Collecting traffic volume data is a vital but costly piece of transportation engineering and urban planning. In recent years, efforts have been made to estimate traffic volumes using passively collected probe data that contain spatiotemporal information. However, the feasibility and underlying principles of traffic volume estimation based on probe data without pseudonyms have not been examined thoroughly. In this paper, we present the exact distribution of the estimated probe traffic volume passing through a road segment based on probe point data without trajectory reconstruction. The distribution of the estimated probe traffic volume can exhibit multimodality, without necessarily being line-symmetric with respect to the actual probe traffic volume. As more probes are present, the distribution approaches a normal distribution. The conformity of the distribution was demonstrated through numerical and microscopic traffic simulations. Theoretically, with a well-calibrated probe penetration rate, traffic volumes in a road segment can be estimated using probe point data with high precision even at a low probe penetration rate. Furthermore, sometimes there is a local optimum cordon length that maximises estimation precision. The theoretical variance of the estimated probe traffic volume can address heteroscedasticity in the modelling of traffic volume estimates.

翻译：采集交通量数据是交通工程与城市规划中至关重要但成本高昂的工作。近年来，研究者利用被动采集的含时空信息的探测数据来估计交通量。然而，基于无匿名标识的探测数据估计交通量的可行性及其基本原理尚未得到充分研究。本文基于不进行轨迹重构的探测点数据，给出了通过路段估计探测交通量的精确分布。该估计探测交通量的分布可能呈现多峰性，且不一定关于真实探测交通量呈线对称。随着探测车辆数量增加，该分布趋近于正态分布。通过数值仿真与微观交通仿真验证了该分布的吻合性。理论上，若探测渗透率经过良好标定，即使渗透率较低，也可利用探测点数据高精度估计路段交通量。此外，在某些情况下存在局部最优检测区间长度，可最大化估计精度。估计探测交通量的理论方差可解决交通量估计建模中的异方差性问题。