The microphone array is widely used in acoustics as a non-contact measurement tool, which can obtain multi-dimensional information about the sound source, such as spatial, time, and frequency. The microphone array is not always used in an ideal anechoic chamber environment, making the sound source signal contaminated with the background interference. The separation of the sound source signal from the complex background interference is very challenging, especially when arrays are used in wind tunnel measurements. A probability model on the time– frequency matrix is constructed in this paper to address this issue. The background interference is constructed by the Gaussian mixture model to fit its complex probability distributions adaptively. The sound source signal is constructed as a low-rank model according to its correlation characteristics on the microphones. The distributions of parameters involved in the low-rank and Gaussian mixture model are estimated through variational Bayesian inference, which can realize the separation of the sound source signal from the complex background interference. The performance of the proposed method is evaluated by the numerical simulation and the DLR closed wind tunnel experimental. The robustness and the effectiveness of extracting the sound source signal from the complex background interference are also verified.