Time delay estimation via multichannel cross-correlation [audio signal processing applications]

Time delay estimation (TDE) in a reverberant acoustical environment is a very challenging and difficult problem. This paper tackles the problem by exploiting the redundant information provided by multiple microphone sensors. To do so, the multichannel crosscorrelation coefficient (MCCC) is re-derived, in a new way, to connect it to the well-known linear interpolation technique. Some interesting properties and bounds of MCCC are discussed, and a recursive algorithm is then introduced so that MCCC can be estimated and updated efficiently when new data snapshots are available. We then apply the MCCC to the TDE problem, resulting a multichannel cross-correlation algorithm that can be treated as a natural generalization of the generalized cross-correlation (GCC) TDE method to the multichannel case. It is shown that this method can take advantage of the redundancy provided by multiple microphone sensors to improve TDE against both reverberation and noise.