Open Access
Translator Disclaimer
February 2004 Stability and uniform approximation of nonlinear filters using the Hilbert metric and application to particle filters
François Le Gland, Nadia Oudjane
Ann. Appl. Probab. 14(1): 144-187 (February 2004). DOI: 10.1214/aoap/1075828050

Abstract

We study the stability of the optimal filter w.r.t. its initial condition and w.r.t. the model for the hidden state and the observations in a general hidden Markov model, using the Hilbert projective metric. These stability results are then used to prove, under some mixing assumption, the uniform convergence to the optimal filter of several particle filters, such as the interacting particle filter and some other original particle filters.

Citation

Download Citation

François Le Gland. Nadia Oudjane. "Stability and uniform approximation of nonlinear filters using the Hilbert metric and application to particle filters." Ann. Appl. Probab. 14 (1) 144 - 187, February 2004. https://doi.org/10.1214/aoap/1075828050

Information

Published: February 2004
First available in Project Euclid: 3 February 2004

zbMATH: 1060.93094
MathSciNet: MR2023019
Digital Object Identifier: 10.1214/aoap/1075828050

Subjects:
Primary: 62E25 , 93E11 , 93E15
Secondary: 60B10 , 60J27 , 62G07 , 62G09 , 62L10

Keywords: Hidden Markov model , Hilbert metric , Mixing , nonlinear filter , particle filter , regularizing kernel , stability , total variation norm

Rights: Copyright © 2004 Institute of Mathematical Statistics

JOURNAL ARTICLE
44 PAGES


SHARE
Vol.14 • No. 1 • February 2004
Back to Top