Traffic state estimation using stochastic Lagrangian dynamics
For traffic engineers and researchers, this work provides a computationally efficient, real-time-capable method for traffic state estimation that handles driver heterogeneity without sampling issues.
This paper introduces a stochastic Lagrangian traffic model that accounts for driver heterogeneity and avoids aggressive oscillations in sample paths. Using ensemble filtering with mean and covariance dynamics derived in the infinite-ensemble limit, the method reduces to a standard Kalman-Bucy filter, enabling real-time traffic state estimation with good agreement to out-of-sample data.
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.