# Improved Multi-GNSS PPP Software for Upgrading the DEMETRA Project Time Monitoring Service
## 3 Processing and Results
### Atomium Constrained PPP  
The constraints were applied to GPS-only PPP and GPS + Galileo PPP results separately, and the results were compared with the original clock results in Figure 5. Both INRIM and ORB have their hydrogen maser clock for the comparison in this experiment, and the values of \(ADev(1s)\) were both set to \(2\times 10^{-13}\). As seen in Figure 5, the constrained PPP can reduce the noise of the clock solution inside the batch and keep the long-term stability as for the original PPP. The noise reduction for the constrained PPP was more visible in an aligned solution using 3 days' clock data, as shown in Figure 6.  
Figure 4: ADEVs for the CCD GPS-only and GPS + Galileo PPP results in the Italian National Metrology Institute (INRIM).  
Figure 5: CCD constrained results in ORB.  
The ADEVs of constrained PPP, using the aligned 3-day results, were compared with the classical PPP ones in Figures 7 and 8 for both the CCD experiments in ORB and INRIM.  
Figure 8: ADEVs of aligned CCD results in INRIM.  
Figure 6: Aligned CCD constrained results in ORB.  
Figure 7: ADEVs of aligned CCD results in ORB.  
It is very clear that constrained PPP improves clock frequency stability (see Figures 7 and 8), especially at short averaging times, as reported in Table 1. It can be observed in both Figures that the best short-term stability was provided by GPS-only constrained PPP, rather than the GPS + Galileo constrained PPP. It is most probably because the GPS + Galileo PPP has more satellite measurements at each epoch, and the relative weight of the constraint gets smaller for GPS+Galileo than for GPS-only.  
The \"PPP--OPT\" experiments were also built here to test the constrained PPP. Since both AO_4 and GUM4 stations receive only GPS signals, GPS + Galileo PPP results were not available for the following \"PPP--OPT\" experiments. The GPS-only results were compared in Figure 9.  
It was found (Figure 9) that the constrained PPP did not reduce the noise obviously as in the former CCD experiments. The reason is that, while the AO_4 is driven by a hydrogen maser, GUM4 is driven by a caesium clock. As a result of its lower ADev(1s), the caesium clock will be constrained in PPP with a much smaller weight than a hydrogen maser, as we can see from Equations (4) and (5). Although the constraint improved the stability dramatically at the AO_4 side, the caesium clock estimation at the GUM4 side was not improved effectively by the constraint, as shown in Figure 10. The noise of caesium clock dominated the stability of the two clock comparison so that the final constrained PPP solution did not show any improvement.  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Averaging Time**} & \multicolumn{2}{c}{**Improvement of Stability**} \\ \cline{2-3}  & **GPS** & **GPS + Galileo** \\ \hline
5 min & 89.3\% & 79.4\% \\
1 h & 50.0\% & 36.7\% \\
3 h & 32.3\% & 23.1\% \\
12 h & 21.1\% & 17.7\% \\ \hline \hline \end{tabular}
\end{table}
Table 1: The stability improvements when applying constraint model to global positioning system (GPS) precise point positioning (PPP) (black to the green line in Figures 7 and 8) and GPS + Galileo PPP (red to the light blue line in Figures 7 and 8), respectively.  
Figure 9: “PPP—OPT” experiments to evaluate constrained PPP.  
In addition to the normal function of constrained PPP, the applications of constrained PPP in different scenarios were also studied in this paper: