Trajectory reconstruction for mixed traffic flow with regular, connected, and connected automated vehicles on freeway

Vehicular trajectory data collected by connected automated vehicles (CAVs) is minimal due to the low penetration rates (PRs) of CAVs, and fail to capture the characteristics of traffic flow. This study proposes a fully sampled trajectory reconstruction method for mixed traffic flow with regular vehicles (RVs), connected vehicles (CVs), and CAVs based on car-following behaviour. Firstly, considering the minimum safety distance constraints between vehicles, an optimization model for minimizing the impact on the acceleration of the known vehicles is developed to obtain the number of inserted RVs. Secondly, the speed of the inserted RVs is estimated based on the traffic flow model. Then, an optimization model is proposed to determine the position of each inserted RV. Finally, numerical simulation is designed to investigate the influence of traffic density and PRs of CAVs and CVs. Results show that the proposed method can better reconstruct the vehicle trajectory on the freeway under the different traffic densities in a congested state. The MAPE of the number and position of inserted RVs is less than 10.7% and 0.37%, respectively. In addition, the proposed method performs well even if the PRs of CAVs and CVs are extremely low.