基于马氏距离的非线性自适应状态估计算法

Mahalanobis-distance-based Adaptive Algorithm for Nonlinear State Estimation

与常规卡尔曼滤波相比,渐消滤波能够克服模型不确定性的影响。然而,异常的测量值将引起先验协方差矩阵异常,甚至导致渐消滤波器失效。针对这一问题,本文从工程数据处理实践出发,引入马氏距离构造判别统计量进行探测,并根据探测结果适时采用渐消因子或协方差膨胀因子,提出了一种基于马氏距离探测的改进自适应滤波器。利用全球导航卫星系统和惯性导航系统在工程实践中采集的数据,进行了多组试验,验证了该算法的有效性。试验结果表明,该算法能有效地控制动态模型偏差和异常测量值的影响,提高滤波解算的稳定性,解算精度较高。

As one of the adaptive Kalman filter,the fading filter is proposed to overcome the shortage of model uncertainty in Kalman filter.However,the anomaly of the prior covariance matrix and even the failure of the fading filter will be caused by the abnormal measured values.Aiming at this problem in the data processing applications,squares of the Mahalanobis distance is introduced as the judging index in this paper,and the fading factor or the covariance inflation factor is adopted according to the detection result.On the basis,a modified Mahalanobis-distance-based adaptive algorithm is proposed.The proposed algorithm is verified to be effective by the practical data collected by the global navigation satellite system(GNSS)and inertial navigation system(INS)integrated navigation systems.Results demonstrate that the influences of both the dynamic model deviations and outlying measurements are controlled effectively with the proposed algorithm,and both the stability and precision of the filtering are improved further.