Plenary Lecture

GPS-based Optimal FIR Filtering of
Discrete-time Clock Models

Professor Yuriy S. Shmaliy
Department of Electronics
FIMEE (Guanajuato University)
Salamanca, 36885, Mexico
E-mail: shmaliy@salamanca.ugto.mx

Abstract: Although Time is a perfect eraser of any information (we have only a few evidences of ancient civilizations), modern digital information technologies rely on an extremely high accuracy of local timescales. The function of time dissemination is ordered to the Global Navigation Satellite Systems (GNSS) such as the Global Positioning System (GPS) measuring up to world standards for signals and systems. Even so, precision of the disseminated time is limited with noise, which standard deviation using commercially available timing receivers is about 30 ns, can reach 10-20 ns and may be improved by removal of systematic errors to no less than 3-5 ns. Precise correction of the local clock errors is hence not always available and optimal estimators are used. The problem we meet here is coupled with the nonstationary random behavior of the clock TIE and the GPS time temporary uncertainties caused by different satellites in a view. It arises in connection with the non Gaussian sawtooth noise induced by the receiver owing to the principle of the one pulse per second (1PPS) signal formation and with the non-white (colored) Gaussian noise of the clock oscillator. Under such conditions, the standard Kalman algorithm cannot always be used properly and may become noisy and unstable.This lecture introduces readers to the finite impulse response (FIR) filtering approach in applications to GPS-based measurements of the local clock errors. Precision of such measurements is limited by the GPS time temporary uncertainty and non Gaussian sawtooth noise induces by the GPS timing receiver. Therefore, optimal solutions are needed to estimate the clock instabilities. We give the fundamentals of FIR filtering, prediction, and smoothing of the polynomial and state space clock models. Unbiased and optimal FIR solutions are observed in line with the basic and thinning algorithms. The trade-off with the Kalman-Bucy algorithm is also discussed. It is noticed that, for large averaging horizons featured to slowly changing with time clock models, simple unbiased FIR solutions become virtually optimal. They may be the best choice in terms of simplicity, precision, stability, and robustness in solving many of the clock problems in GPS-based timekeeping and clock synchronization. Although, we discuss mostly an applied computation problem associated with accurate estimation of clock models, the results are readily extended to general polynomial discrete-time state space models.

Brief Biography of the Speaker:
Dr. Yuriy S. Shmaliy is a Full Professor of Electronics of the School of Mechanical, Electrical, and Electronic Engineering (FIMEE) of the University of Guanajuato, Mexico. He received the B.S., M.S., and Ph.D. degrees in 1974, 1976 and 1982, respectively, from the Kharkiv Aviation Institute, Ukraine, all in Electrical Engineering. 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) working in the field of precision time. In 1999, he joined the Kharkiv National University of Radio Electronics, and, since November 1999, he has been with the Guanajuato University of Mexico as a full professor with tenure. Dr. Shmaliy has 14 books, handbooks, and manuals. He has 240 Journal and Conference papers and 80 patents. His textbooks Continuous-Time Signals and Continuous-Time Systems intended for students of all levels of education were published by Springer. 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 is a Senior Member of the IEEE and belongs to several other professional Societies. He is a member of the Organizing and Program Committees of various Int. Symposia. He is a founder and organizer of the Int. Symposium on Precision Oscillators in Electronics and Optics. His current interests include the stochastic systems theory, precision resonators and oscillators, probabilistic methods of information theory, and computational methods of optimal estimation and statistical signal processing.