On the convergence of the ensemble Kalman filter

Jan Mandel; Loren Cobb; Jonathan D. Beezley

Applications of Mathematics (2011)

  • Volume: 56, Issue: 6, page 533-541
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Mandel, Jan, Cobb, Loren, and Beezley, Jonathan D.. "On the convergence of the ensemble Kalman filter." Applications of Mathematics 56.6 (2011): 533-541. <http://eudml.org/doc/196641>.

@article{Mandel2011,
abstract = {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.},
author = {Mandel, Jan, Cobb, Loren, Beezley, Jonathan D.},
journal = {Applications of Mathematics},
keywords = {data assimilation; ensemble; asymptotics; convergence; filtering; exchangeable random variables; data assimilation; asymptotics; exchangeable random variables},
language = {eng},
number = {6},
pages = {533-541},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the convergence of the ensemble Kalman filter},
url = {http://eudml.org/doc/196641},
volume = {56},
year = {2011},
}

TY - JOUR
AU - Mandel, Jan
AU - Cobb, Loren
AU - Beezley, Jonathan D.
TI - On the convergence of the ensemble Kalman filter
JO - Applications of Mathematics
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 56
IS - 6
SP - 533
EP - 541
AB - 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.
LA - eng
KW - data assimilation; ensemble; asymptotics; convergence; filtering; exchangeable random variables; data assimilation; asymptotics; exchangeable random variables
UR - http://eudml.org/doc/196641
ER -

References

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  8. Frazin, R. A., Butala, M. D., Kemball, A., Kamalabadi, F., 10.1086/499431, Astrophys. J. 635 (2005), L197--L200. (2005) DOI10.1086/499431
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  13. Mandel, J., Beezley, J. D., 10.1007/978-3-642-01973-9_53, Lecture Notes in Computer Science, Vol. 5545 G. Allen, J. Nabrzyski, E. Seidel, G. D. van Albada, J. Dongarra, P. M. A. Sloot Springer (2009), 470-478. (2009) MR2572378DOI10.1007/978-3-642-01973-9_53
  14. Mandel, J., Cobb, L., Beezley, J. D., On the convergence of the ensemble Kalman filter, University of Colorado Denver CCM Report 278, January 2009 http://www.arXiv.org/abs/0901.2951. 
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