Sparse source localization in presence of co-array perturbations

New spatial sampling geometries such as nested and coprime arrays have recently been shown to be capable of localizing O(M²) sources using only M sensors. However, these results are based on the assumption that the sampling locations are exactly known and they obey the specific geometry exactly. In contrast, this paper considers an array with perturbed sensor locations, and studies how such perturbation affects source localization using the co-array of a nested or coprime array. An iterative algorithm is proposed in order to jointly estimate the directions of arrival along with the perturbations. The directions are recovered by solving a sparse representation problem in each iteration. Identifiability issues are addressed by deriving Cramér Rao lower bound for this problem. Numerical simulations reveal successful performance of our algorithm in recovering of the source directions in the presence of sensor location errors.¹