Raol J.R., Gopalratnam G., Twala B. Nonlinear Filtering: Concepts and Engineering Applications

Boca Raton: CRC Press, 2017. — 581 p.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.Mathematical Models, Kalman Filtering and H-Infinity Filters
Dynamic System Models and Basic Concepts
Dynamic Systems: The Need for Modelling, Parameter Estimation and Filtering.
Mathematical Modelling of Systems.
Nonlinear Dynamic Systems.
Signal and System Norms.
Digital Signal Processing, Parameter Estimation and Filtering.
Appendix 1A: Mean Square Estimation.
Appendix 1B: Nonlinear Models Based on Artificial Neural Networks and Fuzzy Logic.
Appendix 1C: Illustrative Examples.
Filtering and Smoothing
Wiener Filtering.
Least Squares Parameter Estimation.
Recursive Least Squares Filter.
State Space Models and Kalman Filtering.
Filter Error Methods.
Information Filtering.
Smoothers.
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.
H_∞ Filtering
H_∞ Norm and Robustness.
H_∞ Filtering Problem.
H_∞ Smoother.
H_∞ Risk-Sensitive Filter.
Mixed H_∞ and Kalman Filtering.
Global H_∞ Filter.
Appendix ЗА: Krein Space and Some Definitions and Theorems.
Appendix 3B: Illustrative Examples.
Adaptive Filtering.
Need of Filter Tuning and Adaptation.
Approaches to Adaptive Filtering.
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).Factorization and Approximation Filters
Factorization Filtering
Divergence of Kalman Filter; Need of Factorization.
UD Factorization Filter.
Filtering Algorithms Based on Square-Root Arrays.
Square-Root Information Filter.
Eigenvalue-Eigenvector Factorization Filtering.
H-Infinity Square-Root Filters.
Approximation Filters for Nonlinear Systems
Continuous Extended Kalman-Bucy Filter.
Continuous-Discrete Extended Kalman-Bucy Filter.
Continuous Discrete Extended Kalman-Bucy Filter for Joint State Parameter Estimation.
Iterated Extended Kalman Filter.
Linearized Kalman Filter.
Continuous Second-Order Minimum Variance Estimator (SOF).
Continuous-Discrete Modified Gaussian Second-Order (CDMGSO) Filter.
Extended Information Filter.
Statistically Linearized Filter.
Derivative-Free Kalman Filter.
Global Approximations Nonlinear Filters.
Extended H-Infinity Filters.
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.
Generalized Model Error Estimators for Nonlinear Systems
Philosophy of Model Error.
Pontryagin's Conditions.
Basic Invariant Embedding Approach.
Generalized Continuous Time Algorithm.
Generalized Discrete Time Algorithm.
Conventional Invariance Embedding Estimators.
Robust Estimation of Model Error in H-Infinity Setting.
Model Fitting Procedure to the Discrepancy/Model Error.
Features of Model Error Algorithm.
Exercises for Section II (Chapters 5-7).
References for Section II (Chapters 5-7).Nonlinear Filtering, Estimation and Implementation Approaches
Nonlinear Estimation and Filtering
The General Estimation Framework.
Continuous Time Dynamic Model and Filtering.
Bayesian Recursive Estimation-Discrete Time Systems.
Continuous Time State-Discrete Time Measurement Estimator.
Benes Filter.
Wonham Filter.
Conditionally Gaussian Filtering.
Daum's Filter.
Schmidt's Design of Nonlinear Filters Based on Daum's Theory.
Cubature Kalman Filter: A Nonlinear Filter for High-Dimensional State Estimation.
Appendix 8A: Innovations Approach to Nonlinear Filtering and Smoothing.
Appendix 8B: Extended Benes Filter.
Appendix 8C: Comparative Aspects of Nonlinear Filters.
Appendix 8D: Illustrative Examples.
Nonlinear Filtering Based on Characteristic Functions
Conditionally Optimal Filtering.
Conditionally Optimal Filters for Continuous Systems.
Conditionally Optimal Filters for Discrete Systems.
Filtering for Continuous Systems with Discrete Measurements.
Nonlinear Filtering for Correlated Noise Processes.
Simulation Results.
Derivations of Conditionally Optimal Gains for CSDM Nonlinear Systems.
Derivations of Conditionally Optimal Gains for CSDM Nonlinear Systems with Correlated Measurement Noise.
Appendix 9A: Finite Dimensional Minmax Algorithm for Nonlinear State Estimation.
Implementation Aspects of Nonlinear Filters
Sequential Monte Carlo Methods: Particle Filters.
Selection of Proposal Probability Density Functions.
Theoretical and Practical Aspects of the Particle Filters.
Evaluation and Implementation of the Particles Filters.
Selection of Structural Functions and Computation of Gains in Conditionally Optimal Filters.
Appendix 10A: Daum's Particle and Non-Particle Filters.
Appendix 10B: Illustrative Examples.
Nonlinear Parameter Estimation
Nonlinear Least Squares.
Gaussian Least Squares Differential Correction Method.
Output Error Method-Maximum Likelihood Approach.
Estimation Before Modelling Approach.
Appendix 11A: Aircraft Real Data Analysis - Illustrative Example.
Appendix 11B: Expectation Maximization Algorithm for Parameter Estimation.
Nonlinear Observers
Continuous Time Full-Order Observer Design.
Discrete Time Full-Order Observer.
Reduced Order Observer.
Nonlinear Observers.
Appendix 12A: Illustrative Examples.
Exercises for Section III and Section IV (Chapters 8-12 and Appendixes A-F).
References for Section III (Chapters 8-12).Appendixes - Basic Concepts and Supporting Material
Appendix A: System Theoretic Concepts - Controllability, Observability, Identifiability and Estimability
Appendix B: Probability, Stochastic Processes and Stochastic Calculus
Appendix C: Bayesian Filtering
Appendix D: Girsanov Theorem
Appendix E: Concepts from Signal and Stochastic Analyses
Appendix F: Notes on Simulation and Some Algorithms
Appendix G: Additional Examples