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Derivation and analysis of simplified filters

Lee, Wongjung and Stuart, Andrew (2017) Derivation and analysis of simplified filters. Communications in Mathematical Sciences, 15 (2). pp. 413-450. ISSN 1539-6746. doi:10.4310/CMS.2017.v15.n2.a6.

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Filtering is concerned with the sequential estimation of the state, and uncertainties, of a Markovian system, given noisy observations. It is particularly difficult to achieve accurate filtering in complex dynamical systems, such as those arising in turbulence, in which effective low-dimensional representation of the desired probability distribution is challenging. Nonetheless recent advances have shown considerable success in filtering based on certain carefully chosen simplifications of the underlying system, which allow closed form filters. This leads to filtering algorithms with significant, but judiciously chosen, model error. The purpose of this article is to analyze the effectiveness of these simplified filters, and to suggest modifications of them which lead to improved filtering in certain time-scale regimes. We employ a Markov switching process for the true signal underlying the data, rather than working with a fully resolved DNS PDE model. Such Markov switching models haven been demonstrated to provide an excellent surrogate test-bed for the turbulent bursting phenomena which make filtering of complex physical models, such as those arising in atmospheric sciences, so challenging.

Item Type:Article
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URLURL TypeDescription Paper
Alternate Title:Derivation and Analysis of Simplified Filters for Complex Dynamical Systems
Additional Information:© 2017 International Press. Received: December 15, 2015; accepted (in revised form): June 11, 2016. Communicated by Arnulf Jentzen. Both authors are supported by the ERC-AMSTAT grant No. 226488. AMS is also supported by EPSRC and ONR.
Funding AgencyGrant Number
European Research Council (ERC)226488
Engineering and Physical Sciences Research Council (EPSRC)UNSPECIFIED
Office of Naval Research (ONR)UNSPECIFIED
Subject Keywords:Bayesian statistics, sequential data assimilation, filtering with model error
Other Numbering System:
Other Numbering System NameOther Numbering System ID
Andrew StuartJ128
Issue or Number:2
Classification Code:AMS subject classifications. 60G35, 93E11, 94A12
Record Number:CaltechAUTHORS:20161221-112623998
Persistent URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:73077
Deposited By: Linda Taddeo
Deposited On:21 Dec 2016 20:48
Last Modified:11 Nov 2021 05:11

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