Relative entropy and error bounds for filtering of Markov processes
type: Item
instance of: scholarly article
title: Relative entropy and error bounds for filtering of Markov processes
zbMATH Open document ID: 0940.93072
DOI: 10.1007/PL00009856
author: J. M. C. Clark
author: C. Coumarbatch
author: Daniel L. Ocone
published in: MCSS. Mathematics of Control, Signals, and Systems
publication date: 2000-03-30T00:00:00Z
review text: The paper considers the general problem of nonlinear filtering for the unobserved components of a Markov process in terms of the observable ones. It studies the sensitivity of the solution to errors arising through incorrect initialization of the filter. This is done using relative entropy as a measure of the discrepancy between the optimal and incorrect filters. A particular decomposition of the relative entropy allows to show that it is a positive supermartingale and as a consequence filters are stable (in the sense of average relative entropy) against erroneous initializations. Finally, for signals observed in additive white noise, it is shown that the incorrectly initialized estimate of the observation function is asymptotically optimal in the infinite time limit.
Mathematics Subject Classification ID: 93E11
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 93E15
Mathematics Subject Classification ID: 93B35
zbMATH DE Number: 1389246
zbMATH Keywords: nonlinear filtering
zbMATH Keywords: relative entropy
zbMATH Keywords: filtering error bounds
zbMATH Keywords: incorrectly initialized filters
zbMATH Keywords: filter stability
zbMATH Keywords: incorrect initialization
zbMATH Keywords: sensitivity
reviewed by: Giovanni Di Masi
MaRDI profile type: Publication
full work available at URL: pl00009856
OpenAlex ID: W2027573726
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description: scientific article; zbMATH DE number 1389246