Optimal and robust state estimation : finite impulse response (FIR) and Kalman approaches /: finite impulse response (FIR) and Kalman approaches. (2022)

• Record Type: Book
• Further Information: Note: Yuriy S. Shmaliy, Shunyi Zhao.
• Authors: Shmaliy, Yuriy; Zhao, Shunyi
• Contents: 1 Introduction 1 1.1 What is System State? 2 1.1.1 Why and How do We Estimate State? 2 1.1.2 What Model to Estimate State? 3 1.1.3 What are Basic State Estimates in Discrete Time? 5 1.2 Properties of State Estimators 6 1.2.1 Structures and Types 6 1.2.2 Optimality 10 1.2.3 Unbiased Optimality (Maximum Likelihood) 11 1.2.4 Suboptimality 14 1.2.5 Unbiasedness 17 1.2.6 Deadbeat 17 1.2.7 Denoising (Noise Power Gain) 17 1.2.8 Stability 18 1.2.9 Robustness 18 1.2.10 Computational Complexity 19 1.2.11 Memory Use 20 1.3 More About FIR State Estimators 20 1.4 Historical Overview and Most Noticeable Works 21 1.5 Summary 26 1.6 Problems 27 2 Probability and Stochastic Processes 31 2.1 Random Variables 31 2.1.1 Moments and Cumulants 33 2.1.2 Product Moments 39 2.1.3 Vector Random Variables 41 2.1.4 Conditional Probability. Bayes’ Rule 42 2.1.5 Transformation of Random Variables 45 2.2 Stochastic Processes 47 2.2.1 Correlation Function 48 2.2.2 Power Spectral Density 51 2.2.3 Gaussian Processes 53 2.2.4 White Gaussian Noise 55 2.2.5 Markov Processes 57 2.3 Stochastic Differential Equation 60 2.3.1 Standard Stochastic Differential Equation 61 2.3.2 Itˆo and Stratonovich Stochastic Calculus 61 2.3.3 Diffusion Process Interpretation 62 2.3.4 Fokker-Planck-Kolmogorov Equation 63 2.3.5 Langevin Equation 64 2.4 Summary 65 2.5 Problems 66 3 State Estimation 71 3.1 Lineal Stochastic Process in State Space 71 3.1.1 Continuous-Time Model 73 3.1.2 Discrete-Time Model 77 3.2 Methods of Linear State Estimation 81 3.2.1 Bayesian Estimator 82 3.2.2 Maximum Likelihood Estimator 85 3.2.3 Least Squares Estimator 86 3.2.4 Unbiased Estimator 87 3.2.5 Kalman Filtering Algorithm 88 3.2.6 Backward Kalman Filter 94 3.2.7 Alternative Forms of Kalman Filter 96 3.2.8 General Kalman Filter 98 3.2.9 Kalman-Bucy Filter 110 3.3 Linear Recursive Smoothing 113 3.3.1 Rauch-Tung-Striebel Algorithm 113 3.3.2 Bryson-Frazier Algorithm 114 3.3.3 Two-Filter (Forward-Backward) Smoothing 115 3.4 Nonlinear Models and Estimators 116 3.4.1 Extended Kalman Filter 117 3.4.2 Unscented Kalman Filter 119 3.4.3 Particle Filtering 122 3.5 Robust State Estimation 126 3.5.1 Robustified Kalman Filter 127 3.5.2 Robust Kalman Filter 128 3.5.3 H8 Filtering 131 3.5.4 Game Theory H8 Filter 132 3.6 Summary 133 3.7 Problems 134 4 Optimal FIR and Limited Memory Filtering 139 4.1 Extended State-Space Model 140 4.2 The a posteriori Optimal FIR Filter 142 4.2.1 Batch Estimate and Error Covariance 143 4.2.2 Recursive Forms 145 4.2.3 System Identification 149 4.3 The a posteriori Optimal Unbiased FIR Filter 149 4.3.1 Batch OUFIR-I Estimate and Error Covariance 150 4.3.2 Recursive Forms for OUFIR-I Filter 151 4.3.3 Batch OUFIR-II Estimate and Error Covariance 153 4.3.4 Recursion Forms for OUFIR-II Filter 154 4.4 Maximum Likelihood FIR Estimator 158 4.4.1 ML-I FIR Filtering Estimate 158 4.4.2 Equivalence of ML-I FIR and OUFIR Filters 159 4.4.3 ML-II FIR Filtering Estimate 162 4.4.4 Properties of ML FIR State Estimators 163 4.5 The a priori FIR Filters 164 4.5.1 The a priori Optimal FIR Filter 164 4.5.2 The a priori Optimal Unbiased FIR Filter 165 4.6 Limited Memory Filtering 165 4.6.1 Batch Limited Memory Filter 166 4.6.2 Iterative LMF Algorithm using Recursions 168 4.7 Continuous-Time Optimal FIR Filter 169 4.7.1 Optimal Impulse Response 169 4.7.2 Differential Equation Form 171 4.8 Extended a posteriori OFIR Filtering 172 4.9 Properties of FIR State Estimators 174 4.10 Summary 179 4.11 Problems 182 5 Optimal FIR Smoothing 187 5.1 Introduction 187 5.2 Smoothing Problem 188 5.3 Forward Filter/Forward Model q-lag OFIR Smoothing 189 5.3.1 Batch Smoothing Estimate 190 5.3.2 Error Covariance 193 5.4 Backward OFIR Filtering 195 5.4.1 Backward State-Space Model 195 5.4.2 Batch Estimate 196 5.4.3 Recursive Estimate and Error Covariance 198 5.5 Backward Filter/Backward Model g-lag OFIR Smoother 202 5.5.1 Batch Smoothing Estimate 203 5.5.2 Error Covariance 204 5.6 Forward Filter/Backward Model q-Lag OFIR Smoother 205 5.6.1 Batch Smoothing Estimate 205 5.6.2 Error Covariance 208 5.7 Backward Filter/Forward Model q-Lag OFIR Smoother 208 5.7.1 Batch Smoothing Estimate 208 5.7.2 Error Covariance 211 5.8 Two-Filter q-lag OFIR Smoother 213 5.9 q-Lag ML FIR Smoothing 214 5.9.1 Batch q-lag ML FIR Estimate 215 5.9.2 Error Covariance 216 5.10 Summary 216 5.11 Problems 217 6 Unbiased FIR State Estimation 221 6.1 Introduction 221 6.2 The a posteriori UFIR Filter 222 6.2.1 Batch Form 222 6.2.2 Iterative Algorithm Using Recursions 224 6.2.3 Recursive Error Covariance 226 6.2.4 Optimal Averaging Horizon 228 6.3 Backward a posteriori UFIR Filter 234 6.3.1 Batch Form 235 6.3.2 Recursions and Iterative Algorithm 236 6.3.3 Recursive Error Covariance 239 6.4 The q-lag UFIR Smoother 240 6.4.1 Batch and Recursive Forms 240 6.4.2 Error Covariance 242 6.4.3 Equivalence of UFIR Smoothers 244 6.5 State Estimation using Polynomial Models 245 6.5.1 Problems Solved with UFIR Structures 246 6.5.2 The p-shift UFIR Filter 247 6.5.3 Filtering of Polynomial Models 250 6.5.4 Discrete Shmaliy Moments 252 6.5.5 Smoothing Filtering and Smoothing 252 6.5.6 Generalized Savitzky-Golay Filter 254 6.5.7 Predictive Filtering and Prediction 255 6.6 UFIR State Estimation under Colored Noise 256 6.6.1 Colored Measurement Noise 256 6.6.2 Colored Process Noise 259 6.7 Extended UFIR Filtering 262 6.7.1 First-Order Extended UFIR Filter 263 6.7.2 Second-Order Extended UFIR Filter 263 6.8 Robustness of UFIR Filter 266 6.8.1 Errors in Noise Covariances and Weighted Matrices 268 6.8.2 Model Errors 271 6.8.3 Temporary Uncertainties 274 6.9 Implementation of Polynomial UFIR Filters 276 6.9.1 Filter Structures in z-Domain 276 6.9.2 Transfer Function in DFT Domain 282 6.10 Summary 287 6.11 Problems 288 7 FIR Prediction and Receding Horizon Filtering 295 7.1 Introduction 295 7.2 Prediction Strategies 296 7.2.1 Kalman Predictor 296 7.3 Extended Predictive State-Space Model 298 7.4 UFIR Predictor 298 7.4.1 Batch UFIR Predictor 299 7.4.2 Iterative Algorithm using Recursions 299 7.4.3 Recursive Error Covariance 303 7.5 Optimal FIR Predictor 304 7.5.1 Batch Estimate and Error Covariance 305 7.5.2 Recursive Forms and Iterative Algorithm 306 7.6 Receding Horizon FIR Filtering 308 7.6.1 MVF-I Filter for Stationary Processes 309 7.6.2 MVF-II Filter for Nonstationary Processes 311 7.7 Maximum Likelihood FIR Predictor 313 7.7.1 ML-I FIR Predictor 314 7.7.2 M
• Edition: 1st
• Publisher Details: Hoboken : Wiley-IEEE Press
• Publication Date: 2022
• Extent: 1 online resource
• Subjects: 629.8312; Observers (Control theory); Systems engineering
• Languages: English
• ISBNs: 9781119863090
• Related ISBNs: 9781119863076
• Notes: Note: Includes bibliographical references and index.; Note: Description based on CIP data; resource not viewed.
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