Оглавление
Simon Haykin. Nonlinear Filters
Table of Contents
List of Tables
List of Illustrations
Guide
Pages
Nonlinear Filters. Theory and Applications
List of Figures
List of Table
Preface
Acknowledgments
Acronyms
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
2 Observability. 2.1 Introduction
2.2 State‐Space Model
2.3 The Concept of Observability
2.4 Observability of Linear Time‐Invariant Systems
2.4.1 Continuous‐Time LTI Systems
2.4.2 Discrete‐Time LTI Systems
2.4.3 Discretization of LTI Systems
2.5 Observability of Linear Time‐Varying Systems
2.5.1 Continuous‐Time LTV Systems
2.5.2 Discrete‐Time LTV Systems
2.5.3 Discretization of LTV Systems
2.6 Observability of Nonlinear Systems
2.6.1 Continuous‐Time Nonlinear Systems
2.6.2 Discrete‐Time Nonlinear Systems
2.6.3 Discretization of Nonlinear Systems
2.7 Observability of Stochastic Systems
2.8 Degree of Observability
2.9 Invertibility
2.10 Concluding Remarks
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
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
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
5.12.1 Information Fusion
5.12.2 Augmented Reality
5.12.3 Urban Traffic Network
5.12.4 Cybersecurity of Power Systems
5.12.5 Incidence of Influenza
5.12.6 COVID‐19 Pandemic
5.13 Concluding Remarks
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
6.9.1 Simultaneous Localization and Mapping
6.10 Concluding Remarks
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
7.12.1 Multiple Target Tracking
7.12.2 Battery State‐of‐Charge Estimation
7.12.3 Robotics
7.13 Concluding Remarks
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
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
9.13.1 Prediction of Drug Effect
9.13.2 Autonomous Driving
9.14 Concluding Remarks
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
10.9.1 Stochastic Volatility
10.9.2 Physical Reasoning
10.9.3 Speech, Music, and Video Modeling
10.10 Concluding Remarks
11 Reinforcement Learning‐Based Filter. 11.1 Introduction
11.2 Reinforcement Learning
11.3 Variational Inference as Reinforcement Learning
11.4 Application
11.4.1 Battery State‐of‐Charge Estimation
11.5 Concluding Remarks
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
12.11.1 Multiple Object Tracking
12.11.2 Data‐Driven Probabilistic Optimal Power Flow
12.11.3 Analyzing Single‐Molecule Tracks
12.12 Concluding Remarks
References
Index. a
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