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.