Peyman Setoodeh, Saeid Habibi, Simon Haykin

Nonlinear Filters (eBook, ePUB)

Theory and Applications

• Format: ePub

Produktbeschreibung

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.

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Produktdetails

• Verlag: Jossey-Bass
• Seitenzahl: 304
• Erscheinungstermin: 4. März 2022
• Englisch
• ISBN-13: 9781119078159
• Artikelnr.: 63584577

Autorenporträt

Peyman Setoodeh, PhD, is Visiting Professor with the Centre for Mechatronics and Hybrid Technologies (CMHT) at McMaster University. He is a Senior Member of the IEEE. Saeid Habibi, PhD, is Professor and former Chair of the Department of Mechanical Engineering and the Director of the Centre for Mechatronics and Hybrid Technologies (CMHT) at McMaster University. He is a Fellow of the ASME and the CSME as well as a Canada Research Chair and a Senior NSERC Industrial Research Chair. Simon Haykin, PhD, is Distinguished University Professor with the Department of Electrical and Computer Engineering and the Director of the Cognitive Systems Laboratory (CSL) at McMaster University. He is a Fellow of the IEEE and the Royal Society of Canada. He is a recipient of the Henry Booker Gold Medal from the International Union of Radio Science, the IEEE James H. Mulligan Jr. Education Medal, and the IEEE Denis J. Picard Medal for Radar Technologies and Applications.

Inhaltsangabe

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-Charg