Navigation and timing accuracy at the 30 centimeter and subnanosecond level

Clocks with accuracies exceeding 1/spl times/10/sup -13/ can now be placed in orbit. Here we carry out a worst case systematic error analysis of ground-based Doppler observations of signals from such a satellite to ascertain how well all the SV orbital parameters can be determined. The classical Keplerian relationship, T/sup 2/=4/spl pi//sup 2/a/sup 3//GM, provides a way for accurate determination of the semi-major axis, a, through measurement of the orbital period, T, of a SV-borne clock. Simple calculations show that an accuracy of 1/spl times/10/sup -13/ translates to an uncertainty in the length of the radius vector of 7.2 cm. To achieve such accuracy, a drag-free system is needed in the satellite to satisfy the free-fall orbital conditions. Because of the potential importance of such accuracy, the purpose of this paper to consider all relevant relativistic effects, and other important error terms.