  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.
