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A sequential importance sampling filter with a new proposal distribution for state and parameter estimation of nonlinear dynamical systems

Ghosh, Shuva J and Manohar, CS and Roy, D (2008) A sequential importance sampling filter with a new proposal distribution for state and parameter estimation of nonlinear dynamical systems. In: Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences, 464 (2089). pp. 25-47.

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Abstract

The problem of estimating parameters of nonlinear dynamical systems based on incomplete noisy measurements is considered within the framework of Bayesian filtering using Monte Carlo simulations. The measurement noise and unmodelled dynamics are represented through additive and/or multiplicative Gaussian white noise processes. Truncated Ito–Taylor expansions are used to discretize these equations leading to discrete maps containing a set of multiple stochastic integrals. These integrals, in general, constitute a set of non-Gaussian random variables. The system parameters to be determined are declared as additional state variables. The parameter identification problem is solved through a new sequential importance sampling filter. This involves Ito–Taylor expansions of nonlinear terms in the measurement equation and the development of an ideal proposal density function while accounting for the non-Gaussian terms appearing in the governing equations. Numerical illustrations on parameter identification of a few nonlinear oscillators and a geometrically nonlinear Euler–Bernoulli beam reveal a remarkably improved performance of the proposed methods over one of the best known algorithms, i.e. the unscented particle filter.

Item Type: Journal Article
Additional Information: Copyright of this article belongs to Royal Society.
Keywords: dynamic state estimation;particle filter;structural system identification;stochastic Taylor expansion.
Department/Centre: Division of Mechanical Sciences > Civil Engineering
Date Deposited: 05 Jun 2008
Last Modified: 27 Aug 2008 13:25
URI: http://eprints.iisc.ernet.in/id/eprint/14199

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