Ensemble Kalman Filters with Resampling

IF 2.1 3区工程技术 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2024-05-23 DOI:10.1137/23m1594935

Omar Al-Ghattas, Jiajun Bao, Daniel Sanz-Alonso

引用次数: 0

Abstract

SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 2, Page 411-441, June 2024.
Abstract.Filtering is concerned with online estimation of the state of a dynamical system from partial and noisy observations. In applications where the state of the system is high dimensional, ensemble Kalman filters are often the method of choice. These algorithms rely on an ensemble of interacting particles to sequentially estimate the state as new observations become available. Despite the practical success of ensemble Kalman filters, theoretical understanding is hindered by the intricate dependence structure of the interacting particles. This paper investigates ensemble Kalman filters that incorporate an additional resampling step to break the dependency between particles. The new algorithm is amenable to a theoretical analysis that extends and improves upon those available for filters without resampling, while also performing well in numerical examples.

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带有重采样功能的集合卡尔曼滤波器

SIAM/ASA 不确定性量化期刊》，第 12 卷第 2 期，第 411-441 页，2024 年 6 月。摘要.滤波涉及从部分和噪声观测中在线估计动态系统的状态。在系统状态为高维的应用中，集合卡尔曼滤波器通常是首选方法。这些算法依赖于相互作用的粒子集合，在获得新的观测数据时依次对状态进行估计。尽管集合卡尔曼滤波器在实践中取得了成功，但由于相互作用粒子的依赖结构错综复杂，理论上的理解受到了阻碍。本文研究的集合卡尔曼滤波器包含一个额外的重采样步骤，以打破粒子之间的依赖关系。新算法可用于理论分析，扩展并改进了不带重采样滤波器的理论分析，同时在数值示例中表现良好。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Siam-Asa Journal on Uncertainty Quantification Mathematics-Statistics and Probability

CiteScore

3.70

自引率

0.00%

发文量

期刊介绍： SIAM/ASA Journal on Uncertainty Quantification (JUQ) publishes research articles presenting significant mathematical, statistical, algorithmic, and application advances in uncertainty quantification, defined as the interface of complex modeling of processes and data, especially characterizations of the uncertainties inherent in the use of such models. The journal also focuses on related fields such as sensitivity analysis, model validation, model calibration, data assimilation, and code verification. The journal also solicits papers describing new ideas that could lead to significant progress in methodology for uncertainty quantification as well as review articles on particular aspects. The journal is dedicated to nurturing synergistic interactions between the mathematical, statistical, computational, and applications communities involved in uncertainty quantification and related areas. JUQ is jointly offered by SIAM and the American Statistical Association.