Trajectory reconstruction for travel time estimation

In this article, we propose a Trajectory Reconstruction Model as an improvement to existing speed-based travel time estimation models. The proposed model utilizes point-based speed data collected by existing Intelligent Transportation Systems (ITS). Using the smoothing scheme proposed, it is possible to construct a speed surface as a function of space and time. Then, one can reconstruct the trajectory of an imaginary vehicle by allowing it to adopt the local speed determined by the speed surface wherever the vehicle travels. Therefore, the travel time of this vehicle can be readily determined from its trajectory. This article develops an analytical formulation of the model. Meanwhile, a discrete version of the formulation is also provided as a computational algorithm to facilitate real world implementation. In comparison with existing models, the proposed model accounts for continuous speed variation in both time and space. This ensures that the model preserves vehicle trajectories and provides sound estimates of travel time. Empirical studies were conducted based on comparison of the reconstructed travel time (estimated by the proposed model) against the Ground Truth travel time and the Instantaneous and Linear Model travel time. The empirical results showed that (1) the reconstructed travel time agrees well with the Ground Truth travel time; (2) the reconstructed travel time is more smooth than the Ground Truth, Instantaneous, and Linear Model travel times; (3) the Instantaneous and Linear Model travel time does not exhibit much difference from the other two when traffic condition is good (e.g., low travel time for the same stretch of road); (4) the difference is noticeable when traffic condition deteriorates; and (5) the difference reaches its peak under severe congestion. Quantitatively, the reconstructed travel time is not statistically different from the Ground Truth travel time and the corresponding mean absolute percentage error (MAPE) is 6.3%. In contrast, the Linear and Instantaneous travel time is statistically different from the Ground Truth travel time and the corresponding MAPE is 11.7% and 14.0%, respectively.