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This paper derives relationships which express the contribution of ground-receiver noise and round-trip transit time to the errors in two-way radio Doppler measurements. Only one method of Doppler measurement is considered. This is the method of counting the number of cycles in a given time interval. From this measurement the signal frequency may then be determined. In usual tracking systems this frequency measurement is further utilized to determine the range-rate of the vehicle with respect to the tracking station. The power-spectral densities of additive-receiver noise and oscillator-frequency noise are assumed white. This situation prevails when the random disturbances are thermal in origin. This is a tractable assumption when one seeks fundamental accuracy limitations for Doppler measurement. The results of this paper should be useful to those concerned with radio tracking and, in particular, tracking of space probes.