A Novel Method Based on Dynamic Model Correction on Train Integrated Navigation Positioning
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摘要: 扩展卡尔曼滤波(Extended Kalman filter, EKF)的准确性依赖于观测的质量、观测对象的非线性程度及动态模型的准确性. 该方法通常假设其动态模型是不变的, 而且默认为非线性程度较弱, 这些在实际的车辆运动中都是不可靠的处理方式. 本文提出了一种利用最小二乘支持向量机(Least squares support vector machine, LSSVM)的技术增强扩展卡尔曼滤波的新算法. LSSVM改进后的EKF算法(LSSVM-EKF)一定程度上弥补了EKF处理强非线性问题的不足; 而且可以自适应地估计历史数据的动态建模偏差, 并使用估计偏差来补偿动态模型. 开发了一种引入Allan方差的K折交叉验证方法来确定LSSVM的训练参数; 将动态模型偏差通过有限数据集与LSSVM一起训练; 并引入无损变换将LSSVM与EKF进行了集成. 为了验证算法, 最后设计了车载试验, 并采用列车数据验证了文中所提的方法, 结果表明LSSVM-EKF可以较好地适应实际车辆运动环境, 可以提供一种可用的车辆定位方法.Abstract: The accuracy of extended Kalman filter (EKF) depends on the quality of the observation, the degree of nonlinearity of the observed object, and the accuracy of the dynamic model. The default is that the degree of nonlinearity is weak, and it is usually assumed that the dynamic model is constant, which is an unreliable treatment in actual vehicle motion. This paper proposes a new algorithm for enhancing the extended Kalman filtering using the technique of least squares support vector machine (LSSVM). The improved EKF algorithm (LSSVM-EKF) of LSSVM compensates for the insufficiency of the strong nonlinear problem of the EKF processing to some extent; and it can adaptively estimate the dynamic modeling deviation of historical data and use the estimated bias to compensate the dynamic model. A K-fold cross-validation method that introduces the Allan variance is developed to determine the training parameters of the LSSVM. The dynamic model deviation is trained with the LSSVM through the finite data set. The lossless transform is introduced to integrate the LSSVM with the EKF. In order to verify the algorithm, the paper finally designs the vehicle test, and uses the train data to verify the proposed method. The results show that LSSVM-EKF can adapt to the actual vehicle motion environment and provide a usable vehicle positioning method.1) 收稿日期 2019-03-18 录用日期 2019-09-12 Manuscript received March 18, 2019; accepted September 12, 2019 国家自然科学基金 (61863024, 71761023), 甘肃省高等学校科研项目 (2018C-11, 2018A-22), 甘肃省自然基金 (17JR5RA089, 18JR3RA130) 资助 Supported by National Natural Science Foundation of China (61863024, 71761023), Gansu Provincial Higher Education Research Project Funding (2018C-11, 2018A-22), and Natural Science Foundation of Gansu Provinaial of China (17JR5RA089, 18JR3RA130) 本文责任编委 阳春华2) Recommended by Associate Editor YANG Chun-Hua 1. 甘肃省高原交通信息工程及控制重点实验室, 兰州 7300702. 上海交通大学电子信息与电气工程学院, 上海 200240 3. 兰州交通大学交通运输学院, 兰州 730070 1. Gansu Provincial Key Laboratory of Traffic Information Engineering and Control, Lanzhou 730070 2. School of Electronic Information and Electrical Engineering, Shanghai Jiaotong University, Shanghai 200240 3. School of Traffic and Transportation, Lanzhou Jiaotong University, Lanzhou 730070
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表 1 计算量对比结果
Table 1 Comparison of calculation results
算法名称 绝对误差 (%) 具体运行时间 (s) NN 3.35 10.6 SVM 5.83 7.2 LSSVM 3.58 3.5 
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表 2 车载定位测量硬件主要参数
Table 2 Main parameters of vehicle positioning measurement hardware
性能指标 参数 IMU更新率 30 (Hz) 陀螺仪分辨率 0.007 (°/s) 陀螺仪零偏稳定性 0.007 (25 ℃, 1δ) (°/s) 陀螺仪随机游走 2.4 (25 ℃, 1δ) (°/ √Hz) 加速度计分辨率 0.33 (mg) 加速度计零偏稳定性 0.2 (25 ℃, 1δ) (mg) 加速度计随机游走 0.2 (25 ℃, 1δ) (m/s√Hz) 卫星板卡更新率 10 (Hz) 卫星单点定位精度 H: 3.0; V: 5.0 (m) 卫星测速精度 0.03 (m/s)
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表 3 车载实验速度误差的分析
Table 3 Analysis of the speed error in vehicle test
误差类型 算法 EKF SVM-EKF LSSVM-EKF 东向速度误差最大值) 2.44991596 1.64263965 1.08354018 东向速度误差均值 −0.51657986 −0.29959351 −0.21635647 东向速度平均绝对误差 0.57636153 0.35360989 0.23635647 东向速度误差均方差 0.46827009 0.17819068 0.10034921 北向速度误差最大值 5.95754509 4.48745292 1.98934116 北向速度误差均值 −0.17019196 −0.18793186 −0.08884883 北向速度平均绝对误差 0.81400385 0.65518412 0.30342385 北向速度误差均方差 0.92862895 0.59494707 0.12433562
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表 4 车载实验位置误差的分析
Table 4 Analysis of the position error in vehicle test
误差类型 算法 EKF SVM-EKF LSSVM-EKF 东向位置平均绝对误差 5.51618956 2.98874558 1.56598758 东向位置误差均方差 115.59446073 43.27129604 7.76993031 北向位置平均绝对误差 7.02954699 2.58372839 1.47242455 北向位置误差均方差 137.35228157 21.28974173 6.65581029
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表 5 卫星失锁情况下位置误差的分析
Table 5 Analysis of position error in case of satellite losing lock
误差类型 算法 EKF SVM-EKF LSSVM-EKF 东向速度误差最大值 71.277860 65.305870 32.099340 东向位置误差标准差 15.482577 10.476818 5.175138 北向位置误差最大值 57.812430 31.018930 15.966400 北向位置误差标准差 14.494762 6.471339 3.008621
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表 6 列车北向位置误差对比
Table 6 Comparison of train northward position error
算法名称 北向位置误差标准差 KF 7.303605 EKF 3.888531 LSSVM-EKF 1.682587
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