Observer-Informed Deep Learning for Traffic State Estimation With Boundary Sensing

Traffic state estimation (TSE) refers to the inference of macroscopic traffic states, including density, speed, and flow, based on partially observed traffic data and some prior knowledge of traffic dynamics. TSE plays a key role in traffic management since traffic control relies on accurate estimation of traffic states. This paper proposes a novel hybrid TSE approach called Observer-Informed Deep Learning (OIDL), which integrates a Partial Differential Equation (PDE) observer and deep learning paradigm to estimate spatial-temporal traffic states from boundary sensing data. The proposed OIDL consists of two modules, an Observer-Uninformed Neural Network (OUNN) to generate preliminary traffic state estimation, and an Observer-Informed Neural Network (OINN) constructed from a boundary observer with theoretical convergence guarantee to regularize the estimation. Furthermore, we propose Adaptive OIDL (aOIDL) to simultaneously estimate traffic states and model parameters. Experiments on the NGSIM dataset demonstrate that the proposed OIDL reduces the estimation error by up to 30 percent compared to the model-based observer, data-driven neural networks, and some hybrid TSE approaches. The OIDL also has smaller variance of the estimation error and presents more accurate pattern for congested traffic.