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Localization of wireless sensors using compressive sensing for manifold learning

In this paper, a novel compressive sensing for manifold learning protocol (CSML) is proposed for localization in wireless sensor networks (WSNs). Intersensor communication costs are reduced significantly by applying the theory of compressive sensing, which indicates that sparse signals can be recovered from far fewer samples than that needed by the Nyquist sampling theorem. We represent the pair-wise distance measurement as a sparse matrix. Instead of sending full pair-wise measurement data to a central node, each sensor transmits only a small number of compressive measurements. And the full pair-wise distance matrix can be well reconstructed from these noisy compressive measurements in the central node, only through an ℓ1-minimization algorithm. The proposed method reduces the overall communication bandwidth requirement per sensor such that it increases logarithmically with the number of sensors and linearly with the number of neighbors, while achieves high localization accuracy. CSML is especially suitable for manifold learning based localization algorithms. Simulation results demonstrate the performance of the proposed protocol on both the localization accuracy and the communication cost reduction.