Abstract: Measurement is always provided with analog sensors, whereas processing and estimation is typically obtained using DSP power. This lecture examines the problem of optimal filtering, interpolation, and extrapolation of dynamic analog quantities existing in continuous-time with the discrete-time state-space finite impulse response (FIR) structures on an interval of N past measurement points. An important feature of such structures is that the optimal and unbiased estimates converge when N is large, N >> 1, that is typical for highly oversampled quantities. In line with the general theory and estimation algorithms, we discuss the estimation error and error bound (EB) derived via the noise power gain (NPG). We show that the EB specialized via the NPG in the three-sigma sense can also be useful for Kalman filtering. A fast unbiased Kalman-like estimation algorithm ignoring noise and initial errors is discussed in detail. We show that this algorithm is bounded input/bounded output (BIBO) stable and more robust than the Kalman filter against outliers, noise tails, and temporary model uncertainties. Examples of applications are given for the Global Positioning System (GPS)-based measurement of time errors in ovenized crystal clocks that is provided with the fixed horizon estimators, controlled system outputs estimated on full-horizons, and extrapolation of errors in National Time scales. Based upon these and other examples, we show that the Kalman-like FIR estimator is able to outperform the Kalman one if the noise covariances are not known exactly, noise is not white, and both the system and measurement noise components need to be filtered out.

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 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 286 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.