基于迭代Sherman-Morrison公式的集合卡尔曼滤波器的高效实现
An Efficient Implementation of the Ensemble Kalman Filter Based on an Iterative Sherman-Morrison Formula
AI总结：
提出一种基于迭代Sherman-Morrison公式的集合卡尔曼滤波器实现方法，通过利用集合估计误差协方差矩阵的特殊结构高效求解分析步骤中的线性系统，在观测数远大于集合成员数时计算复杂度与最优实现相当，且无需矩阵分解，数值实验表明该方法在精度相似下显著更快。
摘要：
我们提出了一种基于迭代Sherman-Morrison公式的集合卡尔曼滤波器（EnKF）的实用实现。这种新直接方法利用了集合估计误差协方差矩阵的特殊结构，以高效求解EnKF分析步骤中涉及的线性系统。当观测数量远大于集合成员数量时，所提出的实现的计算复杂度与文献中最佳EnKF实现相当。即使在不满足此条件的情况下，由于该方法不使用矩阵分解，预期也能表现良好。我们使用Lorenz 96和海洋准地转模型进行了计算实验，以比较所提出的算法与使用矩阵分解的EnKF实现。在精度方面，所有实现的结果相似。即使当观测数量相对于集合成员数量较大时，所提出的方法也明显快于其他EnKF变体。
英文摘要：
We present a practical implementation of the ensemble Kalman (EnKF) filter based on an iterative Sherman-Morrison formula. The new direct method exploits the special structure of the ensemble-estimated error covariance matrices in order to efficiently solve the linear systems involved in the analysis step of the EnKF. The computational complexity of the proposed implementation is equivalent to that of the best EnKF implementations available in the literature when the number of observations is much larger than the number of ensemble members. Even when this conditions is not fulfilled, the proposed method is expected to perform well since it does not employ matrix decompositions. Computational experiments using the Lorenz 96 and the oceanic quasi-geostrophic models are performed in order to compare the proposed algorithm with EnKF implementations that use matrix decompositions. In terms of accuracy, the results of all implementations are similar. The proposed method is considerably faster than other EnKF variants, even when the number of observations is large relative to the number of ensemble members.
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