A novel filtering framework through Girsanov correction for the identification of nonlinear dynamical systems

Raveendran, Tara and Sarkar, Saikat and Roy, D and Vasu, RM (2013) A novel filtering framework through Girsanov correction for the identification of nonlinear dynamical systems. In: Inverse Problems, 29 (6). 065002_1-065002_21.

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Abstract

Using a Girsanov change of measures, we propose novel variations within a particle-filtering algorithm, as applied to the inverse problem of state and parameter estimations of nonlinear dynamical systems of engineering interest, toward weakly correcting for the linearization or integration errors that almost invariably occur whilst numerically propagating the process dynamics, typically governed by nonlinear stochastic differential equations (SDEs). Specifically, the correction for linearization, provided by the likelihood or the Radon-Nikodym derivative, is incorporated within the evolving flow in two steps. Once the likelihood, an exponential martingale, is split into a product of two factors, correction owing to the first factor is implemented via rejection sampling in the first step. The second factor, which is directly computable, is accounted for via two different schemes, one employing resampling and the other using a gain-weighted innovation term added to the drift field of the process dynamics thereby overcoming the problem of sample dispersion posed by resampling. The proposed strategies, employed as add-ons to existing particle filters, the bootstrap and auxiliary SIR filters in this work, are found to non-trivially improve the convergence and accuracy of the estimates and also yield reduced mean square errors of such estimates vis-a-vis those obtained through the parent-filtering schemes.

Item Type:	Journal Article
Publication:	Inverse Problems
Publisher:	IOP Publishing Ltd
Additional Information:	Copyright of this article belongs to IOP Publishing Ltd.
Department/Centre:	Division of Mechanical Sciences > Civil Engineering Division of Physical & Mathematical Sciences > Instrumentation Appiled Physics
Date Deposited:	19 Jul 2013 07:20
Last Modified:	19 Jul 2013 07:20
URI:	http://eprints.iisc.ac.in/id/eprint/46856

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