Suboptimal Bayesian state estimators for linear high-dimensional dynamic processes

Abstract 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).