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Seminar on Control Theory and Nonlinear Filtering
The Stochastic Stability Analysis for Outlier Robustness of Kalman-type Filtering Framework Based on Correntropy-Induced Cost
The Stochastic Stability Analysis for Outlier Robustness of Kalman-type Filtering Framework Based on Correntropy-Induced Cost
Organizer
Speaker
Yangtianze Tao
Time
Tuesday, September 12, 2023 4:00 PM - 5:00 PM
Venue
数学系理科楼A-203
Abstract
In this presentation, we reformulate the update step of extended Kalman filter (EKF) within the nonlinear regression framework called modified EKF (MEKF). Under this framework, a robust cost criterion, i.e., minimum correntropy-induced cost (MCIC) is applied to develop a novel outlier-robust MEKF scheme with adaptive Kalman-type update step called MCIC-MEKF. Moreover, we provide a theoretical understanding for its outlier robustness from the perspective of stochastic stability. 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. In particular, we have an explicit upper bound of our posterior estimation error. 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 MCIC-MEKF and above empirical arguments are confirmed by simulation results compared with several filtering benchmarks in presence of various non-Gaussian noises with large outliers.