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Long-time stability and accuracy of the ensemble Kalman--Bucy filter for fully observed processes and small measurement noise

de Wiljes, J., Reich, S. and Stannat, W. (2018) Long-time stability and accuracy of the ensemble Kalman--Bucy filter for fully observed processes and small measurement noise. SIAM Journal on Applied Dynamical Systems, 17 (2). pp. 1152-1181. ISSN 1536-0040

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To link to this item DOI: 10.1137/17M1119056

Abstract/Summary

The ensemble Kalman filter has become a popular data assimilation technique in the geosciences. However, little is known theoretically about its long term stability and accuracy. In this paper, we investigate the behavior of an ensemble Kalman--Bucy filter applied to continuous-time filtering problems. We derive mean field limiting equations as the ensemble size goes to infinity as well as uniform-in-time accuracy and stability results for finite ensemble sizes. The later results require that the process is fully observed and that the measurement noise is small. We also demonstrate that our ensemble Kalman--Bucy filter is consistent with the classic Kalman--Bucy filter for linear systems and Gaussian processes. We finally verify our theoretical findings for the Lorenz-63 system.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:78674
Publisher:Society for Industrial and Applied Mathematics

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