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Kurzbeschreibung This book presents a practical approach to estimation methods that are designed to provide a clear path to programming all algorithms. The coverage gives readers a firm understanding of Bayesian estimation methods and their interrelatedness. Starting with fundamental principles of Bayesian theory, the book presents a conceptually cohesive roadmap that begins with fundamental principles and leads directly to derivations of the Gaussian estimation methods currently in use within a Bayesian framework. Thoroughly classroom-tested for the past few years, this book serves as both a graduate-level text and as a professional reference.
Aus dem Inhalt 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
