{"product_id":"bayesian-estimation-and-tracking-isbn-9780470621707","title":"Bayesian Estimation and Tracking","description":"\u003cp\u003e\u003cb\u003eA practical approach to estimating and tracking dynamic systems in real-worl applications\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eMuch of the literature on performing estimation for non-Gaussian systems is short on practical methodology, while Gaussian methods often lack a cohesive derivation. \u003ci\u003eBayesian Estimation and Tracking\u003c\/i\u003e 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.\u003c\/p\u003e \u003cp\u003eFeaturing 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.\u003c\/p\u003e \u003cp\u003eCase 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.\u003c\/p\u003e \u003cp\u003e\u003ci\u003eBayesian Estimation and Tracking\u003c\/i\u003e 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.\u003c\/p\u003e \u003cp\u003ePreface xv\u003c\/p\u003e \u003cp\u003eAcknowledgments xvii\u003c\/p\u003e \u003cp\u003eList of Figures Xix\u003c\/p\u003e \u003cp\u003eList of Tables xxv\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePART I PRELIMINARIES\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction 3\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Bayesian Inference 4\u003c\/p\u003e \u003cp\u003e1.2 Bayesian Hierarchy of Estimation Methods 5\u003c\/p\u003e \u003cp\u003e1.3 Scope of This Text 6\u003c\/p\u003e \u003cp\u003e1.3.1 Objective 6\u003c\/p\u003e \u003cp\u003e1.3.2 Chapter Overview and Prerequisites 6\u003c\/p\u003e \u003cp\u003e1.4 Modeling and Simulation with MATLAB\u003csup\u003e®\u003c\/sup\u003e 8\u003c\/p\u003e \u003cp\u003eReferences 9\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Preliminary Mathematical Concepts 11\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 A Very Brief Overview of Matrix Linear Algebra 11\u003c\/p\u003e \u003cp\u003e2.1.1 Vector and Matrix Conventions and Notation 11\u003c\/p\u003e \u003cp\u003e2.1.2 Sums and Products 12\u003c\/p\u003e \u003cp\u003e2.1.3 Matrix Inversion 13\u003c\/p\u003e \u003cp\u003e2.1.4 Block Matrix Inversion 14\u003c\/p\u003e \u003cp\u003e2.1.5 Matrix Square Root 15\u003c\/p\u003e \u003cp\u003e2.2 Vector Point Generators 16\u003c\/p\u003e \u003cp\u003e2.3 Approximating Nonlinear Multidimensional Functions with Multidimensional Arguments 19\u003c\/p\u003e \u003cp\u003e2.3.1 Approximating Scalar Nonlinear Functions 19\u003c\/p\u003e \u003cp\u003e2.3.2 Approximating Multidimensional Nonlinear Functions 23\u003c\/p\u003e \u003cp\u003e2.4 Overview of Multivariate Statistics 29\u003c\/p\u003e \u003cp\u003e2.4.1 General Definitions 29\u003c\/p\u003e \u003cp\u003e2.4.2 The Gaussian Density 32\u003c\/p\u003e \u003cp\u003eReferences 40\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 General Concepts of Bayesian Estimation 42\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Bayesian Estimation 43\u003c\/p\u003e \u003cp\u003e3.2 Point Estimators 43\u003c\/p\u003e \u003cp\u003e3.3 Introduction to Recursive Bayesian Filtering of Probability Density Functions 46\u003c\/p\u003e \u003cp\u003e3.4 Introduction to Recursive Bayesian Estimation of the State Mean and Covariance 49\u003c\/p\u003e \u003cp\u003e3.4.1 State Vector Prediction 50\u003c\/p\u003e \u003cp\u003e3.4.2 State Vector Update 51\u003c\/p\u003e \u003cp\u003e3.5 Discussion of General Estimation Methods 55\u003c\/p\u003e \u003cp\u003eReferences 55\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Case Studies: Preliminary Discussions 56\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 The Overall Simulation\/Estimation\/Evaluation Process 57\u003c\/p\u003e \u003cp\u003e4.2 A Scenario Simulator for Tracking a Constant Velocity Target Through a DIFAR Buoy Field 58\u003c\/p\u003e \u003cp\u003e4.2.1 Ship Dynamics Model 58\u003c\/p\u003e \u003cp\u003e4.2.2 Multiple Buoy Observation Model 59\u003c\/p\u003e \u003cp\u003e4.2.3 Scenario Specifics 59\u003c\/p\u003e \u003cp\u003e4.3 DIFAR Buoy Signal Processing 62\u003c\/p\u003e \u003cp\u003e4.4 The DIFAR Likelihood Function 67\u003c\/p\u003e \u003cp\u003eReferences 69\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePART II THE GAUSSIAN ASSUMPTION: A FAMILY OF KALMAN FILTER ESTIMATORS\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 The Gaussian Noise Case: Multidimensional Integration of Gaussian-Weighted Distributions 73\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Summary of Important Results From Chapter 3 74\u003c\/p\u003e \u003cp\u003e5.2 Derivation of the Kalman Filter Correction (Update) Equations \u003ci\u003eRevisited\u003c\/i\u003e 76\u003c\/p\u003e \u003cp\u003e5.3 The General Bayesian Point Prediction Integrals for Gaussian Densities 78\u003c\/p\u003e \u003cp\u003e5.3.1 Refining the Process Through an Affine Transformation 80\u003c\/p\u003e \u003cp\u003e5.3.2 General Methodology for Solving Gaussian-Weighted Integrals 82\u003c\/p\u003e \u003cp\u003eReferences 85\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 The Linear Class of Kalman Filters 86\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Linear Dynamic Models 86\u003c\/p\u003e \u003cp\u003e6.2 Linear Observation Models 87\u003c\/p\u003e \u003cp\u003e6.3 The Linear Kalman Filter 88\u003c\/p\u003e \u003cp\u003e6.4 Application of the LKF to DIFAR Buoy Bearing Estimation 88\u003c\/p\u003e \u003cp\u003eReferences 92\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 The Analytical Linearization Class of Kalman Filters: The Extended Kalman Filter 93\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 One-Dimensional Consideration 93\u003c\/p\u003e \u003cp\u003e7.1.1 One-Dimensional State Prediction 94\u003c\/p\u003e \u003cp\u003e7.1.2 One-Dimensional State Estimation Error Variance Prediction 95\u003c\/p\u003e \u003cp\u003e7.1.3 One-Dimensional Observation Prediction Equations 96\u003c\/p\u003e \u003cp\u003e7.1.4 Transformation of One-Dimensional Prediction Equations 96\u003c\/p\u003e \u003cp\u003e7.1.5 The One-Dimensional Linearized EKF Process 98\u003c\/p\u003e \u003cp\u003e7.2 Multidimensional Consideration 98\u003c\/p\u003e \u003cp\u003e7.2.1 The State Prediction Equation 99\u003c\/p\u003e \u003cp\u003e7.2.2 The State Covariance Prediction Equation 100\u003c\/p\u003e \u003cp\u003e7.2.3 Observation Prediction Equations 102\u003c\/p\u003e \u003cp\u003e7.2.4 Transformation of Multidimensional Prediction Equations 103\u003c\/p\u003e \u003cp\u003e7.2.5 The Linearized Multidimensional Extended Kalman Filter Process 105\u003c\/p\u003e \u003cp\u003e7.2.6 Second-Order Extended Kalman Filter 105\u003c\/p\u003e \u003cp\u003e7.3 An Alternate Derivation of the Multidimensional Covariance Prediction Equations 107\u003c\/p\u003e \u003cp\u003e7.4 Application of the EKF to the DIFAR Ship Tracking Case Study 108\u003c\/p\u003e \u003cp\u003e7.4.1 The Ship Motion Dynamics Model 108\u003c\/p\u003e \u003cp\u003e7.4.2 The DIFAR Buoy Field Observation Model 109\u003c\/p\u003e \u003cp\u003e7.4.3 Initialization for All Filters of the Kalman Filter Class 111\u003c\/p\u003e \u003cp\u003e7.4.4 Choosing a Value for the Acceleration Noise 112\u003c\/p\u003e \u003cp\u003e7.4.5 The EKF Tracking Filter Results 112\u003c\/p\u003e \u003cp\u003eReferences 114\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 The Sigma Point Class: The Finite Difference Kalman Filter 115\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 One-Dimensional Finite Difference Kalman Filter 116\u003c\/p\u003e \u003cp\u003e8.1.1 One-Dimensional Finite Difference State Prediction 116\u003c\/p\u003e \u003cp\u003e8.1.2 One-Dimensional Finite Difference State Variance Prediction 117\u003c\/p\u003e \u003cp\u003e8.1.3 One-Dimensional Finite Difference Observation Prediction Equations 118\u003c\/p\u003e \u003cp\u003e8.1.4 The One-Dimensional Finite Difference Kalman Filter Process 118\u003c\/p\u003e \u003cp\u003e8.1.5 Simplified One-Dimensional Finite Difference Prediction Equations 118\u003c\/p\u003e \u003cp\u003e8.2 Multidimensional Finite Difference Kalman Filters 120\u003c\/p\u003e \u003cp\u003e8.2.1 Multidimensional Finite Difference State Prediction 120\u003c\/p\u003e \u003cp\u003e8.2.2 Multidimensional Finite Difference State Covariance Prediction 123\u003c\/p\u003e \u003cp\u003e8.2.3 Multidimensional Finite Difference Observation Prediction Equations 124\u003c\/p\u003e \u003cp\u003e8.2.4 The Multidimensional Finite Difference Kalman Filter Process 125\u003c\/p\u003e \u003cp\u003e8.3 An Alternate Derivation of the Multidimensional Finite Difference Covariance Prediction Equations 125\u003c\/p\u003e \u003cp\u003eReferences 127\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 The Sigma Point Class: The Unscented Kalman Filter 128\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Introduction to Monomial Cubature Integration Rules 128\u003c\/p\u003e \u003cp\u003e9.2 The Unscented Kalman Filter 130\u003c\/p\u003e \u003cp\u003e9.2.1 Background 130\u003c\/p\u003e \u003cp\u003e9.2.2 The UKF Developed 131\u003c\/p\u003e \u003cp\u003e9.2.3 The UKF State Vector Prediction Equation 134\u003c\/p\u003e \u003cp\u003e9.2.4 The UKF State Vector Covariance Prediction Equation 134\u003c\/p\u003e \u003cp\u003e9.2.5 The UKF Observation Prediction Equations 135\u003c\/p\u003e \u003cp\u003e9.2.6 The Unscented Kalman Filter Process 135\u003c\/p\u003e \u003cp\u003e9.2.7 An Alternate Version of the Unscented Kalman Filter 135\u003c\/p\u003e \u003cp\u003e9.3 Application of the UKF to the DIFAR Ship Tracking Case Study 137\u003c\/p\u003e \u003cp\u003eReferences 138\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 The Sigma Point Class: The Spherical Simplex Kalman Filter 140\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 One-Dimensional Spherical Simplex Sigma Points 141\u003c\/p\u003e \u003cp\u003e10.2 Two-Dimensional Spherical Simplex Sigma Points 142\u003c\/p\u003e \u003cp\u003e10.3 Higher Dimensional Spherical Simplex Sigma Points 144\u003c\/p\u003e \u003cp\u003e10.4 The Spherical Simplex Kalman Filter 144\u003c\/p\u003e \u003cp\u003e10.5 The Spherical Simplex Kalman Filter Process 145\u003c\/p\u003e \u003cp\u003e10.6 Application of the SSKF to the DIFAR Ship Tracking Case Study 146\u003c\/p\u003e \u003cp\u003eReference 147\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 The Sigma Point Class: The Gauss–Hermite Kalman Filter 148\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 One-Dimensional Gauss–Hermite Quadrature 149\u003c\/p\u003e \u003cp\u003e11.2 One-Dimensional Gauss–Hermite Kalman Filter 153\u003c\/p\u003e \u003cp\u003e11.3 Multidimensional Gauss–Hermite Kalman Filter 155\u003c\/p\u003e \u003cp\u003e11.4 Sparse Grid Approximation for High Dimension\/High Polynomial Order 160\u003c\/p\u003e \u003cp\u003e11.5 Application of the GHKF to the DIFAR Ship Tracking Case Study 163\u003c\/p\u003e \u003cp\u003eReferences 163\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 The Monte Carlo Kalman Filter 164\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 The Monte Carlo Kalman Filter 167\u003c\/p\u003e \u003cp\u003eReference 167\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Summary of Gaussian Kalman Filters 168\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 Analytical Kalman Filters 168\u003c\/p\u003e \u003cp\u003e13.2 Sigma Point Kalman Filters 170\u003c\/p\u003e \u003cp\u003e13.3 A More Practical Approach to Utilizing the Family of Kalman Filters 174\u003c\/p\u003e \u003cp\u003eReferences 175\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 Performance Measures for the Family of Kalman Filters 176\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e14.1 Error Ellipses 176\u003c\/p\u003e \u003cp\u003e14.1.1 The Canonical Ellipse 177\u003c\/p\u003e \u003cp\u003e14.1.2 Determining the Eigenvalues of P 178\u003c\/p\u003e \u003cp\u003e14.1.3 Determining the Error Ellipse Rotation Angle 179\u003c\/p\u003e \u003cp\u003e14.1.4 Determination of the Containment Area 180\u003c\/p\u003e \u003cp\u003e14.1.5 Parametric Plotting of Error Ellipse 181\u003c\/p\u003e \u003cp\u003e14.1.6 Error Ellipse Example 182\u003c\/p\u003e \u003cp\u003e14.2 Root Mean Squared Errors 182\u003c\/p\u003e \u003cp\u003e14.3 Divergent Tracks 183\u003c\/p\u003e \u003cp\u003e14.4 Cramer–Rao Lower Bound 184\u003c\/p\u003e \u003cp\u003e14.4.1 The One-Dimensional Case 184\u003c\/p\u003e \u003cp\u003e14.4.2 The Multidimensional Case 186\u003c\/p\u003e \u003cp\u003e14.4.3 A Recursive Approach to the CRLB 186\u003c\/p\u003e \u003cp\u003e14.4.4 The Cramer–Rao Lower Bound for Gaussian Additive Noise 190\u003c\/p\u003e \u003cp\u003e14.4.5 The Gaussian Cramer–Rao Lower Bound with Zero Process Noise 191\u003c\/p\u003e \u003cp\u003e14.4.6 The Gaussian Cramer–Rao Lower Bound with Linear Models 191\u003c\/p\u003e \u003cp\u003e14.5 Performance of Kalman Class DIFAR Track Estimators 192\u003c\/p\u003e \u003cp\u003eReferences 198\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePART III MONTE CARLO METHODS\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 Introduction to Monte Carlo Methods 201\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e15.1 Approximating a Density From a Set of Monte Carlo Samples 202\u003c\/p\u003e \u003cp\u003e15.1.1 Generating Samples from a Two-Dimensional Gaussian Mixture Density 202\u003c\/p\u003e \u003cp\u003e15.1.2 Approximating a Density by Its Multidimensional Histogram 202\u003c\/p\u003e \u003cp\u003e15.1.3 Kernel Density Approximation 204\u003c\/p\u003e \u003cp\u003e15.2 General Concepts Importance Sampling 210\u003c\/p\u003e \u003cp\u003e15.3 Summary 215\u003c\/p\u003e \u003cp\u003eReferences 216\u003c\/p\u003e \u003cp\u003e\u003cb\u003e16 Sequential Importance Sampling Particle Filters 218\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e16.1 General Concept of Sequential Importance Sampling 218\u003c\/p\u003e \u003cp\u003e16.2 Resampling and Regularization (Move) for SIS Particle Filters 222\u003c\/p\u003e \u003cp\u003e16.2.1 The Inverse Transform Method 222\u003c\/p\u003e \u003cp\u003e16.2.2 SIS Particle Filter with Resampling 226\u003c\/p\u003e \u003cp\u003e16.2.3 Regularization 227\u003c\/p\u003e \u003cp\u003e16.3 The Bootstrap Particle Filter 230\u003c\/p\u003e \u003cp\u003e16.3.1 Application of the BPF to DIFAR Buoy Tracking 231\u003c\/p\u003e \u003cp\u003e16.4 The Optimal SIS Particle Filter 233\u003c\/p\u003e \u003cp\u003e16.4.1 Gaussian Optimal SIS Particle Filter 235\u003c\/p\u003e \u003cp\u003e16.4.2 Locally Linearized Gaussian Optimal SIS Particle Filter 236\u003c\/p\u003e \u003cp\u003e16.5 The SIS Auxiliary Particle Filter 238\u003c\/p\u003e \u003cp\u003e16.5.1 Application of the APF to DIFAR Buoy Tracking 242\u003c\/p\u003e \u003cp\u003e16.6 Approximations to the SIS Auxiliary Particle Filter 243\u003c\/p\u003e \u003cp\u003e16.6.1 The Extended Kalman Particle Filter 243\u003c\/p\u003e \u003cp\u003e16.6.2 The Unscented Particle Filter 243\u003c\/p\u003e \u003cp\u003e16.7 Reducing the Computational Load Through Rao-Blackwellization 245\u003c\/p\u003e \u003cp\u003eReferences 245\u003c\/p\u003e \u003cp\u003e\u003cb\u003e17 The Generalized Monte Carlo Particle Filter 247\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e17.1 The Gaussian Particle Filter 248\u003c\/p\u003e \u003cp\u003e17.2 The Combination Particle Filter 250\u003c\/p\u003e \u003cp\u003e17.2.1 Application of the CPF–UKF to DIFAR Buoy Tracking 252\u003c\/p\u003e \u003cp\u003e17.3 Performance Comparison of All DIFAR Tracking Filters 253\u003c\/p\u003e \u003cp\u003eReferences 255\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePART IV ADDITIONAL CASE STUDIES\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e18 A Spherical Constant Velocity Model for Target Tracking in Three Dimensions 259\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e18.1 Tracking a Target in Cartesian Coordinates 261\u003c\/p\u003e \u003cp\u003e18.1.1 Object Dynamic Motion Model 262\u003c\/p\u003e \u003cp\u003e18.1.2 Sensor Data Model 263\u003c\/p\u003e \u003cp\u003e18.1.3 GaussianTracking Algorithms for a Cartesian StateVector 264\u003c\/p\u003e \u003cp\u003e18.2 Tracking a Target in Spherical Coordinates 265\u003c\/p\u003e \u003cp\u003e18.2.1 State Vector Position and Velocity Components in Spherical Coordinates 266\u003c\/p\u003e \u003cp\u003e18.2.2 Spherical State Vector Dynamic Equation 267\u003c\/p\u003e \u003cp\u003e18.2.3 Observation Equations with a Spherical State Vector 270\u003c\/p\u003e \u003cp\u003e18.2.4 GaussianTracking Algorithms for a Spherical StateVector 270\u003c\/p\u003e \u003cp\u003e18.3 Implementation of Cartesian and Spherical Tracking Filters 273\u003c\/p\u003e \u003cp\u003e18.3.1 Setting Values for q 273\u003c\/p\u003e \u003cp\u003e18.3.2 Simulating Radar Observation Data 274\u003c\/p\u003e \u003cp\u003e18.3.3 Filter Initialization 276\u003c\/p\u003e \u003cp\u003e18.4 Performance Comparison for Various Estimation Methods 278\u003c\/p\u003e \u003cp\u003e18.4.1 Characteristics of the Trajectories Used for Performance Analysis 278\u003c\/p\u003e \u003cp\u003e18.4.2 Filter Performance Comparisons 282\u003c\/p\u003e \u003cp\u003e18.5 Some Observations and Future Considerations 293\u003c\/p\u003e \u003cp\u003eAPPENDIX 18.A Three-Dimensional Constant Turn Rate Kinematics 294\u003c\/p\u003e \u003cp\u003e18.A.1 General Velocity Components for Constant Turn Rate Motion 294\u003c\/p\u003e \u003cp\u003e18.A.2 General Position Components for Constant Turn Rate Motion 297\u003c\/p\u003e \u003cp\u003e18.A.3 Combined Trajectory Transition Equation 299\u003c\/p\u003e \u003cp\u003e18.A.4 Turn Rate Setting Based on a Desired Turn Acceleration 299\u003c\/p\u003e \u003cp\u003eAPPENDIX 18.B Three-Dimensional Coordinate Transformations 301\u003c\/p\u003e \u003cp\u003e18.B.1 Cartesian-to-Spherical Transformation 302\u003c\/p\u003e \u003cp\u003e18.B.2 Spherical-to-Cartesian Transformation 305\u003c\/p\u003e \u003cp\u003eReferences 306\u003c\/p\u003e \u003cp\u003e\u003cb\u003e19 Tracking a Falling Rigid Body Using Photogrammetry 308\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e19.1 Introduction 308\u003c\/p\u003e \u003cp\u003e19.2 The Process (Dynamic) Model for Rigid Body Motion 311\u003c\/p\u003e \u003cp\u003e19.2.1 Dynamic Transition of the Translational Motion of a Rigid Body 311\u003c\/p\u003e \u003cp\u003e19.2.2 Dynamic Transition of the Rotational Motion of a Rigid Body 313\u003c\/p\u003e \u003cp\u003e19.2.3 Combined Dynamic Process Model 316\u003c\/p\u003e \u003cp\u003e19.2.4 The Dynamic Process Noise Models 317\u003c\/p\u003e \u003cp\u003e19.3 Components of the Observation Model 318\u003c\/p\u003e \u003cp\u003e19.4 Estimation Methods 321\u003c\/p\u003e \u003cp\u003e19.4.1 A Nonlinear Least Squares Estimation Method 321\u003c\/p\u003e \u003cp\u003e19.4.2 An Unscented Kalman Filter Method 323\u003c\/p\u003e \u003cp\u003e19.4.3 Estimation Using the Unscented Combination Particle Filter 325\u003c\/p\u003e \u003cp\u003e19.4.4 Initializing the Estimator 326\u003c\/p\u003e \u003cp\u003e19.5 The Generation of Synthetic Data 328\u003c\/p\u003e \u003cp\u003e19.5.1 Synthetic Rigid Body Feature Points 328\u003c\/p\u003e \u003cp\u003e19.5.2 Synthetic Trajectory 328\u003c\/p\u003e \u003cp\u003e19.5.3 Synthetic Cameras 333\u003c\/p\u003e \u003cp\u003e19.5.4 Synthetic Measurements 333\u003c\/p\u003e \u003cp\u003e19.6 Performance Comparison Analysis 334\u003c\/p\u003e \u003cp\u003e19.6.1 Filter Performance Comparison Methodology 335\u003c\/p\u003e \u003cp\u003e19.6.2 Filter Comparison Results 338\u003c\/p\u003e \u003cp\u003e19.6.3 Conclusions and Future Considerations 341\u003c\/p\u003e \u003cp\u003eAPPENDIX 19.A Quaternions Axis-Angle Vectors and Rotations 342\u003c\/p\u003e \u003cp\u003e19.A.1 Conversions Between Rotation Representations 342\u003c\/p\u003e \u003cp\u003e19.A.2 Representation of Orientation and Rotation 343\u003c\/p\u003e \u003cp\u003e19.A.3 Point Rotations and Frame Rotations 344\u003c\/p\u003e \u003cp\u003eReferences 345\u003c\/p\u003e \u003cp\u003e\u003cb\u003e20 Sensor Fusion Using Photogrammetric and Inertial Measurements 346\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e20.1 Introduction 346\u003c\/p\u003e \u003cp\u003e20.2 The Process (Dynamic) Model for Rigid Body Motion 347\u003c\/p\u003e \u003cp\u003e20.3 The Sensor Fusion Observational Model 348\u003c\/p\u003e \u003cp\u003e20.3.1 The Inertial Measurement Unit Component of the Observation Model 348\u003c\/p\u003e \u003cp\u003e20.3.2 The Photogrammetric Component of the Observation Model 350\u003c\/p\u003e \u003cp\u003e20.3.3 The Combined Sensor Fusion Observation Model 351\u003c\/p\u003e \u003cp\u003e20.4 The Generation of Synthetic Data 352\u003c\/p\u003e \u003cp\u003e20.4.1 Synthetic Trajectory 352\u003c\/p\u003e \u003cp\u003e20.4.2 Synthetic Cameras 352\u003c\/p\u003e \u003cp\u003e20.4.3 Synthetic Measurements 352\u003c\/p\u003e \u003cp\u003e20.5 Estimation Methods 354\u003c\/p\u003e \u003cp\u003e20.5.1 Initial Value Problem Solver for IMU Data 354\u003c\/p\u003e \u003cp\u003e20.6 Performance Comparison Analysis 357\u003c\/p\u003e \u003cp\u003e20.6.1 Filter Performance Comparison Methodology 359\u003c\/p\u003e \u003cp\u003e20.6.2 Filter Comparison Results 360\u003c\/p\u003e \u003cp\u003e20.7 Conclusions 361\u003c\/p\u003e \u003cp\u003e20.8 Future Work 362\u003c\/p\u003e \u003cp\u003eReferences 364\u003c\/p\u003e \u003cp\u003eIndex 367\u003c\/p\u003e  \u003cp\u003e\u003cb\u003eANTON J. HAUG, PhD,\u003c\/b\u003e 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.\u003c\/p\u003e  \u003cp\u003e\u003cb\u003eA practical approach to estimating and tracking dynamic systems in real-world applications\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eMuch of the literature on performing estimation for non-Gaussian systems is short on practical methodology, while Gaussian methods often lack a cohesive derivation. \u003ci\u003eBayesian Estimation and Tracking\u003c\/i\u003e 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 noises.\u003c\/p\u003e \u003cp\u003eFeaturing 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 each 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.\u003c\/p\u003e \u003cp\u003eCase 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.\u003c\/p\u003e \u003cp\u003e\u003ci\u003eBayesian Estimation and Tracking\u003c\/i\u003e 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.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47988793770213,"sku":"NP9780470621707","price":146.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9780470621707.jpg?v=1761781613","url":"https:\/\/k12savings.com\/products\/bayesian-estimation-and-tracking-isbn-9780470621707","provider":"K12savings","version":"1.0","type":"link"}