Contents
Part I Kalman Filtering: Preliminaries
1 Introduction to Kalman Filtering 3
1.1 What Is Filtering? 3
1.2 Historical Remarks 5
1.3 Wiener Filter 7
1.4 Kalman Filter 7
1.5 Conclusion 9
References 9
2 Challenges in Kalman Filtering11
2.1 Standard Kalman Filter 11
2.2 Requirements of Standard Kalman Filtering 14
2.3 Effects of System Uncertainties 15
2.4 Effects of Multiple Sensors 16
2.5 Effects of System Couplings 16
2.6 Conclusion 17
References 17
Part II Kalman Filtering for Uncertain Systems
3 Kalman Filter with Recursive Process Noise Covariance Estimation 21
3.1 Introduction 21
3.2 Problem Formulation 23
3.2.1 Standard Kalman Filter 23
3.2.2 Problem To Be Resolved 23
3.3 Basic Idea: Estimating Covariance Matrix 26
3.4 Kalman Filter Based on Algorithm RecursiveCovarianceEstimation 31
3.5 Stability Analysis 33
3.6 Simulations 41
3.6.1 One-Dimensional Simulation 41
3.6.2 Multidimensional Simulation 42
3.6.3 Integrated Navigations Simulation 43
3.7 Conclusion 46
References 48
4 Kalman Filter with Recursive Covariance Estimation Revisited with Technical Conditions Reduced 51
4.1 Introduction 51
4.2 Problem Formulation 53
4.3 Kalman Filter with Recursive Covariance Estimation 56
4.3.1 Basic Method: Covariance Matrix Estimation 56
4.3.2 KF-RCE Algorithm for LTI Systems 58
4.4 Stability Analysis 60
4.5 Simulation Experiments 65
4.6 Conclusion 68
References 68
5 Modified Kalman Filter with Recursive Covariance Estimation for Gyroscope Denoising 71
5.1 Introduction 71
5.2 Problem Formulation 73
5.2.1 Kalman Filter 73
5.2.2 Problem to Be Resolved 74
5.3 Modified Kalman Filter with Recursive Covariance Matrix 76
5.3.1 Basic Idea: Estimating Covariance Matrix 76
5.3.2 Modified Kalman Filter with Recursive Covariance Matrix 77
5.3.3 Stability Analysis 79
5.3.4 Simulation Study 86
5.4 Experimental Tests 87
5.5 Conclusion 93
References 93
6 Real-Time State Estimator Without Noise Covariance Matrices Knowledge 95
6.1 Introduction 95
6.2 Problem Formulation 97
6.3 The Fast Minimum Norm Filtering Algorithm 99
6.3.1 Time Update 100
6.3.2 Measurement Update 100
6.4 Numerical Examples 106
6.4.1 Example I: Measurement Feedback Simulation 107
6.4.2 Example II: Data Fusion Simulation 107
6.4.3 Example III: Integrated Navigation Simulation 115
6.5 Conclusion 115
References 118
7 A Framework of Finite-Model Kalman Filter with Case Study: MVDP-FMKF Algorithm 119
7.1 Introduction 119
7.2 Kalman Filter 121
7.3 Framework of Finite-Model Kalman Filter 122
7.4 MVDP Finite-Model Kalman Filter Algorithm 125
7.4.1 Derivation of di 126
7.4.2 Two-Model MVDP-FMKF Algorithm 131
7.4.3 General MVDP-FMKF Algorithm 134
7.5 Simulation of the MVDP-FMKF Algorithm 136
7.5.1 One-Dimensional Simulation 137
7.5.2 Multidimensional Simulation 142
7.6 Experimental Test 143
7.7 Conclusion 144
References 145
8 Kalman Filters for Continuous Parametric Uncertain Systems 147
8.1 Introduction 147
8.2 Problem Formulation 149
8.3 The Estimation Algorithm 150
8.3.1 The Kalman Filtering-Based Parameter Estimation 150
8.3.2 The Kalman Filtering-Based State Estimation 153
8.4 Convergence Analysis 156
8.5 Numerical Example 158
8.6 Conclusions 160
References 160
Part III Kalman Filtering for Multi-sensor Systems
9 Optimal Centralized， Recursive， and Distributed Fusion for Stochastic Systems with Coupled Noises 165
9.1 Introduction 165
9.2 Problem Formulation 166
9.3 Optimal Fusion Algorithms 167
9.4 Performance Analysis and Computer Simulation 182
9.5 Summary 196
References 197
10 Optimal Estimation for Multirate Systems with Unreliable Measurements and Correlated Noise 199
10.1 Problem Formulations 201
10.2 Optimal Distributed Fusion Algorithm 203
10.2.1 Local State Estimation with Normal Measurements 203
10.2.2 Local State Estimation with Unreliable Measurements 206
10.2.3 Optimal Distributed Fusion Estimation with Unreliable Measurements 208
10.3 Numerical Example 214
10.4 Summary 220
References 220
11 CKF-Based State Estimation of Nonlinear System by Fusion of Multirate Multisensor Unreliable Measurements 223
11.1 Introduction 223
11.2 Problem Formulation 225
11.3 Multirate Multisensor Data Fusion Algorithm 225
11.4 Numerical Simulation 230
11.4.1 Simple Example on Tracking of a Ship 230
11.4.2 Target Tracking on Aircraft 234
11.5 Summary 236
References 237
Part IV Kalman Filtering for Multi-agent Systems
12 Decentralized Adaptive Filtering for Multi-agent Systems with Uncertain Couplings 241
12.1 Introduction 241
12.2 Problem Statement 243
12.2.1 Model 1: Linear Model with Output Coupling 243
12.2.2 Model 2: Linear Model with State Coupling 244
12.2.3 Model 3: Nonlinear Model with Output Couplin