带有噪声递推估计的自适应集合卡尔曼滤波

卡尔曼滤波(KF)广泛应用于线性系统的状态估计问题.然而,它需要精确已知过程噪声的统计特性,这在实际应用中往往是不能满足的.在这个背景下,首先,根据协方差匹配原理建立一种带有过程噪声递推估计的自适应KF算法;然后,为了突破KF只能处理线性系统估计问题的局限,将过程噪声递推估计引入集合卡尔曼滤波(EnKF)中,提出一种自适应EnKF算法;最后,采用估计理论证明所提出算法的稳定性.与标准EnKF相比,该自适应算法在过程噪声统计特性未知的情况下滤波依然收敛,滤波精度及稳定性显著提升.仿真结果验证了所提出算法的有效性.

Adaptive ensemble Kalman filter with recursive noise estimation

The Kalman filter(KF) is widely used for state estimation of linear systems. However, it requires accurate statistic of process noise, which is not plausible in practical applications. In this paper, an adaptive KF algorithm with recursive process noise estimation is constructed firstly by utilizing the covariance matching principle. Then, in order to break through the limitation of the KF that can only deal with the estimation problem of linear systems, the recursive process noise estimation is introduced into the ensemble Kalman filter(EnKF), so that an adaptive EnKF algorithm is proposed. Finally, the stability of the novel algorithm is proved through the estimation theory. Under the condition of unknown process noise statistic, the proposed adaptive EnKF algorithm still converges, moreover its filtering precision and stability are better than those of the standard EnKF. Simulation results validate the effectiveness of the presented algorithm.