中文摘要：

标准卡尔曼滤波假设系统的过程噪声和量测噪声是均值为零的高斯白噪声,但在实际应用中,经常会遇到噪声为非高斯分布的有色噪声,因此不能直接使用卡尔曼滤波算法。针对该问题,提出一种有色噪声条件下的高斯和卡尔曼滤波算法。分别采用状态扩增法和量测扩增法对过程噪声和量测噪声进行白化处理;根据高斯和滤波思想,用多个高斯项的叠加来近似非高斯分布,实现对系统的状态估计。实验结果表明,该算法能够有效去除有色噪声影响,提高滤波精度。

英文摘要：

It is assumed that the process noise and measurement noise are Gaussian white noises with zero mean in the standard Kalman filter.However,there are often colored noises with non-Gaussian distribution in applications.At this time,the standard Kalman filter does not work.To address this problem,a Gaussian sum Kalman filter with colored noises was proposed.The colored noises were whited using state augmentation and measurement augmentation.According to the idea of the Gaussian sum filter,non-Gaussian distribution was approximated using the summation of multiple Gaussian items,and the state was estimated accurately.Experimental results show that the proposed algorithm can eliminate the influence of colored noises effectively and enhance the filtering accuracy.