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The gravitational time dilation, or gravitational redshift effect is a direct consequence of the Einstein equivalence principle. Accurate measurement of this effect is of great importance for the search of possible violations of general relativity and anticipated discovery of the ``new physics''. The best measurement of this effect to date was performed by the Gravity Probe A mission which reached an accuracy of $1.4\times10^{-4}$. The Spektr-R spacecraft, which serves the radio astronomy mission RadioAstron, is currently being used to measure the effect with an accuracy of $\sim10^{-5}$. The satellite's relatively long expected lifetime promises prolonged data accumulation and substantially contributes to the expected accuracy value. The task is complicated by the problem of extracting the tiny gravitational redshift from a number of much larger effects. Preliminary tests confirmed that the developed techniques are appropriate to measuring the gravitational time dilation effect with an order of magnitude better accuracy than obtained with Gravity Probe A more than 40 years ago. In the talk we'll focus on the experiment methodology centered around the non-relativistic Doppler compensation and present preliminary results of performed observations.