In this case, the coherent source is the celestial object being observed. The problem here is that the "combining" step is being performed in software, and the sequence of digital samples have time- and phase-offsets that are ever-changing.
The two options are to keep those offsets under control (i.e., lock everything to a common clock) or to rapidly measure the offsets as they change and try to compensate in software (difficult).
In intensity interferometry the phase is not measured, and the timing accuracy is I believe only proportional to the desired effective bandwidth of the measurement. It was done in 1950's with bandwidths ~10 MHz -> 0.1microsec accuracy, should be do-able with SDR. Intensity interferometry is a bit of mind-twister...
(Another at first surprising thing is that radiation received from celestial sources is only coherent because of their very small apparent size -- the sources themselves are not coherent at all, because their physical size is very large)
The two options are to keep those offsets under control (i.e., lock everything to a common clock) or to rapidly measure the offsets as they change and try to compensate in software (difficult).