Bayesian Estimation and Tracking: A Practical Guide

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John Wiley & Sons, May 29, 2012 - Mathematics - 448 pages
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A practical approach to estimating and tracking dynamic systems in real-worl applications

Much of the literature on performing estimation for non-Gaussian systems is short on practical methodology, while Gaussian methods often lack a cohesive derivation. Bayesian Estimation and Tracking addresses the gap in the field on both accounts, providing readers with a comprehensive overview of methods for estimating both linear and nonlinear dynamic systems driven by Gaussian and non-Gaussian noices.

Featuring a unified approach to Bayesian estimation and tracking, the book emphasizes the derivation of all tracking algorithms within a Bayesian framework and describes effective numerical methods for evaluating density-weighted integrals, including linear and nonlinear Kalman filters for Gaussian-weighted integrals and particle filters for non-Gaussian cases. The author first emphasizes detailed derivations from first principles of eeach estimation method and goes on to use illustrative and detailed step-by-step instructions for each method that makes coding of the tracking filter simple and easy to understand.

Case studies are employed to showcase applications of the discussed topics. In addition, the book supplies block diagrams for each algorithm, allowing readers to develop their own MATLABŪ toolbox of estimation methods.

Bayesian Estimation and Tracking is an excellent book for courses on estimation and tracking methods at the graduate level. The book also serves as a valuable reference for research scientists, mathematicians, and engineers seeking a deeper understanding of the topics.


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115 Application of the GHKF to the DIFAR Ship Tracking Case Study
121 The Monte Carlo Kalman Filter
131 Analytical Kalman Filters
132 Sigma Point Kalman Filters
133 A More Practical Approach to Utilizing the Family of Kalman Filters
141 Error Ellipses
142 Root Mean Squared Errors
143 Divergent Tracks

31 Bayesian Estimation
32 Point Estimators
33 Introduction to Recursive Bayesian Filtering of Probability Density Functions
34 Introduction to Recursive Bayesian Estimation of the State Mean and Covariance
35 Discussion of General Estimation Methods
41 The Overall SimulationEstimationEvaluation Process
42 A Scenario Simulator for Tracking a Constant Velocity Target Through a DIFAR Buoy Field
43 DIFAR Buoy Signal Processing
44 The DIFAR Likelihood Function
51 Summary of Important Results From Chapter 3
52 Derivation of the Kalman Filter Correction Update Equations Revisited
53 The General Bayesian Point Prediction Integrals for Gaussian Densities
61 Linear Dynamic Models
62 Linear Observation Models
63 The Linear Kalman Filter
71 OneDimensional Consideration
72 Multidimensional Consideration
73 An Alternate Derivation of the Multidimensional Covariance Prediction Equations
74 Application of the EKF to the DIFAR Ship Tracking Case Study
81 OneDimensional Finite Difference Kalman Filter
82 Multidimensional Finite Difference Kalman Filters
83 An Alternate Derivation of the Multidimensional Finite Difference Covariance Prediction Equations
91 Introduction to Monomial Cubature Integration Rules
92 The Unscented Kalman Filter
93 Application of the UKF to the DIFAR Ship Tracking Case Study
101 OneDimensional Spherical Simplex Sigma Points
102 TwoDimensional Spherical Simplex Sigma Points
103 Higher Dimensional Spherical Simplex Sigma Points
104 The Spherical Simplex Kalman Filter
105 The Spherical Simplex Kalman Filter Process
111 OneDimensional GaussHermite Quadrature
112 OneDimensional GaussHermite Kalman Filter
113 Multidimensional GaussHermite Kalman Filter
114 Sparse Grid Approximation for High DimensionHigh Polynomial Order
145 Performance of Kalman Class DIFAR Track Estimators
151 Approximating a Density From a Set of Monte Carlo Samples
152 General Concepts Importance Sampling
153 Summary
161 General Concept of Sequential Importance Sampling
162 Resampling and Regularization Move for SIS Particle Filters
163 The Bootstrap Particle Filter
164 The Optimal SIS Particle Filter
165 The SIS Auxiliary Particle Filter
166 Approximations to the SIS Auxiliary Particle Filter
167 Reducing the Computational Load Through RaoBlackwellization
171 The Gaussian Particle Filter
172 The Combination Particle Filter
173 Performance Comparison of All DIFAR Tracking Filters
181 Tracking a Target in Cartesian Coordinates
182 Tracking a Target in Spherical Coordinates
183 Implementation of Cartesian and Spherical Tracking Filters
184 Performance Comparison for Various Estimation Methods
185 Some Observations and Future Considerations
Appendix 18B ThreeDimensional Coordinate Transformations
191 Introduction
192 The Process Dynamic Model for Rigid Body Motion
193 Components of the Observation Model
194 Estimation Methods
195 The Generation of Synthetic Data
196 Performance Comparison Analysis
Appendix 19A quaternions AxisAngle Vectors and Rotations
201 Introduction
202 The Process Dynamic Model for Rigid Body Motion
204 The Generation of Synthetic Data
205 Estimation Methods
206 Performance Comparison Analysis
207 Conclusions

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About the author (2012)

ANTON J. HAUG, PhD, is member of the technical staff at the Applied Physics Laboratory at The Johns Hopkins University, where he develops advanced target tracking methods in support of the Air and Missile Defense Department. Throughout his career, Dr. Haug has worked across diverse areas such as target tracking; signal and array processing and processor design; active and passive radar and sonar design; digital communications and coding theory; and time- frequency analysis.

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