Traffic Volume Estimation for both Undersaturated and Oversaturated Signalized Intersections With Stopbar Location Estimation Using Trajectory Data

Abstract

We proposed an estimator for traffic volumes at signalized intersections using only sparse trajectory data. Each pair of observed trajectories defined a statistical event, from which traffic volume was inferred. The interaction between trajectory stop distances, arrival speeds, and signal plan defined different classes of statistical events, with distinct likelihood expressions. Contrary to recent approaches found in the literature, our method addressed oversaturation and residual queues. We also proposed a method to estimate stopbar location, crucial to properly estimating stop distances and queue lengths. Arrivals were assumed to follow a negative exponential distribution., and the method was compatible with any kind of control. The signal plan was assumed to be known, but an estimated signal plan could also be used. The estimation was formulated as a maximum marginal likelihood problem. We showed the problem to be globally concave and, thus, optimally solvable by standard gradient-based methods. The estimator was first validated by an event-based Lighthill–Whitham–Richards simulation, suppressing any measurement errors from trajectories and uncertainty from driver behavior. The estimator was found to consistently show bias below 10% in low-penetration-rate situations, when the $\upsilon /c$ ratio was medium to high. Finally, the estimator was tested at a real-world intersection set by the authors in Beijing, China, which obtained a bias of similar of magnitude.