Freeway traffic state estimation using extended Kalman filter for first-order traffic model in Lagrangian coordinates

Freeway traffic state estimation is one of the central components in real-time traffic management and information applications. Recent studies show that the classic kinematic wave model can be formulated and solved more efficiently and accurately in Lagrangian (vehicle number-time) coordinates. This paper investigates the opportunities of the Lagrangian form for state estimation. The main advantage for state estimation is that in Lagrangian coordinates, the numerical solution scheme is reduced to an upwind scheme. We propose a new model-based extended Kalman filter (EKF) state estimator where the discretized Lagrangian model is used as the model equation. This state estimator is applied to freeway traffic state estimation and validated using synthetic data. Different filter design specifications with respect to measurement aspects are considered. The achieved results are very promising for subsequent studies.