# An optimal control approach to particle filtering

arXiv: https://arxiv.org/abs/2110.03199 · HTML: https://mlsanity.com/paper/2110.03199/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Oct 2021.

## Built on by (most cited first, 4 of 4)

- [SURGE: Approximation and Training Free Particle Filter for Diffusion Surrogate](https://mlsanity.com/paper/2605.18745/) (2026)
- [Myopically Verifiable Probabilistic Certificates for Safe Control and Learning](https://mlsanity.com/paper/2404.16883/) (2024)
- [Safe Beyond the Horizon: Efficient Sampling-based MPC with Neural Control Barrier Functions](https://mlsanity.com/paper/2502.15006/) (2025)
- [Pathwise Learning of Stochastic Dynamical Systems with Partial Observations](https://mlsanity.com/paper/2601.21860/) (2026)

## Abstract (arXiv)

We present a novel particle filtering framework for continuous-time dynamical systems with continuous-time measurements. Our approach is based on the duality between estimation and optimal control, which allows reformulating the estimation problem over a fixed time window into an optimal control problem. The resulting optimal control problem has a cost function that depends on the measurements and the closed-loop dynamics under optimal control coincides with the posterior distribution over the trajectories for the corresponding estimation problem. This type of stochastic optimal control problem can be solved using a remarkable technique known as path integral control. By recursively solving these optimal control problems using path integral control as new measurements become available we obtain an optimal control-based particle filtering algorithm. A distinguishing feature of the proposed method is that it uses the measurements over a finite-length time window instead of a single measurement for the estimation at each time step, resembling the batch methods of filtering, and improving fault tolerance. The efficacy of our algorithm is illustrated with several numerical examples.