Relation-diffusion augmented network-wide traffic state estimation under sparse sensor deployment

Network-wide traffic state estimation (TSE) under sparse sensor deployment aimed to infer traffic conditions at unobserved road segments from limited sensor observations. Existing diffusion graph convolutional methods mainly propagate node features over physical topology or adaptive graphs, but the adaptive relationships involving unobserved nodes are often weakly supported because their traffic features are missing, zero-padded, or represented only by initialized embeddings. To address this limitation, this study proposed the relation-augmented diffusion graph convolution network (RADGCN), a relation-aware adaptive diffusion framework for TSE under sparse observations. RADGCN first learned functional relationships among observed nodes using reliable temporal traffic features and graph-aware attention and then propagated these relationships to the full network through learnable bilateral diffusion kernels. The resulting relation matrix was incorporated into diffusion graph convolution as an additional transition operator, allowing traffic states to be estimated through both physical topology and learned functional dependencies. An auxiliary edge prediction task was further introduced to regularize node embeddings under inductive K-order neighborhood subgraph training. Experiments across three benchmark datasets showed that RADGCN consistently outperformed state-of-the-art baselines across different sparse-sensor settings, achieving average improvements of 2.97%–11.82% in mean absolute error (MAE), root mean square error (RMSE), and mean absolute percentage error (MAPE). Additional ablation results verified the effectiveness of relation diffusion, relation-augmented feature propagation, and K-order subgraph sampling. Further experiments also validated RADGCN's generalizability across datasets and robustness to sensor sparsity.