Recursive State Estimation: Optimal? Robust? Or What?
Prof. Yuriy S. Shmaliy
IEEE Life Fellow, AIIA Fellow, AAIA Fellow, SNI-III Emeritus
Universidad de Guanajuato, Guanajuato, Μexico
Abstract:
Optimality and robustness often go along with the requirements of accuracy and precision in state estimation and control, especially under harsh operation conditions. If the process and observation are both represented in state space with linear equations and noise is Gaussian (white or Gauss-Markov), then the Kalman filter gives best and thus optimal estimates. Otherwise, its performance degrades due to mismodeling, uncertainties, disturbances, bad initial values, and errors in noise statistics. Better robustness is inherent to finite impulse response (FIR) and limited memory filters. Robust filters can also be obtained by solving the minimax problem for norm-bounded errors. In this talk we discuss the most efficient recursive state estimators such as the optimal, optimal unbiased, unbiased (UFIR), LMF, maximum likelihood, as well as estimators having the robust performances: H 2 , H ∞ , generalized H 2 or l 2 -l ∞ , and L 1 . We show that at one pole is the optimal Kalman filter, at the other is the robust UFIR filter, and all other suboptimal and robust algorithms lie in between. A comparison of different estimators is supported with several practical examples taken from tracking, robotics, navigation, signal processing, control, and medical applications.
Brief Biography of the Speaker:
Dr. Yuriy S. Shmaliy, SNI-III Emeritus, IEEE Life Fellow, AAIA Fellow, AIIA Fellow, has
been a full professor in Electrical Engineering, since 1999 and headed the Electronics
Engineering Department, from 2013 to 2016, of the Universidad de Guanajuato, Mexico. He
received the B.S., M.S., and Ph.D. degrees in 1974, 1976 and 1982, respectively, from the
Kharkiv Aviation Institute, Ukraine, and Dr.Sc. degree, in 1991. In March 1985, he joined the
Kharkiv Military University. He serves as full professor beginning in 1986. In 1993, he founded
and, by 2001, had been a director of the Scientific Center “Sichron” (Kharkiv, Ukraine) working
in the field of precise time and frequency. His books Continuous-Time Signals (2006) and
Continuous-Time Systems (2007) were published by Springer. His book GPS-based Optimal FIR
Filtering of Clock Models (2009) was published by Nova Science Publ., New York. He also
edited a book Probability: Interpretation, Theory and Applications (Nova Science Publ., New
York, 2012). His book (2022) Optimal and Robust State Estimation: Finite Impulse response
(FIR) and Kalman Approaches was published by Wiley & Sons and recognized by
BookAuthority as One of the Best Estimation Theory Books of All Time. His discrete orthogonal
polynomials are called discrete Shmaliy moments. He pioneered and developed the theory of
optimal and robust FIR state estimation and founded the widely used robust UFIR filter.
Dr. Shmaliy has authored more than 550 Journal and Conference papers and holds 81 patents. He
was rewarded a title, Honorary Radio Engineer of the USSR, in 1991; was listed in Outstanding
People of the 20th Century, Cambridge, England in 1999; and was granted with the Royal
Academy of Engineering Newton Collaboration Program Award in 2015. He has received the
IEEE Latin America Eminent Engineer Award, in 2021, and several best conference paper
awards. He was with the Ukrainian State Award Committee on Science and Technology, in
1998-1999, and has been IEEE Fellow Committee Member, in 2023-2026. He has been a visiting
professor-researcher in City University London in 2015-2016 and in TELECOM SudParis in
2015, 2017-2019. His current interests include statistical signal processing, optimal and robust
state estimation, and stochastic system theory.