Traffic Estimation and Prediction via Online Variational Bayesian Subspace Filtering

With the increased proliferation of smart devices, the transit passengers of today expect a higher quality of service in the form of real-time traffic updates, accurate expected time-of-arrival (ETA) predictions. Providing these services requires public transit agencies and private transportation players to maintain full situational awareness of the city-wide traffic. However, most such agencies and companies are resource-constrained and do not have access to city-wide traffic data. The availability of sparsely sampled and outlier-corrupted traffic data renders the resulting traffic maps patchy and unreliable and necessitates the use of sophisticated real-time traffic interpolation and prediction algorithms. Moreover, since the traffic data is measured and collected in a sequential manner, the estimations must also be generated online. Thankfully, the traffic matrices are spatially and temporally structured, allowing the use of time-series and matrix/tensor completion algorithms. This work puts forth a generative model for the traffic density and subsequently uses a variational Bayesian formalism to learn the parameters of the model. Specifically, we consider low-rank traffic matrices whose subspace evolves according to a state-space model with possible sparse outliers. Unlike most matrix/tensor completion algorithms, the proposed model is equipped with automatic relevance determination priors that allow it to learn the parameters in an entirely data-driven manner. A forward-backward algorithm is proposed that enables the updates to be carried out at low-complexity. Simulations carried out on real traffic speed data demonstrate that the proposed algorithm better predicts the future traffic densities as compared to the state-of-the-art matrix/tensor completion algorithms.