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Author Haug, Anton J
Title Bayesian Estimation and Tracking : A Practical Guide
Imprint Hoboken : Wiley, 2012
©2012
book jacket
Edition 1st ed
Descript 1 online resource (398 pages)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
Note Cover -- Title Page -- Copyright -- Contents -- Preface -- Acknowledgments -- List of Figures -- List of Tables -- Part I: Preliminaries -- 1 Introduction -- 1.1 Bayesian Inference -- 1.2 Bayesian Hierarchy of Estimation Methods -- 1.3 Scope of This Text -- 1.3.1 Objective -- 1.3.2 Chapter Overview and Prerequisites -- 1.4 Modeling and Simulation with MATLAB® -- References -- 2 Preliminary Mathematical Concepts -- 2.1 A Very Brief Overview of Matrix Linear Algebra -- 2.1.1 Vector and Matrix Conventions and Notation -- 2.1.2 Sums and Products -- 2.1.3 Matrix Inversion -- 2.1.4 Block Matrix Inversion -- 2.1.5 Matrix Square Root -- 2.2 Vector Point Generators -- 2.3 Approximating Nonlinear Multidimensional Functions withMultidimensional Arguments -- 2.3.1 Approximating Scalar Nonlinear Functions -- 2.3.2 Approximating Multidimensional Nonlinear Functions -- 2.4 Overview of Multivariate Statistics -- 2.4.1 General Definitions -- 2.4.2 The Gaussian Density -- References -- 3 General Concepts of Bayesian Estimation -- 3.1 Bayesian Estimation -- 3.2 Point Estimators -- 3.3 Introduction to Recursive Bayesian Filtering of Probability DensityFunctions -- 3.4 Introduction to Recursive Bayesian Estimation of the State Mean andCovariance -- 3.4.1 State Vector Prediction -- 3.4.2 State Vector Update -- 3.5 Discussion of General Estimation Methods -- References -- 4 Case Studies: Preliminary Discussions -- 4.1 The Overall Simulation/Estimation/Evaluation Process -- 4.2 A Scenario Simulator for Tracking a Constant Velocity TargetThrough a DIFAR Buoy Field -- 4.2.1 Ship Dynamics Model -- 4.2.2 Multiple Buoy Observation Model -- 4.2.3 Scenario Specifics -- 4.3 DIFAR Buoy Signal Processing -- 4.4 The DIFAR Likelihood Function -- References -- Part II: The Gaussian Assumption: A Family of Kalmanfilter Estimators
5 The Gaussian Noise Case: Multidimensional Integration ofGaussian-Weighted Distributions -- 5.1 Summary of Important Results From Chapter 3 -- 5.2 Derivation of the Kalman Filter Correction (Update) EquationsRevisited -- 5.3 The General Bayesian Point Prediction Integrals for GaussianDensities -- 5.3.1 Refining the Process Through an Affine Transformation -- 5.3.2 General Methodology for Solving Gaussian-WeightedIntegrals -- References -- 6 The Linear Class of Kalman Filters -- 6.1 Linear Dynamic Models -- 6.2 Linear Observation Models -- 6.3 The Linear Kalman Filter -- 6.4 Application of the LKF to DIFAR Buoy Bearing Estimation -- References -- 7 The Analytical Linearization Class of Kalman Filters:The Extended Kalman Filter -- 7.1 One-Dimensional Consideration -- 7.1.1 One-Dimensional State Prediction -- 7.1.2 One-Dimensional State Estimation Error VariancePrediction -- 7.1.3 One-Dimensional Observation Prediction Equations -- 7.1.4 Transformation of One-Dimensional Prediction Equations -- 7.1.5 The One-Dimensional Linearized EKF Process -- 7.2 Multidimensional Consideration -- 7.2.1 The State Prediction Equation -- 7.2.2 The State Covariance Prediction Equation -- 7.2.3 Observation Prediction Equations -- 7.2.4 Transformation of Multidimensional PredictionEquations -- 7.2.5 The Linearized Multidimensional Extended Kalman FilterProcess -- 7.2.6 Second-Order Extended Kalman Filter -- 7.3 An Alternate Derivation of the Multidimensional CovariancePrediction Equations -- 7.4 Application of the EKF to the DIFAR Ship Tracking Case Study -- 7.4.1 The Ship Motion Dynamics Model -- 7.4.2 The DIFAR Buoy Field Observation Model -- 7.4.3 Initialization for All Filters of the Kalman Filter Class -- 7.4.4 Choosing a Value for the Acceleration Noise -- 7.4.5 The EKF Tracking Filter Results -- References
8 The Sigma Point Class: The Finite Difference Kalman Filter -- 8.1 One-Dimensional Finite Difference Kalman Filter -- 8.1.1 One-Dimensional Finite Difference State Prediction -- 8.1.2 One-Dimensional Finite Difference State VariancePrediction -- 8.1.3 One-Dimensional Finite Difference Observation PredictionEquations -- 8.1.4 The One-Dimensional Finite Difference Kalman FilterProcess -- 8.1.5 Simplified One-Dimensional Finite Difference PredictionEquations -- 8.2 Multidimensional Finite Difference Kalman Filters -- 8.2.1 Multidimensional Finite Difference State Prediction -- 8.2.2 Multidimensional Finite Difference State CovariancePrediction -- 8.2.3 Multidimensional Finite Difference Observation PredictionEquations -- 8.2.4 The Multidimensional Finite Difference Kalman FilterProcess -- 8.3 An Alternate Derivation of the Multidimensional Finite DifferenceCovariance Prediction Equations -- References -- 9 The Sigma Point Class: The Unscented Kalman Filter -- 9.1 Introduction to Monomial Cubature Integration Rules -- 9.2 The Unscented Kalman Filter -- 9.2.1 Background -- 9.2.2 The UKF Developed -- 9.2.3 The UKF State Vector Prediction Equation -- 9.2.4 The UKF State Vector Covariance Prediction Equation -- 9.2.5 The UKF Observation Prediction Equations -- 9.2.6 The Unscented Kalman Filter Process -- 9.2.7 An Alternate Version of the Unscented Kalman Filter -- 9.3 Application of the UKF to the DIFAR Ship Tracking Case Study -- References -- 10 The Sigma Point Class: The Spherical Simplex Kalman Filter -- 10.1 One-Dimensional Spherical Simplex Sigma Points -- 10.2 Two-Dimensional Spherical Simplex Sigma Points -- 10.3 Higher Dimensional Spherical Simplex Sigma Points -- 10.4 The Spherical Simplex Kalman Filter -- 10.5 The Spherical Simplex Kalman Filter Process -- 10.6 Application of the SSKF to the DIFAR Ship Tracking Case Study -- Reference
11 The Sigma Point Class: The Gauss-Hermite Kalman Filter -- 11.1 One-Dimensional Gauss-Hermite Quadrature -- 11.2 One-Dimensional Gauss-Hermite Kalman Filter -- 11.3 Multidimensional Gauss-Hermite Kalman Filter -- 11.4 Sparse Grid Approximation for High Dimension/High PolynomialOrder -- 11.5 Application of the GHKF to the DIFAR Ship Tracking Case Study -- References -- 12 The Monte Carlo Kalman Filter -- 12.1 The Monte Carlo Kalman Filter -- Reference -- 13 Summary of Gaussian Kalman Filters -- 13.1 Analytical Kalman Filters -- 13.2 Sigma Point Kalman Filters -- 13.3 A More Practical Approach to Utilizing the Family of KalmanFilters -- References -- 14 Performance Measures for the Family of Kalman Filters -- 14.1 Error Ellipses -- 14.1.1 The Canonical Ellipse -- 14.1.2 Determining the Eigenvalues of P -- 14.1.3 Determining the Error Ellipse Rotation Angle -- 14.1.4 Determination of the Containment Area -- 14.1.5 Parametric Plotting of Error Ellipse -- 14.1.6 Error Ellipse Example -- 14.2 Root Mean Squared Errors -- 14.3 Divergent Tracks -- 14.4 Cramer-Rao Lower Bound -- 14.4.1 The One-Dimensional Case -- 14.4.2 The Multidimensional Case -- 14.4.3 A Recursive Approach to the CRLB -- 14.4.4 The Cramer-Rao Lower Bound for Gaussian AdditiveNoise -- 14.4.5 The Gaussian Cramer-Rao Lower Bound with Zero ProcessNoise -- 14.4.6 The Gaussian Cramer-Rao Lower Bound with LinearModels -- 14.5 Performance of Kalman Class DIFAR Track Estimators -- References -- Part III: Monte Carlo Methods -- 15 Introduction to Monte Carlo Methods -- 15.1 Approximating a Density From a Set of Monte Carlo Samples -- 15.1.1 Generating Samples from a Two-Dimensional GaussianMixture Density -- 15.1.2 Approximating a Density by Its MultidimensionalHistogram -- 15.1.3 Kernel Density Approximation -- 15.3 Summary -- References -- 16 Sequential Importance Sampling Particle Filters
16.1 General Concept of Sequential Importance Sampling -- 16.2 Resampling and Regularization (Move) for SIS Particle Filters -- 16.2.1 The Inverse Transform Method -- 16.2.2 SIS Particle Filter with Resampling -- 16.2.3 Regularization -- 16.3 The Bootstrap Particle Filter -- 16.3.1 Application of the BPF to DIFAR Buoy Tracking -- 16.4 The Optimal SIS Particle Filter -- 16.4.1 Gaussian Optimal SIS Particle Filter -- 16.4.2 Locally Linearized Gaussian Optimal SIS Particle Filter -- 16.5 The SIS Auxiliary Particle Filter -- 16.5.1 Application of the APF to DIFAR Buoy Tracking -- 16.6 Approximations to the SIS Auxiliary Particle Filter -- 16.6.1 The Extended Kalman Particle Filter -- 16.6.2 The Unscented Particle Filter -- 16.7 Reducing the Computational Load ThroughRao-Blackwellization -- References -- 17 The Generalized Monte Carlo Particle Filter -- 17.1 The Gaussian Particle Filter -- 17.2 The Combination Particle Filter -- 17.2.1 Application of the CPF-UKF to DIFAR Buoy Tracking -- 17.3 Performance Comparison of All DIFAR Tracking Filters -- References -- Part IV: Additional Case Studies -- 18 A Spherical Constant Velocity Model for Target Trackingin Three Dimensions -- 18.1 Tracking a Target in Cartesian Coordinates -- 18.1.1 Object Dynamic Motion Model -- 18.1.2 Sensor Data Model -- 18.1.3 GaussianTracking Algorithms for a Cartesian StateVector -- 18.2 Tracking a Target in Spherical Coordinates -- 18.2.1 State Vector Position and Velocity Components in SphericalCoordinates -- 18.2.2 Spherical State Vector Dynamic Equation -- 18.2.3 Observation Equations with a Spherical State Vector -- 18.2.4 GaussianTracking Algorithms for a Spherical StateVector -- 18.3 Implementation of Cartesian and Spherical Tracking Filters -- 18.3.1 Setting Values for q -- 18.3.2 Simulating Radar Observation Data -- 18.3.3 Filter Initialization
18.4 Performance Comparison for Various Estimation Methods
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
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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries
Link Print version: Haug, Anton J. Bayesian Estimation and Tracking : A Practical Guide Hoboken : Wiley,c2012 9780470621707
Subject Bayesian statistical decision theory.;Automatic tracking -- Mathematics.;Estimation theory
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