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 1 -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.

Sparsity Based Efficient Cross-Correlation Techniques in Sensor Networks

“…30 observations were collected for every experiment. While the ranging performance of S-XCorr in the absolute sense was studied in our previous work [29], here we study the relative performance of S-XCorr and StructS-XCorr with respect to the (best-case) X-Corr in terms of the relative mean error and its deviation (Fig. 11).…”

“…• Case-C {indoor, high multipath}: A quiet meeting room ([7 × 6 × 6] m) with a big wooden table in the center and other office furnitures. The transmitter and the receiver were fixed at a constant separation distance of 5 m. The transmit power was varied such that the received SNR were recorded within the limits: [0-5) dB, [5][6][7][8][9][10] dB, [10][11][12][13][14][15][16][17][18][19][20] dB, [20][21][22][23][24][25][26][27][28][29][30] dB. For reasons that will be explained in the next subsection, we slightly modified the peak selection criteria of the detection algorithm to choose the tallest peak if there was no valid peak (6 standard deviation above the mean).…”

“…Fig. 6(a) for Case-A presents the most clear characterization by negating the effect of channel multipaths (though introducing an increased background noise level), where observations with a high SNR of [20][21][22][23][24][25][26][27][28][29][30] dB provide reliable range estimates by using only 15% projections while those having low SNR of [0-5) dB show confident result only with α = 0.30 (i.e., using more projections). in Case-C (due to high multipath), and so, the errors are as large as 1 m with α = 0.05, but attain stability after α = 0.25.…”

Learn to Recognise: Exploring Priors of Sparse Face Recognition on Smartphones

“…In sparse representation, random matrices are often used to reduce the dimensionality of the problem while preserving the accuracy of the applications. They have been applied to speed up background subtraction on embedded system [29] and cross-correlation computation in sensor networks [30]. In [5], SRC is used for acoustic classification and a column reduction procedure is proposed to reduce the dimension of ' 1 minimisation.…”

Real-Time and Robust Compressive Background Subtraction for Embedded Camera Networks

“…Also the sparse representation is attracting increasingly attentions with compressive sensing. One of the examples is [22]. In this paper, the authors deal with cross-correlation problem (which is widely used in sensor networks) efficiently via sparse representation.…”