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

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    Type
    Article
    Authors
    Luo, Xiaodong
    Hoteit, Ibrahim cc
    KAUST Department
    Earth Fluid Modeling and Prediction Group
    Earth Science and Engineering Program
    Physical Science and Engineering (PSE) Division
    Date
    2011-12
    Preprint Posting Date
    2011-07-31
    Permanent link to this record
    http://hdl.handle.net/10754/552781
    
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    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.
    Citation
    Robust Ensemble Filtering and Its Relation to Covariance Inflation in the Ensemble Kalman Filter 2011, 139 (12):3938 Monthly Weather Review
    Publisher
    American Meteorological Society
    Journal
    Monthly Weather Review
    DOI
    10.1175/MWR-D-10-05068.1
    arXiv
    1108.0158
    Additional Links
    http://journals.ametsoc.org/doi/abs/10.1175/MWR-D-10-05068.1
    http://arxiv.org/abs/1108.0158
    ae974a485f413a2113503eed53cd6c53
    10.1175/MWR-D-10-05068.1
    Scopus Count
    Collections
    Articles; Physical Science and Engineering (PSE) Division; Earth Science and Engineering Program

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