# Asymptotic Expansion for Nonlinear Filtering in the Small System Noise Regime

arXiv: https://arxiv.org/abs/2509.23920 · HTML: https://mlsanity.com/paper/2509.23920/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 29 references that are in the map.
- First posted on arXiv 28 Sep 2025.

## Builds on (most cited first, 1 of 1)

- [A New Proof for the Linear Filtering and Smoothing Equations, and Asymptotic Expansion of Nonlinear Filtering](https://mlsanity.com/paper/2501.16333/) (2024)

## Abstract (arXiv)

We propose a new asymptotic expansion method for nonlinear filtering, based on a small parameter in the system noise. The conditional expectation is expanded as a power series in the noise level, with each coefficient computed by solving a system of ordinary differential equations. This approach mitigates the trade-off between computational efficiency and accuracy inherent in existing methods such as Gaussian approximations and particle filters. Moreover, by incorporating an Edgeworth-type expansion, our method captures complex features of the conditional distribution, such as multimodality, with significantly lower computational cost than conventional filtering algorithms.