TY  - JOUR
A1  - de Wiljes, Jana
A1  - Reich, Sebastian
A1  - Stannat, Wilhelm
T1  - Long-Time stability and accuracy of the ensemble Kalman-Bucy Filter for fully observed processes and small measurement noise
T2  - SIAM Journal on Applied Dynamical Systems
N2  - 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.
KW  - data assimilation
KW  - Kalman Bucy filter
KW  - ensemble Kalman filter
KW  - stability
KW  - accuracy
KW  - asymptotic behavior
Y1  - 2018
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/54487
SN  - 1536-0040
VL  - 17
IS  - 2
SP  - 1152
EP  - 1181
PB  - Society for Industrial and Applied Mathematics
CY  - Philadelphia
ER  -