Cross-correlation is a popular signal processing technique used in numerous localization and tracking systems for obtaining reliable range information. However, a practical efficient implementation has not yet been achieved on resource constrained wireless sensor network platforms . In this paper, we propose : SparseXcorr: cross-correlation via  sparse representation, a new  framework for ranging based on L1-minimization  . The key idea is to compress the  signal samples on the mote platform by efficient random projections and transfer them to a central device , where a convex optimization process estimates the range by exploiting its sparsity in our proposed correlation domain. Through sparse representation theory validation, extensive empirical studies and experiments on an end-to-end acoustic ranging system implemented on resource limited off-the-shelf sensor nodes, we show that the proposed framework , together with the proposed correlation domain achieved up to two orders of magnitude better performance compared to naive approaches such as working on DCT domain and downsampling. Compared to  standard cross-correlation, SparseXcorr uses only 30-40\% measurements to obtain precise range estimates with an additional bias of only 2-6 cm for applications with high accuracy requirement; whereas for applications with less constrained accuracy levels, only 5\% measurements are adequate to achieve approximately 100cm ranging precision. We also present StructSparseXcorr: cross-correlation via structured sparse representation, an addendum to the proposed computing framework to overcome shortcoming due to dictionary coherence. For cases of high compression factor and low signal-to-noise ratio , we show that StructSparseXcorr improves the performance of SparseXcorr by approximately 40\% .
Cross-correlation is a popular signal processing technique used in numerous location tracking systems for obtaining reliable range information. However, its efficient design and practical implementation has not yet been achieved on mote platforms that are typical in wireless sensor network due to resource constrains . In this paper, we propose SparseS-XCorr: cross-correlation via structured sparse representation, a new computing framework for ranging based on L1-minimization and structured sparsity . The key idea is to compress the ranging signal samples on the mote by efficient random projections and transfer them to a central device ; where a convex optimization process estimates the range by exploiting the sparse signal structure in the proposed correlation dictionary. Through theoretical validation, extensive empirical studies and experiments on an end-to-end acoustic ranging system implemented on resource limited off-the-shelf sensor nodes, we show that the proposed framework can achieve up to two orders of magnitude better performance compared to other approaches such as working on DCT domain and downsampling. Compared to the standard cross-correlation, it is able to obtain range estimates with a bias of 2-6cm with 30\% and approximately 100cm with 5\% compressed measurements. Its structured sparsity model is able to improve the ranging accuracy by 40\% under challenging recovery conditions (such as high compression factor and low signal-to-noise ratio ) by overcoming limitations due to dictionary coherence .
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, we show that StructSparseXcorr improves the performance of SparseXcorr by approximately 40\%
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