Читать книгу Nonlinear Filters - Simon Haykin - Страница 2
Table of Contents
Оглавление1 Cover
7 Preface
9 Acronyms
10 1 Introduction 1.1 State of a Dynamic System 1.2 State Estimation 1.3 Construals of Computing 1.4 Statistical Modeling 1.5 Vision for the Book
11 2 Observability 2.1 Introduction 2.2 State‐Space Model 2.3 The Concept of Observability 2.4 Observability of Linear Time‐Invariant Systems 2.5 Observability of Linear Time‐Varying Systems 2.6 Observability of Nonlinear Systems 2.7 Observability of Stochastic Systems 2.8 Degree of Observability 2.9 Invertibility 2.10 Concluding Remarks
12 3 Observers 3.1 Introduction 3.2 Luenberger Observer 3.3 Extended Luenberger‐Type Observer 3.4 Sliding‐Mode Observer 3.5 Unknown‐Input Observer 3.6 Concluding Remarks
13 4 Bayesian Paradigm and Optimal Nonlinear Filtering 4.1 Introduction 4.2 Bayes' Rule 4.3 Optimal Nonlinear Filtering 4.4 Fisher Information 4.5 Posterior Cramér–Rao Lower Bound 4.6 Concluding Remarks
14 5 Kalman Filter 5.1 Introduction 5.2 Kalman Filter 5.3 Kalman Smoother 5.4 Information Filter 5.5 Extended Kalman Filter 5.6 Extended Information Filter 5.7 Divided‐Difference Filter 5.8 Unscented Kalman Filter 5.9 Cubature Kalman Filter 5.10 Generalized PID Filter 5.11 Gaussian‐Sum Filter 5.12 Applications 5.13 Concluding Remarks
15 6 Particle Filter 6.1 Introduction 6.2 Monte Carlo Method 6.3 Importance Sampling 6.4 Sequential Importance Sampling 6.5 Resampling 6.6 Sample Impoverishment 6.7 Choosing the Proposal Distribution 6.8 Generic Particle Filter 6.9 Applications 6.10 Concluding Remarks
16 7 Smooth Variable‐Structure Filter 7.1 Introduction 7.2 The Switching Gain 7.3 Stability Analysis 7.4 Smoothing Subspace 7.5 Filter Corrective Term for Linear Systems 7.6 Filter Corrective Term for Nonlinear Systems 7.7 Bias Compensation 7.8 The Secondary Performance Indicator 7.9 Second‐Order Smooth Variable Structure Filter 7.10 Optimal Smoothing Boundary Design 7.11 Combination of SVSF with Other Filters 7.12 Applications 7.13 Concluding Remarks
17 8 Deep Learning 8.1 Introduction 8.2 Gradient Descent 8.3 Stochastic Gradient Descent 8.4 Natural Gradient Descent 8.5 Neural Networks 8.6 Backpropagation 8.7 Backpropagation Through Time 8.8 Regularization 8.9 Initialization 8.10 Convolutional Neural Network 8.11 Long Short‐Term Memory 8.12 Hebbian Learning 8.13 Gibbs Sampling 8.14 Boltzmann Machine 8.15 Autoencoder 8.16 Generative Adversarial Network 8.17 Transformer 8.18 Concluding Remarks
18 9 Deep Learning‐Based Filters 9.1 Introduction 9.2 Variational Inference 9.3 Amortized Variational Inference 9.4 Deep Kalman Filter 9.5 Backpropagation Kalman Filter 9.6 Differentiable Particle Filter 9.7 Deep Rao–Blackwellized Particle Filter 9.8 Deep Variational Bayes Filter 9.9 Kalman Variational Autoencoder 9.10 Deep Variational Information Bottleneck 9.11 Wasserstein Distributionally Robust Kalman Filter 9.12 Hierarchical Invertible Neural Transport 9.13 Applications 9.14 Concluding Remarks
19 10 Expectation Maximization 10.1 Introduction 10.2 Expectation Maximization Algorithm 10.3 Particle Expectation Maximization 10.4 Expectation Maximization for Gaussian Mixture Models 10.5 Neural Expectation Maximization 10.6 Relational Neural Expectation Maximization 10.7 Variational Filtering Expectation Maximization 10.8 Amortized Variational Filtering Expectation Maximization 10.9 Applications 10.10 Concluding Remarks
20 11 Reinforcement Learning‐Based Filter 11.1 Introduction 11.2 Reinforcement Learning 11.3 Variational Inference as Reinforcement Learning 11.4 Application 11.5 Concluding Remarks
21 12 Nonparametric Bayesian Models 12.1 Introduction 12.2 Parametric vs Nonparametric Models 12.3 Measure‐Theoretic Probability 12.4 Exchangeability 12.5 Kolmogorov Extension Theorem 12.6 Extension of Bayesian Models 12.7 Conjugacy 12.8 Construction of Nonparametric Bayesian Models 12.9 Posterior Computability 12.10 Algorithmic Sufficiency 12.11 Applications 12.12 Concluding Remarks
22 References
23 Index
