{"product_id":"nonlinear-filters-9781118835814","title":"Nonlinear Filters","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eList of Figures xiii\u003c\/p\u003e \u003cp\u003eList of Table xv\u003c\/p\u003e \u003cp\u003ePreface xvii\u003c\/p\u003e \u003cp\u003eAcknowledgments xix\u003c\/p\u003e \u003cp\u003eAcronyms xxi\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction \u003c\/b\u003e\u003cb\u003e1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 State of a Dynamic System 1\u003c\/p\u003e \u003cp\u003e1.2 State Estimation 1\u003c\/p\u003e \u003cp\u003e1.3 Construals of Computing 2\u003c\/p\u003e \u003cp\u003e1.4 Statistical Modeling 3\u003c\/p\u003e \u003cp\u003e1.5 Vision for the Book 4\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Observability \u003c\/b\u003e\u003cb\u003e7\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Introduction 7\u003c\/p\u003e \u003cp\u003e2.2 State-Space Model 7\u003c\/p\u003e \u003cp\u003e2.3 The Concept of Observability 9\u003c\/p\u003e \u003cp\u003e2.4 Observability of Linear Time-Invariant Systems 10\u003c\/p\u003e \u003cp\u003e2.4.1 Continuous-Time LTI Systems 10\u003c\/p\u003e \u003cp\u003e2.4.2 Discrete-Time LTI Systems 12\u003c\/p\u003e \u003cp\u003e2.4.3 Discretization of LTI Systems 14\u003c\/p\u003e \u003cp\u003e2.5 Observability of Linear Time-Varying Systems 14\u003c\/p\u003e \u003cp\u003e2.5.1 Continuous-Time LTV Systems 14\u003c\/p\u003e \u003cp\u003e2.5.2 Discrete-Time LTV Systems 16\u003c\/p\u003e \u003cp\u003e2.5.3 Discretization of LTV Systems 17\u003c\/p\u003e \u003cp\u003e2.6 Observability of Nonlinear Systems 17\u003c\/p\u003e \u003cp\u003e2.6.1 Continuous-Time Nonlinear Systems 18\u003c\/p\u003e \u003cp\u003e2.6.2 Discrete-Time Nonlinear Systems 21\u003c\/p\u003e \u003cp\u003e2.6.3 Discretization of Nonlinear Systems 22\u003c\/p\u003e \u003cp\u003e2.7 Observability of Stochastic Systems 23\u003c\/p\u003e \u003cp\u003e2.8 Degree of Observability 25\u003c\/p\u003e \u003cp\u003e2.9 Invertibility 26\u003c\/p\u003e \u003cp\u003e2.10 Concluding Remarks 27\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Observers \u003c\/b\u003e\u003cb\u003e29\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Introduction 29\u003c\/p\u003e \u003cp\u003e3.2 Luenberger Observer 30\u003c\/p\u003e \u003cp\u003e3.3 Extended Luenberger-Type Observer 31\u003c\/p\u003e \u003cp\u003e3.4 Sliding-Mode Observer 33\u003c\/p\u003e \u003cp\u003e3.5 Unknown-Input Observer 35\u003c\/p\u003e \u003cp\u003e3.6 Concluding Remarks 39\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Bayesian Paradigm and Optimal Nonlinear Filtering \u003c\/b\u003e\u003cb\u003e41\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Introduction 41\u003c\/p\u003e \u003cp\u003e4.2 Bayes’ Rule 42\u003c\/p\u003e \u003cp\u003e4.3 Optimal Nonlinear Filtering 42\u003c\/p\u003e \u003cp\u003e4.4 Fisher Information 45\u003c\/p\u003e \u003cp\u003e4.5 Posterior Cramér–Rao Lower Bound 46\u003c\/p\u003e \u003cp\u003e4.6 Concluding Remarks 47\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Kalman Filter \u003c\/b\u003e\u003cb\u003e49\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Introduction 49\u003c\/p\u003e \u003cp\u003e5.2 Kalman Filter 50\u003c\/p\u003e \u003cp\u003e5.3 Kalman Smoother 53\u003c\/p\u003e \u003cp\u003e5.4 Information Filter 54\u003c\/p\u003e \u003cp\u003e5.5 Extended Kalman Filter 54\u003c\/p\u003e \u003cp\u003e5.6 Extended Information Filter 54\u003c\/p\u003e \u003cp\u003e5.7 Divided-Difference Filter 54\u003c\/p\u003e \u003cp\u003e5.8 Unscented Kalman Filter 60\u003c\/p\u003e \u003cp\u003e5.9 Cubature Kalman Filter 60\u003c\/p\u003e \u003cp\u003e5.10 Generalized PID Filter 64\u003c\/p\u003e \u003cp\u003e5.11 Gaussian-Sum Filter 65\u003c\/p\u003e \u003cp\u003e5.12 Applications 67\u003c\/p\u003e \u003cp\u003e5.12.1 Information Fusion 67\u003c\/p\u003e \u003cp\u003e5.12.2 Augmented Reality 67\u003c\/p\u003e \u003cp\u003e5.12.3 Urban Traffic Network 67\u003c\/p\u003e \u003cp\u003e5.12.4 Cybersecurity of Power Systems 67\u003c\/p\u003e \u003cp\u003e5.12.5 Incidence of Influenza 68\u003c\/p\u003e \u003cp\u003e5.12.6 COVID-19 Pandemic 68\u003c\/p\u003e \u003cp\u003e5.13 Concluding Remarks 70\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Particle Filter \u003c\/b\u003e\u003cb\u003e71\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Introduction 71\u003c\/p\u003e \u003cp\u003e6.2 Monte Carlo Method 72\u003c\/p\u003e \u003cp\u003e6.3 Importance Sampling 72\u003c\/p\u003e \u003cp\u003e6.4 Sequential Importance Sampling 73\u003c\/p\u003e \u003cp\u003e6.5 Resampling 75\u003c\/p\u003e \u003cp\u003e6.6 Sample Impoverishment 76\u003c\/p\u003e \u003cp\u003e6.7 Choosing the Proposal Distribution 77\u003c\/p\u003e \u003cp\u003e6.8 Generic Particle Filter 78\u003c\/p\u003e \u003cp\u003e6.9 Applications 81\u003c\/p\u003e \u003cp\u003e6.9.1 Simultaneous Localization and Mapping 81\u003c\/p\u003e \u003cp\u003e6.10 Concluding Remarks 82\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Smooth Variable-Structure Filter \u003c\/b\u003e\u003cb\u003e85\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Introduction 85\u003c\/p\u003e \u003cp\u003e7.2 The Switching Gain 86\u003c\/p\u003e \u003cp\u003e7.3 Stability Analysis 90\u003c\/p\u003e \u003cp\u003e7.4 Smoothing Subspace 93\u003c\/p\u003e \u003cp\u003e7.5 Filter Corrective Term for Linear Systems 96\u003c\/p\u003e \u003cp\u003e7.6 Filter Corrective Term for Nonlinear Systems 102\u003c\/p\u003e \u003cp\u003e7.7 Bias Compensation 105\u003c\/p\u003e \u003cp\u003e7.8 The Secondary Performance Indicator 107\u003c\/p\u003e \u003cp\u003e7.9 Second-Order Smooth Variable Structure Filter 108\u003c\/p\u003e \u003cp\u003e7.10 Optimal Smoothing Boundary Design 108\u003c\/p\u003e \u003cp\u003e7.11 Combination of SVSF with Other Filters 110\u003c\/p\u003e \u003cp\u003e7.12 Applications 110\u003c\/p\u003e \u003cp\u003e7.12.1 Multiple Target Tracking 111\u003c\/p\u003e \u003cp\u003e7.12.2 Battery State-of-Charge Estimation 111\u003c\/p\u003e \u003cp\u003e7.12.3 Robotics 111\u003c\/p\u003e \u003cp\u003e7.13 Concluding Remarks 111\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Deep Learning \u003c\/b\u003e\u003cb\u003e113\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Introduction 113\u003c\/p\u003e \u003cp\u003e8.2 Gradient Descent 114\u003c\/p\u003e \u003cp\u003e8.3 Stochastic Gradient Descent 115\u003c\/p\u003e \u003cp\u003e8.4 Natural Gradient Descent 119\u003c\/p\u003e \u003cp\u003e8.5 Neural Networks 120\u003c\/p\u003e \u003cp\u003e8.6 Backpropagation 122\u003c\/p\u003e \u003cp\u003e8.7 Backpropagation Through Time 122\u003c\/p\u003e \u003cp\u003e8.8 Regularization 122\u003c\/p\u003e \u003cp\u003e8.9 Initialization 125\u003c\/p\u003e \u003cp\u003e8.10 Convolutional Neural Network 125\u003c\/p\u003e \u003cp\u003e8.11 Long Short-Term Memory 127\u003c\/p\u003e \u003cp\u003e8.12 Hebbian Learning 129\u003c\/p\u003e \u003cp\u003e8.13 Gibbs Sampling 131\u003c\/p\u003e \u003cp\u003e8.14 Boltzmann Machine 131\u003c\/p\u003e \u003cp\u003e8.15 Autoencoder 135\u003c\/p\u003e \u003cp\u003e8.16 Generative Adversarial Network 136\u003c\/p\u003e \u003cp\u003e8.17 Transformer 137\u003c\/p\u003e \u003cp\u003e8.18 Concluding Remarks 139\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Deep Learning-Based Filters \u003c\/b\u003e\u003cb\u003e141\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Introduction 141\u003c\/p\u003e \u003cp\u003e9.2 Variational Inference 142\u003c\/p\u003e \u003cp\u003e9.3 Amortized Variational Inference 144\u003c\/p\u003e \u003cp\u003e9.4 Deep Kalman Filter 144\u003c\/p\u003e \u003cp\u003e9.5 Backpropagation Kalman Filter 146\u003c\/p\u003e \u003cp\u003e9.6 Differentiable Particle Filter 148\u003c\/p\u003e \u003cp\u003e9.7 Deep Rao–Blackwellized Particle Filter 152\u003c\/p\u003e \u003cp\u003e9.8 Deep Variational Bayes Filter 158\u003c\/p\u003e \u003cp\u003e9.9 Kalman Variational Autoencoder 167\u003c\/p\u003e \u003cp\u003e9.10 Deep Variational Information Bottleneck 172\u003c\/p\u003e \u003cp\u003e9.11 Wasserstein Distributionally Robust Kalman Filter 176\u003c\/p\u003e \u003cp\u003e9.12 Hierarchical Invertible Neural Transport 178\u003c\/p\u003e \u003cp\u003e9.13 Applications 182\u003c\/p\u003e \u003cp\u003e9.13.1 Prediction of Drug Effect 182\u003c\/p\u003e \u003cp\u003e9.13.2 Autonomous Driving 183\u003c\/p\u003e \u003cp\u003e9.14 Concluding Remarks 183\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Expectation Maximization \u003c\/b\u003e\u003cb\u003e185\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Introduction 185\u003c\/p\u003e \u003cp\u003e10.2 Expectation Maximization Algorithm 185\u003c\/p\u003e \u003cp\u003e10.3 Particle Expectation Maximization 188\u003c\/p\u003e \u003cp\u003e10.4 Expectation Maximization for Gaussian Mixture Models 190\u003c\/p\u003e \u003cp\u003e10.5 Neural Expectation Maximization 191\u003c\/p\u003e \u003cp\u003e10.6 Relational Neural Expectation Maximization 194\u003c\/p\u003e \u003cp\u003e10.7 Variational Filtering Expectation Maximization 196\u003c\/p\u003e \u003cp\u003e10.8 Amortized Variational Filtering Expectation Maximization 198\u003c\/p\u003e \u003cp\u003e10.9 Applications 199\u003c\/p\u003e \u003cp\u003e10.9.1 Stochastic Volatility 199\u003c\/p\u003e \u003cp\u003e10.9.2 Physical Reasoning 200\u003c\/p\u003e \u003cp\u003e10.9.3 Speech, Music, and Video Modeling 200\u003c\/p\u003e \u003cp\u003e10.10 Concluding Remarks 201\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Reinforcement Learning-Based Filter \u003c\/b\u003e\u003cb\u003e203\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Introduction 203\u003c\/p\u003e \u003cp\u003e11.2 Reinforcement Learning 204\u003c\/p\u003e \u003cp\u003e11.3 Variational Inference as Reinforcement Learning 207\u003c\/p\u003e \u003cp\u003e11.4 Application 210\u003c\/p\u003e \u003cp\u003e11.4.1 Battery State-of-Charge Estimation 210\u003c\/p\u003e \u003cp\u003e11.5 Concluding Remarks 210\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Nonparametric Bayesian Models \u003c\/b\u003e\u003cb\u003e213\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Introduction 213\u003c\/p\u003e \u003cp\u003e12.2 Parametric vs Nonparametric Models 213\u003c\/p\u003e \u003cp\u003e12.3 Measure-Theoretic Probability 214\u003c\/p\u003e \u003cp\u003e12.4 Exchangeability 219\u003c\/p\u003e \u003cp\u003e12.5 Kolmogorov Extension Theorem 221\u003c\/p\u003e \u003cp\u003e12.6 Extension of Bayesian Models 223\u003c\/p\u003e \u003cp\u003e12.7 Conjugacy 224\u003c\/p\u003e \u003cp\u003e12.8 Construction of Nonparametric Bayesian Models 226\u003c\/p\u003e \u003cp\u003e12.9 Posterior Computability 227\u003c\/p\u003e \u003cp\u003e12.10 Algorithmic Sufficiency 228\u003c\/p\u003e \u003cp\u003e12.11 Applications 232\u003c\/p\u003e \u003cp\u003e12.11.1 Multiple Object Tracking 233\u003c\/p\u003e \u003cp\u003e12.11.2 Data-Driven Probabilistic Optimal Power Flow 233\u003c\/p\u003e \u003cp\u003e12.11.3 Analyzing Single-Molecule Tracks 233\u003c\/p\u003e \u003cp\u003e12.12 Concluding Remarks 233\u003c\/p\u003e \u003cp\u003eReferences 235\u003c\/p\u003e \u003cp\u003eIndex 253\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49406931599703,"sku":"9781118835814","price":100.76,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781118835814.jpg?v=1730497598","url":"https:\/\/bookcurl.com\/products\/nonlinear-filters-9781118835814","provider":"Book Curl","version":"1.0","type":"link"}