BeiDou Navigation Satellite System/Inertial Measurement Unit Integrated Train Positioning Method Based on Improved Unscented Kalman Filter Algorithm
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摘要: 为提高列车定位的精确性和连续性，采用北斗卫星接收机和惯性测量单元构建车载组合定位系统. 针对多传感器组合定位信息融合估计的非线性和鲁棒性需求，将抗差估计理论的等价权原理应用于标准无迹卡尔曼滤波（unscented Kalman filter，UKF）算法，构造了一种改进的UKF算法，通过对标准UKF算法的噪声协方差进行等价替换，从而起到调节滤波增益的作用，使得滤波算法对传感器观测粗差具有较强的抑制能力. 将改进的UKF算法与标准UKF算法应用于列车组合定位进行仿真比较，结果表明：传感器无观测异常时，改进UKF算法的滤波精度总体上略优于标准UKF算法；当传感器观测值含有随机粗差时，改进UKF算法的滤波精度及稳定性明显优于标准UKF算法，北向、东向位置平均估计误差分别降低了48.5%、48.8%，北向、东向速度平均估计误差分别降低了43.7%、48.9%.Abstract: In order to improve the accuracy and continuity of train positioning, BeiDou satellite receiver and inertial measurement unit were employed to construct an on-board integrated positioning system. Given the nonlinearity and robustness in the information fusion estimation of mulit-sensor positioning, an improved unscented Kalman filter (UKF) algorithm was proposed by applying the equivalence of robustness to the standard UKF. With the equivalent transformation of noise covariance in the standard UKF algorithm, the filter gain was adjusted, such that the filtering algorithm has a strong ability to suppress gross errors in sensor observation. The improved UKF algorithm and the standard UKF algorithm were applied to the integrated positioning for simulation comparison. The results show that, the filtering accuracy of the improved UKF is slightly higher than that of the standard UKF under normal conditions; the filtering accuracy and stability of the improved UKF is significantly better than the standard UKF when sensor observations contain gross errors. The average estimation errors of north and east positioning are respectively decreased by 48.5% and 48.8%. The average estimation errors of north and east speed are respectively declined by 43.7% and 48.9%.
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表 1 误差统计结果（0～300 s）
Table 1. Error statistics（0−300 s）
参数 标准UKF 改进UKF 北向
位置/m东向
位置/m北向速度
/（m•s−1）东向速度
/（m•s−1）北向
位置/m东向
位置/m北向速度
/（m•s−1）东向速度
/（m•s−1）AVE 4.32 3.27 0.28 0.21 4.26 3.14 0.25 0.20 RMSE 3.34 2.51 0.22 0.16 3.18 2.45 0.19 0.15 
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表 2 误差统计结果（300～400 s）
Table 2. Error statistics（300−400 s）
参数 标准UKF 改进UKF 北向
位置/m东向
位置/m北向速度
/（m•s−1）东向速度
/（m•s−1）北向
位置/m东向
位置/m北向速度
/（m•s−1）东向速度
/（m•s−1）AVE 8.73 6.87 0.48 0.45 4.49 3.52 0.27 0.23 RMSE 6.49 5.11 0.35 0.33 3.23 2.74 0.21 0.17
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