Optimal and Robust State Estimation - Finite Impulse Response (Fir) and Kalman Approaches

A unified and systematic theoretical framework for solving problems related to finite impulse response (FIR) estimate
 
Optimal and Robust State Estimation: Finite Impulse Response (FIR) and Kalman Approaches is a comprehensive investigation into batch state estimators and recursive forms. The work begins by introducing the reader to the state estimation approach and provides a brief historical overview. Next, the work discusses the specific properties of finite impulse response (FIR) state estimators. Further chapters give the basics of probability and stochastic processes, discuss the available linear and nonlinear state estimators, deal with optimal FIR filtering, and consider a limited memory batch and recursive algorithms.
 
Other topics covered include solving the q-lag FIR smoothing problem, introducing the receding horizon (RH) FIR state estimation approach, and developing the theory of FIR state estimation under disturbances. The book closes by discussing the theory of FIR state estimation for uncertain systems and providing several applications where the FIR state estimators are used effectively. Key concepts covered in the work include:
* A holistic overview of the state estimation approach, which arose from the need to know the internal state of a real system, given that the input and output are both known
* Optimal, optimal unbiased, maximum likelihood, and unbiased and robust finite impulse response (FIR) structures
* FIR state estimation approach along with the infinite impulse response (IIR) and Kalman approaches
* Cost functions and the most critical properties of FIR and IIR state estimates
 
Optimal and Robust State Estimation: Finite Impulse Response (FIR) and Kalman Approaches was written for professionals in the fields of microwave engineering, system engineering, and robotics who wish to move towards solving finite impulse response (FIR) estimate issues in both theoretical and practical applications. Graduate and senior undergraduate students with coursework dealing with state estimation will also be able to use the book to gain a valuable foundation of knowledge and become more adept in their chosen fields of study.

List of 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 It^o 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

About the author

YURIY S. SHMALIY, PhD, is a Professor with the Universidad de Guanajuato, Mexico. He serves as an Editorial Board Member in various scientific journals and is an IEEE Fellow. He also developed the theory of FIR state estimation, gave many keynote and plenary lectures, and his discrete orthogonal polynomials are called discrete Shmaliy moments.
SHUNYI ZHAO, PhD, is a Professor with the Jiangnan University, China. His current research interests include statistical signal processing, Bayesian estimation theory, and fault detection and diagnosis.

Summary

A unified and systematic theoretical framework for solving problems related to finite impulse response (FIR) estimate

Optimal and Robust State Estimation: Finite Impulse Response (FIR) and Kalman Approaches is a comprehensive investigation into batch state estimators and recursive forms. The work begins by introducing the reader to the state estimation approach and provides a brief historical overview. Next, the work discusses the specific properties of finite impulse response (FIR) state estimators. Further chapters give the basics of probability and stochastic processes, discuss the available linear and nonlinear state estimators, deal with optimal FIR filtering, and consider a limited memory batch and recursive algorithms.

Other topics covered include solving the q-lag FIR smoothing problem, introducing the receding horizon (RH) FIR state estimation approach, and developing the theory of FIR state estimation under disturbances. The book closes by discussing the theory of FIR state estimation for uncertain systems and providing several applications where the FIR state estimators are used effectively. Key concepts covered in the work include:
* A holistic overview of the state estimation approach, which arose from the need to know the internal state of a real system, given that the input and output are both known
* Optimal, optimal unbiased, maximum likelihood, and unbiased and robust finite impulse response (FIR) structures
* FIR state estimation approach along with the infinite impulse response (IIR) and Kalman approaches
* Cost functions and the most critical properties of FIR and IIR state estimates

Optimal and Robust State Estimation: Finite Impulse Response (FIR) and Kalman Approaches was written for professionals in the fields of microwave engineering, system engineering, and robotics who wish to move towards solving finite impulse response (FIR) estimate issues in both theoretical and practical applications. Graduate and senior undergraduate students with coursework dealing with state estimation will also be able to use the book to gain a valuable foundation of knowledge and become more adept in their chosen fields of study.

Product details

• Authors: Shmaliy, Ys Shmaliy, Yuriy S Shmaliy, Yuriy S. Shmaliy, Yuriy S. (Universidad De Guanajuato Shmaliy, Yuriy S. Zhao Shmaliy, Shmaliy Yuriy S., Shunyi Zhao
• Publisher: Wiley, John and Sons Ltd
• Languages: English
• Product format: Hardback
• Released: 31.08.2022
• EAN: 9781119863076
• ISBN: 978-1-119-86307-6
• No. of pages: 480
• Subjects: Natural sciences, medicine, IT, technology > Technology > Electronics, electrical engineering, communications engineering; Regelungstechnik, Systemtechnik, Electrical & Electronics Engineering, Elektrotechnik u. Elektronik, Mikrowellen- u. Hochfrequenztechnik u. Theorie, RF / Microwave Theory & Techniques, Systemtechnik u. -management, Systems Engineering & Management, Control Systems Technology