Source localization using a sparse representation of sensor measurements

Abstract

International audienceWe propose a non-parametric technique for source localization with passive sensor arrays, using the concept of a sparse representation of sensor measurements. We give an interpretation of sensor data by sparsely representing these data in an overcomplete basis, stressing the fact that the source position is usually sparse relative to entire spatial domain. In this way, the estimation problem is put in a model-fitting framework in which source position is achieved by finding the sparsest representation of the data. The approach presented in the communication is based on the singular value decomposition (SVD) of multiple samples of the array output and the use of a second-order cone programming for optimization of a resulting objective function. We formulate the problem in a variational framework, where we minimize a regularized objective function for finding an estimate of the signal energy as a function of acoustical source position. The key is to use an appropriate non-quadratic regularizing functional which leads to sparsity constraints and superresolution. The acoustical sources can be correlated or uncorrelated, wideband or narrowband, in nearfield or farfield. Numerical and experimental results in an anechoic room are presented. Our algorithm is compared to traditional algorithms such as beamforming, Capon and MUSIC