论文标题
基于独立ENKF估计器的样本平均值的多级集合卡尔曼过滤
Multilevel Ensemble Kalman Filtering based on a sample average of independent EnKF estimators
论文作者
论文摘要
我们引入了一种新的多级集合Kalman滤波器方法（MLENKF），该方法由集合Kalman过滤器（ENKF）的独立样本组成。这种新的MLENKF方法与Hoel，Law和Tempone在2016年介绍的先前存在的方法根本不同，并且适用于对基于多数元素的蒙特卡洛过滤方法的扩展。强大的理论分析和支持的数值示例表明，在适当的规律性假设下，Mlenkf方法在大型和细分限制中具有比普通的香草ENKF更好的复杂性，对于较弱的利益量近似值。该方法是针对具有有限维状态空间的离散时间过滤问题的开发，以及通过加性高斯噪声污染的线性观测值。
We introduce a new multilevel ensemble Kalman filter method (MLEnKF) which consists of a hierarchy of independent samples of ensemble Kalman filters (EnKF). This new MLEnKF method is fundamentally different from the preexisting method introduced by Hoel, Law and Tempone in 2016, and it is suitable for extensions towards multi-index Monte Carlo based filtering methods. Robust theoretical analysis and supporting numerical examples show that under appropriate regularity assumptions, the MLEnKF method has better complexity than plain vanilla EnKF in the large-ensemble and fine-resolution limits, for weak approximations of quantities of interest. The method is developed for discrete-time filtering problems with finite-dimensional state space and linear observations polluted by additive Gaussian noise.
