**Titre : ** Robustness of the Kalman, H∞, and UFIR Filters

**Date : ** le lundi 28 août à 15h

**Lieu :** en salle C06, à Télécom Sud Paris

**Intervenant : ** Pr. Yuriy Shmaliy (Université de Guanajuato, Mexique)

**Abstract:** Optimal state estimation in diverse environments is a key problem for many branches of engineering, such as navigation, indoor robot localization, communications, etc. However, not each estimator is sufficiently robust when the model and environments are not well specified or undergo uncertainties. This lecture provides a comparative analysis for robustness of the three fast filtering algorithms: the Kalman filter (KF), which is optimal but not robust; the H∞ filter, which was derived using the game theory to be a robust alternative to the KF; and the unbiased finite impulse response (UFIR) filter, which ignores the noise statistics and the initial values. We test these filters using the Gaussian model by the three main factors: imprecisely defined noise covariances, which exact values are typically unavailable in practice; mismodeling, which occurs when the model does not fit the process; and temporary uncertainties such as jumps in phase, frequency, and velocity, which cannot be modeled in view of their unpredictable nature. Under the ideal conditions, the KF produces best estimates, which cannot be improved using the H∞ filter. Provided that errors in the model are maximized correctly or overrated and the tuning factor is chosen properly, the H∞ filter performs better than the KF. But an incorrectly chosen tuning factor may bring the H∞ filter to instability and divergence. The H∞ filter will also be unable to improve estimates with an allowed positive tuning factor if the maximum errors are underrated. On the other hand, much smaller efforts are required to find an optimal horizon (a single tuning factor) for the UFIR filter, which therefore may be a better choice for robust estimation. These findings were verified experimentally based on long-term temperature measurements with missing data.

**Brief Biography of the Speaker:**

Dr. Yuriy S. Shmaliy has been a full professor in Electrical Engineering of the Universidad de Guanajuato, Mexico, since 1999. He is presently a visiting researcher in TELECOM SudParis. 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. (technical) 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 Full Professor, since 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 authored 385 Journal and Conference papers and holds 81 patents. He is IEEE Fellow; was rewarded a title, Honorary Radio Engineer of the USSR, in 1991; was listed in Outstanding People of the 20th Century, Cambridge, England in 1999; and was granted with the Royal Academy of Engineering Newton Collaboration Program Award in 2015. He currently serves on the Editorial Boards of several International Journals and is a member of the Program Committees of various Int. Symposia. His current interests include statistical signal processing, optimal estimation, and stochastic system theory.