Approach to robust estimation of radiation sources in an array of electric dipoles when measurement data are distorted by additive noise as well as by random impulses is suggested. It is based on a non-linear optimization technique where objective function is built by the idea of minimization of “spatial extent.” The model of radiation sources is described by a set of ideal Hertzian dipoles. The case, when dipoles are located along a straight line, which is parallel to measurement line of electric field, and when their electric moments are perpendicular to the measurement plane, is considered. Algorithm, based on conjugate gradient method, is proposed. Numerical simulations are presented.