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Bayesian Estimation and Tracking: A Practical Guide

Book Description

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.

Table of Contents

  1. Cover
  2. Title Page
  3. Copyright
  4. Dedication
  5. Preface
  6. Acknowledgments
  7. List of Figures
  8. List of Tables
  9. Part I: Preliminaries
    1. Chapter 1: Introduction
      1. 1.1 Bayesian Inference
      2. 1.2 Bayesian Hierarchy of Estimation Methods
      3. 1.3 Scope of this Text
      4. 1.4 Modeling and Simulation with Matlab®
      5. References
    2. Chapter 2: Preliminary Mathematical Concepts
      1. 2.1 A Very Brief Overview of Matrix Linear Algebra
      2. 2.2 Vector Point Generators
      3. 2.3 Approximating Nonlinear Multidimensional Functions with Multidimensional Arguments
      4. 2.4 Overview of Multivariate Statistics
      5. References
    3. Chapter 3: General Concepts of Bayesian Estimation
      1. 3.1 Bayesian Estimation
      2. 3.2 Point Estimators
      3. 3.3 Introduction to Recursive Bayesian Filtering of Probability Density Functions
      4. 3.4 Introduction to Recursive Bayesian Estimation of the State Mean and Covariance
      5. 3.5 Discussion of General Estimation Methods
      6. References
    4. Chapter 4: Case Studies: Preliminary Discussions
      1. 4.1 The Overall Simulation/Estimation/Evaluation Process
      2. 4.2 A Scenario Simulator for Tracking a Constant Velocity Target Through a DIFAR Buoy Field
      3. 4.3 DIFAR Buoy Signal Processing
      4. 4.4 The DIFAR Likelihood Function
      5. References
  10. Part II: The Gaussian Assumption: A Family of Kalman Filter Estimators
    1. Chapter 5: The Gaussian Noise Case: Multidimensional Integration of Gaussian-Weighted Distributions
      1. 5.1 Summary of Important Results From Chapter 3
      2. 5.2 Derivation of the Kalman Filter Correction (Update) Equations Revisited
      3. 5.3 The General Bayesian Point Prediction Integrals for Gaussian Densities
      4. References
    2. Chapter 6: The Linear Class of Kalman Filters
      1. 6.1 Linear Dynamic Models
      2. 6.2 Linear Observation Models
      3. 6.3 The Linear Kalman Filter
      4. 6.4 Application of the LKF to DIFAR Buoy Bearing Estimation
      5. References
    3. Chapter 7: The Analytical Linearization Class of Kalman Filters: The Extended Kalman Filter
      1. 7.1 One-Dimensional Consideration
      2. 7.2 Multidimensional Consideration
      3. 7.3 An Alternate Derivation of the Multidimensional Covariance Prediction Equations
      4. 7.4 Application of the EKF to the DIFAR Ship Tracking Case Study
      5. References
    4. Chapter 8: The Sigma Point Class: The Finite Difference Kalman Filter
      1. 8.1 One-Dimensional Finite Difference Kalman Filter
      2. 8.2 Multidimensional Finite Difference Kalman Filters
      3. 8.3 An Alternate Derivation of the Multidimensional Finite Difference Covariance Prediction Equations
      4. References
    5. Chapter 9: The Sigma Point Class: The Unscented Kalman Filter
      1. 9.1 Introduction to Monomial Cubature Integration Rules
      2. 9.2 The Unscented Kalman Filter
      3. 9.3 Application of the UKF to the DIFAR Ship Tracking Case Study
      4. References
    6. Chapter 10: The Sigma Point Class: The Spherical Simplex Kalman Filter
      1. 10.1 One-Dimensional Spherical Simplex Sigma Points
      2. 10.2 Two-Dimensional Spherical Simplex Sigma Points
      3. 10.3 Higher Dimensional Spherical Simplex Sigma Points
      4. 10.4 The Spherical Simplex Kalman Filter
      5. 10.5 The Spherical Simplex Kalman Filter Process
      6. 10.6 Application of the SSKF to the DIFAR Ship Tracking Case Study
      7. References
    7. Chapter 11: The Sigma Point Class: The Gauss–Hermite Kalman Filter
      1. 11.1 One-Dimensional Gauss–Hermite Quadrature
      2. 11.2 One-Dimensional Gauss–Hermite Kalman Filter
      3. 11.3 Multidimensional Gauss–Hermite Kalman Filter
      4. 11.4 Sparse Grid Approximation for High Dimension/High Polynomial Order
      5. 11.5 Application of the GHKF to the DIFAR Ship Tracking Case Study
      6. References
    8. Chapter 12: The Monte Carlo Kalman Filter
      1. 12.1 The Monte Carlo Kalman Filter
      2. References
    9. Chapter 13: Summary of Gaussian Kalman Filters
      1. 13.1 Analytical Kalman Filters
      2. 13.2 Sigma Point Kalman Filters
      3. 13.3 A More Practical Approach to Utilizing the Family of Kalman Filters
      4. References
    10. Chapter 14: Performance Measures for the Family of Kalman Filters
      1. 14.1 Error Ellipses
      2. 14.2 Root Mean Squared Errors
      3. 14.3 Divergent Tracks
      4. 14.4 Cramer–Rao Lower Bound
      5. 14.5 Performance of Kalman Class DIFAR Track Estimators
      6. References
  11. Part III: Monte Carlo Methods
    1. Chapter 15: Introduction to Monte Carlo Methods
      1. 15.1 Approximating a Density From a Set of Monte Carlo Samples
      2. 15.2 General Concepts Importance Sampling
      3. 15.3 Summary
      4. References
    2. Chapter 16: Sequential Importance Sampling Particle Filters
      1. 16.1 General Concept of Sequential Importance Sampling
      2. 16.2 Resampling and Regularization (Move) for SIS Particle Filters
      3. 16.3 The Bootstrap Particle Filter
      4. 16.4 The Optimal SIS Particle Filter
      5. 16.5 The SIS Auxiliary Particle Filter
      6. 16.6 Approximations to the SIS Auxiliary Particle Filter
      7. 16.7 Reducing the Computational Load Through Rao-Blackwellization
      8. References
    3. Chapter 17: The Generalized Monte Carlo Particle Filter
      1. 17.1 The Gaussian Particle Filter
      2. 17.2 The Combination Particle Filter
      3. 17.3 Performance Comparison of All DIFAR Tracking Filters
      4. References
  12. Part IV: Additional Case Studies
    1. Chapter 18: A Spherical Constant Velocity Model for Target Tracking in Three Dimensions
      1. 18.1 Tracking a Target in Cartesian Coordinates
      2. 18.2 Tracking a Target in Spherical Coordinates
      3. 18.3 Implementation of Cartesian and Spherical Tracking Filters
      4. 18.4 Performance Comparison for Various Estimation Methods
      5. 18.5 Some Observations and Future Considerations
      6. Appendix 18.A Three-Dimensional Constant Turn Rate Kinematics
      7. Appendix 18.B Three-Dimensional Coordinate Transformations
      8. References
    2. Chapter 19: Tracking a Falling Rigid Body Using Photogrammetry
      1. 19.1 Introduction
      2. 19.2 The Process (Dynamic) Model for Rigid Body Motion
      3. 19.3 Components of the Observation Model
      4. 19.4 Estimation Methods
      5. 19.5 The Generation of Synthetic Data
      6. 19.6 Performance Comparison Analysis
      7. Appendix 19.A quaternions, Axis-Angle Vectors, and Rotations
      8. References
    3. Chapter 20: Sensor Fusion using Photogrammetric and Inertial Measurements
      1. 20.1 Introduction
      2. 20.2 The Process (Dynamic) Model for Rigid Body Motion
      3. 20.3 The Sensor Fusion Observational Model
      4. 20.4 The Generation of Synthetic Data
      5. 20.5 Estimation Methods
      6. 20.6 Performance Comparison Analysis
      7. 20.7 Conclusions
      8. 20.8 Future Work
      9. References
  13. Index