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Analysis of the 3DVAR filter for the partially observed Lorenz'63 model

Law, Kody and Shukla, Abishek and Stuart, Andrew (2014) Analysis of the 3DVAR filter for the partially observed Lorenz'63 model. Discrete and Continuous Dynamical Systems A, 34 (3). pp. 1061-1078. ISSN 1553-5231. doi:10.3934/dcds.2014.34.1061.

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The problem of effectively combining data with a mathematical model constitutes a major challenge in applied mathematics. It is particular challenging for high-dimensional dynamical systems where data is received sequentially in time and the objective is to estimate the system state in an on-line fashion; this situation arises, for example, in weather forecasting. The sequential particle filter is then impractical and ad hoc filters, which employ some form of Gaussian approximation, are widely used. Prototypical of these ad hoc filters is the 3DVAR method. The goal of this paper is to analyze the 3DVAR method, using the Lorenz '63 model to exemplify the key ideas. The situation where the data is partial and noisy is studied, and both discrete time and continuous time data streams are considered. The theory demonstrates how the widely used technique of variance inflation acts to stabilize the filter, and hence leads to asymptotic accuracy.

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Additional Information:© 2014 American Institute of Mathematical Sciences. Received December 2012; revised April 2013. KJHL is supported by ESA and ERC. AbS is supported by the EPSRC-MASDOC graduate training scheme. AMS is supported by ERC, EPSRC, ESA and ONR. The authors are grateful to Daniel Sanz, Mike Scott and Kostas Zygalakis for helpful comments on earlier versions of the manuscript. AMS is grateful to Arieh Iserles for his inspirational research at the interface of Dynamical Systems and Numerical Analysis.
Funding AgencyGrant Number
European Space Agency (ESA)UNSPECIFIED
European Research Council (ERC)UNSPECIFIED
Engineering and Physical Sciences Research Council (EPSRC)UNSPECIFIED
Office of Naval Research (ONR)UNSPECIFIED
Subject Keywords:Data assimilation, synchronization, stochastic dynamics
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Other Numbering System NameOther Numbering System ID
Andrew StuartJ108
Issue or Number:3
Classification Code:2010 Mathematics Subject Classification. Primary: 34F05, 37H10; Secondary: 60H10.
Record Number:CaltechAUTHORS:20160719-152032603
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:69120
Deposited By: Linda Taddeo
Deposited On:20 Jul 2016 17:30
Last Modified:11 Nov 2021 04:09

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