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摘要: 针对基于卫星导航系统的列车定位对数字轨道地图的实际需求, 提出了一种基于无迹卡尔曼滤波的线路估计方法, 生成线路的三维数字轨道地图; 对于铁路线路的3种平面线形(直线、缓和曲线和圆曲线), 采用以里程为参数的菲涅尔(Fresnel)积分模型统一建模; 对于纵断面的直线和曲线, 采用二次曲线模型建模; 用无迹卡尔曼滤波对模型的状态(里程、三维坐标)和参数(方位角、曲率、曲率变化率、坡度、坡度变化率)进行联合估计; 将归一化新息平方和估计距离误差作为线路分段的判断条件, 最终用分段点和几何参数完成三维线路的生成; 采用仿真的平面线路数据对比了离散点法、三次多项式法和本文Fresnel法, 利用青藏线14.7 km的实测数据进一步对Fresnel法进行了验证。仿真结果表明: 在相同的误差要求下, 3种方法的平面距离误差均值都在0.024 m以内, 但Fresnel法采用了最少的分段点, 数据约简率高达99.76%; Fresnel法的最大累积里程误差最小, 由0.964 m降低为0.060 m, 减少了93.77%;Fresnel法比三次多项式法的方位角和曲率估计精度都高, 更加接近真值; 实际数据测试结果表明Fresnel法分别采用22个和20个分段点及参数即可完成线路的平面曲线和纵断面曲线生成, 平面和纵断面曲线距离误差均值都在0.03 m以内, 累积里程误差最大只有0.078 m, 位置精度和几何精度都较高。Abstract: To meet the requirements of digital track maps for the satellite-navigation-system-based train positioning, an unscented Kalman filter(UKF)-based track estimation method was proposed and a three-dimensional digital track map for railway tracks was generated. For the three basic curve elements(straight line, transition curve, and circular arc) in the horizontal profile of railway track, a mileage-parameterized Fresnel integral model was used for a unified modeling. For the straight line and curve in the vertical profile, a quadratic curve model was used for modeling. The states(mileage, three-dimensional coordinates) and parameters(heading, curvature, curvature rate, slope, and slope rate) of models were jointly estimated using the UKF. The normalized innovation squared and estimated distance error were introduced as the criteria to segment the track. The three-dimensional railway track was generated using the breakpoints along with the geometric parameters. The discrete point, cubic polynomial, and proposed Fresnel integral methods were compared by using the simulated horizontal track data. The Fresnel method was verified by using the 14.7 km field data from the Qinghai-Tibet Railway Line. Simulation result shows that the mean horizontal distance errors are below 0.024 m for all three methods under the same error requirement. However, the Fresnel method uses the fewest break points, with a data reduction rate of 99.76%. In addition, the maximum chainage error of Fresnel method is the smallest, which decreases from 0.964 m to only 0.060 m, with a reduction of 93.77%. The heading and curvature of Fresnel method are considerably more accurate than those of the cubic polynomial method, which are closer to the true value. The field data test results demonstrate that the Fresnel method can use 22 and 20 break points with their parameters to generate the horizontal and vertical curves, respectively. The mean distance errors of horizontal and vertical curves are below 0.03 m, while the maximum accumulative mileage error is only 0.078 m, which indicates high accuracies of both position and geometry.
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表 1 仿真结果误差对比
Table 1. Error comparison of simulation results
误差类别 方法 最大值 平均值 标准差 平面距离/m DP算法 0.079 0.024 0.018 三次多项式法 0.079 0.019 0.012 Fresnel法 0.077 0.019 0.013 累积里程/m DP算法 0.091 0.015 0.022 三次多项式法 0.964 0.467 0.269 Fresnel法 0.060 -0.008 0.021 方位角/rad 三次多项式法 4.759×10-3 2.964×10-6 7.002×10-4 Fresnel法 1.316×10-4 2.956×10-6 1.703×10-5 曲率/(rad·m-1) 三次多项式法 2.415×10-4 1.232×10-6 4.258×10-5 Fresnel法 3.046×10-5 7.253×10-8 1.117×10-6 
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表 2 实际线路数据平纵面误差结果
Table 2. Horizontal and vertical error results of field track
类别 约简率/% 距离误差最大值/m 距离误差均值/m 距离误差标准差/m 平面曲线 99.64 0.100 0.030 0.024 纵断面曲线 99.67 0.100 0.024 0.021
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