A homogenization approach to multiscale filtering

Peter Imkeller, N. Sri Namachchivaya, Nicolas Perkowski, Hoong C. Yeong

Research output: Contribution to journalConference articlepeer-review

Abstract

We present a homogenized nonlinear filter for multi-timescale systems, which allows the reduction of the dimension of filtering equation. We prove that the actual nonlinear filter converges to our homogenized filter. This is achieved by a suitable asymptotic expansion of the dual of the Zakai equation, and probabilistically representing the correction terms with the help of backward doubly-stochastic differential equations. This homogenized filter provides a rigorous mathematical basis for the development of reduced-dimension nonlinear filters for multiscale systems. A filtering scheme, based on the homogenized filtering equation and the technique of importance sampling, is applied to a chaotic multiscale system in Lingala et al. [1].

Original languageEnglish (US)
Pages (from-to)34-45
Number of pages12
JournalProcedia IUTAM
Volume5
DOIs
StatePublished - 2012
EventIUTAM Symposium on 50 Years of Chaos: Applied and Theoretical - Kyoto, Japan
Duration: Nov 28 2011Dec 2 2011

Keywords

  • Asymptotic expansion
  • BDSDE
  • Dimensional reduction
  • Homogenization
  • Nonlinear filtering
  • Particle filter
  • SPDE

ASJC Scopus subject areas

  • Mechanical Engineering

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