Time-delay estimation via linear interpolation and cross correlation

Time-delay estimation (TDE), which aims at measuring the relative time difference of arrival (TDOA) between different channels is a fundamental approach for identifying, localizing, and tracking radiating sources. Recently, there has been a growing interest in the use of TDE based locator for applications such as automatic camera steering in a room conferencing environment where microphone sensors receive not only the direct-path signal, but also attenuated and delayed replicas of the source signal due to reflections from boundaries and objects in the room. This multipath propagation effect introduces echoes and spectral distortions into the observation signal, termed as reverberation, which severely deteriorates a TDE algorithm in its performance. This paper deals with the TDE problem with emphasis on combating reverberation using multiple microphone sensors. The multichannel cross correlation coefficient (MCCC) is rederived here, in a new way, to connect it to the well-known linear interpolation technique. Some interesting properties and bounds of the MCCC are discussed and a recursive algorithm is introduced so that the MCCC can be estimated and updated efficiently when new data snapshots are available. We then apply the MCCC to the TDE problem. The resulting new algorithm can be treated as a natural generalization of the generalized cross correlation (GCC) TDE method to the multichannel case. It is shown that this new algorithm can take advantage of the redundancy provided by multiple microphone sensors to improve TDE against both reverberation and noise. Experiments confirm that the relative time-delay estimation accuracy increases with the number of sensors.