Discrete-Time Optimal FIR Estimation in State-Space

Lecture / Panel
For NYU Community

Speaker: Professor Yuriy S. Shmaliy

Faculty Host: Ivan Selesnick


Filtering, smoothing, and prediction have become key tools of statistical signal, image, and speech processing and found applications in algorithms of various electronic systems. Estimation can be provided using methods of finite impulse response (FIR) linear optimal filtering having strong features, such as the inherent bounded input/bounded output stability and robustness against temporary model uncertainties and round-off errors. In this talk, I will show that the general p-shift optimal linear FIR estimator follows straightforwardly from the real discrete-time state space model (from n and n-1 to n) used in signal processing, rather than from the prediction one (from n to n+1) used in control. This general estimator allows solving universally the problems of filtering (p 0), prediction (p > 0), and smoothing (p < 0) on a horizon of N points. I will then present different batch and recursive algorithms and give an analysis of the estimation errors along with the noise power gain. Applications will be given for polynomial state space modeling, clock state estimation and synchronization, and image processing.

About the Speaker

Dr. Yuriy S. Shmaliy is a Full Professor of the Guanajuato University, Mexico. He received the Ph.D degree in 1982 from the Kharkiv Aviation Institute, Ukraine. In 1992 he received the Doctor of Technical Sc. degree from the Kharkiv Railroad Institute. In March 1985, he joined the Kharkiv Military University of Ukraine. He serves as Full Professor beginning in 1986 and has a Certificate of Professor from the Ukrainian Government in 1993. Since 1993 to 1999, he has been a director-collaborator of the Scientific Center “Sichron” (Kharkiv, Ukraine). Since 1999 to 2009, he has been with the Kharkiv National University of Radio Electronics, and, since November 1999, he has been with the Guanajuato University of Mexico. Dr. Shmaliy has several books, handbooks, and manuals. He has 251 Journal and Conference papers and 80 patents. 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” was published by Nova Science Publ., New York, in 2009. He also authored and co-authored several invited chapter to books. He was rewarded a title, Honorary Radio Engineer of the USSR, in 1991; was listed in Marquis Who's Who in the World in 1998; and was listed in Outstanding People of the 20th Century, Cambridge, England in 1999. He has Certificates of appreciation and recognition from the IEEE, WSEAS, and IASTED. He is a member of the Organizing and Program Committees of various Int. Symposia. He is an Associate Editor of Recent Patents on Space Technology. He is a founder and organizer of the Int. Conference on Precision Oscillators in Electronics and Optics. He is a Senior Member of the IEEE and belongs to several other professional Societies.  His current interests include optimal estimation, statistical signal processing, and stochastic system theory.