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Cross-correlation is a popular signal processing technique used in numerouslocation tracking systems for obtaining reliable range information. However,its efficient design and practical implementation has not yet been achieved onmote platforms that are typical in wireless sensor network due to resourceconstrains. In this paper, we propose SparseS-XCorr: cross-correlation viastructured sparse representation, a new computing framework for ranging basedon L1-minimization and structured sparsity. The key idea is to compress theranging signal samples on the mote by efficient random projections and transferthem to a central device; where a convex optimization process estimates therange by exploiting the sparse signal structure in the proposed correlationdictionary. Through theoretical validation, extensive empirical studies andexperiments on an end-to-end acoustic ranging system implemented on resourcelimited off-the-shelf sensor nodes, we show that the proposed framework canachieve up to two orders of magnitude better performance compared to otherapproaches such as working on DCT domain and downsampling. Compared to thestandard cross-correlation, it is able to obtain range estimates with a bias of2-6cm with 30% and approximately 100cm with 5% compressed measurements. Itsstructured sparsity model is able to improve the ranging accuracy by 40% underchallenging recovery conditions (such as high compression factor and lowsignal-to-noise ratio) by overcoming limitations due to dictionary coherence.

Sparsity based Efficient Cross-Correlation Techniques in Sensor Networks