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A method has been developed for precision measurement of the gravitationalfrequency shift of communication radio signals between the spacecraft and theground tracking station based on the maximum likelihood principle, using theRao-Cramer limit estimates for the kinematic parameters associated with orbitalmotion. Numerical illustrations of the efficiency of the method are presentedusing the example of data obtained in experiments with the Spectr-R satelliteas part of the VLBI system in the "Radioastron" mission. A compensatory"on-line" technique for suppressing Doppler and atmospheric noise has beenimplemented due to the presence of two modes of communication in gravitysessions: unidirectional (1w) and looped (2w). Recipes for reducing themagnitude of systematic errors are discussed.

Precision measurement of gravitational frequency shift of radio signals using Rao-Cramer estimates