On Persistence of Convergence of Kernel Density Estimates in Particle Filtering

Abstract

A sufficient condition is provided for keeping the character of the filtering density in the filtering task. This is done for the Sobolev class of filtering densities.

As a consequence, estimating the filtering density in particle filtering persists its convergence at any time of filtering. Specifying the condition complements previous results on using the kernel density estimates in particle filtering.

Keywords

• Particle filtering
• Kernel density estimates
• Convergence