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October 2015 Can local particle filters beat the curse of dimensionality?
Patrick Rebeschini, Ramon van Handel
Ann. Appl. Probab. 25(5): 2809-2866 (October 2015). DOI: 10.1214/14-AAP1061

Abstract

The discovery of particle filtering methods has enabled the use of nonlinear filtering in a wide array of applications. Unfortunately, the approximation error of particle filters typically grows exponentially in the dimension of the underlying model. This phenomenon has rendered particle filters of limited use in complex data assimilation problems. In this paper, we argue that it is often possible, at least in principle, to develop local particle filtering algorithms whose approximation error is dimension-free. The key to such developments is the decay of correlations property, which is a spatial counterpart of the much better understood stability property of nonlinear filters. For the simplest possible algorithm of this type, our results provide under suitable assumptions an approximation error bound that is uniform both in time and in the model dimension. More broadly, our results provide a framework for the investigation of filtering problems and algorithms in high dimension.

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Patrick Rebeschini. Ramon van Handel. "Can local particle filters beat the curse of dimensionality?." Ann. Appl. Probab. 25 (5) 2809 - 2866, October 2015. https://doi.org/10.1214/14-AAP1061

Information

Received: 1 March 2013; Revised: 1 May 2014; Published: October 2015
First available in Project Euclid: 30 July 2015

zbMATH: 1325.60058
MathSciNet: MR3375889
Digital Object Identifier: 10.1214/14-AAP1061

Subjects:
Primary: 60G35 , 60K35 , 62M20 , 65C05 , 68Q87

Keywords: curse of dimensionality , data assimilation , decay of correlations , filter stability , Filtering in high dimension , interacting Markov chains , local particle filters

Rights: Copyright © 2015 Institute of Mathematical Statistics

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Vol.25 • No. 5 • October 2015
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