505
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IGPM505.pdf June 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 |