# Evaluating Optical Clock Performance for GNSS Positioning
## 6 Discussion  
In this section, the potentiality of optical clocks in GNSS positioning is discussed based on the research findings, the stability analysis, and the estimated clock impacts on satellite observations used for positioning. According to the stability analysis, the optical clock stability is superior to the satellite atomic clocks estimated, and therefore optical clocks could potentially surpass the current GNSS timing capability, thus positioning  
Figure 4: Calculated ADEV of the GNSS satellite clocks (averaged as per the satellite types) in 2022 against the CROC, Iodine MTS, and Sr Lattice Clock. The optical clock ADEV values are sourced from the existing literature [11; 12; 13]. \begin{table}
\begin{tabular}{l l l l l l l l l l l l l} \hline \hline \multirow{2}{*}{**Constellation**} & \multirow{2}{*}{**SV Type**} & \multicolumn{3}{c}{**ADEV Averaging Times**} & \multicolumn{3}{c}{} \\ \cline{3-14}  & & **30 s** & **60 s** & **120 s** & **240 s** & **480 s** & **900 s** & **1800 s** & **3600 s** & **7200 s** & **14,400 s** & **28,800 s** \\ \hline BEIDOU & BD52 GEO \& ICSO & 4.89\(\times\) & 3.22 \(\times\) & 2.17 \(\times\) & 1.51 \(\times\) & 1.08 \(\times\) & 8.44 \(\times\) & 6.43 \(\times\) & 4.71 \(\times\)  
and navigation. For example, the most stable satellite clocks--the Galileo FOC satellite clocks--showed 1.2 \(\times\) 10\({}^{-13}\) at 30 s averaging time, whereas the three optical clocks; Sr Lattice, Iodine MTS, and CROC, had significantly better stability yielding 7.5 \(\times\) 10\({}^{-17}\), 2.8 \(\times\) 10\({}^{-15}\), and 7.3 \(\times\) 10\({}^{-14}\) respectively. Such short-term stability between 30 s and 900 s is of interest for GNSS Precise Point Positioning (PPP) real-time application users because the performance driving factor of the PPP application is IGS precise orbit and clock products. For longer averaging times over 900 s, the stability of three optical clocks is still better, outweighing the satellite clocks by orders of magnitudes. Regarding use cases, clock long-term stability is pertinent in predicting satellite clock errors for broadcast navigation messages, which GNSS Single Point Positioning (SPP) application, for example, is reliant on. GPS and GLONASS navigation messages are uploaded daily from the ground segments to the satellites, where a set of ephemerides data is transmitted to receivers every 120 min and 30 min, respectively. In comparison, Galileo and BeiDou constellations upload their navigation messages in a much shorter period of 10 and 60 min, respectively. So, the averaging time for a clock prediction must be limited in line with the navigation message uploading intervals [7] because the predicted clock information is refreshed upon the uploads. Following that, simple calculations have been completed here to gauge the clock ADEV contribution (solely) to GNSS range measurement errors. As formulated by [7], assuming the clock drift and drift rate are perfectly determined, the standard deviation of range errors--\(SD(\tau)\)--over different averaging times resulting from clock ADEV values can be estimated as  
\[SD(\tau)=c\times\sigma_{y}(\tau)\times\tau \tag{2}\]  
where \(c\) is the speed of light. Figure 5 displays the calculated standard deviations of range errors as a function of averaging time for the GNSS satellite and optical clocks. The typical upload intervals (first update) of broadcast navigation messages are also highlighted in the figure. At first glance, the overall standard deviation of clock prediction from the GNSS satellite clocks is less than 1 m over eight hours of averaging time, whereas the optical clock contributions are under a decimetre to millimetre level. Further in detail, at 30 s averaging time, where PPP real-time application is concerned, the optical clocks may reduce the prediction errors to 1 mm level from 14 mm, which is the greatest of all.