| Title:
|
On the convergence of the ensemble Kalman filter (English) |
| Author:
|
Mandel, Jan |
| Author:
|
Cobb, Loren |
| Author:
|
Beezley, Jonathan D. |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
56 |
| Issue:
|
6 |
| Year:
|
2011 |
| Pages:
|
533-541 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
data assimilation |
| Keyword:
|
ensemble |
| Keyword:
|
asymptotics |
| Keyword:
|
convergence |
| Keyword:
|
filtering |
| Keyword:
|
exchangeable random variables |
| MSC:
|
60F05 |
| MSC:
|
60F25 |
| MSC:
|
60G09 |
| MSC:
|
62M20 |
| MSC:
|
93E11 |
| idZBL:
|
Zbl 1248.62164 |
| idMR:
|
MR2886236 |
| DOI:
|
10.1007/s10492-011-0031-2 |
| . |
| Date available:
|
2011-12-16T15:03:23Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141765 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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[13] Mandel, J., Beezley, J. D.: An ensemble Kalman-particle predictor-corrector filter for non-Gaussian data assimilation. ICCS 2009.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. MR 2572378, 10.1007/978-3-642-01973-9_53 |
| Reference:
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[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 \hfil http://www.arXiv.org/abs/0901.2951. |
| Reference:
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