# Evaluating Optical Clock Performance for GNSS Positioning
## 2 Optical Clock Development  
Since its inception a few decades ago, the revolutionary OFS has significantly improved current timing capabilities and opened up more opportunities. So far, the best optical clock has achieved an uncertainty beyond \(10^{-18}\) and has been recognised as the most stable and accurate timing solution to date [4; 27; 28; 29]. Figure 1 shows the continuous development of AFS and OFS with regard to their fractional frequency uncertainties (ultimate), as summarised in [21].  
The principle of optical clock working is very similar to atomic clocks except for the source of oscillation. Replacing the primal oscillator--quartz crystal--with an ultra-stable laser was the key enhancement that amplifies the standard atomic frequencies five orders  
Figure 1: The evolution of AFS and OFS with their fractional frequency uncertainties. The data points shown are referenced from [21].  
of magnitude higher, up to 1.1 \(\times\) 10\({}^{15}\) Hz [4; 30; 31]. On the other hand, however, counting such high frequencies (10\({}^{15}\) Hz) with the current electronic detector was a challenge [32]. In the 2000s, [PERSON] and [PERSON] invented an optical frequency comb [33; 34], allowing OFS to be measured or converted to microwave frequencies and vice versa. Their remarkable invention of this device was recognised in the industry, and they received the Nobel Prize in Physics in 2005. Optical frequency combs are now the essential component of optical clocks and have contributed significantly to the development of the optical domain. In [34], the authors provide a comprehensive review of optical frequency comb development and applications. In addition, significant improvements in atomic controls and laser stabilisation capabilities have empowered OFS to become more mature [20].  
Throughout the development of OFS, neutral atom and trapped ion frequency standards have been improved the most [20] and adopted various elements in the system. For example, optical lattice clocks that require hundreds to thousands of \({}^{87,88}\)Strontium, \({}^{171,174}\)Ytterbium, or \({}^{199}\)Mercury atoms in the system while \({}^{27,40}\)Aluminum, \({}^{88}\)Calcium\({}^{+}\), \({}^{171}\)Ytterbium\({}^{+}\), and \({}^{199}\)Mercury\({}^{+}\) ions are used in making trapped ion optical clocks [3]. There are other clock types simultaneously developed as well, namely Rubidium two-photon transition and modulation transfer spectroscopy clocks [12].  
Making a portable, robust, and miniaturised (chip-scale) optical clock is seemingly the main target in the clock community, besides improving the clock stability performance. For instance, an indication of its transportability was introduced by the authors of [35], who created a \({}^{40}\)Ca\({}^{+}\) ion optical clock and achieved 7.3 \(\times\) 10\({}^{-16}\) stability over 1000 s, whilst [36] established an \({}^{87}\)Sr optical lattice clock in a car trailer set-up and showed 4.1 \(\times\) 10\({}^{-17}\) stability at a similar averaging time. Lately, Chip-Scale Optical Clock (CSOC) development with integrated photonics has also occurred [37; 38; 39]. Furthermore, some experiments to test optical clock performance in space scenarios were proposed using a lattice optical clock aboard the International Space Station [40] and a molecular iodine optical clock to be on board the TEXUS 54 sounding rocket to assess the maturity of the clock [41]. This sounding rocket mission was accomplished later in 2018 [42]. Moreover, optical clocks have been recommended for scientific experiments including a test of fundamental physics [4; 43], gravity field determination due to their high sensitivity [28; 44; 45; 46; 47], a new type of frequency transfer method using a free-space laser link, and fibre optic [4], or via Very Long Baseline Interferometry (VLBI) technique [48]. In addition, Refs. [27; 29; 49] introduced their successfully developed optical lattice clocks in striving for better timing performance. An extensive review of the evolution of optical clocks can be found in [3; 16; 20].