Abstract This paper studies Deep Convolutional Neural Networks (DCNNs) for the accurate estimation of space–time traffic speeds given sparse data on freeways. Several aspects are highlighted which are crucial for the large-scale application of DCNNs to empirical probe data. (i) A methodology is proposed that allows to effectively train DCNNs on variable-sized space–time domains given empirical data prone to a varying penetration rate. Therefore, space–time domains are decomposed into small unified grids, which are processed separately. Second, in order to cope with varying penetration rates of available probe data, the network input is designed as two input matrices: grid-based speed data and grid occupancies. (ii) Using empirical probe data collected during 43 congestion scenarios on a freeway of 143 km length a shallow encoding–decoding CNN and a deep CNN are trained to reconstruct heterogeneous congestion types, such as moving and stationary congestion. It is demonstrated that for training only data of a single sparse data source is needed but no complete Ground Truth (GT), and still heterogeneous congestion types are reconstructed accurately. (iii) The estimation accuracy of a shallow encoding–decoding CNN and a DCNN, based on the U-net, are compared with traditional methods such as the ASM and PSM. An unseen complex congestion scenario is studied with all approaches and the estimation results are analyzed qualitatively and quantitatively. It is shown, that the DCNN outperforms the other approaches significantly.

Highlights • Extensive study of deep convolutional neural networks (DCNN) to traffic speed estimation with probe data. • Novel methodology to handle variable-sized space–time domains and varying penetration rate. • Training is accomplished with large empirical dataset comprising Floating Car Data. • Trained network reconstructs heterogeneous congestion patterns with high accuracy. • The studied deep neural network architecture outperforms the ASM, PSM and two shallow CNNs.