MIT-Harvard CINCS (Communications Information Networks Circuits and Signals) / Hamilton Institute Seminar
Speaker: Professor Subhra Dey, Maynooth University
Title: "A Tale of Heavy Tails: Kalman Filtering with information loss"
Abstract: The area of estimation and control where information/control actions are received over lossy networks has been extremely active over the last 15 years. One of the key results is that the second moment of the estimation error in Kalman filtering (linear state estimation algorithm) for unstable systems becomes unbounded if the measurement packets are randomly lost at a probability higher than a certain threshold. While many of the subsequent studies have largely focused on the investigation of second moments only, a more fundamental quantity - the estimation/prediction error itself has not been investigated deeply under such scenarios involving information loss.
In this talk, we will study the existence of a steady-state distribution and its tail behaviour for the estimation error arising from Kalman filtering for unstable linear dynamical systems.
First we will show that if the system is strictly unstable and packet loss probability is strictly less than unity, then the steady-state distribution (if it exists) must be heavy tail, i.e. its absolute moments beyond a certain order do not exist. Then, by drawing results from Renewal Theory, we will further provide sufficient conditions for the existence of such stationary distribution. Moreover, we will show that under additional technical assumptions and in the scalar scenario, the steady-state distribution of the Kalman prediction error has an asymptotic power-law tail, where the exponent of the power-law can be explicitly computed. Finally, we will explore how to optimally select the sampling period assuming an exponential decay of packet loss probability with respect to the sampling period. In order to minimize the expected value of the second moment or the confidence bounds, we illustrate that in general a larger sampling period will need to be chosen in the latter case as a result of the heavy tail behaviour.
Bio: Subhrakanti Dey received the Bachelor in Technology and Master in Technology degrees from the Department of Electronics and Electrical Communication Engineering, Indian Institute of Technology, Kharagpur, in 1991 and 1993, respectively, and the Ph.D. degree from the Department of Systems Engineering, Research School of Information Sciences and Engineering, Australian National University, Canberra, in 1996.
He is currently a Professor with the Hamilton Institute, National University of Ireland, Maynooth, Ireland. Prior to this, he was a Professor with the Dept. of Engineering Sciences in Uppsala University, Sweden (2013-2017), Professor with the Department of Electrical and Electronic Engineering, University of Melbourne, Parkville, Australia, from 2000 until early 2013, and a Professor of Telecommunications at University of South Australia during 2017-2018. From September 1995 to September 1997, and September 1998 to February 2000, he was a Postdoctoral Research Fellow with the Department of Systems Engineering, Australian National University. From September 1997 to September 1998, he was a Postdoctoral Research Associate with the Institute for Systems Research, University of Maryland, College Park.
His current research interests include wireless communications and networks, signal processing for sensor networks, networked control systems, and distributed machine learning.
Professor Dey currently serves as a Senior Editor on the Editorial Board IEEE Transactions on Control of Network Systems, and as an Associate Editor/Editor for Automatica, IEEE Control Systems Letters, and IEEE Transactions on Wireless Communications. He was also an Associate Editor for IEEE and Transactions on Signal Processing, (2007-2010, 2014-2018), IEEE Transactions on Automatic Control (2004-2007), and Elsevier Systems and Control Letters (2003-2013).