When performing measurements with wall-installed microphone array, the turbulent boundary layer (TBL) that develops over the measuring system can induce pressure fluctuations that are much greater than those of acoustic sources. It then becomes necessary to process the data to extract each component of the measured field. For this purpose, it is proposed in this paper to decompose the measured spectral matrix into the sum of matrices associated with the acoustic and aerodynamic contributions. This decomposition exploits the statistical properties of each pressure field. On the one hand, assuming that the acoustic contribution is highly correlated over the sensors, the rank of the corresponding cross-spectral matrix is limited to a finite number. On the other hand, the correlation structure of the aerodynamic noise matrix is constrained to resemble a Corcos-like model, with physical parameters estimated within the separation procedure. This separation problem is solved by a Bayesian inference approach, which takes into account the uncertainties on each component of the model. The performance of the method is first evaluated on wind tunnel measurements and then on a particularly noisy industrial measurement setup: microphones flush mounted on the fuselage of a large aircraft.