Two-Sample Kalman Filter for Steady-State Data Assimilation

Abstract

In this paper, a new iterative algorithm for computing a steady-state Kalman gain is proposed. This algorithm utilizes two model forecasts with statistically independent random perturbations to determine the error covariance used to define a Kalman gain matrix for steady-state data assimilation. It is based on the assumption that the error process is weakly stationary and ergodic. The algorithm consists of an iterative procedure for improving the covariance estimate, which requires a fixed observation network. Two twin experiments using a simple wave model and an operational storm surge prediction model are performed to demonstrate the performance of the proposed algorithm. The experiments show that the results obtained by using the proposed algorithm converge to the ones produced by the classic Kalman filter algorithm. An additional experiment using the three-variable Lorenz model is also performed to demonstrate its potential applicability in unstable dynamical systems.