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This paper combines recent developments in sparse approximation and distributed consensus theory to efficiently perform decentralized localization in wireless networks. To this goal, we exploit the Compressed Sensing (CS) framework, which provides a new paradigm for recovering signals being sparse in some basis by means of a limited amount of random incoherent projections. In particular, we propose a novel decentralized technique that considers the spatial correlations among the received measurements at the base stations (BSs) to provide global accurate position estimation, while reducing significantly the amount of measurements exchanged among the BSs and required for accurate positioning. We exploit the common structure of the received measurements to design a gossip-based algorithm in order to alleviate the effects of radio channel-induced signal variations on the estimation accuracy. Experimental evaluation with real data demonstrates the superiority of the proposed decentralized CS-based localization technique over traditional fingerprinting methods in terms of the achieved positioning accuracy.