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 MATLAB®
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.
Autorentext
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.
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. 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® 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.
Inhalt
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 51
3.5 Discussion of General Estimation Methods 55
References 55
4 Case Studies: Preliminary Discussions 56
4.1 The Overall Simulation/Estimation/Evaluation Process 57
4.2 A Scenario Simulator for Tracking a Constant Velocity Target Through a DIFAR Buoy Field 58
4.2.1 Ship Dynamics Model 58
4.2.2 Multiple Buoy Observation Model 59
4.2.3 Scenario Specifics 59
4.3 DIFAR Buoy Signal Processing 62
4.4 The DIFAR Likelihood Function 67
References 69
PART II THE GAUSSIAN ASSUMPTION: A FAMILY OF KALMAN FILTER ESTIMATORS
5 The Gaussian Noise Case: Multidimensional Integration of Gaussian-Weighted Distributions 73
5.1 Summary of Important Results From Chapter 3 74
5.2 Derivation of the Kalman Filter Correction (Update) Equations Revisited 76
5.3 The General Bayesian Point Prediction Integrals for Gaussian Densities 78
5.3.1 Refining the Process Through an Affine Transformation 80
5.3.2 General Methodology for Solving Gaussian-Weighted Integrals 82
References 85
6 The Linear Class of Kalman Filters 86
6.1 Linear Dynamic Models 86
6.2 Linear Observation Models 87
6.3 The Linear Kalman Filter 88
6.4 Application of the LKF to DIFAR Buoy Bearing Estimation 88
References 92
7 The Analytical Linearization Class of Kalman Filters: The Extended Kalman Filter 93
7.1 One-Dimensional Consideration 93
7.1.1 One-Dimensional State Prediction 94
7.1.2 One-Dimensional State Estimation Error Variance Prediction 95
7.1.3 One-Dimensional Observation Prediction Equations 96
7.1.4 Transformation of One-Dimensional Prediction Equations 96
7.1.5 The One-Dimensional Linearized EKF Process 98
7.2 Multidimensional Consideration 98
7.2.1 The State Prediction Equation 99
7.2.2 The State Covariance Prediction Equation 100
7.2.3 Observation Prediction Equations 102
7.2.4 Transformation of Multidimensional Prediction Equations 103
7.2.5 The Linearized Multidimensional Extended Kalman Filter Process 105
7.2.6 Second-Order Extended Kalman Filter 105
7.3 An Alternate Derivation of the Multidimensional Covariance Prediction Equations 107
7.4 Application of the EKF to the DIFAR Ship Tracking Case Study 108...