Optimal FIR Estimation of Discrete-Time State-Space Models
Optimal estimation of signal parameters and system models is often required to formalize a posteriori knowledge about undergoing processes in the presence of noise. Therefore 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 model (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 the unique low-degree polynomial gains for unbiased FIR estimators. Applications will be given for polynomial state space modeling, clock state estimation and synchronization, and image processing.
Dr. Yuriy S. Shmaliy is a professor at Guanajuato University. He received his PhD in 1982 from the Kharkiv Aviation Institute in Ukraine. In 1992 he received a doctor of technical science degree from the Kharkiv Railroad Institute. From 1993 to 1999 he was a director-collaborator of the Scientific Center “Sichron” in Ukraine. In 1999 he joined the Kharkiv National University of Radio Electronics, and since November 1999 he has been with Guanajuato University of Mexico. He has authored several books, handbooks and manuals. He has published 245 journal and conference papers and holds 80 patents. His textbooks “Continuous-Time Signals” (2006) and “Continuous-Time Systems” (2007) were published by Springer. His book “GPS-based Optimal FIR Filtering of Clock Models” and the invited chapter to the book “Global Positioning System” are to be published by Nova Science Publishers in 2009. He also co-authored an invited chapter for the book “Image Processing” published by In-Tech. He is a founder and organizer of the International Conference on Precision Oscillators in Electronics and Optics, an editorial board member of several journals and a senior member of IEEE.