Geodesic
On the convergence of the ensemble Kalman filter
Applications of Mathematics, Tome 56 (2011) no. 6, pp. 533-541

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Convergence of the ensemble Kalman filter in the limit for large ensembles to the Kalman filter is proved. In each step of the filter, convergence of the ensemble sample covariance follows from a weak law of large numbers for exchangeable random variables, the continuous mapping theorem gives convergence in probability of the ensemble members, and $L^{p}$ bounds on the ensemble then give $L^{p}$ convergence.
DOI : 10.1007/s10492-011-0031-2
Classification : 60F05, 60F25, 60G09, 62M20, 93E11
Keywords: data assimilation; ensemble; asymptotics; convergence; filtering; exchangeable random variables 
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     title = {On the convergence of the ensemble {Kalman} filter},
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Mandel, Jan; Cobb, Loren; Beezley, Jonathan D. On the convergence of the ensemble Kalman filter. Applications of Mathematics, Tome 56 (2011) no. 6, pp. 533-541. doi: 10.1007/s10492-011-0031-2

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