Convergence of Ensemble Kalman Filter |
Jan Mandel, University of Colorado, Denver
Monday, October 5, 2009
4:00 p.m., 223 Weber
ABSTRACT |
Based on joint work with Loren Cobb and Jonathan Beezley.
Convergence of the ensemble Kalman filter (EnKF) 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, Slutsky's theorem gives weak convergence of
ensemble members, and $L^{p}$ bounds on the ensemble then give $L^{p}$
convergence.
In practice, the EnKF is of interest primarily in very high dimension.
However, the convergence analysis is formulated using weak convergence
in the given fixed state space, and so it does not provide convergence
uniformly with respect to the dimension of the state space. This
motivates ongoing work on extending the theory to infinitely
dimensional Hilbert space, and the the talk will discuss some recent
progress.