  The Ensemble Kalman Filter method can be used as an iterative numerical
scheme for parameter identification or nonlinear filtering problems. We study
the limit of infinitely large ensemble size and derive the corresponding
mean-field limit of the ensemble method. The solution of the inverse problem is
provided by the expected value of the distribution of the ensembles and the
kinetic equation allows, in simple cases, to analyze stability of these
solutions. Further, we present a slight but stable modification of the method
which leads to a Fokker-Planck-type kinetic equation. The kinetic methods
proposed here are able to solve the problem with a reduced computational
complexity in the limit of a large ensemble size. We illustrate the properties
and the ability of the kinetic model to provide solution to inverse problems by
using examples from the literature.
