book

Nonlinear Filters

Name: Nonlinear Filters
ISBN: 9781118835814

by Peyman Setoodeh, Saeid Habibi, Simon Haykin

April 2022

Intermediate to advanced

304 pages

8h 12m

English

Wiley

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Cover
Title Page
Copyright
Dedication
List of Figures
List of Table
Preface
Acknowledgments
Acronyms
1 Introduction
1.1 State of a Dynamic System1.2 State Estimation1.3 Construals of Computing1.4 Statistical Modeling1.5 Vision for the Book

2 Observability
2.1 Introduction2.2 State‐Space Model2.3 The Concept of Observability2.4 Observability of Linear Time‐Invariant Systems2.5 Observability of Linear Time‐Varying Systems2.6 Observability of Nonlinear Systems2.7 Observability of Stochastic Systems2.8 Degree of Observability2.9 Invertibility2.10 Concluding Remarks
3 Observers
3.1 Introduction3.2 Luenberger Observer3.3 Extended Luenberger‐Type Observer3.4 Sliding‐Mode Observer3.5 Unknown‐Input Observer3.6 Concluding Remarks
4 Bayesian Paradigm and Optimal Nonlinear Filtering
4.1 Introduction4.2 Bayes' Rule4.3 Optimal Nonlinear Filtering4.4 Fisher Information4.5 Posterior Cramér–Rao Lower Bound4.6 Concluding Remarks
5 Kalman Filter
5.1 Introduction5.2 Kalman Filter5.3 Kalman Smoother5.4 Information Filter5.5 Extended Kalman Filter5.6 Extended Information Filter5.7 Divided‐Difference Filter5.8 Unscented Kalman Filter5.9 Cubature Kalman Filter5.10 Generalized PID Filter5.11 Gaussian‐Sum Filter5.12 Applications5.13 Concluding Remarks
6 Particle Filter
6.1 Introduction6.2 Monte Carlo Method6.3 Importance Sampling6.4 Sequential Importance Sampling6.5 Resampling6.6 Sample Impoverishment6.7 Choosing the Proposal Distribution6.8 Generic Particle Filter6.9 Applications6.10 Concluding Remarks
7 Smooth Variable‐Structure Filter
7.1 Introduction7.2 The Switching Gain7.3 Stability Analysis7.4 Smoothing Subspace7.5 Filter Corrective Term for Linear Systems7.6 Filter Corrective Term for Nonlinear Systems7.7 Bias Compensation7.8 The Secondary Performance Indicator7.9 Second‐Order Smooth Variable Structure Filter7.10 Optimal Smoothing Boundary Design7.11 Combination of SVSF with Other Filters7.12 Applications7.13 Concluding Remarks
8 Deep Learning
8.1 Introduction8.2 Gradient Descent8.3 Stochastic Gradient Descent8.4 Natural Gradient Descent8.5 Neural Networks8.6 Backpropagation8.7 Backpropagation Through Time8.8 Regularization8.9 Initialization8.10 Convolutional Neural Network8.11 Long Short‐Term Memory8.12 Hebbian Learning8.13 Gibbs Sampling8.14 Boltzmann Machine8.15 Autoencoder8.16 Generative Adversarial Network8.17 Transformer8.18 Concluding Remarks
9 Deep Learning‐Based Filters
9.1 Introduction9.2 Variational Inference9.3 Amortized Variational Inference9.4 Deep Kalman Filter9.5 Backpropagation Kalman Filter9.6 Differentiable Particle Filter9.7 Deep Rao–Blackwellized Particle Filter9.8 Deep Variational Bayes Filter9.9 Kalman Variational Autoencoder9.10 Deep Variational Information Bottleneck9.11 Wasserstein Distributionally Robust Kalman Filter9.12 Hierarchical Invertible Neural Transport9.13 Applications9.14 Concluding Remarks
10 Expectation Maximization
10.1 Introduction10.2 Expectation Maximization Algorithm10.3 Particle Expectation Maximization10.4 Expectation Maximization for Gaussian Mixture Models10.5 Neural Expectation Maximization10.6 Relational Neural Expectation Maximization10.7 Variational Filtering Expectation Maximization10.8 Amortized Variational Filtering Expectation Maximization10.9 Applications10.10 Concluding Remarks
11 Reinforcement Learning‐Based Filter
11.1 Introduction11.2 Reinforcement Learning11.3 Variational Inference as Reinforcement Learning11.4 Application11.5 Concluding Remarks
12 Nonparametric Bayesian Models
12.1 Introduction12.2 Parametric vs Nonparametric Models12.3 Measure‐Theoretic Probability12.4 Exchangeability12.5 Kolmogorov Extension Theorem12.6 Extension of Bayesian Models12.7 Conjugacy12.8 Construction of Nonparametric Bayesian Models12.9 Posterior Computability12.10 Algorithmic Sufficiency12.11 Applications12.12 Concluding Remarks
References
Index
Wiley End User License Agreement

Content preview from Nonlinear Filters

List of Table

Table 11.1

Reinforcement learning and variational inference viewed as expectation maximization.

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Nonlinear Filters

by Peyman Setoodeh, Saeid Habibi, Simon Haykin

List of Table

Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
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