Efficient cross-correlation via sparse representation in sensor networks

Abstract

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. We propose 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 order of magnitude better performance compared to naive approaches such as working on DCT domain and downsampling. Furthermore, compared to cross-correlation results, 30-40% measurements are sufficient to obtain precise range estimates with an additional bias of only 2-6 cm for high accuracy application requirements, while 5% measurements are adequate to achieve approximately 100 cm precision for lower accuracy applications.