Sparsity Based Efficient Cross-Correlation Techniques in Sensor Networks

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 StructS-XCorr: cross-correlation via structured sparse representation, a new computing framework for ranging based on l(1)-norm minimization [1] 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 2-6 cm with 30 percent and approximately 100 cm with 5 percent compressed measurements. Its structured sparsity model is able to improve the ranging accuracy by 40 percent under challenging recovery conditions (such as high compression factor and low signal-to-noise ratio) by overcoming limitations due to dictionary coherence.