Geopotential Determination Based on Precise Point Positioning Time Comparison: A Case Study Using Simulated Observation

Based on the general relativity theory, the geopotential difference 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 high-performance clocks for determining the geopotential difference using this approach, and conducted the simulation experiments to validate this approach. In the experiment, we consider three cases for evaluating the performance of this approach with different types of atomic clocks, namely, the fractional frequency stabilities of the clocks equipped at three selected ground stations (BRUX, OPMT, and PTBB) are <inline-formula> <tex-math notation="LaTeX">$4.0 \times 10^{-13} / \sqrt {\tau }$ </tex-math></inline-formula> (Case 1), <inline-formula> <tex-math notation="LaTeX">$2.3 \times 10^{-14} / \sqrt {\tau }$ </tex-math></inline-formula> (Case 2), and <inline-formula> <tex-math notation="LaTeX">$2.8 \times 10^{-15} / \sqrt {\tau }$ </tex-math></inline-formula> (Case 3) at averaging time <inline-formula> <tex-math notation="LaTeX">${\tau }$ </tex-math></inline-formula>, respectively, and the accuracy of these clock have been evaluated to be <inline-formula> <tex-math notation="LaTeX">$5.3 \times 10^{-16}$ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$7.8 \times 10^{-17}$ </tex-math></inline-formula>, and <inline-formula> <tex-math notation="LaTeX">$8.6 \times 10^{-18}$ </tex-math></inline-formula>. Two main conclusions can be drawn from the experimental results. First, high-performance clocks can significantly improve the precision for GNSS PPP time transfer. Compared to Case 1, the long-term stabilities of the time link OPMT-BRUX as well as PTBB-BRUX are improved in Cases 2 and 3. Second, the geopotential difference between any two stations can be determined at the decimeter level, and the accuracy of geopotential difference is 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, m<sup>2</sup>/<sup>2</sup> with an uncertainty of 1.11 m<sup>2</sup>/s<sup>2</sup>, whereas the deviation error between PTBB and BRUX is 0.76 m<sup>2</sup>/s<sup>2</sup> with an uncertainty of 1.79 m<sup>2</sup>/s<sup>2</sup>. The results of this study suggest that a one decimeter-level geopotential difference between two arbitrary stations can be determined based on this approach.

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