Beijing Institute of Mathematical Sciences and Applications

Shing Toung Yau

Weixian He

Wednesday, June 26, 2024 4:00 PM - 5:00 PM

理科楼A-304

State estimation presents a critical challenge across diverse engineering domains, particularly when dealing with the nonlinear and non-Gaussian characteristics in complex control systems. Conventional approaches often resort to approximations like model linearization or Monte Carlo sampling, which may compromise precision or encounter significant computational overhead. This paper proposes a data-driven offline estimation method called datatic approximate optimal filter (DAOF), which is tailored for nonlinear systems under non-Gaussian conditions. Due to its structural flexibility, this method allows for both model-based and model-free estimation, depending on the availability of the state-space model. To obtain DAOF, we formulate the reinforced estimation problem (REP), where the optimal state estimate is computed to minimize accumulated estimation error, establishing a connection with reinforcement learning (RL). We design a model-based filter similar to Kalman filter (KF) for nonlinear and non-Gaussian systems, incorporating prediction and update components. We further design the filtering structure for model-free estimation by directly choosing the state estimate as the policy output. An actor-critic learning algorithm is employed to obtain a parameterized filtering policy for both filtering structures. We integrate a sliding window on the input of the policy, enabling the retention of historical observation information while maintaining high online computational efficiency. Experimental results on the 2-DOF nonlinear vehicle system and the Lorenz system showcases the superior accuracy and computational efficiency of DAOF compared to representative nonlinear filters. The model-free estimation capability of DAOF is validated with a 14-DOF vehicle dynamic model without explicitly providing the transition or observation functions.