A Girsanov particle filter in nonlinear engineering dynamics

Saha, Nilanjan and Roy, D (2009) A Girsanov particle filter in nonlinear engineering dynamics. In: Physics Letters A, 373 (6). pp. 627-635.

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Abstract

In this Letter, we propose a novel variant of the particle filter (PF) for state and parameter estimations of nonlinear engineering dynamical systems, modelled through stochastic differential equations (SDEs). The aim is to address a possible loss of accuracy in the estimates due to the discretization errors, which are inevitable during numerical integration of the SDEs. In particular, we adopt an explicit local linearization of the governing nonlinear SDEs and the resulting linearization errors in the estimates are corrected using Girsanovtransformation of measures. Indeed, the linearization scheme via transformation of measures provides a weak framework for computing moments and this fits in well with any stochastic filtering strategy wherein estimates are themselves statistical moments. We presently implement the strategy using a bootstrap PF and numerically illustrate its performance for state and parameter estimations of the Duffing oscillator with linear and nonlinear measurement equations.

Item Type:	Journal Article
Publication:	Physics Letters A
Publisher:	Elsevier Science
Additional Information:	Copyright of this article belongs to Elsevier Science.
Keywords:	Stochastic filtering;Local linearization;Girsanov transformation;State and parameter estimations;Weak Monte Carlo simulations.
Department/Centre:	Division of Mechanical Sciences > Civil Engineering
Date Deposited:	23 Jul 2009 04:55
Last Modified:	19 Sep 2010 05:27
URI:	http://eprints.iisc.ac.in/id/eprint/19168

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