A sparse regularization technique for source localization with non-uniform sensor gain

A robust sparse regularization technique with applications to source localization in the presence of non-uniform gain distribution is presented. As a key component in sparse optimization, a proper choice of the regularization parameter is crucial. It renders high impact on the localization performance and has to account for any kind of model perturbation. Our proposed technique utilizes a statistical framework to provide a direct relation between the physical system parameters and the regularization parameter of the resulting optimization problem. It addresses the joint effects of sensor gain variations and noise. As a figure of merit, we consider the mean-squared error (MSE) between the perturbed measurements and the assumed underlying model. An upper bound of the MSE is attained in order to estimate the regularization parameter. The presented method shows good performance for moderate gain variances even in low SNR regimes.