A cascading Kalman filtering framework for real-time urban network flow estimation

In this work we develop a kalman filtering approach for the problem of traffic state estimation in urban networks. The proposed approach employs concepts developed in the field of traffic flow observability, to derive both i) a minimal set of locations wherein traffic sensing infrastructure the network should be equipped and ii) topological relationships to be employed in the filtering technique's error covariance matrices, to improve the estimation process. A Linear Time-Variant formulation of first-order traffic flow theory is employed to model node-node vehicle propagation, allowing to predict the evolution of Cumulative Vehicle Numbers at intersections. This model is then embedded in the proposed cascading Kalman Filter framework. Validation of the proposed filtering approach is performed on a simple grid-like network, bearing considerable congestion, spillback and rerouting behaviour. We generate experimental data through a microscopic simulation software (SUMO). Test results showcase how the proposed approach successfully exploits observability-based information to reconstruct data in unmeasured segments of the network. Particular care should however be devoted to appropriate inference of turning fractions at intersections, in order to achieve the lowest possible estimation error.