SATORIS-N: Spectral Analysis based Traffic Observation Recovery via Informed Subspaces and Nuclear-norm minimization

Traffic-density matrices from different days exhibit both low rank and stable correlations in their singular-vector subspaces. Leveraging this, we introduce SATORIS-N, a framework for imputing partially observed traffic-density by informed subspace priors from neighboring days. Our contribution is a subspace-aware semidefinite programming (SDP)} formulation of nuclear norm that explicitly informs the reconstruction with prior singular-subspace information. This convex formulation jointly enforces low rank and subspace alignment, providing a single global optimum and substantially improving accuracy under medium and high occlusion. We also study a lightweight implicit subspace-alignment} strategy in which matrices from consecutive days are concatenated to encourage alignment of spatial or temporal singular directions. Although this heuristic offers modest gains when missing rates are low, the explicit SDP approach is markedly more robust when large fractions of entries are missing. Across two real-world datasets (Beijing and Shanghai), SATORIS-N consistently outperforms standard matrix-completion methods such as SoftImpute, IterativeSVD, statistical, and even deep learning baselines at high occlusion levels. The framework generalizes to other spatiotemporal settings in which singular subspaces evolve slowly over time. In the context of intelligent vehicles and vehicle-to-everything (V2X) systems, accurate traffic-density reconstruction enables critical applications including cooperative perception, predictive routing, and vehicle-to-infrastructure (V2I) communication optimization. When infrastructure sensors or vehicle-reported observations are incomplete - due to communication dropouts, sensor occlusions, or sparse connected vehicle penetration-reliable imputation becomes essential for safe and efficient autonomous navigation.

SMILE: Robust Network Localization via Sparse and Low-Rank Matrix Decomposition

Motivated by collaborative localization in robotic sensor networks, we consider the problem of large-scale network localization where location estimates are derived from inter-node radio signals. Well-established methods for network localization commonly assume that all radio links are line-of-sight and subject to Gaussian noise. However, the presence of obstacles which cause non-line-of-sight attenuation present distinct challenges. To enable robust network localization, we present Sparse Matrix Inference and Linear Embedding (SMILE), a novel approach which draws on both the well-known Locally Linear Embedding (LLE) algorithm and recent advances in sparse plus low-rank matrix decomposition. We demonstrate that our approach is robust to noisy signal propagation, severe attenuation due to non-line-of-sight, and missing pairwise measurements. Our experiments include simulated large-scale networks, an 11-node sensor network, and an 18-node network of mobile robots and static anchor radios in a GPS-denied limestone mine. Our findings indicate that SMILE outperforms classical multidimensional scaling (MDS) which ignores the effect of non-line of sight (NLOS), as well as outperforming state-of-the-art robust network localization algorithms that do account for NLOS attenuation including a graph convolutional network-based approach. We demonstrate that this improved accuracy is not at the cost of complexity, as SMILE sees reduced computation time for very large networks which is important for position estimation updates in a dynamic setting, e.g for mobile robots.