Filtering a nonlinear slow-fast system with strong fast forcing
type: Item
instance of: scholarly article
title: Filtering a nonlinear slow-fast system with strong fast forcing
zbMATH Open document ID: 1202.62128
author: B. Gershgorin
author: Andrew J. Majda
published in: Communications in Mathematical Sciences
publication date: 2010-05-28T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.cms/1266935014
review text: The authors study the problem of the filtering of atmospheric signals with multiple time scales. They start by introducing the nonlinear multiple time test model with fast forcing (a model introduced first by the same authors in 2008) and give more interesting motivations and concrete application for this model. They study the exact solutions and exactly solvable statistics giving a way to find an analytic solution, extending some results given by \textit{R. Kubo} [J. Math. Phys. 4, 174--183 (1963; Zbl 0135.45102)] and \textit{A.J. Majda} et al [Proc. Natl. Acad. Sci. USA 96, No.26, 14687--14691 (1999; Zbl 0966.86003)]. They also present some more numerical examples. We have to remark, that the authors pointed out the non-Gaussianity of the statistics of the fast mode. In the next part, they introduced two adequate filters: the exact Nonlinear Extended Kalman Filter (NEKF) and the linear Kalman Filter (KF) with model errors for the slow-fast system with fast forcing (both filters are based on the classical Kalman filter. They compare the performance of both filters under various filtering parameters. An important result of this study presents their discovering that for the observation time and observation variance larger than certain values and all three types of observations, the linear KF with model errors performs surprisingly better than the exact NEKF on the slowly varying amplitude of the fast mode.
reviewed by: Romeo Negrea
Mathematics Subject Classification ID: 62M20
Mathematics Subject Classification ID: 86A10
Mathematics Subject Classification ID: 93E11
zbMATH DE Number: 5713682
zbMATH Keywords: nonlinear model
zbMATH Keywords: extended Kalman filter
MaRDI profile type: Publication
OpenAlex ID: W2092546785
DOI: 10.4310/CMS.2010.V8.N1.A5
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description: scientific article; zbMATH DE number 5713682