A method is proposed for measuring the levels of extended spatially uncorrelated sound sources in the near field using a linear antenna array. It is supposed that these sources are located in the region of a given size (in the plane that is perpendicular to the plane of the array) but their exact position is unknown. A robust algorithm to synthesize weight coefficients providing the given value of methodological measurement error under maximum suppression of external noise is developed. The results of numerical simulation, as well as experimental results obtained under sea conditions, have shown the method to be efficient.