基于改进的反距离权重插值的车辆轨迹重构方法
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摘要
为解决车辆行驶过程中,时常出现的信息丢失、数据接收障碍等问题,提出了反距离权重插值方法。反距离权重插值算法因其简单,普适性强被广泛用于车辆轨迹重构,但车辆轨迹数据的分布多呈现离散、不均匀状态,当分布点采集不均匀时反距离权重插值方法会严重影响插值精度。针对这一问题,结合自然邻近关系的良好自适应分布特性,提出一种改进的反距离权重插值方法。首先,将车辆轨迹数据与道路路网数据进行匹配后,采用3σ准则法对车辆轨迹数据进行粗差剔除预处理。其次,对轨迹数据构建初始路网,并通过逐点插值法对初始路网进行插值,局部调整得到新的车辆轨迹,以待插点的一阶邻近点作为反距离权重插值参考点,通过建立自适应规则,调整各子区域内的变化参数,使其均匀地分布在待插值点周围,再进行反距离权重插值计算。最后,采用山东省淄博市的出租车轨迹数据对提出改进的反距离权重插值方法进行验证,收到了良好的效果。并在插值精度方面与当下应用较广的插值算法进行对比试验,试验表明,改进的反距离权重插值算法在原有性能的基础上具有更高的插值精度,可以应用于车辆轨迹数据丢失后的修补工作。
In order to solve the problem of loss of information and obstacles to data reception,an inverse distance weight interpolation method is proposed. The inverse distance weight interpolation algorithm is widely used in vehicle trajectory reconstruction because of its simplicity and universal applicability. However,the distribution of vehicle trajectory data is mostly discrete and uneven,and the interpolation method can seriously affect the interpolation accuracy when the distribution points are not uniform. In order to solve this problem,an improved inverse distance weighted interpolation method is proposed based on the good selfadaptive distribution of natural neighbor relations. First,the vehicle trajectory data are matched with the road network data,and the gross error elimination pretreatment of vehicle trajectory data is performed by the 3σcriterion method. Second,an initial road network is built for trajectory data,and through point by point interpolation method is used for initial network interpolation,and partial adjustment is performed to get new vehicle trajectory. Taking the first-order neighbor point of the point to be interpolated as a reference point forinverse distance weight interpolation,through the establishment of self-adaptive rules,the change parameters in each subarea are adjusted so that they are evenly distributed around the points to be interpolated,and then the calculation of inverse distance weight interpolation is performed. Finally,by using the trajectory data of taxis in Zibo City of Shandong Province,of the proposed improved inverse distance weighted interpolation method is validated,which has received the good effect. The comparative experiment in the precision between the proposed method and the current widely used interpolation algorithm is conducted,the result shows that the improved inverse distance weight interpolation algorithm has higher interpolation precision than the original performance,and can be applied to the repair work after the loss of vehicle trajectory data.
In order to solve the problem of loss of information and obstacles to data reception,an inverse distance weight interpolation method is proposed. The inverse distance weight interpolation algorithm is widely used in vehicle trajectory reconstruction because of its simplicity and universal applicability. However,the distribution of vehicle trajectory data is mostly discrete and uneven,and the interpolation method can seriously affect the interpolation accuracy when the distribution points are not uniform. In order to solve this problem,an improved inverse distance weighted interpolation method is proposed based on the good selfadaptive distribution of natural neighbor relations. First,the vehicle trajectory data are matched with the road network data,and the gross error elimination pretreatment of vehicle trajectory data is performed by the 3σcriterion method. Second,an initial road network is built for trajectory data,and through point by point interpolation method is used for initial network interpolation,and partial adjustment is performed to get new vehicle trajectory. Taking the first-order neighbor point of the point to be interpolated as a reference point forinverse distance weight interpolation,through the establishment of self-adaptive rules,the change parameters in each subarea are adjusted so that they are evenly distributed around the points to be interpolated,and then the calculation of inverse distance weight interpolation is performed. Finally,by using the trajectory data of taxis in Zibo City of Shandong Province,of the proposed improved inverse distance weighted interpolation method is validated,which has received the good effect. The comparative experiment in the precision between the proposed method and the current widely used interpolation algorithm is conducted,the result shows that the improved inverse distance weight interpolation algorithm has higher interpolation precision than the original performance,and can be applied to the repair work after the loss of vehicle trajectory data.
引文
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[18]张金秋,赵庶旭,屈睿涛.基于点与热度的交通时空数据可视化[J].兰州交通大学学报,2017,36(3):63-69,75.ZHANG Jin-qiu, ZHAO Shu-xu, QU Rui-tao.Visualization of Traffic Spatio-Temporal Data Based on Point and Heatmap[J]. Journal of Lanzhou Jiaotong University,2017,36(3):63-69,75.
[2] JENELIUS E, KOUTSOPOULOS H N. Travel Time Estimation for Urban Road Networks Using Low Frequency Probe Vehicle Data[J]. Transportation Research Part B:Methodological,2013,53(4):64-81.
[3] FRENTZOS E, GRATSIAS K, PELEKIS N, et al.Algorithms for Nearest Neighbor Search on Moving Object Trajectories[J]. Geoinformatica,2007,11(2):159-193.
[4] XING Y,XU R,TAN J,et al. A Class of Generalized Bspline Quaternion Curves[J]. Applied Mathematics and Computation,2015,271:288-300.
[5] BOGORNY V, RENSO C, AQUINO A R, et al.Constant:A Conceptual Data Model for Semantic Trajectories of Moving Objects[J]. Transactions in GIS,2014,18(1):66-88.
[6]陈志军,吴超仲,吕能超,等.基于改进三次Hermite插值的车辆时空轨迹重构研究[J].交通信息与安全,2013,31(6):43-46.CHEN Zhi-jun,WU Chao-zhong,LNeng-chao,et al.Vehicle Trajectory Reconstruction Based on Improved Cubic Hermite Interpolation[J]. Journal of Transport Information and Safety,2013,31(6):43-46.
[7]张健钦,李明轩,段颖超,等.一种改进的快速浮动车地图匹配方法[J].测绘通报,2017(1):87-92.ZHANG Jian-qin,LI Ming-xuan,DUAN Ying-chao,et al. An Improved Algorithm for Fast Map-matching of Floating Car[J]. Bulletin of Surveying and Mapping,2017(1):87-92.
[8] SHEPARD D. Geography and the Properties of Surfaces.A Two-dimensional Interpolation Function for Computer Mapping of Irregularly Spaced Data[C]//ACM'68Proceedings of the 1968 23rd ACM National Conference.New York:ACM,1968.
[9]孔龙星,汤晓安,张俊达,等.顾及局部特性的自适应3D矢量场反距离权重插值法[J].系统工程与电子技术,2016,38(7):1697-1702.KONG Long-Xing,TANG Xiao-an,ZHANG Jun-da,et al. Adaptive IDW Interpolation Method Involving Local Behavior for 3D Vector Field[J]. Systems Engineering and Electronics,2016,38(7):1697-1702.
[10] DE MESNARD L. Pollution Models and Inverse Distance Weighting:Some Critical Remarks[J]. Computers&Geosciences,2013,52(1):459-469.
[11] LI Y,WANG W,YA L,et al. Study of an Atomic Clock Steering Method Based on Least Square[C]//Frequency Control Symposium(FCS), 2014 IEEE International.Taipei:IEEE,2014:1-4.
[12] MARTINI A,COCO D,SORCE A,et al. Gross Error Detection Based on Serial Elimination:Applications to an Industrial Gas Turbine[C]//ASME Turbo Expo 2014:Turbine Technical Conference and Exposition. Dusseldorf:American Society of Mechanical Engineers,2014.
[13]高鹏,石为人,周伟,等.基于图论模糊聚类的室内自适应RSSI定位算法[J].仪器仪表学报,2013,34(9):1998-2004.GAO Peng, SHI Wei-ren, ZHOU Wei, et al, Indoor Adaptive RSSI Localization Algorithm Based on Graph Theory and Fuzzy Clustering in Wireless Sensor Networks[J]. Chinese Journal of Scientific Instrument,2013,34(9):1998-2004.
[14] PIAH A R M,SAABAN A,ABD M A. Range Restricted Positivity-preserving Scattered Data Interpolation[J].Journal of Fundamental and Applied Sciences,2014,2(1/2):63-75.
[15] CUOMO S,GALLETTI A,GIUNTA G,et al. A Novel Triangle-based Method for Scattered Data Interpolation[J]. Applied Mathematical Sciences,2014,8(134):6717-6724.
[16] PENG J,YU Y,ZHOU W,et al. Using Triangle-based Cubic Interpolation in Generation of Object-adaptive Fringe Pattern[J]. Optics and Lasers in Engineering,2014,52(1):41-52.
[17] DECLERCQ F A N. Interpolation Methods for Scattered Sample Data:Accuracy,Spatial Patterns,Processing Time[J]. Cartography and Geographic Information Systems,2006,23(3):128-144.
[18]张金秋,赵庶旭,屈睿涛.基于点与热度的交通时空数据可视化[J].兰州交通大学学报,2017,36(3):63-69,75.ZHANG Jin-qiu, ZHAO Shu-xu, QU Rui-tao.Visualization of Traffic Spatio-Temporal Data Based on Point and Heatmap[J]. Journal of Lanzhou Jiaotong University,2017,36(3):63-69,75.