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.
The Ensemble Kalman Filter (EnKF) belongs to the class of iterative particle filtering methods and can be used for solving control--to--observable inverse problems. In this context, the EnKF is known as Ensemble Kalman Inversion (EKI). 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 possible drawbacks in the phase space of moments provided by the continuous limits of the EKI, but observed also in the multi--dimensional setting . 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 by using test inverse problems from the literature and comparing it with the classical continuous limit formulation of the method.
R
ensemble Kalman filter
Ensemble Kalman Filter (EnKF)
A
this context, the EnKF is known as Ensemble Kalman Inversion (EKI). In
R
a possible instability of the solution
possible drawbacks in the phase space of moments
R
continuous--time limit of the ensemble Kalman filter for inverse problems
continuous limits of the EKI, but observed also in the multi--dimensional setting
D
of the ensemble Kalman filter
A
continuous limit