From Optimality to Robustness in State Estimation: The FIR Approach

Professor Yuriy S. Shmaliy, PhD, DSc, IEEE Fellow,
Department of Electronics Engineering,
Universidad de Guanajuato,
DICIS, Salamanca, Mexico

Abstract: Optimality and robustness often go along with the requirement of accuracy in system state estimation, especially under harsh operation conditions. If a system and its observation are both represented with linear state-space equations, the statistics of Gaussian noise (white or colored) are known exactly, then the Kalman filter provides best state estimates. Otherwise, its performance degrades due to mismodeling, temporary uncertainties, bad initial values, and errors in the noise statistics. Better robustness is inherent to estimators with a finite impulse response (FIR), limited memory filters (LMF), and norm-bounded solutions. In this talk we review most efficient FIR state estimators such as the optimal, optimal unbiased, unbiased (UFIR), LMF, maximum likelihood, as well as estimators having the H 2 , H ∞ , and generalized H 2 or l 2 -l ∞ nominal performances. We show that the UFIR filter, which completely ignores noise and initial conditions, may be a better choice than the optimal and norm-bounded filters under different kinds of uncertainties. Unlike other estimators, the UFIR filter requires only one tuning factor, an averaging horizon of N opt points. Of importance is that much smaller efforts are required to find N opt than for the noise or error statistics, initial values, and norm bounds. A comparison of different estimators is supported with a number of practical examples taken from tracking, robotics, navigation, signal processing, control, and medical applications.

Brief Biography of the Speaker: Dr. Yuriy S. Shmaliy has been a full professor in Electrical Engineering, since 1999, and headed the Electronics Engineering Department, from 2012 to 2015, 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. In 1992 he received the Dr.Sc. (technical) degree from the USSR Government. 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, New York. 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 discrete orthogonal polynomials are called Shmaliy moments. Dr. Shmaliy has authored more than 450 Journal and Conference papers and holds 81 patents. He is IEEE Fellow; 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 been a visiting professor- researcher in City University London in 2015-2016 and in TELECOM SudParis in 2015, 2017- 2019. He was invited many times to give tutorial, keynote, and plenary lectures. He currently serves on the Editorial Boards of several International Journals and is a member of the Program Committees of various Int. Symposia. His current interests include statistical signal processing, optimal and robust state estimation, and stochastic system theory.