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

Abstract

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). This paper introduces a non-linear 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 non-linear relationship between traffic data and time-dependent OD-flows. Specifically, we propose a model that takes advantage of Principal Component Analysis (PCA) to capture spatial correlations between variables and better exploit the local nature of a specific KF recently proposed in literature, the Local Ensemble Transformed Kalman filter (LETKF). The main advantage of the LETKF is that the Kalman gain is not explicitly formulated which means that, differently from other approaches proposed in the literature, there is no need to compute the assignment matrix or its approximation. The paper shows that the LETKF can easily incorporate different data sources, such as traffic counts and link speeds. Additionally, thanks to the PCA, the model can identify local patterns within the data and better explain the correlation between variables and data. The effectiveness of the proposed methodology is demonstrated first through synthetic experiments where non-linear functions are used to benchmark the model in different conditions 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.