| Description |
1 online resource (xxii, 273 pages) : illustrations |
| Bibliography |
Includes bibliographical references and index. |
| Summary |
"This book fills the gap between the literature on nonlinear filters and nonlinear observers by presenting a new state estimation strategy, the smooth variable structure filter (SVSF). The book is a valuable resource to researchers outside of the control society, where literature on nonlinear observers is less well-known. SVSF is a predictor-corrector estimator that is formulated based on a stability theorem, to confine the estimated states within a neighborhood of their true values. It has the potential to improve performance in the presence of severe and changing modeling uncertainties and noise. An important advantage of the SVSF is the availability of a set of secondary performance indicators that pertain to each estimate. This allows for dynamic refinement of the filter model. The combination of SVSF's robust stability and its secondary indicators of performance make it a powerful estimation tool, capable of compensating for uncertainties that are abruptly introduced in the system"-- Provided by publisher. |
| Contents |
List of Figures xiii -- List of Table xv -- Preface xvii -- Acknowledgments xix -- Acronyms xxi -- 1 Introduction 1 -- 1.1 State of a Dynamic System 1 -- 1.2 State Estimation 1 -- 1.3 Construals of Computing 2 -- 1.4 Statistical Modeling 3 -- 1.5 Vision for the Book 4 -- 2 Observability 7 -- 2.1 Introduction 7 -- 2.2 State-Space Model 7 -- 2.3 The Concept of Observability 9 -- 2.4 Observability of Linear Time-Invariant Systems 10 -- 2.4.1 Continuous-Time LTI Systems 10 -- 2.4.2 Discrete-Time LTI Systems 12 -- 2.4.3 Discretization of LTI Systems 14 -- 2.5 Observability of Linear Time-Varying Systems 14 -- 2.5.1 Continuous-Time LTV Systems 14 -- 2.5.2 Discrete-Time LTV Systems 16 -- 2.5.3 Discretization of LTV Systems 17 -- 2.6 Observability of Nonlinear Systems 17 -- 2.6.1 Continuous-Time Nonlinear Systems 18 -- 2.6.2 Discrete-Time Nonlinear Systems 21 -- 2.6.3 Discretization of Nonlinear Systems 22 -- 2.7 Observability of Stochastic Systems 23 -- 2.8 Degree of Observability 25 -- 2.9 Invertibility 26 -- 2.10 Concluding Remarks 27 -- 3 Observers 29 -- 3.1 Introduction 29 -- 3.2 Luenberger Observer 30 -- 3.3 Extended Luenberger-Type Observer 31 -- 3.4 Sliding-Mode Observer 33 -- 3.5 Unknown-Input Observer 35 -- 3.6 Concluding Remarks 39 -- 4 Bayesian Paradigm and Optimal Nonlinear Filtering 41 -- 4.1 Introduction 41 -- 4.2 Bayes' Rule 42 -- 4.3 Optimal Nonlinear Filtering 42 -- 4.4 Fisher Information 45 -- 4.5 Posterior Cramér-Rao Lower Bound 46 -- 4.6 Concluding Remarks 47 -- 5 Kalman Filter 49 -- 5.1 Introduction 49 -- 5.2 Kalman Filter 50 -- 5.3 Kalman Smoother 53 -- 5.4 Information Filter 54 -- 5.5 Extended Kalman Filter 54 -- 5.6 Extended Information Filter 54 -- 5.7 Divided-Difference Filter 54 -- 5.8 Unscented Kalman Filter 60 -- 5.9 Cubature Kalman Filter 60 -- 5.10 Generalized PID Filter 64 -- 5.11 Gaussian-Sum Filter 65 -- 5.12 Applications 67 -- 5.12.1 Information Fusion 67 -- 5.12.2 Augmented Reality 67 -- 5.12.3 Urban Traffic Network 67 -- 5.12.4 Cybersecurity of Power Systems 67 -- 5.12.5 Incidence of Influenza 68 -- 5.12.6 COVID-19 Pandemic 68 -- 5.13 Concluding Remarks 70 -- 6 Particle Filter 71 -- 6.1 Introduction 71 -- 6.2 Monte Carlo Method 72 -- 6.3 Importance Sampling 72 -- 6.4 Sequential Importance Sampling 73 -- 6.5 Resampling 75 -- 6.6 Sample Impoverishment 76 -- 6.7 Choosing the Proposal Distribution 77 -- 6.8 Generic Particle Filter 78 -- 6.9 Applications 81 -- 6.9.1 Simultaneous Localization and Mapping 81 -- 6.10 Concluding Remarks 82 -- 7 Smooth Variable-Structure Filter 85 -- 7.1 Introduction 85 -- 7.2 The Switching Gain 86 -- 7.3 Stability Analysis 90 -- 7.4 Smoothing Subspace 93 -- 7.5 Filter Corrective Term for Linear Systems 96 -- 7.6 Filter Corrective Term for Nonlinear Systems 102 -- 7.7 Bias Compensation 105 -- 7.8 The Secondary Performance Indicator 107 -- 7.9 Second-Order Smooth Variable Structure Filter 108 -- 7.10 Optimal Smoothing Boundary Design 108 -- 7.11 Combination of SVSF with Other Filters 110 -- 7.12 Applications 110 -- 7.12.1 Multiple Target Tracking 111 -- 7.12.2 Battery State-of-Charge Estimation 111 -- 7.12.3 Robotics 111 -- 7.13 Concluding Remarks 111 -- 8 Deep Learning 113 -- 8.1 Introduction 113 -- 8.2 Gradient Descent 114 -- 8.3 Stochastic Gradient Descent 115 -- 8.4 Natural Gradient Descent 119 -- 8.5 Neural Networks 120 -- 8.6 Backpropagation 122 -- 8.7 Backpropagation Through Time 122 -- 8.8 Regularization 122 -- 8.9 Initialization 125 -- 8.10 Convolutional Neural Network 125 -- 8.11 Long Short-Term Memory 127 -- 8.12 Hebbian Learning 129 -- 8.13 Gibbs Sampling 131 -- 8.14 Boltzmann Machine 131 -- 8.15 Autoencoder 135 -- 8.16 Generative Adversarial Network 136 -- 8.17 Transformer 137 -- 8.18 Concluding Remarks 139 -- 9 Deep Learning-Based Filters 141 -- 9.1 Introduction 141 -- 9.2 Variational Inference 142 -- 9.3 Amortized Variational Inference 144 -- 9.4 Deep Kalman Filter 144 -- 9.5 Backpropagation Kalman Filter 146 -- 9.6 Differentiable Particle Filter 148 -- 9.7 Deep Rao-Blackwellized Particle Filter 152 -- 9.8 Deep Variational Bayes Filter 158 -- 9.9 Kalman Variational Autoencoder 167 -- 9.10 Deep Variational Information Bottleneck 172 -- 9.11 Wasserstein Distributionally Robust Kalman Filter 176 -- 9.12 Hierarchical Invertible Neural Transport 178 -- 9.13 Applications 182 -- 9.13.1 Prediction of Drug Effect 182 -- 9.13.2 Autonomous Driving 183 -- 9.14 Concluding Remarks 183 -- 10 Expectation Maximization 185 -- 10.1 Introduction 185 -- 10.2 Expectation Maximization Algorithm 185 -- 10.3 Particle Expectation Maximization 188 -- 10.4 Expectation Maximization for Gaussian Mixture Models 190 -- 10.5 Neural Expectation Maximization 191 -- 10.6 Relational Neural Expectation Maximization 194 -- 10.7 Variational Filtering Expectation Maximization 196 -- 10.8 Amortized Variational Filtering Expectation Maximization 198 -- 10.9 Applications 199 -- 10.9.1 Stochastic Volatility 199 -- 10.9.2 Physical Reasoning 200 -- 10.9.3 Speech, Music, and Video Modeling 200 -- 10.10 Concluding Remarks 201 -- 11 Reinforcement Learning-Based Filter 203 -- 11.1 Introduction 203 -- 11.2 Reinforcement Learning 204 -- 11.3 Variational Inference as Reinforcement Learning 207 -- 11.4 Application 210 -- 11.4.1 Battery State-of-Charge Estimation 210 -- 11.5 Concluding Remarks 210 -- 12 Nonparametric Bayesian Models 213 -- 12.1 Introduction 213 -- 12.2 Parametric vs Nonparametric Models 213 -- 12.3 Measure-Theoretic Probability 214 -- 12.4 Exchangeability 219 -- 12.5 Kolmogorov Extension Theorem 221 -- 12.6 Extension of Bayesian Models 223 -- 12.7 Conjugacy 224 -- 12.8 Construction of Nonparametric Bayesian Models 226 -- 12.9 Posterior Computability 227 -- 12.10 Algorithmic Sufficiency 228 -- 12.11 Applications 232 -- 12.11.1 Multiple Object Tracking 233 -- 12.11.2 Data-Driven Probabilistic Optimal Power Flow 233 -- 12.11.3 Analyzing Single-Molecule Tracks 233 -- 12.12 Concluding Remarks 233 -- References 235 -- Index 253. |
| Subject |
Nonlinear control theory.
|
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Digital filters (Mathematics)
|
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Signal processing -- Digital techniques.
|
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Commande non linéaire. |
|
Filtres numériques (Mathématiques) |
|
Traitement du signal -- Techniques numériques. |
|
Digital filters (Mathematics) |
|
Nonlinear control theory |
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Signal processing -- Digital techniques |
| Added Author |
Habibi, Saeid, author.
|
|
Haykin, Simon S., 1931- author.
|
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John Wiley & Sons, publisher.
|
| Other Form: |
Print version: Setoodeh, Peyman, 1974- Nonlinear filters Hoboken, NJ : Wiley, 2022 9781118835814 (DLC) 2022000943 |
| ISBN |
9781119078159 electronic book |
|
1119078156 electronic book |
|
1119078180 electronic book |
|
9781119078166 electronic book |
|
1119078164 electronic book |
|
9781119078180 (electronic bk.) |
|
hardcover |
|
hardcover |
| Standard No. |
10.1002/9781119078166 doi |
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