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, andLpbounds on the ensemble then giveLpconvergence.
Denver, CO, USA.
Jan
J
Mandel
Denver, CO, USA.
Loren
L
Cobb
Denver, CO, USA.
Jonathan D
JD
Beezley
Data assimilation; asymptotics; convergence; ensemble; exchangeable random variables; filtering