BIMSA > Seminar on Control Theory and Nonlinear Filtering Extension of the Kalman–Bucy Filter to Elementary Linear Systems with Fractional Brownian Noises
Extension of the Kalman–Bucy Filter to Elementary Linear Systems with Fractional Brownian Noises
Organizer
Shing Toung Yau
Speaker
Jia Yi Kang
Time
Wednesday, May 22, 2024 3:00 PM - 3:30 PM
Venue
理科楼A-304
Abstract
I will report a paper on investigating the optimal filtering problem in the simplest Gaussian linear system driven by fractional Brownian motions. At first they extend to this setting the Kalman–Bucy filtering equations which are well-known in the specific case of usual Brownian motions. Closed form Volterra type integral equations are derived both for the mean of the optimal filter and the variance of the filtering error. Then the asymptotic stability of the filter is analyzed. It is shown that the variance of the filtering error converges to a finite limit as the observation time tends to infinity.