On Convergence of Kernel Density Estimates in Particle Filtering

0469752 - ÚI 2017 RIV CZ eng J - Journal Article
Coufal, David
On Convergence of Kernel Density Estimates in Particle Filtering.
Kybernetika. Roč. 52, č. 5 (2016), s. 735-756. ISSN 0023-5954
Grant - others: GA ČR(CZ) GA16-03708S; SVV(CZ) 260334/2016
Institutional support: RVO:67985807
Keywords : Fourier analysis * kernel methods * particle filter
Subject RIV: BB - Applied Statistics, Operational Research
Impact factor: 0.379, year: 2016

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. An upper bound on the convergence rate is given. The result is provided 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.
Permanent Link: http://hdl.handle.net/11104/0267550