Nonlinear filters : theory and applications /

"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 o...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Setoodeh, Peyman, 1974- (Autor), Habibi, Saeid (Autor), Haykin, Simon S., 1931- (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Hoboken, NJ : John Wiley & Sons, Inc., 2022.
Temas:
Nonlinear control theory.
Digital filters (Mathematics)
Signal processing > Digital techniques.
Commande non linéaire.
Filtres numériques (Mathématiques)
Traitement du signal > Techniques numériques.
Acceso en línea:Texto completo (Requiere registro previo con correo institucional)
Tabla de Contenidos:
  • 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.

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