The so-called “phase delay tracking” attempts to estimate the effects of the turbulence on the phase of the interferograms in order to numerically cophase the measured complex visibilities and to coherently integrate them. This is implemented by the “coherent fringe analysis” of MIDI instrument 1 but has only been used for high SNR data. In this paper, we investigate whether the sensitivity of this technique can be pushed to its theoretical limits and thus applied to fainter sources. In the general framework of the maximum likelihood and exploiting the chromatic behavior of the turbulence effects, we propose a global optimization strategy to compute various estimators of the differential pistons between two data frames. The most efficient estimators appear to be the ones based on the phasors, even though they do not yet reach the theoretical limits.