Filter Comparison for Estimation on Discretized PDEs Modeling Traffic: Ensemble Kalman Filter and Minimax Filter

Traffic State Estimation (TSE) refers to the estimation of the state (i.e., density, speed, or other parameters) of vehicular traffic on roads based on partial observation data (e.g., road-side detectors and on-vehicle GPS devices). It can be used as a component in applications such as traffic control systems as a means to identify and alleviate congestion. In existing studies, the Kalman Filter and its extensions, notably the Ensemble Kalman Filter (EnKF), are commonly employed for TSE. Recently, the MF has been newly adapted to this domain as a filtering algorithm for TSE. In this article, we compare the performance of the EnKF and the MF on discretized PDE models of traffic flow traffic. Specifically, for the EnKF study, the estimation is performed using stationary and mobile sensor information based on actual traffic data, by employing EnKF in conjunction with a Godunov discretization of the Lighthill-Whitham-Richards (LWR) model. For the minimax study, the discontinuous Galerkin formulation of the LWR model is used in conjunction with the implicitly-linearized MF to obtain state estimates using the same data. The advantages and disadvantages of each of the filters are empirically quantified. Insights for practical application and future research directions are presented.