8.8 Numerical Examples
340(17)
Appendix 8.A Example Track Initiation Equations
346(1)
8.A.1 Applying the Fixed Interval Smoother to Compute Initial Conditions
346(1)
8.A.2 Applying First Order Polynomial Smoothing to Radar Measurements to Obtain Initial State Estimate and Covariance for a Tracking Filter in Cartesian Coordinates
347(7)
Homework Problems
354(1)
References
354(3)
9 Multiple Hypothesis Tracking Algorithm
357(34)
9.1 Introduction
357(2)
9.2 Multiple Hypothesis Tracking Illustrations
359(20)
9.2.1 Measurement-Oriented MHT
359(8)
9.2.2 Track-Oriented MHT
367(8)
9.2.3 Track and Hypothesis Generation Example; Multiple Target Case
375(2)
9.2.4 Additional Implementation Methods
377(2)
9.3 Track and Hypothesis Scoring and Pruning
379(5)
9.3.1 Definition of Track Status
380(1)
9.3.2 Track and Hypothesis Scoring
381(2)
9.3.3 Track Scoring Example
383(1)
9.4 Multiple Hypothesis Tracker Implementation Using Nassi--Shneiderman Chart
384(3)
9.5 Extending It to Multiple Sensors with Measurement Fusion
387(1)
9.6 Concluding Remarks
387(4)
Homework Problems
388(1)
References
388(3)
10 Multiple Sensor Correlation and Fusion with Biased Measurements
391(22)
10.1 Introduction
391(1)
10.2 Bias Estimation Directly with Sensor Measurements
392(6)
10.2.1 Problem Statement
392(2)
10.2.2 Comparison of Two Bias Estimation Approaches
394(4)
10.3 State-to-State Correlation and Bias Estimation
398(15)
10.3.1 Review of Fundamental Approaches to Correlation Without Bias
399(2)
10.3.2 Bias Estimation
401(2)
10.3.3 Joint Correlation and Bias Estimation
403(6)
Homework Problems
409(1)
References
410(3)
Concluding Remarks
413(4)
Estimation
413(2)
Association/Correlation
415(2)
Appendix A Matrix Inversion Lemma 417(2)
Appendix B Notation and Variables 419(6)
Appendix C Definition of Terminology Used in Tracking 425(6)
Index 431
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