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

arXiv: https://arxiv.org/abs/2505.07043 · HTML: https://mlsanity.com/paper/2505.07043/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods.
- Builds on 6 of its 31 references that are in the map.
- First posted on arXiv 11 May 2025.

## Placed in

- Deep reinforcement learning methods / [RL theory and sample complexity](https://mlsanity.com/deeprl/rl-theory-and-sample-complexity/)

## Builds on (most cited first, 6 of 6)

- [A Brief Survey of Deep Reinforcement Learning](https://mlsanity.com/paper/1708.05866/) (2017)
- [Deep Variational Bayes Filters: Unsupervised Learning of State Space Models from Raw Data](https://mlsanity.com/paper/1605.06432/) (2016)
- [KalmanNet: Neural Network Aided Kalman Filtering for Partially Known Dynamics](https://mlsanity.com/paper/2107.10043/) (2021)
- [Distributional Soft Actor-Critic with Three Refinements](https://mlsanity.com/paper/2310.05858/) (2023)
- [DynaNet: Neural Kalman Dynamical Model for Motion Estimation and Prediction](https://mlsanity.com/paper/1908.03918/) (2019)
- [Expectation-Maximization for Adaptive Mixture Models in Graph Optimization](https://mlsanity.com/paper/1811.04748/) (2018)

## Abstract (arXiv)

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.