Can local particle filters beat the curse of dimensionality?

Patrick Rebeschini, Ramon Van Handel

Research output: Contribution to journalArticle

70 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)2809-2866
Number of pages58
JournalAnnals of Applied Probability
Volume25
Issue number5
DOIs
StatePublished - Oct 1 2015

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • Curse of dimensionality
  • Data assimilation
  • Decay of correlations
  • Filter stability
  • Filtering in high dimension
  • Interacting Markov chains
  • Local particle filters

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