- 控制理论和非线性滤波讨论班

Data-driven Optimal Filtering for Linear Systems with Unknown Noise Covariances

组织者

丘成栋

演讲者

冯敏立

时间

2023年08月21日 15:00 至 15:30

地点

数学系理科楼A-203

摘要

The objective of this presentation is to provide fresh insights into the classical estimation problem by leveraging the duality between control and estimation and incorporating recent advances in data-driven optimal control. Specifically, building on the fundamental connection between the optimal mean-squared error estimation problem and the LQR problem, we reformulate determining the optimal Kalman gain as a problem of synthesizing an optimal policy for the adjoint system, under conditions. Upon utilizing this relationship, we propose a SGD algorithm for learning the optimal Kalman gain, accompanied by novel non-asymptotic error guarantees in presence of biased gradient and stability constraint. Our approach opens up promising avenues for addressing the estimation problem with robust and efficient data-driven techniques.