Kernel density estimates in particle filter
Computation
2014-07-29 v2
Abstract
The paper deals with kernel density estimates of filtering densities in the particle filter. The convergence of the estimates is investigated by means of Fourier analysis. It is shown that the estimates converge to the theoretical filtering densities in the mean integrated squared error under a certain assumption on the Sobolev character of the filtering densities. A sufficient condition is presented for the persistence of this Sobolev character over time. Both results are extended to partial derivatives of the estimates and filtering densities.
Cite
@article{arxiv.1402.3466,
title = {Kernel density estimates in particle filter},
author = {David Coufal},
journal= {arXiv preprint arXiv:1402.3466},
year = {2014}
}
Comments
Substantially revised version. The extension of results to partial derivatives has been provided