The estimation of the relative acoustic transfer function is a prerequisite for implementing multi-reference non-synchronous measurements with a microphone array. In industrial test scenarios, strong background noise poses a significant challenge, resulting in substantial errors in multi-reference non-synchronous measurements. To address such issue, an identification approach for the relative acoustic transfer function matrix based on total least squares is established. The cross-spectral matrix obtained by scanning the microphone array is completed, and acoustic holography imaging is achieved using the partial field derived from the decomposition of the spectral correlation matrix. The results indicate that the proposed method can effectively mitigate the influence of background noise on the completion of the spectral correlation matrix of microphone measurements under low signal-to-noise ratio scenarios. When the signal-to-noise ratio is below 10 dB, the error can be reduced by more than 2%, thereby enhancing the non-synchronous imaging accuracy of the microphone array.