BIMSA > Seminar on Control Theory and Nonlinear Filtering The Stochastic Stability Analysis of A Modified Extended Kalman Filter Framework Under Maximum Correntropy Criterion
The Stochastic Stability Analysis of A Modified Extended Kalman Filter Framework Under Maximum Correntropy Criterion
Organizer
Shing Toung Yau
Speaker
Yangtianze Tao
Time
Tuesday, January 17, 2023 9:00 PM - 9:30 PM
Venue
Online
Abstract
In this presentation we reformulate the update step of extended Kalman filter (EKF) within a dynamical optimization framework called modified EKF (MEKF). Under this framework, we derive a novel robust EKF scheme with adaptive Kalman-type update step based on maximum correntropy criterion (MCC) called MCC-MEKF. Moreover, we provide a theoretical understanding for its robustness from the perspective of stochastic stability, which allows us to investigate the robustness of MCC-based filters in a quantitative way for the first time. Under some natural conditions, we give the estimate of prior estimation error between two adjacent steps and prove that its posterior estimation error is exponentially bounded in mean square. The explicit upper bound is provided in particular. In addition, motivated by these theoretical insights, we propose a technical approximation for this adaptive Kalman gain, which can maintain good performance while avoid iteratively solving a fixed-point problem at each update step used in previous works. At last, the robustness of our proposed MCC-MEKF and above empirical arguments are confirmed by simulation results compared with several filtering benchmarks.