DOA estimation in the presence of array imperfections: A sparse regularization parameter selection problem

A robust sparse regularization technique for source localization that accounts for the joint effects of sensor position errors and noise is presented. Finding a good choice of the regularization parameter is a key component in sparse optimization problems and its automated determination is typically a non-trivial task. Our approach attempts to statistically determine an upper bound of the mean-squared error resulting from noise and from uncertainty about the exact sensor positions. Hereby, we aim at finding a direct relation between the physical parameters of the array, i.e. the sensor position errors, and the hyperparameter in the constrained formulation of the optimization problem. We will show that the proposed method provides proper sparse regularization even in low SNR regimes and in the presence of severe array imperfections.