Robust Kalman filtering based on Mahalanobis distance as outlier judging criterion
Robust Kalman filtering based on Mahalanobis distance as outlier judging criterion
复制标题
基于马氏距离作为异常值判断标准的鲁棒卡尔曼滤波
DOI：
10.1007/s00190-013-0690-8
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发表时间：
2014-04-01
影响因子：
4.4
通讯作者：
Chang, Guobin
中科院分区：
文献类型：
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作者：
Chang, Guobin
提出了一种抗野值影响的鲁棒卡尔曼滤波方法。研究了两种观测误差，实际观测值中的异常值和观测噪声的重尾分布。这两种误差中的任何一种都会严重降低标准卡尔曼滤波器的性能。在该方法中，一个判断指标被定义为从观测到其预测的马氏距离的平方。假设观测值服从高斯分布，均值和协方差为观测值的预测值及其协方差，则判断指标应以观测向量的维数为自由度，服从卡方分布。将上述高斯分布作为原假设，将判断指标作为检验统计量，对实际观测值进行假设检验。如果零假设应被拒绝，则可以得出结论，观察值中存在离群值。在存在离群值的情况下，可以引入缩放因子来重新缩放观测噪声或新息向量的协方差，这两者都导致滤波器增益降低。并且可以使用牛顿迭代法或以解析方式求解比例因子。该方法能有效地抵抗这两种误差的不利影响，具有较强的鲁棒性。此外，由于迭代方法中所需的迭代次数可能相当大，因此应首选解析计算的比例因子。
A robust Kalman filter scheme is proposed to resist the influence of the outliers in the observations. Two kinds of observation error are studied, i.e., the outliers in the actual observations and the heavy-tailed distribution of the observation noise. Either of the two kinds of errors can seriously degrade the performance of the standard Kalman filter. In the proposed method, a judging index is defined as the square of the Mahalanobis distance from the observation to its prediction. By assuming that the observation is Gaussian distributed with the mean and covariance being the observation prediction and its associate covariance, the judging index should be Chi-square distributed with the dimension of the observation vector as the degree of freedom. Hypothesis test is performed to the actual observation by treating the above Gaussian distribution as the null hypothesis and the judging index as the test statistic. If the null hypothesis should be rejected, it is concluded that outliers exist in the observations. In the presence of outliers scaling factors can be introduced to rescale the covariance of the observation noise or of the innovation vector, both resulting in a decreased filter gain. And the scaling factors can be solved using the Newton’s iterative method or in an analytical manner. The harmful influence of either of the two kinds of errors can be effectively resisted in the proposed method, so robustness can be achieved. Moreover, as the number of iterations needed in the iterative method may be rather large, the analytically calculated scaling factor should be preferred.