# Optimal Transport Particle Filters

arXiv: https://arxiv.org/abs/2304.00392 · HTML: https://mlsanity.com/paper/2304.00392/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Apr 2023.

## Built on by (most cited first, 7 of 7)

- [Conditional Optimal Transport on Function Spaces](https://mlsanity.com/paper/2311.05672/) (2023)
- [Nonlinear Filtering with Brenier Optimal Transport Maps](https://mlsanity.com/paper/2310.13886/) (2023)
- [Fast filtering of non-Gaussian models using Amortized Optimal Transport Maps](https://mlsanity.com/paper/2503.12633/) (2025)
- [Closed-form conditional diffusion models for data assimilation](https://mlsanity.com/paper/2603.21291/) (2026)
- [Preserving linear invariants in ensemble filtering methods](https://mlsanity.com/paper/2404.14328/) (2024)
- [Conditional Normalizing Flows for Forward and Backward Joint State and Parameter Estimation](https://mlsanity.com/paper/2601.07013/) (2026)
- [Generative models for simulation based filtering: Formulations and Empirical Comparisons](https://mlsanity.com/paper/2609.16317/) (2026)

## Abstract (arXiv)

This paper is concerned with the theoretical and computational development of a new class of nonlinear filtering algorithms called the optimal transport particle filters (OTPF). The algorithm is based on a recently introduced variational formulation of the Bayes' rule, which aims to find the Brenier optimal transport map between the prior and the posterior distributions as the solution to a stochastic optimization problem. On the theoretical side, the existing methods for the error analysis of particle filters and stability results for optimal transport map estimation are combined to obtain uniform error bounds for the filter's performance in terms of the optimization gap in solving the variational problem. The error analysis reveals a bias-variance trade-off that can ultimately be used to understand if/when the curse of dimensionality can be avoided in these filters. On the computational side, the proposed algorithm is evaluated on a nonlinear filtering example in comparison with the ensemble Kalman filter (EnKF) and the sequential importance resampling (SIR) particle filter.