Vehicle Trajectory Reconstruction from Sparse Data Using a Hybrid Approach

Vehicle trajectories deliver precious information, supporting traffic state estimation and congested traffic mitigation. However, collecting fully sampled vehicle trajectories is difficult due to unaffordable data-collection costs and maintenance costs of data collection equipment. This study aims to accurately reconstruct missing vehicle trajectories by proposing a novel approach based on sparse data collected from different types of urban roads. First, an improved map-matching algorithm combining a hidden Markov model (HMM) and a bidirectional Dijkstra algorithm is proposed to ensure the high quality of the input data for trajectory reconstruction. The matched trajectory points are then converted into a two-dimensional time-space map. Subsequently, a piecewise cubic Hermite interpolating polynomial (PCHIP) algorithm is developed to reconstruct vehicle trajectories based on a total of 371 taxi trajectories on three types of urban roads. The results demonstrate that the speed-based mean relative error (MRE) value is less than 9%, and the speed-based root mean square error (RMSE_v) value is less than 6 km/h. Furthermore, the location-based MAE is found to be less than 5.86 m, and the location-based RMSE_x value is less than 7 m. Additionally, a model comparison is conducted, and the outcomes evidence that the combined method performs better than state-of-the-art approaches.