Plenary
Lecture
Optimal FIR Filtering of State-Space Models in
non-Gaussian Environment with Uncertainties
Professor Yuriy S. Shmaliy
Department of Electronics
DICIS, Guanajuato University
Salamanca, 36855, Mexico
E-mail:
shmaliy@salamanca.ugto.mx
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.
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