# Bayesian Estimation and Tracking: A Practical Guide

John Wiley & Sons, May 29, 2012 - Mathematics - 448 pages

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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### Contents

 11 Bayesian Inference 12 Bayesian Hierarchy of Estimation Methods 13 Scope of this Text 14 Modeling and Simulation with Matlab 21 A Very Brief Overview of Matrix Linear Algebra 22 Vector Point Generators 23 Approximating Nonlinear Multidimensional Functions with Multidimensional Arguments 24 Overview of Multivariate Statistics
 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 Copyright

### 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.