Abstract: In this lecture, we examine recently developed the p-shift finite impulse response (FIR) unbiased estimator (UE) intended for filtering (p = 0), p-step prediction (p > 0), and p-lag smoothing (p < 0) of linear discrete time-varying state-space models. The estimator is investigated for robustness in Gaussian and non-Gaussian noise environments with outliers and temporary uncertainties in a comparison to the Kalman filter. The FIR UE algorithm is designed to have no requirements for noise and initial conditions and thus has strong engineering features. It is first presented in a batch form and then developed in the computationally efficient iterative Kalman-like one having the guarantied bounded input/bounded output (BIBO) stability, unlike the Kalman filter. Owing to the imbedded BIBO stability and without any other special solutions, such as those used in robust filtering, the FIR UE is show to have better robustness than the Kalman filter against the heavy-tailed noise and Gaussian noise with outliers. It is also shown to have a bit better robustness against temporary model uncertainties. Errors in the Kalman-like FIR UE are compared to the error bound (EB) specified via the noise power gain (NPG) serving as a limiter of errors in transversal estimators. We show that the EB specialized via the NPG in the three-sigma sense can also be useful in Kalman filtering. Examples of applications are taken from signal and image processing, clock synchronization, and control. Based upon these examples, we demonstrate that the Kalman-like FIR UE overperforms the Kalman filter one if the noise covariances and initial conditions are not known exactly, the noise constituents are not white sequences, and both the system and measurement noise components need to be filtered out. Otherwise, the errors are similar.

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.