Nonlinear Filters: Theory and Applications

✍ Scribed by Peyman Setoodeh, Saeid Habibi, Simon Haykin

• Publisher: Wiley
• Year: 2022
• Tongue: English
• Leaves: 307
• Category: Library

✦ Synopsis

NONLINEAR FILTERS

Discover the utility of using deep learning and (deep) reinforcement learning in deriving filtering algorithms with this insightful and powerful new resource

Nonlinear Filters: Theory and Applications delivers an insightful view on state and parameter estimation by merging ideas from control theory, statistical signal processing, and machine learning. Taking an algorithmic approach, the book covers both classic and machine learning-based filtering algorithms.

Readers of Nonlinear Filters will greatly benefit from the wide spectrum of presented topics including stability, robustness, computability, and algorithmic sufficiency. Readers will also enjoy:

• Organization that allows the book to act as a stand-alone, self-contained reference
• A thorough exploration of the notion of observability, nonlinear observers, and the theory of optimal nonlinear filtering that bridges the gap between different science and engineering disciplines
• A profound account of Bayesian filters including Kalman filter and its variants as well as particle filter
• A rigorous derivation of the smooth variable structure filter as a predictor-corrector estimator formulated based on a stability theorem, used to confine the estimated states within a neighborhood of their true values
• A concise tutorial on deep learning and reinforcement learning
• A detailed presentation of the expectation maximization algorithm and its machine learning-based variants, used for joint state and parameter estimation
• Guidelines for constructing nonparametric Bayesian models from parametric ones

Perfect for researchers, professors, and graduate students in engineering, computer science, applied mathematics, and artificial intelligence, Nonlinear Filters: Theory and Applications will also earn a place in the libraries of those studying or practicing in fields involving pandemic diseases, cybersecurity, information fusion, augmented reality, autonomous driving, urban traffic network, navigation and tracking, robotics, power systems, hybrid technologies, and finance.

✦ Table of Contents

Cover
Title Page
Copyright
Contents
List of Figures
List of Table
Preface
Acknowledgments
Acronyms
Chapter 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
Chapter 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
Chapter 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
Chapter 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
Chapter 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
Chapter 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
Chapter 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
Chapter 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
Chapter 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
Chapter 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
Chapter 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
Chapter 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
EULA