This book presents a practical approach to estimation methods that are designed to provide a clear path to programming all algorithms. Readers are provided with a firm understanding of Bayesian estimation methods and their interrelatedness. Starting with fundamental principles of Bayesian theory, the book shows how each tracking filter is derived from a slight modification to a previous filter. Such a development gives readers a broader understanding of the hierarchy of Bayesian estimation and tracking. Following the discussions about each tracking filter, the filter is put into block diagram form for ease in future recall and reference. The book presents a completely unified approach toBayesian estimation and tracking, and this is accomplished by showing that the current posterior density for a state vector can be linked to its previous posterior density through the use of Bayes' Law and the Chapman-Kolmogorov integral. Predictive point estimates are then shown to be density-weighted integrals of nonlinear functions. The book also presents a methodology that makes implementation of the estimation methods simple (or, rather, simpler than they have been in the past). Each algorithm is accompanied by a block diagram thatillustrates how all parts of the tracking filter are linked in a never-endingchain, from initialization to the loss of track. These filter block diagramsprovide a ready picture for implementing the algorithms into programmable code. In addition, four completely worked out case studies give readers examplesof implementation, from simulation models that generate noisy observations toworked-out applications for all tracking algorithms. This book also presentsthe development and application of track performance metrics, including how to generate error ellipses when implementing in real-world applications, how tocalculate RMS errors in simulation environments, and how to calculate Cramer-Rao lower bounds for the RMS errors. These are also illustrated in the case study presentations. INDICE: List of Figures xiList of Tables xxiPart I. Prelininaries1. Introduction 31.1 Bayesian Inference 51.2 Bayesian Hierarchy of Estimation Methods 71.3 Scope of this Text 81.4 Modeling and Simulation with Matlab® 132. Preliminary Mathematical Concepts 192.1 A Very Brief Overview of Matrix Linear Algebra202.2 Vector Point Generators 272.3 Approximating Nonlinear Multidimensional Functions with Multidimensional Arguments 322.4 Overview of Multivariate Statistics 473. General Concepts of Bayesian Estimation 693.1 Bayesian Estimation 703.2 Point Estimators 723.3 Introduction to Recursive Bayesian Filtering of Probability Density Functions 763.4 Introduction to Recursive Bayesian Estimation of the State Mean and Covariance 813.5 Discussion of General Estimation Methods 884. Case Studies: Preliminary Discussions 934.1 The Overall Simulation/Estimation/Evaluation Process 944.2 A Scenario Simulator for Tracking a Constant-Velocity Target Through a DIFAR Buoy Field 974.3 DIFAR Buoy Signal Processing1024.4 The DIFAR Likelihood Function 111Part II. The Gaussian Assumption: A Family of Kalman Filter Estimators5. The Gaussian Noise Case: Multidimensional Integration of Gaussian-Weighted Distributions 1195.1 Summary of Important Results From Chapter 3 1225.2 Derivation of the Kalman Filter Correction (Update)Equations Revisted 1245.3 The General Bayesian Point Prediction Integrals forGaussian Densities 1286. The Linear Class of Kalman Filters 1416.1 Linear Dynamic Models 1426.2 Linear Observation Models 1436.3 The Linear Kalman Filter 1446.4 Application of the LKF to DIFAR Buoy Bearing Estimation 1467. The Analytical Linearization Class of Kalman Filters: The Extended Kalman Filter 1537.1 One-Dimensional Consideration 1547.2 Multidimensional Consideration 1597.3 An Alternate Derivation of the Multidimensional Covariance Prediction Equations 1727.4 Application of the EKF to the DIFAR Ship Tracking Case Study 1748. The Sigma Point Class: The Finite Difference Kalman Filter 1878.1 One-Dimensional Finite Difference Kalman Filter 1898.2 Multidimensional Finite Difference Kalman Filters 1958.3 An Alternate Derivation of the Multidimensional Finite Difference Covariance Prediction Equations 2019. The Sigma Point Class: The Unscented Kalman Filter 2079.1 Introduction to Monomial Cubature Integration Rules 2079.2 The Unscented Kalman Filter 2119.3 Applications of the UKF to the DIFAR Ship Tracking Case Study 22110. The Sigma Point Class: The Spherical Simplex Kalman Filter 22710.1 One-Dimensional Spherical Simplex Sigma Points 22810.2 Two-Dimensional Spherical Simplex Sigma Points 22910.3 Higher-Dimensional Spherical Simplex Sigma Points 23310.4 The Spherical Simplex Kalman Filter 23310.5 TheSpherical Simplex Kalman Filter Process 23610.6 Application of the SSKF to the DIFAR Ship Tracking Case Study 23611. The Sigma Point Class: The Gauss-Hermite Kalman Filter 24111.1 One-Dimensional Gauss-Hermite Quadrature 24211.2 One-Dimensional Gauss-Hermite Kalman Filter 24811.3 Multidimensional Gauss-HermiteKalman Filter 25111.4 Sparse Grid Approximation for High Dimension/High Polynomial Order 25711.5 Application of the GHKF to the DIFAR Ship Tracking Case Study 26112. The Monte Carlo Kalman Filter 26512.1 The Monte Carlo Kalman Filter26813. Summary of Gaussian Kalman Filters 27313.1 Analytical Kalman Filters 27413.2 Sigma-Point Kalman Filters 27613.3 A More Practical Approach to Utilizing the Family of Kalman Filters 28414. Performance Measures for the Family of Kalman Filters 28914.1 Error Ellipses 29014.2 Root Mean Squared Errors 29914.3Divergent Tracks 30114.4 Cramer-Rao Lower Bound 30214.5 Performance of KalmanClass DIFAR Track Estimators 315Part III. Monte Carlo Methods15. Introductionto Monte Carlo Methods 32315.1 Approximating a Density From a Set of Monte Carlo Samples 32515.2 General Concepts Importance Sampling 34015.3 Summary 34716. Sequential Importance Sampling Particle Filters 35116.1 General Concept of Sequential Importance Sampling 35116.2 Resampling and Regularization (Move) forSIS Particle Filters 35716.3 The Bootstrap Particle Filter 37216.4 The Optimal SIS Particle Filter 37816.5 The SIS Auxiliary Particle Filter 38516.6 Approximations to the SIS Auxiliary Particle Filter 39316.7 Reducing the Computational Load Through Rao-Blackwellization 39617. The Generalized Sequential Monte Carlo Particle Filter 40317.1 The Gaussian Particle Filter 40417.2 The Combination Particle Filter 40617.3 Performance Comparison of all DIFAR Tracking Filters 411Part IV Additional Case Studies18. A Spherical Constant Velocity Model for Target Tracking in Three Dimensions 42118.1 Tracking a Target in Cartesian Coordinates 42618.2 Tracking a Target in Spherical Coordinates 43318.3 Implementation of Cartesian and Spherical Tracking Filters 44318.4 Performance Comparison for Various Estimation Methods 45318.5 Some Observations and Future Considerations 46919. Tracking a Falling Rigid Body Using Photogrammetry 49719.1 Introduction 49719.2 The Process (Dynamic) Model for Rigid Body Motion 50219.3 Components of the Observation Model 51319.4 Estimation Methods 51719.5 The Generation of Synthetic Data 52919.6 Performance Comparison Analysis 53820. SensorFusion using Photogrammetric and Inertial Measurements 55920.1 Introduction 55920.2 The Process (Dynamic) Model for Rigid Body Motion 56220.3 The Sensor Fusion Observational Model56320.4 The Generation of Synthetic Data 56920.5 Estimation Methods 57220.6 Performance Comparison Analysis 57720.7 Conclusions 58520.8 Future Work 586References 589
- ISBN: 978-0-470-62170-7
- Editorial: John Wiley & Sons
- Encuadernacion: Cartoné
- Páginas: 400
- Fecha Publicación: 29/06/2012
- Nº Volúmenes: 1
- Idioma: Inglés