# Error Analysis for the Particle Filter: Methods and Theoretical Support

## TL;DR

This paper analyzes the error behavior of particle filters in nonlinear, non-Gaussian settings, providing theoretical insights and empirical validation of asymptotic normality with frequent resampling.

## Contribution

It offers a decomposition of particle filter error and proves asymptotic normality under continuous resampling, supported by practical examples.

## Key findings

- Error decomposes into two terms with asymptotic normality.
- Frequent resampling ensures the estimator's distribution converges to normal.
- Empirical examples confirm theoretical predictions.

## Abstract

The particle filter is a popular Bayesian filtering algorithm for use in cases where the state-space model is nonlinear and/or the random terms (initial state or noises) are non-Gaussian distributed. We study the behavior of the error in the particle filter algorithm as the number of particles gets large. After a decomposition of the error into two terms, we show that the difference between the estimator and the conditional mean is asymptotically normal when the resampling is done at every step in the filtering process. Two nonlinear/non-Gaussian examples are tested to verify this conclusion.