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

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    2011mwr36401.pdf
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    Type
    Article
    Authors
    Hoteit, Ibrahim cc
    Luo, Xiaodong
    Pham, Dinh-Tuan
    KAUST Department
    Earth Fluid Modeling and Prediction Group
    Earth Science and Engineering Program
    Physical Science and Engineering (PSE) Division
    Date
    2012-02
    Preprint Posting Date
    2011-07-31
    Permanent link to this record
    http://hdl.handle.net/10754/552775
    
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    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.
    Citation
    Particle Kalman Filtering: A Nonlinear Bayesian Framework for Ensemble Kalman Filters* 2012, 140 (2):528 Monthly Weather Review
    Publisher
    American Meteorological Society
    Journal
    Monthly Weather Review
    DOI
    10.1175/2011MWR3640.1
    arXiv
    1108.0168
    Additional Links
    http://journals.ametsoc.org/doi/abs/10.1175/2011MWR3640.1
    http://arxiv.org/abs/1108.0168
    ae974a485f413a2113503eed53cd6c53
    10.1175/2011MWR3640.1
    Scopus Count
    Collections
    Articles; Physical Science and Engineering (PSE) Division; Earth Science and Engineering Program

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