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探讨定常线性系统被多种有色噪声污染下的Kalman滤波模型。首先,借助于经典的AR模型及QR分解,寻求系统噪声与量测有色噪声无关的增广系统;其次,利用外推法扩展此增广系统为系统噪声与量测噪声均为白噪声且相关的线性随机系统;进而,获得加性复合有色噪声下的Kalman滤波模型。数值实验说明所获模型比已报道的Kalman滤波模型更能有效地估计系统的状态。
The Kalman filter model which is contaminated by a variety of colored noises is investigated. First of all, by means of classical AR model and QR decomposition, the augmented system with system noise and non-colored noise is sought out. Secondly, the augmented system is extended by extrapolation as the system noise and the measured noise are both white noise and correlated Then, the Kalman filter model under additive composite colored noise is obtained. Numerical experiments show that the obtained model can estimate the state of the system more effectively than the reported Kalman filter.