505 IGPM505.pdf        2020
TITLE A Stabilization of a Continuous Limit of the Ensemble Kalman Filter
AUTHORS Dieter Armbruster, Michael Herty, Giuseppe Viscont
ABSTRACT The ensemble Kalman filter belongs to the class of iterative particle filtering methods and can be used for solving control–to–observable inverse problems. In recent years several continuous limits in the number of iteration and particles have been performed in order to study properties of the method. In particular, a one–dimensional linear stability analysis reveals a possible instability of the solution provided by the continuous–time limit of the ensemble Kalman filter for inverse problems. In this work we address this issue by introducing a stabilization of the dynamics which leads to a method with globally asymptotically stable solutions. We illustrate the performance of the stabilized version of the ensemble Kalman filter by using test inverse problems from the literature and comparing it with the classical formulation of the method.
KEYWORDS dynamical systems, inverse problems, regularization, stabilization, nonlinear filtering methods, moment equations