Robust time delay estimation exploiting redundancy among multiple microphones

To find the position of an acoustic source in a room, typically, a set of relative delays among different microphone pairs needs to be determined. The generalized cross-correlation (GCC) method is the most popular to do so and is well explained in a landmark paper by Knapp and Carter. In this paper, the idea of cross-correlation coefficient between two random signals is generalized to the multichannel case by using the notion of spatial prediction. The multichannel spatial correlation matrix is then deduced and its properties are discussed. We then propose a new method based on the multichannel spatial correlation matrix for time delay estimation. It is shown that this new approach can take advantage of the redundancy when more than two microphones are available and this redundancy can help the estimator to better cope with noise and reverberation.