Robust Ensemble Filtering and Its Relation to Covariance Inflation in the Ensemble Kalman Filter

Handle URI:
http://hdl.handle.net/10754/552781
Title:
Robust Ensemble Filtering and Its Relation to Covariance Inflation in the Ensemble Kalman Filter
Authors:
Luo, Xiaodong; Hoteit, Ibrahim ( 0000-0002-3751-4393 )
Abstract:
A robust ensemble filtering scheme based on the H∞ filtering theory is proposed. The optimal H∞ filter is derived by minimizing the supremum (or maximum) of a predefined cost function, a criterion different from the minimum variance used in the Kalman filter. By design, the H∞ filter is more robust than the Kalman filter, in the sense that the estimation error in the H∞ filter in general has a finite growth rate with respect to the uncertainties in assimilation, except for a special case that corresponds to the Kalman filter. The original form of the H∞ filter contains global constraints in time, which may be inconvenient for sequential data assimilation problems. Therefore a variant is introduced that solves some time-local constraints instead, and hence it is called the time-local H∞ filter (TLHF). By analogy to the ensemble Kalman filter (EnKF), the concept of ensemble time-local H∞ filter (EnTLHF) is also proposed. The general form of the EnTLHF is outlined, and some of its special cases are discussed. In particular, it is shown that an EnKF with certain covariance inflation is essentially an EnTLHF. In this sense, the EnTLHF provides a general framework for conducting covariance inflation in the EnKF-based methods. Some numerical examples are used to assess the relative robustness of the TLHF–EnTLHF in comparison with the corresponding KF–EnKF method.
KAUST Department:
Physical Sciences and Engineering (PSE) Division
Citation:
Robust Ensemble Filtering and Its Relation to Covariance Inflation in the Ensemble Kalman Filter 2011, 139 (12):3938 Monthly Weather Review
Journal:
Monthly Weather Review
Issue Date:
Dec-2011
DOI:
10.1175/MWR-D-10-05068.1
ARXIV:
arXiv:1108.0158
Type:
Article
ISSN:
0027-0644; 1520-0493
Additional Links:
http://journals.ametsoc.org/doi/abs/10.1175/MWR-D-10-05068.1; http://arxiv.org/abs/1108.0158
Appears in Collections:
Articles; Physical Sciences and Engineering (PSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorLuo, Xiaodongen
dc.contributor.authorHoteit, Ibrahimen
dc.date.accessioned2015-05-14T07:09:52Zen
dc.date.available2015-05-14T07:09:52Zen
dc.date.issued2011-12en
dc.identifier.citationRobust Ensemble Filtering and Its Relation to Covariance Inflation in the Ensemble Kalman Filter 2011, 139 (12):3938 Monthly Weather Reviewen
dc.identifier.issn0027-0644en
dc.identifier.issn1520-0493en
dc.identifier.doi10.1175/MWR-D-10-05068.1en
dc.identifier.urihttp://hdl.handle.net/10754/552781en
dc.description.abstractA robust ensemble filtering scheme based on the H∞ filtering theory is proposed. The optimal H∞ filter is derived by minimizing the supremum (or maximum) of a predefined cost function, a criterion different from the minimum variance used in the Kalman filter. By design, the H∞ filter is more robust than the Kalman filter, in the sense that the estimation error in the H∞ filter in general has a finite growth rate with respect to the uncertainties in assimilation, except for a special case that corresponds to the Kalman filter. The original form of the H∞ filter contains global constraints in time, which may be inconvenient for sequential data assimilation problems. Therefore a variant is introduced that solves some time-local constraints instead, and hence it is called the time-local H∞ filter (TLHF). By analogy to the ensemble Kalman filter (EnKF), the concept of ensemble time-local H∞ filter (EnTLHF) is also proposed. The general form of the EnTLHF is outlined, and some of its special cases are discussed. In particular, it is shown that an EnKF with certain covariance inflation is essentially an EnTLHF. In this sense, the EnTLHF provides a general framework for conducting covariance inflation in the EnKF-based methods. Some numerical examples are used to assess the relative robustness of the TLHF–EnTLHF in comparison with the corresponding KF–EnKF method.en
dc.relation.urlhttp://journals.ametsoc.org/doi/abs/10.1175/MWR-D-10-05068.1en
dc.relation.urlhttp://arxiv.org/abs/1108.0158en
dc.rights© Copyright 2011 American Meteorological Society (AMS). Permission to use figures, tables, and brief excerpts from this work in scientific and educational works is hereby granted provided that the source is acknowledged. Any use of material in this work that is determined to be “fair use” under Section 107 of the U.S. Copyright Act September 2010 Page 2 or that satisfies the conditions specified in Section 108 of the U.S. Copyright Act (17 USC §108, as revised by P.L. 94-553) does not require the AMS’s permission. Republication, systematic reproduction, posting in electronic form, such as on a web site or in a searchable database, or other uses of this material, except as exempted by the above statement, requires written permission or a license from the AMS. Additional details are provided in the AMS Copyright Policy, available on the AMS Web site located at (http://www.ametsoc.org/) or from the AMS at 617-227-2425 or copyrights@ametsoc.org.en
dc.subjectFiltering techniquesen
dc.subjectKalman filtersen
dc.subjectEnsemblesen
dc.titleRobust Ensemble Filtering and Its Relation to Covariance Inflation in the Ensemble Kalman Filteren
dc.typeArticleen
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.identifier.journalMonthly Weather Reviewen
dc.eprint.versionPublisher's Version/PDFen
dc.identifier.arxividarXiv:1108.0158en
kaust.authorLuo, Xiaodongen
kaust.authorHoteit, Ibrahimen
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