1  Cover

      2  Title Page

      3  Copyright

      4  Dedication

      5  List of Figures

      6  List of Table

      7  Preface

      8  Acknowledgments

      9  Acronyms

      10  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

      11  2 Observability 2.1 Introduction 2.2 State‐Space Model 2.3 The Concept of Observability 2.4 Observability of Linear Time‐Invariant Systems 2.5 Observability of Linear Time‐Varying Systems 2.6 Observability of Nonlinear Systems 2.7 Observability of Stochastic Systems 2.8 Degree of Observability 2.9 Invertibility 2.10 Concluding Remarks

      12  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

      13  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

      14  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 5.13 Concluding Remarks

      15  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 6.10 Concluding Remarks

      16  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