Relativistic models of phase and Doppler observations of electromagnetic signals

The paper deals with special definitions of phase and Doppler observations of electromagnetic signals and their modeling in four-dimensional space times of general relativity with an earth related metric. Particular attention is paid to phase measurements in GPS and, in addition, to possible contributions of clock transports. After a short explanation of the most essential fundamentals of physical theories and observations with standard clocks solutions of the direct and inverse geodetic problems in media are treated, which are directly or indirectly important for all observation equations concerning coordinate determinations. Then, based on the theory of electromagnetic wave propagation in a refractive medium the observation equations for phase measurements with standard clocks (oscillators) are derived. Finally, the observation equations of clock transports along terrestrial paths, directly resulting from the fundamental form of general relativity, are discussed. It can be shown that their application yields a valuable improvement in the accuracy of coordinate determinations.