Geodesic
On convergence of kernel density estimates in particle filtering
Kybernetika, Tome 52 (2016) no. 5, pp. 735-756 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.14736/kyb-2016-5-0735
Classification : 65C35
Keywords: particle filter; kernel methods; Fourier analysis 
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Coufal, David. On convergence of kernel density estimates in particle filtering. Kybernetika, Tome 52 (2016) no. 5, pp. 735-756. doi: 10.14736/kyb-2016-5-0735

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