Nonlinear Filtering : Concepts and Engineering Applications

"Nonlinear Filtering covers linear and nonlinear filtering in a comprehensive manner, with appropriate theoretic and practical development. Aspects of modeling, estimation, recursive filtering, linear filtering, and nonlinear filtering are presented with appropriate and sufficient mathematics. A modeling-control-system approach is used when applicable, and detailed practical applications are presented to elucidate the analysis and filtering concepts. MATLAB routines are included, and examples from a wide range of engineering applications - including aerospace, automated manufacturing, robotics, and advanced control systems - are referenced throughout the text."--Provided by publisher Appendix 6A: Approximate Filters -- Appendix 6B: Basic Numerical Approximation Approaches -- Appendix 6C: Satellite Orbit Determination as a Nonlinear Filtering Problem - Application of the Extended Kalman Filter, Extended UD Filter and Extended UD-RTS Smoother -- Appendix 6D: Application to Planar Tracking Problem - Illustrative Example -- Chapter 7. Generalized Model Error Estimators for Nonlinear Systems -- 7.1 Philosophy of Model Error -- 7.2 Pontryagin's Conditions -- 7.3 Basic Invariant Embedding Approach -- 7.4 Generalized Continuous Time Algorithm -- 7.5 Generalized Discrete Time Algorithm -- 7.6 Conventional Invariance Embedding Estimators -- 7.7 Robust Estimation of Model Error in H-Infinity Setting -- 7.7.1 Performance Norm -- 7.7.2 Constraint on Cost Function -- 7.7.3 Semi-Robust/Adaptive Invariant Embedding Estimators -- 7.8 Model Fitting Procedure to the Discrepancy/Model Error -- 7.9 Features of Model Error Algorithm -- Exercises for Section II (Chapters 5-7) -- References for Section II (Chapters 5-7) -- Section III Nonlinear Filtering, Estimation and Implementation Approaches -- Chapter 8. Nonlinear Estimation and Filtering -- 8.1 The General Estimation Framework -- 8.2 Continuous Time Dynamic Model and Filtering -- 8.2.1 Fokker-Planck Equation -- 8.2.2 Kushner-Stratonovich Equation -- 8.2.3 Minimum Variance Estimation -- 8.2.4 Bayesian Approach to Continuous Time Filtering -- 8.2.4.1 Bayes Formula -- 8.2.4.2 Nonlinear Filtering for Stochastic Differential Equation-Continuous Time Systems -- 8.2.5 Computation of the Filtered Estimates -- 8.3 Bayesian Recursive Estimation-Discrete Time Systems -- 8.3.1 Measurement Data Update/Filtering -- 8.3.2 Prediction-Time Propagation/Evolution -- 8.4 Continuous Time State-Discrete Time Measurement Estimator -- 8.4.1 Filtering/Measurement Data Update -- 8.4.2 Prediction-Time Propagation/Evolution 3.3 H∞ Smoother -- 3.4 H∞ Risk-Sensitive Filter -- 3.4.1 A Posteriori-Risk Sensitive Filter -- 3.4.2 A Priori Risk-Sensitive Filter -- 3.4.3 Risk-Sensitive Smoother -- 3.5 Mixed H∞ and Kalman Filtering -- 3.6 Global H∞ Filter -- Appendix 3A: Krein Space and Some Definitions and Theorems -- Appendix 3B: Illustrative Examples -- Chapter 4. Adaptive Filtering -- 4.1 Need of Filter Tuning and Adaptation -- 4.2 Approaches to Adaptive Filtering -- 4.2.1 Heuristic Approach -- 4.2.2 Bayesian Approach -- 4.2.3 Maximum Likelihood-Based Optimal Adaptive Filtering -- 4.2.4 Correlation-Based Adaptation -- 4.2.5 Concept of Covariance Matching -- 4.2.6 Fuzzy Logic-Based Adaptation -- 4.2.6.1 Fuzzy Inference System for R with Known Q -- 4.2.6.2 Fuzzy Inference System for Q with Known R -- 4.3 H∞ Finite Memory Adaptive Filter -- Appendix 4A: Maneuvering Target - Illustrative Examples -- Appendix 4B: Adaptive Kalman Filter - Illustrative Example -- Exercises for Section I (Chapters 1-4) -- References for Section I (Chapters 1-4) -- Section II Factorization and Approximation Filters -- Chapter 5. Factorization Filtering -- 5.1 Divergence of Kalman Filter -- Need of Factorization -- 5.2 UD Factorization Filter -- 5.2.1 Time Propagation -- 5.2.2 Measurement Data Update -- 5.2.3 Filter for Correlated Process Noise and Bias Parameters -- 5.3 Filtering Algorithms Based on Square-Root Arrays -- 5.3.1 H2 Square-Root Arrays -- 5.3.2 Chandrasekhar Recursions -- 5.3.3 H2 Chandrasekhar Recursions -- 5.4 Square-Root Information Filter -- 5.4.1 Inclusion of A Priori Information in the Least Squares Cost Function -- 5.4.2 Measurements Data Update -- 5.4.3 State Propagation of Square- Root Information Filter -- 5.4.4 Measurements Data Update of Square- Root Information Filter -- 5.5 Eigenvalue-Eigenvector Factorization Filtering -- 5.5.1 V-D Discrete Time Measurement Update 2.4.1.1 State and Covariance Matrix Propagation -- 2.4.1.2 Measurement Update -- 2.4.1.3 Kalman Gain -- 2.4.2 Continuous Time Kalman Filter -- 2.4.3 Interpretation of Kalman Filter -- 2.4.3.1 Continuous Time Filter -- 2.4.3.2 Discrete Time Filter -- 2.4.4 Filters for Correlated/Coloured Process and Measurement Noises -- 2.4.4.1 Kalman Filter for the Correlated Process and Measurement Noises -- 2.4.4.2 Handling of Coloured Process Noise and Coloured Measurement Noise in Kalman Filters -- 2.4.5 Time-Varying Linear Kalman Filters -- 2.4.6 Steady State Filtering -- 2.4.7 Kalman Filter Implementation Aspects -- 2.4.8 Parallelization of Kalman Filters -- 2.4.8.1 Measurement Update Parallelization -- 2.4.8.2 Time Propagation Parallelization -- 2.5 Filter Error Methods -- 2.5.1 Output Error Method -- 2.5.2 Process Noise Algorithms for Linear Systems -- 2.5.2.1 Natural Formulation -- 2.5.2.2 Innovations Formulation -- 2.5.2.3 Mixed Formulation -- 2.5.3 Process Noise Algorithms for Nonlinear Systems -- 2.5.3.1 Steady-State Filter -- 2.5.3.2 Time-Varying Filter -- 2.6 Information Filtering -- 2.6.1 Fisher's Information Concept -- 2.6.2 Linear Information Filter -- 2.7 Smoothers -- 2.7.1 Smoothing as a Combination of Forward and Backward Filtering -- 2.7.2 Fixed Interval RTS Smoother -- 2.7.3 Fixed Point Smoother -- 2.7.4 Fixed Lag Smoother -- Appendix 2A: Innovations Approach to Linear Least Squares Estimation -- Appendix 2B: Filtering Algorithms for Delayed State and Missing Measurements - Illustrative Example -- Appendix 2C: Artificial Neural Network Based Filtering -- Appendix 2D: Image Centroid Tracking with Fuzzy Logic in Filtering Algorithms - Illustrative Example -- Appendix 2E: Illustrative Examples -- Chapter 3. H∞ Filtering -- 3.1 H∞ Norm and Robustness -- 3.2 H∞ Filtering Problem -- 3.2.1 H∞ A Posteriori Filter -- 3.2.2 H∞ A Priori Filter Cover -- Half Title -- Title -- Copyright -- Dedication -- Contents -- Preface -- Acknowledgements -- Authors -- Introduction -- Section I Mathematical Models, Kalman Filtering and H-Infinity Filters -- Chapter 1. Dynamic System Models and Basic Concepts -- 1.1 Dynamic Systems: The Need for Modelling, Parameter Estimation and Filtering -- 1.2 Mathematical Modelling of Systems -- 1.2.1 Time and Frequency Domain Aspects -- 1.2.2 Differential Equations -- 1.2.3 Difference Equations -- 1.2.4 State Space Models -- 1.2.4.1 Physical Representation -- 1.2.4.2 Controllable Canonical Form -- 1.2.4.3 Observable Canonical Form -- 1.2.4.4 Diagonal Form -- 1.2.4.5 General State Space Models -- 1.2.5 Polynomial Models -- 1.2.6 Time Series Models -- 1.2.6.1 Autoregressive Model -- 1.2.6.2 Least Squares Model -- 1.2.7 Transfer Function Models -- 1.3 Nonlinear Dynamic Systems -- 1.3.1 Nonlinearities in a System -- 1.3.2 Mathematical Models of Nonlinear Systems -- 1.3.2.1 Nonlinear Differential and Difference Equations -- 1.3.2.2 Volterra Series -- 1.3.2.3 Hammerstein Model -- 1.3.2.4 Nonlinear State Space Models -- 1.3.2.5 Nonlinear Time Series Models -- 1.4 Signal and System Norms -- 1.4.1 Signal Norms -- 1.4.2 System Norms -- 1.4.2.1 H2 Norm -- 1.4.2.2 H∞ Norm -- 1.5 Digital Signal Processing, Parameter Estimation and Filtering -- 1.5.1 Signal Processing -- 1.5.2 Parameter Estimation: Recursive Approach -- 1.5.3 Filtering Concepts -- 1.5.4 Simple Recursive Filtering -- Appendix 1A: Mean Square Estimation -- Appendix 1B: Nonlinear Models Based on Artificial Neural Networks and Fuzzy Logic -- Appendix 1C: Illustrative Examples -- Chapter 2. Filtering and Smoothing -- 2.1 Wiener Filtering -- 2.2 Least Squares Parameter Estimation -- 2.3 Recursive Least Squares Filter -- 2.4 State Space Models and Kalman Filtering -- 2.4.1 Discrete Time Filter 5.5.2 V-D Square-Root Filtering -- 5.5.2.1 Continuous Time/Discrete Time Square-Root Filtering Algorithm -- 5.5.2.2 Discrete Time/Discrete Time Square- Root Filtering Algorithm -- 5.6 H-Infinity Square-Root Filters -- 5.6.1 H-Infinity Square-Root Arrays -- 5.6.2 H-Infinity Chandrasekhar Recursions -- Chapter 6. Approximation Filters for Nonlinear Systems -- 6.1 Continuous Extended Kalman-Bucy Filter -- 6.2 Continuous-Discrete Extended Kalman-Bucy Filter -- 6.2.1 Time Propagation Filter -- 6.2.2 Measurement Data Update/Filtering -- 6.3 Continuous Discrete Extended Kalman-Bucy Filter for Joint State Parameter Estimation -- 6.3.1 Time Propagation -- 6.3.2 Measurement Data Update -- 6.4 Iterated Extended Kalman Filter -- 6.5 Linearized Kalman Filter -- 6.6 Continuous Second-Order Minimum Variance Estimator (SOF) -- 6.7 Continuous-Discrete Modified Gaussian Second-Order (CDMGSO) Filter -- 6.7.1 Measurement Update -- 6.7.2 Time Propagation/Prediction Part -- 6.8 Extended Information Filter -- 6.9 Statistically Linearized Filter -- 6.10 Derivative-Free Kalman Filter -- 6.10.1 Derivative-Free Kalman Filter Initialization -- 6.10.2 Sigma Points Computation -- 6.10.3 State and Covariance Propagation -- 6.10.4 State and Covariance Update -- 6.11 Global Approximations Nonlinear Filters -- 6.11.1 Orthogonal Series Expansion Approximations -- 6.11.1.1 Approximation Based on Legendre or Fourier Bases Functions -- 6.11.1.2 Approximation Based on Chebyshev Polynomials -- 6.11.2 Gaussian Sum Approximation -- 6.11.3 Point-Mass Approximation -- 6.11.3.1 Measurement Update -- 6.11.3.2 Time Propagation -- 6.11.3.3 Point Estimates -- 6.11.3.4 Algorithmic Aspects -- 6.11.4 Spline Approximation -- 6.11.4.1 B-Splines -- 6.11.4.2 Spline Filtering -- 6.12 Extended H-Infinity Filters -- 6.12.1 Continuous Time System -- 6.12.2 Discrete Time System Content: PrefaceAcknowledgementsAuthorsIntroductionSection I Mathematical Models, Kalman Filtering and H-Infinity Filters1. Dynamic System Models and Basic Concepts2. Filtering and Smoothing3. Hâ Filtering4. Adaptive FilteringSection II Factorization and Approximation Filters5. Factorization Filtering6. Approximation Filters for Nonlinear Systems7. Generalized Model Error Estimators for Nonlinear SystemsSection III Nonlinear Filtering, Estimation and Implementation Approaches8. Nonlinear Estimation and Filtering9. Nonlinear Filtering Based on Characteristic Functions10. Implementation Aspects of Nonlinear Filters11. Nonlinear Parameter Estimation12. Nonlinear ObserversSection IV Appendixes - Basic Concepts and Supporting MaterialAppendix A: System Theoretic Concepts - Controllability, Observability, Identifiability and EstimabilityAppendix B: Probability, Stochastic Processes and Stochastic CalculusAppendix C: Bayesian FilteringAppendix D: Girsanov TheoremAppendix E: Concepts from Signal and Stochastic AnalysesAppendix F: Notes on Simulation and Some AlgorithmsAppendix G: Additional ExamplesIndex