A conditional diffusion model for probabilistic estimation of traffic states at sensor-free locations

Transportation administrators and urban planners rely on accurate network-wide traffic state estimation to make well-informed decisions. However, due to insufficient sensor coverage, traffic state estimation at sensor-free locations (TSES) poses significant challenges for downstream network-wide traffic analysis. This is because direct observations are not available at these sensor-free locations. Most existing traffic state estimation (TSE) research focuses on inferring several unknown time points based on observed historical data using deterministic models. In contrast, TSES is to infer the entire unknown traffic time series of a given sensor-free node, thereby presenting high predictive difficulty, as we could not learn any historical traffic patterns locally. In this study, we introduce a novel probabilistic model — the conditional diffusion framework with spatio-temporal estimator (CDSTE) — to tackle the TSES problem. When dealing with TSES, deterministic models can only produce point value estimates, which may substantially deviate from the actual traffic states of sensor-free locations. To mitigate this, the proposed CDSTE integrates the conditional diffusion framework with cutting-edge spatio-temporal networks to extract the underlying dependencies in traffic states between sensor-free and sensor-equipped nodes. This integration enables reliable probabilistic traffic state estimations for sensor-free locations, which can be used to quantify the variability of estimations in TSES to support flexible and robust decision-making processes for traffic management and control. Extensive numerical experiments on real-world datasets demonstrate the superior performance of CDSTE for TSES over five widely-used baseline models.