# Evaluating Optical Clock Performance for GNSS Positioning
###### Abstract
But, to achieve an error in a range below 1 m, for example, the timing error must be better than three nanoseconds. Numerous studies have discussed the possibility of optical clocks being employed onboard GNSS satellites [10; 11; 12; 13; 14; 15; 16; 17; 18]; however, an optical clock is yet to be deployed on a GNSS satellite mission. Among the studies, refs. [10; 11] demonstrated a compact rubidium optical clock (CROC) based on two-photon transition achieving \(4\times 10^{-13}/\sqrt{\tau(s)}\) frequency stability over averaging times (\(\tau\)) up to 10,000 s, which was attractive meeting the technical requirement of GPS Block III satellites, though its long-term stability after that period was not appealing. Whereas German Aerospace Center (DLR) developed a different set-up of an optical clock named Iodine Modulation Transfer Spectroscopy (MTS) with exceptional short-term stability of approximately \(10^{-15}\) from 1 to 10,000 s, and they advocated the clock for the next generation of Galileo satellites (Kepler) with an inter-satellite link and orbit verification applications [12; 17; 18]. Further, a miniaturised Strontium (Sr) Lattice optical clock based on bosonic atoms was introduced by [13] with \(4.1\times 10^{-16}/\sqrt{\tau(s)}\), which experienced almost \(10^{-18}\) stability after a couple of hours. Even though the miniaturisation of the clock was insufficient for GNSS satellite criteria, the authors highlighted the clock compactness as a first step towards an optical lattice clock setup in space targeting the International Space Station. Meanwhile, refs. [14; 15; 16] provided a comprehensive review of the current development of space-grade atomic clocks, including the potential use of optical clocks in the future. But the emphases are mainly on the clock development and operating principles. In Timing, the current time and frequency standards are mostly synchronised via GNSS satellites between terrestrial reference atomic clocks to disseminate UTC time scales to the world [19]. With optical clocks, they do not yet play a formal role in this process. In metrology, however, optical clocks have been recommended as a new way of defining the unit of time [20; 21; 22; 23], second, which was redefined last time in 1967 using the ground state of the caesium [133] atomic clock [24; 25]. Additionally, the International Bureau of Weights and Measures (BIPM)--an intergovernmental organisation of more than 63 countries as of 2022 providing the SI standard for a system of measurements throughout the world--has provided the secondary representations of the second based on various OFS with different optical transitions [26]. For clarity, it is important to note that timing is not the focus of this study, and therefore limited information is presented in that respect. In this paper, we overview the current development of emerging optical clocks and discuss the potential improvements optical clocks may bring to GNSS positioning based on the clock stability analysis conducted for the aforementioned optical clocks--Sr Lattice, CROC, and Iodine MTS--in comparison with the current atomic clocks onboard GNSS satellites of the four prominent constellations. The overlapping ADEV method is applied to estimate the satellite clock stability from 24 h of IGS satellite clock products with 30 s intervals prepared by GeoForschungsZentrum Postdam (GFZ) analysis centre for 2022 while the optical clock ADEV values are sourced from the existing literature referenced. The significances of this study, in the authors' view, are first, the stability of satellite atomic clocks (as of 2022) is comprehensively estimated, which was not conducted or found in the existing literature ever since the recent formation of the fully operational four constellations. Secondly, the potentiality of state-of-the-art optical clocks is discussed explicitly from a GNSS positioning user's perspective and in the context of the clock errors, which has impacts on positioning observations and estimates. The paper is structured as follows.