Optimal nudging in particle filters

N. Lingala, N. Sri Namachchivaya, N. Perkowski, H. C. Yeong

Research output: Contribution to journalConference articlepeer-review

Abstract

We present an efficient particle filtering algorithm for multi-scale systems, that is adapted for dynamical systems which are inherently chaotic. We discuss the recent homogenization method developed by the authors that provides a Stochastic Partial Differential Equation (SPDE) for the evolution of the distribution of the coarse-grained variables given the observations. Particle methods are used for approximating the solution to the SPDE. Importance sampling and control methods are then used as a basic and flexible tool for the construction of the proposal density inherent in particle filtering. We superimpose a control on the particle dynamics which drives the particles to locations most representative of the observations. The control is chosen as the one which minimizes certain cost functional that penalizes the particles that are far away from the observations. The measure change, needed to compensate for the addition of control in the "prognostic" equations, corresponds to that involved in optimal importance sampling.

Original languageEnglish (US)
Pages (from-to)18-30
Number of pages13
JournalProcedia IUTAM
Volume6
DOIs
StatePublished - 2013
EventIUTAM Symposium on Multiscale Problems in Stochastic Mechanics 2012 - Karlsruhe, Germany
Duration: Jun 25 2012Jun 28 2012

Keywords

  • Homogenization
  • Importance sampling
  • Multi-scale dynamics
  • Optimal control
  • Particle filter
  • Zakai equation

ASJC Scopus subject areas

  • Mechanical Engineering

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