D2D Cooperative Localization Approach Based on Euclidean Distance Matrix Completion

As one of the key technologies of the 5G, Device-to-device (D2D) can realize communication between terminals without a base station, thus making the cooperative positioning more convenient. In this paper, we propose a D2D cooperative localization approach based on matrix completion, which can tackle the problem of localization with an incomplete Euclidean Distance Matrix (EDM). In concrete terms, first of all, an incomplete EDM is constructed based on the known inadequate distance values between nodes, and then the Singular Value Threshold (SVT) algorithm is used to complete the EDM to obtain a recovered EDM. Secondly, Multidimensional Scaling (MDS) is used to reduce the recovered EDM dimension to obtain the relative position of nodes while maintaining the distance value between nodes. Finally, according to the relative position and global position of the anchor node, Procrustes Analysis (PA) is applied to obtain the transformation relationship, and the global positions of all nodes are further obtained. From extensive experimental results, it is evident that the proposed approach still has high localization performance even when a large proportion of elements are missing in the EDM.