# Improved Multi-GNSS PPP Software for Upgrading the DEMETRA Project Time Monitoring Service
## 3 Processing and Results
### Atomium Integer PPP  
As described before, to check if there was any integer cycle estimation error of \(N_{WL}\) in the integer PPP results, the continuity of the estimated WRB needs to be ensured. Figure 14 shows the estimated WRB at the first step of integer PPP for the station BRUX and RTBS in the CCD experiments, and no integer cycle error was found during the period of estimation.  
Figure 14: Wide-lane receiver bias (WRB) at station BRUX and RTBS estimated by integer PPP.  
Figure 13: “IGRT—GUM4” from PPP and constrained PPP.  
As shown in Figure 15, the common clock comparison results using integer PPP also showed some discontinuities at the daily batch boundaries. However, these discontinuities were only integer multiples of the GPS \(\lambda_{NL}\) (are 1 or \(-\)1 \(\lambda_{NL}\) in Figure 15), and the continuous clock solution could be easily obtained after alignment by adding integer multiples of \(\lambda_{NL}\).  
This continuous integer PPP CCD result was compared to the original Atomium PPP result with daily boundary jumps and the aligned original Atomium PPP result in terms of phase offset and ADEVs, as illustrated in Figures 16 and 17, separately. Compared to the original Atomium PPP results, integer PPP clearly improved the frequency stability from several hours to longer averaging times, and the frequency accuracy of \(1\,\times\,10^{-16}\) could be reached by 4 days averaging. Aligning the daily Atomium PPP results using 2 nd order extrapolation to remove the daily boundary jumps could largely improve the frequency stability as shown in Figure 17, however it caused a drift in the time solution, as shown in Figure 16 (where the aligned data in green line accumulate an error of about 0.6 ns in a month). It is, therefore, not recommended to align the daily time solutions from float ambiguities PPP over a long time span to not affect the time accuracy.  
Figure 16: CCD results in ORB using Atomium integer PPP and original Atomium PPP.  
Figure 15: CCD experiments at ORB with integer PPP.  
The improvements of frequency stability at different averaging times by using Atomium integer PPP instead of Atomium PPP (corresponding to the black and red lines in Figure 17) are recorded in Table 2. It is shown that the largest improvement happened at the averaging time of one day, which was exactly the occurrence rate of the daily boundary jump.  
Figure 18 compares the \"PPP--OPT\" results from integer PPP with the one from NRCAN PPP, which was based on a multi-day batch to avoid the daily jumps within the batch. The NRCAN PPP results showed a slight divergence and reach 0.4 ns at the end of the one-month batch.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Averaging Time** & **Improvement of Stability** \\ \hline
5 min & 13.3\% \\
1 h & 31.2\% \\
3 h & 50.2\% \\
12 h & 63.3\% \\
1 day & 80\% \\
5 days & 65.3\% \\ \hline \hline \end{tabular}
\end{table}
Table 2: The stability improvements applying integer ambiguity resolution to Atomium PPP (GPS).  
Figure 17: ADEVs between integer PPP and PPP CCD results in ORB.  
Figure 18: Comparison of integer PPP and NRCAN PPP results.  
The ADEVs of the clock measurements in Figure 18 are further compared in Figure 19. A similar conclusion can be made as from the CCD experiments: The integer PPP improved the clock frequency stability from an average of 2.5 h to longer times compared to the NRCAN PPP, and at 10 days averaging, the stability of \(1\,\times\,10^{-16}\) was acquired by using integer PPP.