Particle Kalman Filtering: A Nonlinear Bayesian Framework for Ensemble Kalman Filters*

Handle URI:
http://hdl.handle.net/10754/552775
Title:
Particle Kalman Filtering: A Nonlinear Bayesian Framework for Ensemble Kalman Filters*
Authors:
Hoteit, Ibrahim ( 0000-0002-3751-4393 ) ; Luo, Xiaodong; Pham, Dinh-Tuan
Abstract:
This paper investigates an approximation scheme of the optimal nonlinear Bayesian filter based on the Gaussian mixture representation of the state probability distribution function. The resulting filter is similar to the particle filter, but is different from it in that the standard weight-type correction in the particle filter is complemented by the Kalman-type correction with the associated covariance matrices in the Gaussian mixture. The authors show that this filter is an algorithm in between the Kalman filter and the particle filter, and therefore is referred to as the particle Kalman filter (PKF). In the PKF, the solution of a nonlinear filtering problem is expressed as the weighted average of an “ensemble of Kalman filters” operating in parallel. Running an ensemble of Kalman filters is, however, computationally prohibitive for realistic atmospheric and oceanic data assimilation problems. For this reason, the authors consider the construction of the PKF through an “ensemble” of ensemble Kalman filters (EnKFs) instead, and call the implementation the particle EnKF (PEnKF). It is shown that different types of the EnKFs can be considered as special cases of the PEnKF. Similar to the situation in the particle filter, the authors also introduce a resampling step to the PEnKF in order to reduce the risk of weights collapse and improve the performance of the filter. Numerical experiments with the strongly nonlinear Lorenz-96 model are presented and discussed.
KAUST Department:
Physical Sciences and Engineering (PSE) Division
Citation:
Particle Kalman Filtering: A Nonlinear Bayesian Framework for Ensemble Kalman Filters* 2012, 140 (2):528 Monthly Weather Review
Journal:
Monthly Weather Review
Issue Date:
Feb-2012
DOI:
10.1175/2011MWR3640.1
Type:
Article
ISSN:
0027-0644; 1520-0493
Additional Links:
http://journals.ametsoc.org/doi/abs/10.1175/2011MWR3640.1; http://arxiv.org/abs/1108.0168
Appears in Collections:
Articles; Physical Sciences and Engineering (PSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorHoteit, Ibrahimen
dc.contributor.authorLuo, Xiaodongen
dc.contributor.authorPham, Dinh-Tuanen
dc.date.accessioned2015-05-14T07:00:30Zen
dc.date.available2015-05-14T07:00:30Zen
dc.date.issued2012-02en
dc.identifier.citationParticle Kalman Filtering: A Nonlinear Bayesian Framework for Ensemble Kalman Filters* 2012, 140 (2):528 Monthly Weather Reviewen
dc.identifier.issn0027-0644en
dc.identifier.issn1520-0493en
dc.identifier.doi10.1175/2011MWR3640.1en
dc.identifier.urihttp://hdl.handle.net/10754/552775en
dc.description.abstractThis paper investigates an approximation scheme of the optimal nonlinear Bayesian filter based on the Gaussian mixture representation of the state probability distribution function. The resulting filter is similar to the particle filter, but is different from it in that the standard weight-type correction in the particle filter is complemented by the Kalman-type correction with the associated covariance matrices in the Gaussian mixture. The authors show that this filter is an algorithm in between the Kalman filter and the particle filter, and therefore is referred to as the particle Kalman filter (PKF). In the PKF, the solution of a nonlinear filtering problem is expressed as the weighted average of an “ensemble of Kalman filters” operating in parallel. Running an ensemble of Kalman filters is, however, computationally prohibitive for realistic atmospheric and oceanic data assimilation problems. For this reason, the authors consider the construction of the PKF through an “ensemble” of ensemble Kalman filters (EnKFs) instead, and call the implementation the particle EnKF (PEnKF). It is shown that different types of the EnKFs can be considered as special cases of the PEnKF. Similar to the situation in the particle filter, the authors also introduce a resampling step to the PEnKF in order to reduce the risk of weights collapse and improve the performance of the filter. Numerical experiments with the strongly nonlinear Lorenz-96 model are presented and discussed.en
dc.relation.urlhttp://journals.ametsoc.org/doi/abs/10.1175/2011MWR3640.1en
dc.relation.urlhttp://arxiv.org/abs/1108.0168en
dc.rights© Copyright 2012 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.subjectKalman filtersen
dc.subjectBayesian methodsen
dc.subjectData assimilationen
dc.subjectFiltering techniquesen
dc.subjectEnsemblesen
dc.titleParticle Kalman Filtering: A Nonlinear Bayesian Framework for Ensemble Kalman Filters*en
dc.typeArticleen
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.identifier.journalMonthly Weather Reviewen
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.institutionCentre National de la Recherche Scientifique, Grenoble, Franceen
dc.identifier.arxividarXiv:1108.0168en
kaust.authorHoteit, Ibrahimen
kaust.authorLuo, Xiaodongen
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