Name
Abstract | ||
|---|---|---|
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 <= p <= infinity, with the usual rate 1/root 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. |
Year | DOI | Venue |
|---|---|---|
2015 | 10.1137/140965363 | SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION |
Keywords | Field | DocType |
data assimilation,L-p laws of large numbers,Hilbert space,ensemble Kalman filter,continuity,stability,Kalman filter | Applied mathematics,Extended Kalman filter,Alpha beta filter,Fast Kalman filter,Covariance intersection,Minimum mean square error,Data assimilation,Invariant extended Kalman filter,Statistics,Ensemble Kalman filter,Mathematics | Journal |
Volume | Issue | ISSN |
3 | 1 | 2166-2525 |
Citations | PageRank | References |
7 | 1.18 | 0 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| evan kwiatkowski | 1 | 7 | 1.18 |
| Jan Mandel | 2 | 444 | 69.36 |