The source localisation method SODIX is capable of determining the amplitudes and the directivity of sound sources based on measurements with a microphone array. The source model of the method has recently been extended with fully coherent sound sources which improves the application of SODIX to tonal noise. This paper presents a further extension of the SODIX source model with partially coherent sources in order to overcome residual effects that cannot be correctly modelled with a fully coherent source model, e.g. due to propagation effects that decorrelate the sound field radiated by a sound source for different receiver positions. The extension relies on a parameterisation of the source directivities and a compressed-sensing based algorithm in combination with an eigenvalue decomposition of the measured cross-spectral matrix to determine the unknown source directivities. The extended localization method with the partially coherent source model is validated using simulated sound sources that have different source directivities and mutual coherence. The results show that only the new source model with partially coherent sound sources is able to resolve the simulated source directivities accurately, when the sources are partially coherent or both coherent and incoherent sources are present
