Mesoscopic Traffic State Estimation based on a Variational Formulation of the LWR Model in Lagrangian-space Coordinates and Kalman Filter

Abstract This paper proposes a new model-based traffic state estimation framework using the LWR model formulated in vehicle number – space (Lagrangian – space) coordinates. This formulation inherits the numerical benefits and modelling flexibility from Lagrangian (vehicle number – time) models. Specifically, a variational formulation of the LWR model is selected as the underlying process model. Compared to the traditional conservation law approach in the same coordinate system, the current formulation entitles a simplified expression (no complex state updating originated from different traffic conditions), and provides more accurate numerical results in the prediction step of the data assimilation framework (exact solution to the continuous model when the fundamental diagram is bi-linear). More importantly, this formulation is particularly convenient for data assimilation, because in reality, the flow characteristics are mostly observed at fixed point (spatial fixed) or along vehicle trajectories (vehicle number fixed). These observations are located on cell boundaries of the Lagrangian-space grid, which makes any traffic state estimation method convenient with this approach. Its corresponding observation models are also defined to incorporate both spatial-fixed and moving observations. A Kalman filter framework is applied with the underlying traffic system model. Moreover, travel time can be directly derived from system estimates, and no state transformation is required compared to other estimation approaches. Model validation experiment based on a synthetic traffic network has demonstrated the feasibility of the proposed framework, and suggested promising extensions for future applications.