In this paper, we propose an efficient and practical implementation of the ensemble Kalman filter via shrinkage covariance matrix estimation. Our filter implementation combines information brought by an ensemble of model realizations, and that based on our prior knowledge about the dynamical system of interest. We perform the combination of both sources of information via optimal shrinkage factors. The method exploits the rank-deficiency of ensemble covariance matrices to provide an efficient and practical implementation of the analysis step in EnKF based formulations. Localization and inflation aspects are discussed, as well. Experimental tests are performed to assess the accuracy of our proposed filter implementation by employing an Advection Diffusion Model and an Atmospheric General Circulation Model. The experimental results reveal that the use of our proposed filter implementation can mitigate the impact of sampling noise, and even more, it can avoid the impact of spurious correlations during assimilation steps.

在本文中，我们提出了一种通过收缩协方差矩阵估计的集成卡尔曼滤波器的有效而实用的实现。我们的过滤器实现结合了模型实现整体带来的信息，以及基于我们对感兴趣的动力学系统的先验知识而获得的信息。我们通过最佳收缩率将两种信息源进行组合。该方法利用集合协方差矩阵的秩不足，以在基于EnKF的公式中提供分析步骤的有效和实际实现。还讨论了本地化和通货膨胀方面。通过使用对流扩散模型和大气总循环模型进行实验测试，以评估我们提出的滤波器实现方案的准确性。