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Formulation of geopotential difference determination using optical-atomic clocks onboard satellites and on ground based on Doppler cancellation system

In this study, we propose an approach for determining the geopotential difference using high-frequency-stability microwave links between satellite and ground station based on Doppler cancellation system. Suppose a satellite and a ground station are equipped with precise optical-atomic clocks (OACs) and oscillators. The ground oscillator emits a signal with frequency f
 a towards the satellite and the satellite receiver (connected with the satellite oscillator) receives this signal with frequency f
 b which contains the gravitational frequency shift effect and other signals and noises. After receiving this signal, the satellite oscillator transmits and emits, respectively, two signals with frequencies f
 b and f
 c towards the ground station. Via Doppler cancellation technique, the geopotential difference between the satellite and the ground station can be determined based on gravitational frequency shift equation by a combination of these three frequencies. For arbitrary two stations on ground, based on similar procedures as described above, we may determine the geopotential difference between these two stations via a satellite. Our analysis shows that the accuracy can reach 1 m
 2
 s
 − 2
 based on the clocks’ inaccuracy of about 10
 −17
 (s s
 −1
) level. Since OACs with instability around 10
 −18
 in several hours and inaccuracy around 10
 −18
 level have been generated in laboratory, the proposed approach may have prospective applications in geoscience, and especially, based on this approach a unified world height system could be realized with one-centimetre level accuracy in the near future.