We present a optical system with an extended point-spread function (PSF) for the localization of point sources in the visible and IR spectral ranges with a subpixel precision. This compact system involves a random phase mask (RPM) as its unique component. It exhibits original properties, because this RPM is used in a particular regime, called the "filamentation regime," before the speckle region. The localization is performed by calculating the phase correlation between the PSF and the image obtained under off-axis illumination. Numerical simulations are presented to assess the basic optical properties of this RPM in the filamentation regime.