Design and Experimental Test of Datatic Approximate Optimal Filter in Nonlinear Dynamic Systems

Filtering is crucial in engineering fields, providing vital state estimation for control systems. However, the nonlinear nature of complex systems and the presence of non-Gaussian noises pose significant challenges to the performance of conventional filtering methods in terms of estimation accuracy and computational efficiency. In this work, we present a data-driven closed-loop filter, termed datatic approximate optimal filter (DAOF), specifically designed for nonlinear systems under non-Gaussian conditions. We first formulate a Markovian filtering problem (MFP), which inherently shares a connection with reinforcement learning (RL) as it aims to compute the optimal state estimate by minimizing the accumulated error. To solve MFP, we propose DAOF, which primarily incorporates a trained RL policy and features two distinct structural designs: DAOF-v1 and DAOF-v2. Designed for systems with explicit models, DAOF-v1 combines prediction and update phases, with the RL policy generating the update value. Meanwhile, DAOF-v2 bypasses system modeling by directly outputting the state estimate. Then, we utilize an actor-critic algorithm to learn the parameterized policy for DAOF. Experimental results on a 2-degree-of-freedom (2-DOF) vehicle system, equipped with explicit system models, demonstrate the superior accuracy and computational efficiency of DAOF-v1 compared to existing nonlinear filters. Moreover, DAOF-v2 showcases its unique ability to perform filtering without requiring explicit system modeling, as validated by a 14-DOF vehicle system.