On the convergence of the ensemble Kalman filter. (English) Zbl 1248.62164

Mandel, Jan; Cobb, Loren; Beezley, Jonathan D.

Appl. Math., Praha 56, No. 6, 533-541 (2011).

One of the most successful recent data assimilation methods for high-dimensional problems is the ensemble Kalman filter. The present analysis does not assume that the ensemble members are independent or normally distributed. A discrete-time filtering problem is introduced. It is based on the Bayes theorem. The main theorem establishes the convergence of the ensemble Kalman filter in the Lebesgue space \(L^p\) for all \(p\in [1,\infty)\). As a consequence the authors derive that the ensemble mean and covariance converge to the filtering mean and covariance.

Reviewer: Michal Křížek (Praha)

MSC:

62M20	Inference from stochastic processes and prediction
60G09	Exchangeability for stochastic processes

Keywords:

data assimilation; asymptotics; exchangeable random variables

Software:

EnKF

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