近似最小一乘意义下的鲁棒卡尔曼滤波器

Robust Kalman filter based on approximate least absolute deviation

当存在高污染率的野值观测时,现有的鲁棒卡尔曼滤波器的数值稳定性和抗差能力可能会严重退化.为此,基于近似最小一乘估计和修正的高斯牛顿方法提出一种新的鲁棒卡尔曼滤波器,以减小含野量测对滤波器的不利影响.通过条件数分析和影响函数分析,从理论上证明所提出方法的数值稳定性和抗差能力均好于基于Huber估计的卡尔曼滤波器.通过仿真实验对理论分析结果进行验证.仿真结果表明,在只有少量野值观测的情况下,所提出的滤波器与Huber卡尔曼滤波器的估计性能大致相当;而在含有高污染率的野值观测时,所提出的滤波器的估计性能明显好于Huber卡尔曼滤波器.在仿真实验中还对几种滤波器的计算花费进行了比较,发现所提出滤波器的计算代价小于Huber卡尔曼滤波器的计算代价.

If measurements contain a high proportion of outlier data, the numerical stability and robustness of existing robust Kalman filters may be seriously degraded. Therefore, this paper proposes a novel robust Kalman filter based on the approximate least absolute deviation and modified Gauss-Newton method to reduce the adverse effects of the outlier measurement on the filtering. Through the analysis based on the condition number and influence function, it is proved theoretically that the numerical stability and robustness of the proposed approach are preferable to those of Huber-based Kalman filter. The theoretical analysis results are verified by the simulation experiments. The simulation results show that the performance of the proposed filter is almost equivalent to that of the Huber-based Kalman filter in the case with low proportion of outlier measurements. However, the proposed filter exhibits more superior performance than the Huber-based Kalman filter in the case with high proportion of outlier measurements. The comparison of computational cost of several filters is also performed by the simulation experiments. It is found that the computational cost of the proposed filter is less than the computational cost of the Huber-based Kalman filter.