论文标题
基于模型的集合卡尔曼滤波器的稀疏基质公式
A sparse matrix formulation of model-based ensemble Kalman filter
论文作者
论文摘要
我们引入了基于模型的集合Kalman滤波器（ENKF）的计算有效变体。我们建议对原始配方进行两次更改。首先，我们用精确矩阵而不是协方差矩阵来表达设置，并引入了精确矩阵的新先验，以确保其稀疏。其次，我们建议将状态向量分为几个块，并为每个块制定一个近似更新过程。 我们在模拟示例中研究计算速度和使用所提出的方法引起的近似误差。对于高维状态向量的加速度是很大的，可以使所提出的过滤器在比原始配方更大的问题上运行。在仿真示例中，与原始过程和所提出的过程中固有的蒙特卡洛变异性相比，使用引入的块更新引起的近似误差可以忽略不计。
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.
