Plenary Lecture
Nonlinear Tracking: The Approach Based on Extended Kalman-Like UFIR Filtering
Professor Yuriy S. Shmaliy
Department of Electronics
DICIS, Guanajuato University
Salamanca, 36855, Mexico
E-mail: shmaliy@salamanca.ugto.mx
Abstract: Tracking of moving objects is often provided employing the first-order and sometimes the second-order extended Kalman filters. The problem we meet here is associated with the process noise covariance which cannot always be specified correctly and also with the model temporary uncertainties. In this lecture, we show that an efficient remedy against these problems is unbiased averaging associated with finite impulse response (FIR) filtering. For suboptimal nonlinear tracking in discrete-time state-space with additive white noise, we accordingly derive and discuss the first- and second-order extended Kalman-like unbiased FIR filters (EFIR1 and EFIR2, respectively). Unlike the extended Kalman filter (EKF), the EFIR1 one does not require noise covariances and initial errors. By virtue of this, it demonstrates better robustness against temporary uncertainties in real world. Only within a narrow region around an actual process noise covariance, the EFIR filter falls a bit short of EKF and it demonstrates better performance otherwise. We show that the optimal averaging interval for EFIR filters can be determined via measurement in a “learning” circle and then re-determined and updated whenever necessary. We also notice that the second-order approximation can improve the local performance, but it can also deteriorate it. Thus, there can be given no definitive recommendations about its use, at least for tracking problems.
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 Soviet Union Government. 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 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) and contributed to several books with invited chapters. Dr. Shmaliy has 292 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 for Recent Patents on Space Technology. He serves on the Editorial Boards of several International Journals and 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.