Abstract
The ensemble Kalman filter (EnFK) has recently become one of the most popular methods for high dimensional data assimilation and it is widely used in many disciplines such as discretization of partial differential equations in geophysics or image reconstruction. The EnKF has been originally proposed as a Monte Carlo approximation to the extended Kalman filter, which is in practice inapplicable when dimension of the input data is huge Numerous publications have studied applications and asymptotic results of the EnKF, while properties of the Kalman filter (KF) and EnKF for the infinite dimensional Hilbert spaces are still under the development.
The main purpose of this paper is a brief description of the high dimensional EnKF with references to the most valuable publications. Also a short introduction to problems related with KF and EnKF on infinite dimensional Hilbert spaces is included.