BIMSA > Seminar on Control Theory and Nonlinear Filtering The Extended Direct Method for Generalized Time-varying Filtering Systems
The Extended Direct Method for Generalized Time-varying Filtering Systems
Organizer
Shing Toung Yau
Speaker
Minli Feng
Time
Wednesday, September 4, 2024 2:30 PM - 3:00 PM
Venue
理科楼A-304
Abstract
The goal of nonlinear filtering is to determine the conditional mean of the state given the observation history, which requires us to solve the Duncan–Mortensen–Zakai equation in real time and in a memoryless manner. One of our approach is the direct method which works exceptionally well for time-varying Yau filtering system. The error of its estimation result is derived from the Gaussian approximation for a non-Gaussian initial distribution. This paper provides a theoretical proof that, under very mild conditions, this error can be made arbitrary small if the error between this distribution and its Gaussian approximation is sufficiently small in L^1(B_R) sense for a sufficiently large positive number R, which facilitates numerical computation. We additionally show that two assumptions in the original framework of the direct method can be removed provided that there exist proper approximations. We also present numerical experiments demonstrating the superior efficiency of the extended direct method compared to the extended Kalman filter and the particle filter.