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Convergence of the Square Root Ensemble Kalman Filter in the Large Ensemble Limit

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    0439569 - ÚI 2015 RIV US eng J - Článek v odborném periodiku
    Kwiatkowski, E. - Mandel, Jan
    Convergence of the Square Root Ensemble Kalman Filter in the Large Ensemble Limit.
    SIAM/ASA Journal on Uncertainty Quantification. Roč. 3, č. 1 (2015), s. 1-17. ISSN 2166-2525. E-ISSN 2166-2525
    Grant CEP: GA ČR GA13-34856S
    Institucionální podpora: RVO:67985807
    Klíčová slova: data assimilation * Lp laws of large numbers * Hilbert space * ensemble Kalman filter
    Kód oboru RIV: IN - Informatika

    Ensemble filters implement sequential Bayesian estimation by representing the probability distribution by an ensemble mean and covariance. Unbiased square root ensemble filters use deterministic algorithms to produce an analysis (posterior) ensemble with a prescribed mean and covariance, consistent with the Kalman update. This includes several filters used in practice, such as the ensemble transform Kalman filter, the ensemble adjustment Kalman filter, and a filter by Whitaker and Hamill. We show that at every time index, as the number of ensemble members increases to infinity, the mean and covariance of an unbiased ensemble square root filter converge to those of the Kalman filter, in the case of a linear model and an initial distribution of which all moments exist. The convergence is in all $L^p$, $1/leq p</infty$, with the usual rate $1//sqrt{N}$, and the constant does not depend on the model or the data dimensions. The result holds in infinite-dimensional separable Hilbert spaces as well.
    Trvalý link: http://hdl.handle.net/11104/0242826

     
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