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

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.