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A Stabilization of a Continuous Limit of the Ensemble Kalman Inversion
SIAM Journal on Numerical Analysis ( IF 2.9 ) Pub Date : 2022-06-21 , DOI: 10.1137/21m1414000
Dieter Armbruster, Michael Herty, Giuseppe Visconti

SIAM Journal on Numerical Analysis, Volume 60, Issue 3, Page 1494-1515, June 2022.
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 iterations 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 is observed also in the multidimensional 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.


中文翻译:

系综卡尔曼反演连续极限的稳定

SIAM 数值分析杂志,第 60 卷,第 3 期,第 1494-1515 页,2022 年 6 月。
集成卡尔曼滤波器 (EnKF) 属于迭代粒子滤波方法类,可用于解决控制到可观察的逆问题。在这种情况下,EnKF 被称为集合卡尔曼反演 (EKI)。近年来,为了研究该方法的特性,已经对迭代次数和粒子数进行了多次连续限制。特别是,一维线性稳定性分析揭示了由 EKI 的连续限制提供的矩相空间中可能存在的缺陷,但在多维设置中也可以观察到。在这项工作中,我们通过引入动态稳定性来解决这个问题,这导致了一种具有全局渐近稳定解的方法。
更新日期:2022-06-22
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