# Optimal Transportation Methods in Nonlinear Filtering: The feedback particle filter

arXiv: https://arxiv.org/abs/2102.10712 · HTML: https://mlsanity.com/paper/2102.10712/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Feb 2021.

## Built on by (most cited first, 5 of 5)

- [An Optimal Transport Formulation of Bayes' Law for Nonlinear Filtering Algorithms](https://mlsanity.com/paper/2203.11869/) (2022)
- [Closed-form conditional diffusion models for data assimilation](https://mlsanity.com/paper/2603.21291/) (2026)
- [Conditional Sampling via Wasserstein Autoencoders and Triangular Transport](https://mlsanity.com/paper/2604.02644/) (2026)
- [Functional role of synchronization: A mean-field control perspective](https://mlsanity.com/paper/2502.00590/) (2025)
- [Conditional Normalizing Flows for Forward and Backward Joint State and Parameter Estimation](https://mlsanity.com/paper/2601.07013/) (2026)

## Abstract (arXiv)

Feedback particle filter (FPF) is a Monte-Carlo (MC) algorithm to approximate the solution of a stochastic filtering problem. In contrast to conventional particle filters, the Bayesian update step in FPF is implemented via a mean-field type feedback control law. The objective for this paper is to situate the development of FPF and related controlled interacting particle system algorithms within the framework of optimal transportation theory. Starting from the simplest setting of the Bayes' update formula, a coupling viewpoint is introduced to construct particle filters. It is shown that the conventional importance sampling resampling particle filter implements an independent coupling. Design of optimal couplings is introduced first for the simple Gaussian settings and subsequently extended to derive the FPF algorithm. The final half of the paper provides a review of some of the salient aspects of the FPF algorithm including the feedback structure, algorithms for gain function design, and comparison with conventional particle filters. The comparison serves to illustrate the benefit of feedback in particle filtering.