Assignment Matrix Free Algorithms for On-line Estimation of Dynamic Origin-Destination Matrices

Dynamic Traffic Assignment (DTA) models represent fundamental tools to forecast traffic flows on road networks, assessing the effects of traffic management and transport policies. As biased models lead to incorrect predictions, which can cause inaccurate evaluations and huge social costs, the calibration of DTA models is an established and active research field. When it comes to estimating Origin-Destination (OD) demand flows, perhaps the most important input for DTA models, one algorithm suggested to outperform all the others for real-time applications: the Kalman Filter (KF). The paper introduces a nonlinear Kalman Filter framework for online dynamic OD estimation that reduces the number of variables and can easily incorporate heterogeneous data sources to better explain the nonlinear relationship between traffic data and time-dependent OD-flows. Specifically, we propose a model that takes advantage of Principal Component Analysis to better exploit the local nature of a specific KF recently proposed in literature, the Local Ensemble Transformed Kalman filter. The effectiveness of the proposed methodology is demonstrated first through a synthetic experiment where nonlinear functions have been adopted to simulate the assignment process and then on the real-world network of Vitoria, Spain (2.884 nodes, 5.799 links) using the mesoscopic simulator Aimsun. Results show that the proposed method leads to better state estimation performances with respect to other Ensemble-based Kalman filters, providing improvements as high as 64% in terms of traffic data reproduction with a 17-fold problem dimensionality reduction.