# Evaluating Optical Clock Performance for GNSS Positioning
## 5 Results  
This section presents the clock stability analysis results. The averaged overlapping ADEV values of 12 clock products for each satellite clock, \(\sigma_{y}(\tau)\) vs. averaging time, \((\tau)\) are shown on the log-log graph in Figure 3, where four separate graphs are exhibited representing the four constellations. Looking into the GPS constellation, it is found that the new generation of Rb clocks on GPS IIF and GPS III satellites, excluding G08 and G10, have shown more than 10 times better stability yielding almost \(10^{-13}\) at 30 s, compared to that of old Rb atomic clocks onboard GPS IIR or GPS IIR-M block satellites, which have resulted in less than \(10^{-12}\). Furthermore, for a longer averaging time up to 900 s, the GPS IIF and GPS III satellite clocks have consistent slopes in the ADEV values driven by white noises, whereas GPS IIR and GPS IIR-M satellite clocks exhibit significant slope changes after 100 s.  
Considering the Galileo and BeilDou constellations next, the ensemble of two PHM + two Rb clocks on both Galileo Full Operational Capability (FOC) and BDS3 satellites have somewhat similar slopes in the first 900 s or so, except for E07, which shows a flicker noise behaviour after 1800 s. In terms of ADEV, these clocks have shown the best stability amongst all satellite clocks at the averaging time of 30 s and 900 s reaching \(10^{-13}\) and \(10^{-14}\), respectively, which indicates that this unique setup of clocks has an order of magnitude better stability than their older generations of Galileo In-Orbit Verification (IOV) and BDS2 satellite clocks. Lastly, with the GLONASS constellation, no significant difference is found in the performance of M and K1 satellite clocks, given that all clock ADEV values vary around \(10^{-12}\) and \(10^{-13}\) at 30 s and 900 s, respectively. The second assessment conducted is to compare the satellite clocks with the optical clocks with regard to their ADEV. For clarity on the ADEV plot, we classified and averaged the initial ADEV values previously shown in Figure 3 as per the satellite types. As detailed in Table 2, there are 12 different satellite types for the four constellations. Figure 4 presents the averaged ADEV values of the clocks (by satellite types) and the optical clocks. Among them, the ensemble of two PHM and two Rb clocks onboard Galileo FOC satellites are the most stable satellite clocks averaging 1.2 \(\times\)\(10^{-13}\) at 30 s and 1.7 \(\times\)\(10^{-14}\) at 900 s, followed by the similar setup of BeilDou BDS3 Medium Earth Orbit (MEO) clocks that have ADEV of 1.6 \(\times\)\(10^{-13}\) and 2.1 \(\times\)\(10^{-14}\) at 30 s and 900 s, respectively. The three Rb clocks on GPS Block \begin{table}
\begin{tabular}{l l l l} \hline
**Const.** & **SV Type** & **PRN** & **Clocks** \\ \hline GPS & Block IIR & G02 G13 G16 G19 G20 G21 G22 G28 & 3 Rb \\ GPS & Block IIR-M & G05 G07 G12 G15 G17 G29 G31 & 3 Rb \\ GPS & Block IIF & G01 G03 G06 G08 G09 G10 G24 G25 G26 G27 G30 G32 & 2 Rb + 1 Cs \\ GPS & Block III & G04 G11 G14 G18 G23 & 3 Rb \\ GLONASS & M & R01 R02 R03 R04 R05 R07 R08 R12 R13 R14 R15 R17 R18 R19 R20 R21 R24 & 3 Cs \\ GLONASS & K1 & R09 R11 R22 & 2 Cs + 2 Rb \\ GALILEO & IOV & E11 E12 E19 & 2 PHM + 2 Rb \\ GALILEO & FOC & E01 E02 E03 E04 E05 E07 E08 E09 E10 E13 E14 E15 E18 E21 E24 E25 E26 & 2 PHM + 2 Rb \\ BEIDOU & BDS2 MEO & C11 C12 C14 & 4 Rb \\ BEIDOU & BDS2 GEO \& IOSO & C01 C02 C03 C04 C05 C06 C07 C08 C09 C10 C13 C16 & 4 Rb \\ BEIDOU & BDS3 MEO & C19 C20 C21 C22 C23 C24 C25 C26 C27 C28 C29 C30 C32 C33 C34 C35 & 2 PHM + 2 Rb \\ BEIDOU & BDS3 GEO\&IOSO & C38 C39 C40 C59 C60 & 2 PHM + 2 Rb \\ \hline \end{tabular}
\end{table} 
Table 2: Total atomic clocks onboard GNSS satellites in 2022.