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A new test of the gravitational redshift effect, was conducted with the RadioAstron satellite, which has been in a highly eccentric orbit around the Earth for several years. We probed the flow of time on board, which varies while RadioAstron (RA) passes through the varying gravitational potential of the Earth, by recording the spacecraft's downlink signal, which is synchronized to its ultra-stable on-board H-maser, at the ground radio telescopes. The experiment requires us to extract the tiny gravitational redshift signal from the mixture of a number of much larger effects, including those of the nonrelativistic Doppler frequency shift, signal propagation through the Earth's troposphere and ionosphere, higher-order kinematic effects of special relativity, Earth tides, and various instrumental effects. In order to perform the offline filtering of those effects we developed several algorithms adapted to operational modes RA spacecraft, A total of 17 successful experiments were performed while the on-board H-maser was operational. Preliminary analysis of the data from two experiments gives us a fractional accuracy of the gravitational redshift test of at least 2x10^{-4}, which is comparable to that obtained by Gravity Probe A. In this talk we discuss our data analysis algorithms and present arguments in favor of the experiment uncertainty currently being dominated by that of the ionosphere frequency shift. Also we formulate prospects for improving the achieved accuracy further.