Abstract
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 $4.0 \times 10^{-13} / \sqrt {\tau }$ (Case 1), $2.3 \times 10^{-14} / \sqrt {\tau }$ (Case 2), and $2.8 \times 10^{-15} / \sqrt {\tau }$ (Case 3) at averaging time ${\tau }$ , respectively, and the accuracy of these clock have been evaluated to be $5.3 \times 10^{-16}$ , $7.8 \times 10^{-17}$ , and $8.6 \times 10^{-18}$ . 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 xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> / <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> with an uncertainty of 1.11 m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> /s <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , whereas the deviation error between PTBB and BRUX is 0.76 m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> /s <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> with an uncertainty of 1.79 m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> /s <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">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.
Highlights
The geopotential plays a very important role in geodesy and has broad applications in various fields
Considering the advantages of the high-precision of global navigation satellite system (GNSS) precise point positioning (PPP) time transfer technique and rapid development of time and frequency science, for instance at present optical atomic clocks achieve a stability of 4.8×10−17 at 1 s and 6.6×10−19 over an hour-long measurement [26], in this study, we propose an approach that uses the PPP technique to directly compute clock offsets between two clocks at two arbitrary positions for the determination of geopotential difference, referred to as the relativistic PPP time comparison approach, and the accuracy of this approach depends on the both accuracies and stabilities of clocks, and the time transfer technique itself
With the simulated GNSS observation data, we analyzed the performance of the PPP time transfer technique with different cases, and the results of the relativistic PPP time comparison approach are presented
Summary
The geopotential plays a very important role in geodesy and has broad applications in various fields. The classic method of determining geopotential difference is based on leveling with additional gravimetry [1], which has drawbacks in that it is. The associate editor coordinating the review of this manuscript and approving it for publication was Halil Ersin Soken. Labor-intensive and geographically limited [2]. To overcome these drawbacks, Bjerhammar [3] proposed that geopotential difference could be determined using a clock transportation comparison (CTC) approach [4] based on the general relativity theory (GRT) [5]. The CTC technique is based on continuously comparing the change in time difference between a fixed clock with a transportable clock [6]. The key problem lies in the difficulties associated with transporting.
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