Low-Rank Hankel Tensor Completion for Traffic Speed Estimation

This paper studies the traffic state estimation (TSE) problem using sparse observations from mobile sensors. Most existing TSE methods either rely on well-defined physical traffic flow models or require large amounts of simulation data as input to train learning algorithms. Different from previous studies, in this paper we propose a purely data-driven and model-free solution. We consider TSE as a spatiotemporal matrix completion/interpolation problem and apply spatiotemporal delay embedding to transform the original incomplete matrix into a fourth-order Hankel structured tensor. By imposing a low-rank assumption on this tensor structure, we can approximate and characterize both global patterns and local patterns in a data-driven manner. We use a truncated nuclear norm of a balanced spatiotemporal unfolding to approximate the tensor rank and develop an efficient algorithm based on the Alternating Direction Method of Multipliers (ADMM) to solve the problem. The proposed framework only involves two hyperparameters, spatial and temporal window lengths, which are easy to set given the degree of data sparsity. To validate the effectiveness of our proposed method, we conducted numerical experiments on real-world high-resolution trajectory data, which demonstrated its superiority in some challenging scenarios. The proposed method shows great potential for solving the TSE problem using sparse observations from mobile sensors and can be applied in various traffic applications.