Device-to-Device Cooperative Positioning via Matrix Completion and Anchor Selection

Abstract

As one of the key technologies of the 5G, the device-to-device (D2D) can realize communication between terminals without any base station, thus achieving more convenience of cooperative positioning. In this article, we propose a D2D cooperative positioning approach via matrix completion and anchor selection, which tackles the positioning problem with inadequate distance information. Specifically, first, an incomplete Euclidean distance matrix (EDM) is constructed by using insufficient distance information between nodes, and then the singular value thresholding (SVT) algorithm is used to recovery this EDM to obtain completed information. Second, multidimensional scaling (MDS) is performed to reduce dimensions of recovered EDM, which aims to obtain the relative positions of nodes while maintaining the distance relationship among them. Third, a set of suitable anchor nodes is selected by using the Hodges–Lehmann (HL) test for position transformation. Finally, we apply the procrustes analysis (PA) to transform the relative positions to the global ones according to the selected set of suitable anchor nodes. From the extensive experimental results, it is evident that the proposed approach has high positioning accuracy even when a large proportion of elements are missing in the EDM.