Adaptive fast desensitized ensemble Kalman filter for uncertain systems

Abstract

The classical desensitized ensemble Kalman filter can effectively tolerate uncertain parameters of the system. However, the method of solving the gain matrix by algebraic equations must be solved, and the sensitivity-weight must be adjusted in real-time during the filtering process. An adaptive fast desensitized ensemble Kalman filter (AFDEnKF) is proposed to reduce computational cost and adaptively adjust the sensitivity-weight in real-time. In case of the AFDEnKF, an analytical gain matrix is obtained by desensitizing the sensitivity of the state estimation error to the uncertain parameters and minimizing cost functions, and an adaptive factor is introduced to adjust automatically sensitivity-weight by using the orthogonal principle of measurement residuals. Three numerical examples are employed to demonstrate the effectiveness of the proposed AFDEnKF. The simulation results show that the AFDEnKF can effectively improve the computational efficiency and the state estimation accuracy.