Sound Localization using Compressive Sensing

In a sensor network with remote sensor devices, it is important to have a method that can accurately localize a sound event with a small amount of data transmitted from the sensors. In this paper, we propose a novel method for localization of a sound source using compressive sensing. Instead of sampling a large amount of data at the Nyquist sampling rate in time domain, the acoustic sensors take compressive measurements integrated in time. The compressive measurements can be used to accurately compute the location of a sound source. Proc. SENSORNETS, 2012, pp.159-166 Sound sensors x1 x0 x2 d1 d2 Sound source θ d1cos(θ) compressive sensing. In order for localization to be reliable for a variety of sound events, we don’t make the assumption that the sound wave from a sound source is sparse. Instead, we observe that in most reasonable circumstances, the acoustic signal at one sensor has a sparse representation if the acoustic signal at another sensor is known. We regard the signal at one sensor to be the output of a linear system with the input as the signal at another sensor, and we assume that the linear system can be approximated by a finite impulse response filter with a very small number of nonzero coefficients. Consequently, it is possible for sensors to take and transmit very small number of measurements if the signal at one of the sensors is known. By using compressive measurements, a sound sensor is only required to make and transmit samples at a low rate, which improves the reliability of the sensor and reduces the power assumption. Furthermore, since the measurements are made by linear projections, the complexity of acquiring the measurements is also low. The paper is organized as follows. In section 2, we describe existing sound localization techniques. Our method of localization using compressive sensing is described in Section 3. Some simulation and experiment results are presented in Section 4, and the conclusion is provided in Section 5. 2 SOUND LOCALIZATION TECHNIQUES Figure 1 illustrates a distributed sensor network. The sensors are distributed with a known geometry. The sensors make samples of the sound waves, and transmit the samples to a processing center (not shown) for analysis. 2.1 Direction of Arrival (DOA) and Time Difference of Arrival (TDOA) The location of the sound source can be estimated from the time differences between the arrival times of the sound wave at the sensors. For the purpose of this paper, we consider the case where the sound source is sufficiently distant so that the wavefront arriving at the array approximates a plane. Figure 1 shows the derivation of the DOA shown as angle θ between the segment 1 0 x x and the arriving sound. The quantity d1cos(θ) can be calculated by measuring the time delay, τ01, for the wavefront to propagate from x0 to x1. Using c to denote the velocity of sound in air, we have ( ) θ τ cos 1 01 d c = , and thus ( ) 1 01 1 cos d cτ θ − = . In this way, a pair of sensors can be used to determine the relative direction to the sound source. Multiple pairs can be used to triangulate upon the source position. Figure 1 Distributed sensor network. 2.2 Cross-correlation Cross-correlation of the sensor signals, proposed by (Knapp, Carter 1976) is the most straightforward means to measure TDOA. Given a single sound source in a quiet anechoic space, the output of each sensor is a transduction of the source signal affected only by the delay and attenuation associated with the path length between the source and sensor. The cross-correlation of two such signals is maximized at the time lag corresponding to the difference in path delays. Let ) ( 0 i x and ) ( 1 i x represent the samples of signals arriving at sensors x0 and x1. The samples are processed in blocks of length N. For each block of samples, we calculate the cross-correlation function