# A critical analysis of resampling strategies for the regularized particle filter

## TL;DR

This paper critically examines resampling strategies in regularized particle filters, revealing that resampling can hinder convergence and proposing methods like kernel bandwidth modulation to improve performance, supported by numerical experiments.

## Contribution

It provides a detailed analysis of resampling effects in regularized particle filters and introduces techniques to mitigate convergence issues, outperforming traditional bootstrap methods.

## Key findings

- Resampling can prevent convergence to the true posterior.
- Kernel bandwidth modulation improves filter performance.
- Regularized particle filters outperform bootstrap filters with proposed methods.

## Abstract

We analyze the performance of different resampling strategies for the regularized particle filter regarding parameter estimation. We show in particular, building on analytical insight obtained in the linear Gaussian case, that resampling systematically can prevent the filtered density from converging towards the true posterior distribution. We discuss several means to overcome this limitation, including kernel bandwidth modulation, and provide evidence that the resulting particle filter clearly outperforms traditional bootstrap particle filters. Our results are supported by numerical simulations on a linear textbook example, the logistic map and a non-linear plant growth model.