An efficient implementation of the ensemble Kalman filter based on an iterative Sherman–Morrison formula
An efficient implementation of the ensemble Kalman filter based on an iterative Sherman–Morrison formula
复制标题
基于迭代谢尔曼-莫里森公式的集成卡尔曼滤波器的实现效率
DOI：
10.1007/s11222-014-9454-4
复制
发表时间：
2013
影响因子：
2.2
通讯作者：
Jeffrey L. Anderson
中科院分区：
文献类型：
--
作者：
E. Niño;Adrian Sandu;Jeffrey L. Anderson
我们提出了一个实际的实施的集合卡尔曼滤波器（EnKF）的基础上迭代谢尔曼-莫里森公式。新的直接方法利用了集合估计误差协方差矩阵的特殊结构，以有效地解决在EnKF的分析步骤中涉及的线性系统。所提出的实现的计算复杂度是相当于最好的EnKF实现在文献中的观测的数量远大于合奏成员的数量时，通常是在实践中的情况下。此外，所提出的方法提供了最好的理论复杂度相比，通用配方的基础上的谢尔曼-莫里森公式的矩阵求逆。对该方法的稳定性进行了分析，并讨论了一种旋转策略，以减少舍入误差的积累，而不增加计算量。一个并行的实现进行了讨论。使用海洋准地转模型进行的计算实验表明，所提出的算法产生相同的精度作为其他EnKF实现，但规模更好的观测数量方面。
We present a practical implementation of the ensemble Kalman filter (EnKF) 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, as typically is case in practice. Moreover, the proposed method provides the best theoretical complexity when it is compared to generic formulations of matrix inversion based on the Sherman–Morrison formula. The stability analysis of the proposed method is carried out and a pivoting strategy is discussed in order to reduce the accumulation of round-off errors without increasing the computational effort. A parallel implementation is discussed as well. Computational experiments carried out using an oceanic quasi-geostrophic model reveal that the proposed algorithm yields the same accuracy as other EnKF implementations, but scales better with regard to the number of observations.