Gram Matrix Completion for Cooperative Localization in Partially Connected Wireless Sensor Network

The performance of cooperative localization can be degraded in the partially connected wireless sensor network (WSN). In this letter, we address the localization problem based on the incomplete distance information. By considering the input of distance-based localization algorithms, we proposed a novel Gram matrix completion method. With the function of Gram matrix, we indirectly represent the measurement of Gram matrix by the Euclidean distance matrix (EDM). The recovered Gram matrix can directly used for multidimensional scaling (MDS) or semi-definite programming (SDP) to localize the nodes. Then we present the procedure of MDS and rigid transformation estimation to localize the nodes. The performance of the proposed algorithm is evaluated compared with low rank matrix completion and positioning algorithms.