A Matrix Completion-Based Cooperative Localization Scheme for 3D Indoor Environments

Device-to-device communication can realize the measure of terminals without any base station, thus achieving more convenience of cooperative localization. However, the non-line-of-sight (NLoS) condition or interruption may cause missing distance data in the harsh indoor environment, which results in low position accuracy between nodes. To address this issue, we propose a three-dimensional cooperative localization scheme based on matrix completion to estimate the missing localization information. Making full use of Euclidean distance matrix (EDM) properties, we convert the nonconvex rank constraint problem into the convex one with a positive semidefinite condition and improve the completion accuracy. Exploiting Gram matrix, we further obtain the relative positions of nodes while maintaining the distance relationship among them. Finally, we transform the relative positions to the global ones according to very few anchor nodes. Experimental results demonstrate that our scheme has high positioning accuracy even when a large proportion of elements are missing in the EDM.