EE SEminar: Accuracy in linear filtering with fractional noises
(The talk will be given in English)
Speaker: Prof. Pavel Chigansky
Department of Statistics, Hebrew University
Monday, May 6th, 2019
15:00 - 16:00
Room 011, Kitot Bldg., Faculty of Engineering
Accuracy in linear filtering with fractional noises
Abstract
For a pair of random processes, the linear filtering problem consists of finding a causal linear transformation of the observed component, whose output generates an estimator of the hidden state with the minimal mean squared error. In continuous time, construction of the optimal filter in general boils down to solving a certain integral equation. In the Markov case, when the processes are generated by a linear system driven by the Brownian ''white'' noises, it reduces to the Riccati differential equation. This fact lies in the foundation of the Kalman-Bucy filtering theory. Beyond the Markov case, analysis of this integral equation can be quite challenging. In this talk, I will present a new analytic framework applicable to filtering problems with fractional Brownian noises. Such noises are used in modeling of non-white disturbances with long range dependence. The developed theory allows to obtain exact asymptotics of the optimal filtering error in the steady-state and high signal-to-noise regimes.
Joint work with D.Afterman, M.Kleptsyna and D. Marushkevych.
