The Annals of Applied Probability

Can local particle filters beat the curse of dimensionality?

Patrick Rebeschini and Ramon van Handel

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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.

Article information

Source
Ann. Appl. Probab. Volume 25, Number 5 (2015), 2809-2866.

Dates
Received: March 2013
Revised: May 2014
First available in Project Euclid: 30 July 2015

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1438261054

Digital Object Identifier
doi:10.1214/14-AAP1061

Mathematical Reviews number (MathSciNet)
MR3375889

Zentralblatt MATH identifier
1325.60058

Subjects
Primary: 60G35: Signal detection and filtering [See also 62M20, 93E10, 93E11, 94Axx] 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 62M20: Prediction [See also 60G25]; filtering [See also 60G35, 93E10, 93E11] 65C05: Monte Carlo methods 68Q87: Probability in computer science (algorithm analysis, random structures, phase transitions, etc.) [See also 68W20, 68W40]

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

Citation

Rebeschini, Patrick; van Handel, Ramon. Can local particle filters beat the curse of dimensionality?. Ann. Appl. Probab. 25 (2015), no. 5, 2809--2866. doi:10.1214/14-AAP1061. https://projecteuclid.org/euclid.aoap/1438261054


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