# Development of a Submillimetric GNSS-Based Distance Meter for Length Metrology +
## 4 Assessment of the GNSS-Based Distances Accuracy
### Description of the Experiment  
To be prove accurate, the GNSS-based distances had to be compared with the SITraced distances provided by the FGI in 2012. Furthermore, since accuracy comprises both repeatability and reproducibility, the comparison had to be done over time with GNSS measurements carried out under different environmental conditions. Nonetheless, the SI-traced distances provided by the FGI were realized by the pillars in a specific epoch (June 2012), and consequently their stability over time has to be considered as a critical part of the study. Considering the construction features of the pillars, errors due to vibrations and reproducibility of the centre mount can be assumed negligible, but the possible instability of pillars, which chiefly depends on the grounding and the geological profile, would diminish the uncertainty of SI-traced distances of reference. The instability of pillars is normally included in the corresponding uncertainty budget (K  
International Association of Geodesy when the scale is required to be better than 1 ppm. It is worth noting, however, that this formulation has an incorrect sign, as recently pointed out by [51]. Once obtained the actual refraction index, the three meteorological corrections recommended for the ME5000 [11] were computed, though only the first speed correction was retained because the second speed correction and the beam correction were negligible even for the longest distance (330 m). The calibration correction was then applied to the slope distances resulting from the refraction correction. Applying the calibration parameters (zero-error and scale error) improves the accuracy of the measured distances, though the precision of the resulting distances decreases as the uncertainty of the calibration parameters has to be taken into account. Finally, the geometrical reduction is applied to obtain the distances in Table 4.  
Concerning the GNSS campaigns, they were carried out in 12-h static sessions during the nighttime once the daily EDM measurements were finished. Table 5 shows the dates and other details concerning the GNSS campaigns. Since pillars No.1 and No.3 had better GNSS observing conditions than the rest, they were selected to conduct the experiment. Nonetheless, the trees surrounding the baseline had considerably grown from 2013 to 2016, making the multipath error apparent even for the selected pillars. Therefore, we decided to reduce the GNSS data interval from 15 s to 1 s in the 2016 campaign so that the methods to detect and mitigate the multipath error that were being developed at Space Geodesy and Navigation Laboratory of the University College London (SGNL-UCL), which were described in the previous section, could be better implemented and tested. With regard to the GNSS antennas, we always used the same two 3D choke-ring Leica AR25.R4, which were individually calibrated by the University of Bonn by using the anechoic chamber method [52; 53]. The two antennas were set up carefully oriented towards the geodetic north which was rigorously realized by benchmarks that are permanently located near every pillar. The GNSS distances finally obtained are given in Table 6. It is worth noting that all the DD residuals and testing results in this study are consistent with the solution by Bernese 5.2 [21]. \begin{table}
\begin{tabular}{c c c c} \hline
**Year** & **ME5000 Distance** & \(\sigma\) & \(\mathbf{U}_{k=2}\) \\ \hline
2013 & 94.40146 m & 0.08 mm & 0.21 mm \\
2014 & 94.40057 m & 0.09 mm & 0.22 mm \\
2015 & 94.40108 m & 0.08 mm & 0.21 mm \\
2016 & 94.40093 m & 0.07 mm & 0.21 mm \\ \hline \end{tabular}
\end{table} 
Table 4: Electronic Distance Meter (EDM) distances obtained in years 2013–2016 and their corresponding standard deviation and expanded uncertainty \(U\) (\(k=2\)).