论文标题
合奏倒置的连续极限的稳定
A Stabilization of a Continuous Limit of the Ensemble Kalman Inversion
论文作者
论文摘要
集合卡尔曼滤波器（ENKF）属于迭代粒子滤波方法的类别，可用于求解控制 - 到可观察的反问题。在这种情况下，ENKF被称为集合Kalman倒置（EKI）。近年来，为了研究该方法的特性，已经执行了迭代和颗粒数量的连续限制。特别是，一维线性稳定性分析揭示了EKI连续限制提供的矩空间的可能缺点，但在多维设置中也观察到。在这项工作中，我们通过引入动力学的稳定来解决这个问题，该动力学导致一种具有全球渐近稳定解决方案的方法。我们通过使用文献中的测试反问题来说明稳定版本的性能，并将其与该方法的经典连续限制公式进行比较。
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.
