Advances and Applications in Statistics
Volume 32, Issue 2, Pages 151 - 162
(February 2013)
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EXPLORING EnKF CONVERGENCE FOR LINEAR DYNAMICAL SYSTEM
Nina Fitriyati, Sutawanir Darwis, Agus Yodi Gunawan and Asep Kurnia Permadi
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Abstract: The discussion of convergence is important to justify the validity of the ensemble Kalman filter (EnKF) method. In linear system, it is well known theoretically that for the very big number of the ensemble sizes, the state in EnKF hardly differs with the state in Kalman filter. In this paper, we explore numerically such convergence by means of the statistical quality control chart methodology. If the random samples of the average of the forecast step and the update step in EnKF are viewed as production outputs of a process with specific characteristics, namely, the forecast step and the update step in Kalman filter, we can observe their behaviors around these characteristics using control chart. We propose the control limits as a function of the ensemble size which is calculated based on the Chebyshev’s inequality. Simulation study shows that, as the ensemble size increases, the band of control limits will be tighter and the average of state in the forecast step and the update step of the EnKF will be closed to the same Kalman filter quantities. This simulation confirms theoretically the convergence of EnKF to Kalman filter. |
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