On the convergence of the ensemble Kalman filter
نویسندگان
چکیده
منابع مشابه
On the Convergence of the Ensemble Kalman Filter.
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 Lp bounds on the ensemble then give Lp converge...
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The ensemble Kalman filter (EnKF) is a recursive filter suitable for problems with a large number of variables, such as discretizations of partial differential equations in geophysical models. The EnKF originated as a version of the Kalman filter for large problems (essentially, the covariance matrix is replaced by the sample covariance), and it is now an important data assimilation component o...
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Ensemble Kalman filters (EnKF) based on a small ensemble tend to provide collapse of the ensemble over time. It is shown that this collapse is caused by positive coupling of the ensemble members due to use of one common estimate of the Kalman gain for the update of all ensemble members at each time step. This coupling can be avoided by resampling the Kalman gain from its sampling distribution i...
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We present several methods for the efficient implementation of the Ensemble Kalman Filter (EnKF) of Evensen. It is shown that the EnKF can be implemented without access to the observation matrix, and only an observation function is needed; this greatly simplifies software design. New implementations of the EnKF formulas are proposed, with linear computational complexity in the number of data po...
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ژورنال
عنوان ژورنال: Applications of Mathematics
سال: 2011
ISSN: 0862-7940,1572-9109
DOI: 10.1007/s10492-011-0031-2