# Improved Multi-GNSS PPP Software for Upgrading the DEMETRA Project Time Monitoring Service
## 3 Processing and Results
### Atomium Constrained PPP
#### 3.2.2 For an Extreme Noisy Environment  
Station GUM4 was observed to have very noisy receiver measurements for around 2 months, and it returned to normal after some receiver modification. The basic idea was constraining the measurements' noise by constrained PPP, as illustrated in Figure 12.  
Since the cesium clock estimation at GUM4 was not affected much by the constraint model as mentioned before, a larger weight of the clock constraint at GUM4 was set in this experiment to further restrict the abnormal measurements' noise (the same weight as for the hydrogen maser was chosen). The constrained PPP reduced the noise but still not at a satisfactory level, which can be seen in Figure 12. This is because the frequency offset and drift over each day were estimated with larger uncertainties due to the very noisy measurements.  
To further retrieve the correct clock solution from the noisy environment, we needed a more accurate frequency measurement of the clock. For this purpose, we estimated the averaged frequency deviation \"IGRT--GUM4\" (Frq-iCRT--GUM4\") as the difference of Frq-iCRT--AO_4\" and Frq-AO_4--GUM4\". Frq-iCRT--AO_4\" was computed from the clock solution IGRT--AO_4 through Atomium PPP, and Frq-AO_4--GUM4\" was computed from independent clock comparison results of AO_4--GUM4. Then the constraints were computed from the frequency data and applied to Atomium PPP to estimate the constrained \"IGRT--GUM4\". In the present case, we used the optical link for AO_4--GUM4. This link is even more stable than the PPP, so there is no real advantage of using it to get a constrained PPP solution. However, in some other links, the only available independent link might be a two-Way satellite time and frequency transfer (TWSTFT) [34], which provides only 24 data points per day, and therefore, does not provide short-term stability. In that case, using the TWSTFT to get the frequency deviation of the link will be very helpful to get a constrained PPP, and hence, a frequency transfer with very good short-term frequency stability.  
The results of constrained PPP at GUM4 using estimated constraints are displayed in the red line in Figure 13. To further mitigate the daily boundary effect, and also to verify the correctness of the constrained clock results inside the batch, the multi-day constrained PPP computations were also performed: For each daily batch, in addition to the relative constraints, the receiver clock at the first epoch was further absolutely constrained based on the estimated clock at the last epoch of the previous batch and the increment predicted from the frequency model of the previous batch. The corresponding multi-day constrained PPP results are plotted in Figure 13 in the green line. It is observed from Figure 13 that the constrained PPP using the estimated constraints can highly reduce the clock measurements' noise, and the multi-day constrained PPP can further provide continuous  
Figure 12: “IGRT—GUM4” from constrained and non-constrained PPP.  
clock solutions by reducing the size of the daily boundary jump. However, the multi-day constrained method should be used carefully since it may also introduce an artificial variation up to hundreds of ps during 1-month clock measurements. Hence, it is recommended to use this multi-day constrained PPP in extremely noisy environments only to restrict the large daily boundary jump, which is the main factor influencing the stability of the constrained PPP clock solution, as can be seen in Figure 13.  
The correct frequency data are expected to be obtained from external products, e.g., TWSTFT. Though it is also possible to directly use the phase data from external products if it exits, the calibration error of the external measurements will also be introduced. Meanwhile, the estimated frequency data is not affected by these calibration errors and can be used by the target clock without any bias.