On convergence of kernel density estimates in particle filtering

David Coufal

Kybernetika (2016)

  • Volume: 52, Issue: 5, page 735-756
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Coufal, David. "On convergence of kernel density estimates in particle filtering." Kybernetika 52.5 (2016): 735-756. <http://eudml.org/doc/287524>.

@article{Coufal2016,
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. 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.},
author = {Coufal, David},
journal = {Kybernetika},
keywords = {particle filter; kernel methods; Fourier analysis; particle filter; kernel methods; Fourier analysis},
language = {eng},
number = {5},
pages = {735-756},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On convergence of kernel density estimates in particle filtering},
url = {http://eudml.org/doc/287524},
volume = {52},
year = {2016},
}

TY - JOUR
AU - Coufal, David
TI - On convergence of kernel density estimates in particle filtering
JO - Kybernetika
PY - 2016
PB - Institute of Information Theory and Automation AS CR
VL - 52
IS - 5
SP - 735
EP - 756
AB - 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.
LA - eng
KW - particle filter; kernel methods; Fourier analysis; particle filter; kernel methods; Fourier analysis
UR - http://eudml.org/doc/287524
ER -

References

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