Real-Time Lagrangian Traffic State Estimator for Freeways

Freeway traffic state estimation and prediction are central components in real-time traffic management and information applications. Model-based traffic state estimators consist of a dynamic model for the state variables (e.g., a first- or second-order macroscopic traffic flow model), a set of observation equations relating sensor observations to the system state (e.g., the fundamental diagrams), and a data-assimilation technique to combine the model predictions with the sensor observations [e.g., the extended Kalman filter (EKF)]. Commonly, both process and observation models are formulated in Eulerian (space-time) coordinates. Recent studies have shown that this model can be formulated and solved more efficiently and accurately in Lagrangian (vehicle number-time) coordinates. In this paper, we propose a new model-based state estimator based on the EKF technique, in which the discretized Lagrangian Lighthill-Whitham and Richards (LWR) model is used as the process equation, and in which observation models for both Eulerian and Lagrangian sensor data (from loop detectors and vehicle trajectories, respectively) are incorporated. This Lagrangian state estimator is validated and compared with a Eulerian state estimator based on the same LWR model using an empirical microscopic traffic data set from the U.K. The results indicate that the Lagrangian estimator is significantly more accurate and offers computational and theoretical benefits over the Eulerian approach.