Abstract: In industrial applications, optimal estimators of system state often face a necessity to work in non-Gaussian environment in the presence of uncertainties. This lecture introduces readers to the recently developed p-shift iterative Kalman-like finite impulse response (FIR) unbiased estimation (UE) algorithm intended for filtering (p = 0), prediction (p > 0), and smoothing (p < 0) under such conditions of linear discrete time-varying state-space models. The algorithm was designed with no requirements for noise and initial conditions and thus has strong engineering features. A solution is first found in a batch form and then represented in the computationally efficient iterative Kalman-like one with the following advantages peculiar to FIR structures: guarantied bounded input/bounded output (BIBO) stability, better robustness against temporary model uncertainties and round-off errors, and low sensitivity to noise and initial conditions. It is shown that the estimator proposed overperforms the Kalman one when the noise covariances and initial conditions are not known exactly, if noise is not white sequence, and when both the system and measurement noise components need to be filtered out. Otherwise, the estimators produce similar errors. Extensive investigations of the FIR UE have been carried out for the standard Kalman filter regarding different models. Examples of applications have been taken from signal and image processing, clock synchronization, and control. All the way, we lay stress on the trade-off with the Kalman filter in the Gaussian and non-Gaussian environments allowing for temporary model and measurement uncertainties, as well as outliers.

Brief Biography of the Speaker:
Dr. Yuriy S. Shmaliy is Full Professor in Electrical Engineering of the University of Guanajuato, Mexico, since 1999. 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. degree from the Kharkiv Railroad Institute. In March 1985, he joined the Kharkiv Military University. He serves as Full Professor beginning in 1986 and has a certificate of Professor from the Ukrainian Government in 1993. In 1993, he founded and, by 2001, had been a director-collaborator 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 contributed to several books with invited chapters. Dr. Shmaliy has 262 Journal and Conference papers and 80 patents. He is IEEE Fellow; was rewarded a title, Honorary Radio Engineer of the USSR, in 1991; was listed in Marquis Who's Who in the World in 1998; was listed in Outstanding People of the 20th Century, Cambridge, England in 1999; and was listed in The Contemporary Who's Who, American Bibliographical Institute, 2003. He is currently an Associate Editor of Recent Patents on Space Technology. He is a member of the Organizing and Program Committees of various Int. Symposia. His current interests include statistical signal processing, optimal estimation, and stochastic system theory.