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Seminar on Control Theory and Nonlinear Filtering
Data-driven Optimal Filtering for Linear Systems with Unknown Noise Covariances
Data-driven Optimal Filtering for Linear Systems with Unknown Noise Covariances
Organizer
Speaker
Time
Monday, August 21, 2023 3:00 PM - 3:30 PM
Venue
数学系理科楼A-203
Abstract
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.