This paper presents a new state estimation method to ease the heavy computational loads of the Kalman filter (KF) when applied for the processes of large dimensions. The key idea of the proposed methodology is to divide the whole high-dimensional state vector into multiple low-dimensional blocks and suppress the errors introduced by minimizing the corresponding Kullback–Leibler (KL) divergence. Without losing generality, two different scenarios depending on the state dynamics are considered. One is that the state transition matrix is block-diagonal, and the other is not. By doing these, prior knowledge about the processes can be incorporated into, and more importantly, a satisfying trade-off between computational cost and estimation accuracy can be built-in. Simulations results on a numerical model, and a practice-oriented example demonstrate that the proposed method costs much less computational resources than the KF for high-dimensional processes and yields significant improvements than the existing fast Kalman-like estimators, including the ensemble KF (EnKF).

本文提出了一种新的状态估计方法，以减轻卡尔曼滤波器 (KF) 在应用于大维度过程时的繁重计算负载。所提出方法的关键思想是将整个高维状态向量划分为多个低维块，并通过最小化相应的 Kullback-Leibler (KL) 散度来抑制引入的误差。在不失一般性的情况下，考虑了取决于状态动态的两种不同场景。一种是状态转移矩阵是块对角矩阵，另一种不是。通过这样做，可以将有关过程的先验知识纳入其中，更重要的是，可以内置计算成本和估计精度之间的令人满意的权衡。数值模型的模拟结果，