Integrated macro-micro modelling for individual vehicle trajectory reconstruction using fixed and mobile sensor data

Vehicle trajectories can provide a clear picture of the traffic flow that plays a pivotal role in traffic management and control. Two types of traffic sensors, i.e., fixed and mobile sensors, are widely adopted to collect road traffic information. However, fully-sampled vehicle trajectories are far from obtainable through those sensors due to their fixed-location measurements or low penetration rates. To overcome these issues, this study proposes an integrated macro–micro framework to reconstruct individual vehicle trajectories on freeways under a multi-source data environment, in which fixed-location sensor data that collect positions and velocities of vehicles in a certain place and a small fraction of probe vehicle (PV) data that yield continuous trajectories are available. The framework consists of three modules. First, at the macro level, we apply shockwave theory and fundamental diagram to expand the partially detected information to the whole space–time diagram, and then establish a velocity baseline for evaluation of the trajectory fusion thereafter. Second, at the micro level, we develop two trajectory estimation algorithms based on extended car-following models to generate individual trajectories between any two consecutive PVs, in which two candidate trajectories will be generated for each non-probe vehicle. Third, we tailor a trajectory fusion algorithm to integrate the macro- and micro-level models, and apply dynamic programming to solve the optimal trajectories as per the established velocity baseline. The proposed framework is finally tested with NGSIM and HighD datasets. The results show that our integrated method attains a notable improvement in accuracies and smoothness of reconstructed trajectories compared to the non-integrated and the classical Variational Theory-based methods respectively.