Uncertainty quantification for traffic state estimation at signalized intersections with low penetration vehicle trajectory data

This study investigates the problem of traffic state estimation at signalized intersections using low-penetration-rate vehicle trajectory data. While prior research has proposed various methods to estimate unknown traffic states and parameters—such as queue length and penetration rate—most provide only point estimates and do not characterize the uncertainty arising from sparse and noisy observations. However, understanding this uncertainty is essential for assessing the reliability of estimation results and for determining whether the available data are sufficient to support operational decision-making. To address this limitation, we develop a Bayesian estimation framework that yields distributional outputs, explicitly quantifying estimation uncertainty. The framework is built upon a novel hidden Markov model (HMM) formulation, in which a point-queue process captures the latent traffic dynamics, and an observation model connects the observed trajectories with the unknown quantities to be estimated. We also derive a recursive algorithm to estimate the unknown traffic states and parameters simultaneously. The proposed method is evaluated through simulation, and a comprehensive sensitivity analysis is conducted to examine how key factors influence the accuracy and uncertainty of the estimation results.