Traffic state estimation using stochastic Lagrangian dynamics

This paper proposes a new stochastic model of traffic dynamics in Lagrangian coordinates. The source of uncertainty is heterogeneity in driving behavior, captured using driver-specific speed-spacing relations, i.e., parametric uncertainty. It also results in smooth vehicle trajectories in a stochastic context, which is in agreement with real-world traffic dynamics and, thereby, overcoming issues with aggressive oscillation typically observed in sample paths of stochastic traffic flow models. We utilize ensemble filtering techniques for data assimilation (traffic state estimation), but derive the mean and covariance dynamics as the ensemble sizes go to infinity, thereby bypassing the need to sample from the parameter distributions while estimating the traffic states. As a result, the estimation algorithm is just a standard Kalman–Bucy algorithm, which renders the proposed approach amenable to real-time applications using recursive data. Data assimilation examples are performed and our results indicate good agreement with out-of-sample data.