  A method has been developed for precision measurement of the gravitational
frequency shift of communication radio signals between the spacecraft and the
ground tracking station based on the maximum likelihood principle, using the
Rao-Cramer limit estimates for the kinematic parameters associated with orbital
motion. Numerical illustrations of the efficiency of the method are presented
using the example of data obtained in experiments with the Spectr-R satellite
as part of the VLBI system in the "Radioastron" mission. A compensatory
"on-line" technique for suppressing Doppler and atmospheric noise has been
implemented due to the presence of two modes of communication in gravity
sessions: unidirectional (1w) and looped (2w). Recipes for reducing the
magnitude of systematic errors are discussed.
