Extended Kalman filters using explicit and derivative-free local linearizations

Saha, Nilanjan and Roy, D (2009) Extended Kalman filters using explicit and derivative-free local linearizations. In: Applied Mathematical Modelling, 33 (6). pp. 2545-2563.

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Abstract

We propose three variants of the extended Kalman filter (EKF) especially suited for parameter estimations in mechanical oscillators under Gaussian white noises. These filters are based on three versions of explicit and derivative-free local linearizations (DLL) of the non-linear drift terms in the governing stochastic differential equations (SDE-s). Besides a basic linearization of the non-linear drift functions via one-term replacements, linearizations using replacements through explicit Euler and Newmark expansions are also attempted in order to ensure higher closeness of true solutions with the linearized ones. Thus, unlike the conventional EKF, the proposed filters do not need computing derivatives (tangent matrices) at any stage. The measurements are synthetically generated by corrupting with noise the numerical solutions of the SDE-s through implicit versions of these linearizations. In order to demonstrate the effectiveness and accuracy of the proposed methods vis-à-vis the conventional EKF, numerical illustrations are provided for a few single degree-of-freedom (DOF) oscillators and a three-DOF shear frame with constant parameters.

Item Type:	Journal Article
Publication:	Applied Mathematical Modelling
Publisher:	Elsevier Science
Additional Information:	Copyright of this article belongs to Elsevier Science.
Keywords:	Extended Kalman filters;Explicit and derivative-free local linearizations;State and parameter estimations.
Department/Centre:	Division of Mechanical Sciences > Civil Engineering
Date Deposited:	19 Jul 2009 07:05
Last Modified:	19 Sep 2010 05:30
URI:	http://eprints.iisc.ac.in/id/eprint/19753

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