Bayesian Estimation and Tracking - A Practical Guide

Informationen zum Autor 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. Klappentext A practical approach to estimating and tracking dynamic systems in real-worl applicationsMuch 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 MATLAB(r) 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. Zusammenfassung 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. Inhaltsverzeichnis Preface xv Acknowledgments xvii List of Figures Xix List of Tables xxv PART I PRELIMINARIES 1 Introduction 3 1.1 Bayesian Inference 4 1.2 Bayesian Hierarchy of Estimation Methods 5 1.3 Scope of This Text 6 1.3.1 Objective 6 1.3.2 Chapter Overview and Prerequisites 6 1.4 Modeling and Simulation with MATLAB® 8 References 9 2 Preliminary Mathematical Concepts 11 2.1 A Very Brief Overview of Matrix Linear Algebra 11 2.1.1 Vector and Matrix Conventions and Notation 11 2.1.2 Sums and Products 12 2.1.3 Matrix Inversion 13 2.1.4 Block Matrix Inversion 14 2.1.5 Matrix Square Root 15 2.2 Vector Point Generators 16 2.3 Approximating Nonlinear Multidimensional Functions with Multidimensional Arguments 19 2.3.1 Approximating Scalar Nonlinear Functions 19 2.3.2 Approximating Multidimensional Nonlinear Functions 23 2.4 Overview of Multivariate Statistics 29 2.4.1 General Definitions 29 2.4.2 The Gaussian Density 32 References 40 3 General Concepts of Bayesian Estimation 42 3.1 Bayesian Estimation 43 3.2 Point Estimators 43 3.3 Introduction to Recursive Bayesian Filtering of Probability Density Functions 46 3.4 Introduction to Recursive Bayesian Estimation of the State Mean and Covariance 49 3.4.1 State Vector Prediction 50 3.4.2 State Vector Update 5...

List of contents

Preface
 
Acknowledgments
 
List of Figures xi
 

List of Tables xxi
 
Part I. Prelininaries
 
1. Introduction 3
 
1.1 Bayesian Inference 5
 
1.2 Bayesian Hierarchy of Estimation Methods 7
 
1.3 Scope of this Text 8
 
1.4 Modeling and Simulation with Matlab(r) 13
 
2. Preliminary Mathematical Concepts 19
 
2.1 A Very Brief Overview of Matrix Linear Algebra 20
 
2.2 Vector Point Generators 27
 
2.3 Approximating Nonlinear Multidimensional Functions with Multidimensional Arguments 32
 
2.4 Overview of Multivariate Statistics 47
 
3. General Concepts of Bayesian Estimation 69
 
3.1 Bayesian Estimation 70
 
3.2 Point Estimators 72
 
3.3 Introduction to Recursive Bayesian Filtering of Probability Density Functions 76
 
3.4 Introduction to Recursive Bayesian Estimation of the State Mean and Covariance 81
 
3.5 Discussion of General Estimation Methods 88
 
4. Case Studies: Preliminary Discussions 93
 
4.1 The Overall Simulation/Estimation/Evaluation Process 94
 
4.2 A Scenario Simulator for Tracking a Constant-Velocity Target Through a DIFAR Buoy Field 97
 
4.3 DIFAR Buoy Signal Processing 102
 
4.4 The DIFAR Likelihood Function 111
 
Part II. The Gaussian Assumption: A Family of Kalman Filter Estimators
 
5. The Gaussian Noise Case: Multidimensional Integration of Gaussian-Weighted Distributions 119
 
5.1 Summary of Important Results From Chapter 3 122
 
5.2 Derivation of the Kalman Filter Correction (Update) Equations Revisted 124
 
5.3 The General Bayesian Point Prediction Integrals for Gaussian Densities 128
 
6. The Linear Class of Kalman Filters 141
 
6.1 Linear Dynamic Models 142
 
6.2 Linear Observation Models 143
 
6.3 The Linear Kalman Filter 144
 
6.4 Application of the LKF to DIFAR Buoy Bearing Estimation 146
 
7. The Analytical Linearization Class of Kalman Filters: The Extended Kalman Filter 153
 
7.1 One-Dimensional Consideration 154
 
7.2 Multidimensional Consideration 159
 
7.3 An Alternate Derivation of the Multidimensional Covariance Prediction Equations 172
 
7.4 Application of the EKF to the DIFAR Ship Tracking Case Study 174
 
8. The Sigma Point Class: The Finite Difference Kalman Filter 187
 
8.1 One-Dimensional Finite Difference Kalman Filter 189
 
8.2 Multidimensional Finite Difference Kalman Filters 195
 
8.3 An Alternate Derivation of the Multidimensional Finite Difference Covariance Prediction Equations 201
 
9. The Sigma Point Class: The Unscented Kalman Filter 207
 
9.1 Introduction to Monomial Cubature Integration Rules 207
 
9.2 The Unscented Kalman Filter 211
 
9.3 Applications of the UKF to the DIFAR Ship Tracking Case Study 221
 
10. The Sigma Point Class: The Spherical Simplex Kalman Filter 227
 
10.1 One-Dimensional Spherical Simplex Sigma Points 228
 
10.2 Two-Dimensional Spherical Simplex Sigma Points 229
 
10.3 Higher-Dimensional Spherical Simplex Sigma Points 233
 
10.4 The Spherical Simplex Kalman Filter 233
 
10.5 The Spherical Simplex Kalman Filter Process 236
 
10.6 Application of the SSKF to the DIFAR Ship Tracking Case Study 236
 
11. The Sigma Point Class: The Gauss-Hermite Kalman Filter 241
 
11.1 One-Dimensional Gauss-Hermite Quadrature 242
 
11.2 One-Dimensional Gauss-Hermite Kalman Filter 248
 
11.3 Multidimensional Gauss-Hermite Kalman Filter 251
 
11.4 Sparse Grid Approximation for High Dimension/High Polynomial Order 257
 

Product details

• Authors: Haug, AJ Haug, Anton J Haug, Anton J. Haug
• Publisher: Wiley, John and Sons Ltd
• Languages: English
• Product format: Hardback
• Released: 29.06.2012
• EAN: 9780470621707
• ISBN: 978-0-470-62170-7
• No. of pages: 400
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Miscellaneous; Statistik, Statistics, Signalverarbeitung, Signal Processing, Electrical & Electronics Engineering, Elektrotechnik u. Elektronik, Wahrscheinlichkeitsrechnung u. mathematische Statistik, Probability & Mathematical Statistics, Bayessches Verfahren