Robust Traffic Density Estimation Using Discontinuous Galerkin Formulation of a Macroscopic Model

In this paper, we develop a data-assimilation algorithm for a macroscopic model of traffic flow. The algorithm is based on the Discontinuous Galerkin Method and Minimax Estimation, and is applied to a macroscopic model based on a scalar conservation law. We present numerical results which demonstrate the shock-capturing capability of the algorithm under high uncertainty in the initial traffic condition, using only sparse measurements, and under time-dependent boundary conditions. The latter makes it possible for estimation to be performed on merge/diverge sections, allowing the possibility of the deployment of the algorithm to road networks.