Network-wide traffic state estimation using a mixture Gaussian graphical model and graphical lasso

Abstract

This study proposes a model that estimates unobserved highway link speeds by a machine learning technique using historical probe vehicle data. For highway traffic monitoring, probe vehicle data is one of the most promising data source. However, since such data do not always cover an entire study area, we cannot measure traffic speeds on all links in a time-dependent manner; quite a few links are unobserved. To continuously monitor speeds on all links, it is necessary to develop a technique that estimates speeds on unobserved links from historical observed link speeds. For this purpose, we extend the current Gaussian graphical model so as to use two or more multivariate normal distributions to accurately estimate unobserved link speeds. In general, since the number of unknown model parameters (mean parameters and covariance matrices) is enormous and also unobserved links always exist, the EM algorithm and the graphical lasso technique are employed to determine the model parameters. Our proposed model was applied to the Bangkok city center in Thailand as well as to the Fujisawa city in Japan. We confirmed that the model can estimate the unobserved link speeds quite reasonably.