Wireless sensor networks localization based on graph embedding with polynomial mapping

Localization of unknown nodes in wireless sensor networks, especially for new coming nodes, is an important area and attracts considerable research interests because many applications need to locate the source of incoming measurements as precise as possible. In this paper, in order to estimate the geographic locations of nodes in the wireless sensor networks where most sensors are without an effective self-positioning functionality, a new graph embedding method is presented based on polynomial mapping. The algorithm is used to compute an explicit subspace mapping function between the signal space and the physical space by a small amount of labeled data and a large amount of unlabeled data. To alleviate the inaccurate measurement in the complicated environment and obtain the high dimensional localization data, we view the wireless sensor nodes as a group of distributed devices and use the geodesic distance to measure the dissimilarity between every two sensor nodes. Then employing the polynomial mapping algorithm, the relative locations of sensor nodes are determined and aligned to physical locations by using coordinate transformation with sufficient anchors. In addition, the physical location of a new coming unknown node is easily obtained by the sparse preserving ability of the polynomial embedding manifold. At last, compared with several existing approaches, the performances of the presented algorithm are analyzed under various network topology, communication range and signal noise. The simulation results show the high efficiency of the proposed algorithm in terms of location estimation error.