audio signal time delay estimation(TDE) in indiviual and separate mics common TDE problems algorithms(such as GCC) often require audio signals in different mics concurrently, however, is it possible to estimate audio signal time of arrivals(ToA) in different mics separately in the noisy environment in order to estimate TDoA&amp;TDE? 

Also, since memory space limitation, cross-correlation related algorithms may not be feasible, starting point detection may be a possible solution(in noisy environment)
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.