The Kalman filter is currently one of the most popular approaches to solving the data assimilation problem. A major line of the application of the Kalman filter to data assimilation is the ensemble approach. In this paper, a version of the stochastic ensemble Kalman filter is considered. In this algorithm, an ensemble of analysis errors is obtained by transforming an ensemble of forecast errors. The analysis step is made only for a mean value. Thus, the ensemble π-algorithm combines the advantages of stochastic filters and the efficiency and locality of square root filters. A numerical method of implementing the ensemble π-algorithm is proposed, and the validity of this method is proved. This algorithm is used for a test problem in a three-dimensional domain. The results of numerical experiments with model data for estimating the efficiency of the algorithm are presented. A comparative analysis of the behavior of the root-mean-square errors of the ensemble π-algorithm and the Kalman ensemble filter by means of numerical experiments with a one-dimensional Lorentz model is performed.

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带有扰动积分变换的随机积分卡尔曼滤波器

卡尔曼滤波器当前是解决数据同化问题的最流行方法之一。卡尔曼滤波器在数据同化中的主要应用是集成方法。在本文中，考虑了随机集成卡尔曼滤波器的一种形式。在该算法中，通过变换预测误差的集合来获得分析误差的集合。仅针对平均值进行分析步骤。因此，集合π算法结合了随机滤波器的优点以及平方根滤波器的效率和局部性。提出了一种实现集合π算法的数值方法，并证明了该方法的有效性。该算法用于三维域中的测试问题。给出了利用模型数据进行数值实验以估计算法效率的结果。通过一维洛伦兹模型的数值实验，对集合π算法和卡尔曼集合滤波器的均方根误差行为进行了比较分析。