Joint tensor completion anchor selection and coordinate transformation for high precision cooperative positioning in device-to-device systems

Abstract

The synergistic amalgamation of device-to-device (D2D) communication between mobile terminals (MT) and ultra-dense networks in 5G systems enables cooperative positioning. In this paper, we propose a joint tensor completion, anchor selection, and coordinate transformation (JTCASCT) for high precision cooperative positioning in D2D systems. The positioning is achieved by mitigating the challenging issue of recovering the missing values from the corrupted distance between nodes and determining the global positions of unknown stationary nodes. Initially, a hankelized distance tensor structure called Euclidean distance tensor (EDT) is constructed from incomplete EDM. The missing values are recovered as tensor completion by exploiting its latent low rank structure. The optimization problem is solved using simple low rank tensor completion (SiLRTC) and high accuracy low rank tensor completion (HaLRTC) algorithms. The relative position of nodes is determined after applying multidimensionality scaling (MDS). To reduce the data dimension for coordinate transformation and to select the optimal combination of anchor nodes, we propose a low complex Kruskal–Wallis (KW) test. Finally, the global position of unknown nodes is computed using Helmert transformation (HT). Numerical evaluations demonstrate that the cooperative positioning accuracy is significantly improved with the proposed JTCASCT approach compared to the state-of-the-art techniques.