Kernel density estimates in particle filter

0442499 - ÚI 2015 US eng V - Výzkumná zpráva
Coufal, David
Kernel density estimates in particle filter.
Cornell University, 2015. 37 s. arXiv.org e-Print archive, arXiv:1402.3466 [stat.CO].
Grant CEP: GA MŠMT(CZ) LD13002
Institucionální podpora: RVO:67985807
Klíčová slova: particle filter * kernel methods * Fourier transform
Kód oboru RIV: BB - Aplikovaná statistika, operační výzkum
http://arxiv.org/abs/1402.3466

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 char- acter over time. Both results are extended to partial derivatives of the estimates and filtering densities.
Trvalý link: http://hdl.handle.net/11104/0245307