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According to general relativity theory (GRT), by comparing the frequencies between two precise clocks at two different stations, the gravity potential (geopotential) difference between the two stations can be determined due to the gravity frequency shift effect. Here, we provide experimental results of geopotential difference determination based on frequency comparisons between two remote hydrogen atomic clocks, with the help of common-view satellite time transfer (CVSTT) technique. For the first time we apply the ensemble empirical mode decomposition (EEMD) technique to the CVSTT observations for effectively determining the geopotential-related signals. Based on the net frequency shift between the two clocks in two different periods, the geopotential difference between stations of the Beijing 203 Institute Laboratory (BIL) and Luojiashan Time--Frequency Station (LTS) is determined. Comparisons show that the orthometric height (OH) of LTS determined by the clock comparison is deviated from that determined by the Earth gravity model EGM2008 by (38.5$\pm$45.7)~m. The results are consistent with the frequency stabilities of the hydrogen clocks (at the level of $10^{-15}$~day$^{-1}$) used in the experiment. Using more precise atomic or optical clocks, the CVSTT method for geopotential determination could be applied effectively and extensively in geodesy in the future., Comment: 24 pages, 15 figures

In 2022 China Space Station (CSS) will be equipped with atomic clocks and optical clocks with stabilities of $2 \times 10^{-16}$ and $8 \times 10^{-18}$, respectively, which provides an excellent opportunity to test gravitational redshift (GR) with higher accuracy than previous results. Based on high-precise frequency links between CSS and a ground station, we formulated a model and provided simulation experiments to test GR. Simulation results suggest that this method could test the GR at the accuracy level of $(0.27 \pm 2.15) \times10^{-7}$, more than two orders in magnitude higher than the result of the experiment of a hydrogen clock on board a flying rocket more than 40 years ago., Comment: 6 pages, 5 figures

According to general relativity theory (GRT), the geopotential difference (GD) can be determined by comparing the change in time difference between precise clocks using the precise point positioning (PPP) time transfer technique, referred to as the relativistic PPP time comparison approach. We focused on high-precision time comparison between two precise clocks for determining the GD using the relativistic PPP time transfer,and conducted simulation experiments to validate the approach. In the experiments, we consider three cases to evaluate the performance of the approach using clocks with different stabilities, namely, the frequency stabilities of the clocks equipped at three selected ground stations are respectively (Case 1), (Case 2), and (Case 3) at time period. Conclusions are drawn from the experimental results. First, high-precision clocks can significantly improve the accuracy for PPP time transfer, but the improvement is limited by measurement noises. Compared to Case 1, the long-term stabilities of OPMT-BRUX as well as PTBB-BRUX are improved in Cases 2 and 3. The frequency stabilities of Cases 1-3 are approximately 4.28*10-16, 4.00*10-17, and 3.22*10-17 at 10-day averaging time for OPMT-BRUX, respectively, and for PTBB-BRUX, these values are approximately 3.73*10-16, 8.17*10-17, and 4.64*10-17. Second, the geopotential difference between any two stations can be determined at the decimeter level, with its accuracy being consistent with the stabilities of the time links in Cases 1-3. In Case 3, the determined geopotential differences between OPMT and BRUX deviate from the EIGEN-6C4 model values by -0.64 m2/s2 with an uncertainty of 1.11 m2/s2, whereas the deviation error between PTBB and BRUX is 0.76 m2/s2 with an uncertainty of 1.79 m2/s2. The approach proposed in this study can be also applied to testing GRT.

Atomic Clock Ensemble in Space (ACES) is an ESA mission mainly designed to test gravitational redshift with high-performance atomic clocks in space and on the ground. A crucial part of this experiment lies in its two-way Microwave Link (MWL), which uses the uplink of carrier frequency 13.475 GHz (Ku band) and downlinks of carrier frequencies 14.70333 GHz (Ku band) and 2248 MHz (S band) to transfer time and frequency. The formulation based on the time comparison has been studied for over a decade. However, there are advantages of using frequency comparison instead of time comparison to test gravitational redshift. Hence, we develop a tri-frequency combination (TFC) method based on the measurements of the frequency shifts of three independent MWLs between ACES and a ground station. The potential scientific object requires stabilities of atomic clocks at least $3\times10^{-16}$/day, so we must consider various effects, including the Doppler effect, second-order Doppler effect, atmospheric frequency shift, tidal effects, refraction caused by the atmosphere, and Shapiro effect, with accuracy levels of tens of centimeters. The ACES payload will be launched as previously planned in the middle of 2021, and the formulation proposed in this study will enable testing gravitational redshift at an accuracy level of at least $2\times10^{-6}$, which is more than one order higher than the present accuracy level of $7\times10^{-5}$.

Here, we provide preliminary experimental results of the geopotential determination based on time elapse comparisons between two remote atomic clocks located at Beijing and Wuhan, respectively. After synchronizing two hydrogen atomic clocks at Beijing 203 Institute Laboratory (BIL) for 20 days as zero-baseline calibration, we transport one clock to Luojiashan Time-Frequency Station (LTS), Wuhan, without stopping its running. Continuous comparisons between the two remote clocks were conducted for 65 days based on the Common View Satellite Time Transfer (CVSTT) technique. The ensemble empirical mode decomposition (EEMD) technique is applied to removing the uninteresting periodic signals contaminated in the original CVSTT observations to obtain the residual clocks-offsets series, from which the time elapse between the two remote clocks was determined. Based on the accumulated time elapse between these two clocks the geopotential difference between these two stations was determined. Given the orthometric height (OH) of BIL, the OH of the LTS was determined based on the determined geopotential difference. Comparisons show that the OH of the LTS determined by time elapse comparisons deviates from that determined by Earth gravity model EGM2008 by about 98 m. The results are consistent with the frequency stabilities of the hydrogen atomic clocks (at the level of $10^{-15}$/day) applied in our experiments. In addition, we used 85-days original observations to determine the geopotential difference between two remote stations based on the CVSTT technique. Using more precise atomic or optical clocks, the CVSTT method for geopotential determination could be applied effectively and extensively in geodesy in the future.