{"product_id":"bayesian-estimation-and-tracking-9780470621707","title":"Bayesian Estimation and Tracking","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\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 o\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\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","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49402380157271,"sku":"9780470621707","price":102.56,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780470621707.jpg?v=1730480219","url":"https:\/\/bookcurl.com\/products\/bayesian-estimation-and-tracking-9780470621707","provider":"Book Curl","version":"1.0","type":"link"}