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The Ensemble Kalman Filter: theoretical formulation and practical implementation

机译：合奏卡尔曼滤波器：理论公式和实际实现

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The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications. A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias.
机译：本文的目的是对En​​semble Kalman滤波器（EnKF）及其数值实现进行全面的介绍和解释。 EnKF有一个庞大的用户群，许多出版物都讨论了它的应用和理论方面。本文回顾了这些研究的重要结果，并提出了新的观点和替代解释，进一步解释了EnKF的成功。除了提供使用EnKF所需的理论框架外，还重点关注算法公式和最佳数值实现。给出了一些关键子例程的程序列表。本文还涉及特定问题，例如非线性测量的使用，温度和盐度的原地分布图以及及时获得的高频数据。基于集合的最佳插值（EnOI）方案是一种经济高效的方法，在某些应用中可以替代EnKF。与时间相关的模型误差的使用和模型偏差的估计进行了相当广泛的讨论。

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