## 1 Introduction
The use of different kinds of prior information in various regions makes it difficult to unify the elevation datums in these regions. (4) The fourth method is adopting global gravity models (GGMs) with high precision. The EGM2008, for example, is complete with the degree and order of spherical harmonics up to 2159 [12], and we can directly compute the potential \(C(P)\) of any given point in the ITRF coordinates by introducing it into the spherical harmonic expansion equation. However, at present, the GGM method has the problem of a precision and resolution trade-off. For instance, the GOCE series models (see, e.g., [13]); also see the products released from ESA (www.esa.int (accessed on 10 March 2023)) and the International Centre for Global Earth Models (icgem.gfz-potsdam.de/ICGEM (accessed on 10 March 2023)) can reach an accuracy level of 1 cm (even higher) but with a poor resolution of \(1^{\circ}\times 1^{\circ}\). On the contrary, although the EGM2008 model has a relatively high resolution of \(5^{\prime}\times 5^{\prime}\), its average accuracy is only about 10 to 20 cm [12]. Another drawback of the GGM method is that different models usually present discrepancies because of their different standards and conventions. Currently, it is challenging to establish IHRF with high precision by any of the approaches described above. Another method, the relativistic geodetic method, has gained increasing attention and discussion in terms of addressing this challenge. The relativistic geodetic method is based on the general theory of relativity [14]: precise clocks at positions with different geopotentials run at different rates. Therefore, the geopotential difference between two arbitrary stations can be measured by precise clocks. The corresponding height propagation based on this method is referred to as \"chronometric leveling\" [15; 16]. Since the relativistic geodetic method requires ultrahigh precision clocks (e.g., for a precision of 1 cm, the stability of clocks should reach \(1\times 10^{-18}\)), it was not suitable for practical applications for a long time because of the limited clock precision. However, with the fast development of high-precision clock manufacturing technology in recent years, optical atomic clocks (OACs), which have uncertainty and accuracy level of around \(1\times 10^{-18}\) and even higher have been developed in various laboratories [17; 18; 19; 20]. This guarantees the feasibility of actual applications of the relativistic geodetic methods. Consequently, more and more scientists are paying attention to various potential applications of the relativistic geodetic methods [21; 22; 23; 24]. The most precise method for comparing clocks in different places is to connect them via optical fiber links (OFLs) [25]. Therefore, an increasing number of discussions and experiments on clocks connected by OFLs have been carried out and discussed [26; 27; 28; 29]. Recently, the most precise measurement in OFL chronometric leveling was conducted by [30]. They used transportable optical clocks with an uncertainty of around \(5\times 10^{-17}\) to determine the geopotential difference between two points in a mountain area between France and Italy. Though their experiments show a height discrepancy of around 20 cm between the observed OFL result and that determined by the conventional approach (leveling and gravity measurement), the \(1\sigma\) uncertainty is limited to around 17 m [30]. In addition, [PERSON] et al. proposed a method to unify several local height systems by clock networks connected by OFLs [31]. According to their simulation results, the height systems of the West European region can be unified at a precision of better than 1 cm, under the assumption that the clock frequency uncertainty is \(1\times 10^{-18}\). Although relativistic geodetic methods are now practical and can reach high precision, the adoption of OFL limits its development. The cost of optical fibers will increase rapidly as the distance between two clocks increases or the number of stations in a network increases.