audio signal time delay estimation(TDE) in indiviual and separate mics
single mic, i'm not sure.  it seems to me that all you can do is mark different events (perhaps with envelope following or perhaps by comparing the signal or parameters measured from the signal to templates) and just use the time difference of the onset times of each marked event.

for two mics, there is cross-correlation.  but some people have also suggested an adaptive LMS filter (one of the mics is the "desired signal", $d[n]$) of some sort and computing some measure of group delay from the FIR coefficients that result in the LMS.  something in me makes me think is the Julius Smith/Perry Cook thing, but it might be someone else.