Аннотация:We report on a sensitivity study for measurements of the gravitational redshift, with the RadioAstron satellite. Hydrogen masers were used on board the satellite as well as at the tracking stations in Pushchino (ASC LPI RAS, Russia) and Green Bank (NRAO, USA). The report discusses an improved method for processing gravitational data by the phase detection method using the limit of Cramer-Rao bound. With large large signal-to-noise ratios, this method promise to increase the accuracy of relative gravitational frequency measurements significantly to between 10−4 and 10−5. The estimates presented below are limited to the signals received against the background of Gaussian white noise. In this frame it becomes possible to obtain a lower value of the GR violation parameter, close to the estimates obtained from observations of Galileo satellites.