# Analytic solution of the exact Daum-Huang flow equation for particle filters

arXiv: https://arxiv.org/abs/2209.00089 · HTML: https://mlsanity.com/paper/2209.00089/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Aug 2022.

## Built on by (most cited first, 1 of 1)

- [Physics-informed neural particle flow for the Bayesian update step](https://mlsanity.com/paper/2602.23089/) (2026)

## Abstract (arXiv)

State estimation for nonlinear systems, especially in high dimensions, is a generally intractable problem, despite the ever-increasing computing power. Efficient algorithms usually apply a finite-dimensional model for approximating the probability density of the state vector or treat the estimation problem numerically. In 2007 Daum and Huang introduced a novel particle filter approach that uses a homotopy-induced particle flow for the Bayesian update step. Multiple types of particle flows were derived since with different properties. The exact flow considered in this work is a first-order linear ordinary time-varying inhomogeneous differential equation for the particle motion. An analytic solution in the interval [0,1] is derived for the scalar measurement case, which enables significantly faster computation of the Bayesian update step for particle filters.