Reconstructing maximum likelihood trajectory of probe vehicles between sparse updates

•We propose an approach to reconstruct trajectories using sparse probe vehicle data.•An EM algorithm is used to allocate travel time to small segments.•Our approach can estimate stop position and duration at intersection accurately.•Comparison with ground truth data demonstrates the effectiveness. Data from connected probe vehicles can be critical in estimating road traffic conditions. Unfortunately, current available data is usually sparse due to the low reporting frequency and the low penetration rate of probe vehicles. To help fill the gaps in data, this paper presents an approach for estimating the maximum likelihood trajectory (MLT) of a probe vehicle in between two data updates on arterial roads. A public data feed from transit buses in the city of San Francisco is used as an example data source. Low frequency updates (at every 200m or 90s) leaves much to be inferred. We first estimate travel time statistics along the road and queue patterns at intersections from historical probe data. The path is divided into short segments, and an Expectation Maximization (EM) algorithm is proposed for allocating travel time statistics to each segment. Then the trajectory with the maximum likelihood is generated based on segment travel time statistics. The results are compared with high frequency ground truth data in multiple scenarios, which demonstrate the effectiveness of the proposed approach, in estimating both the trajectory while moving and the stop positions and durations at intersections.