We introduce a computationally efficient variant of the model-based ensemble Kalman filter (EnKF). We propose two changes to the original formulation. First, we phrase the setup in terms of precision matrices instead of covariance matrices, and introduce a new prior for the precision matrix which ensures it to be sparse. Second, we propose to split the state vector into several blocks and formulate an approximate updating procedure for each of these blocks. We study in a simulation example the computational speedup and the approximation error resulting from using the proposed approach. The speedup is substantial for high dimensional state vectors, allowing the proposed filter to be run on much larger problems than can be done with the original formulation. In the simulation example the approximation error resulting from using the introduced block updating is negligible compared to the Monte Carlo variability inherent in both the original and the proposed procedures.

翻译：我们提出了一种计算效率更高的基于模型的集合卡尔曼滤波器（EnKF）变体。对原始公式进行了两项改进：首先，将问题的表述从协方差矩阵改为精度矩阵，并引入一种新的先验条件以保证精度矩阵的稀疏性；其次，将状态向量划分为多个模块，并为每个模块设计近似更新流程。通过仿真实验，我们研究了该方法的计算加速效果及近似误差。对于高维状态向量，该方法能显著提升计算速度，使得滤波器能够处理远大于原始公式所能处理的问题规模。在仿真案例中，与原始方法及所提方法中固有的蒙特卡洛变异性相比，采用模块更新引入的近似误差可忽略不计。