# Experimental Validation of a GNSS Receiver Antenna Absolute Field Calibration System
## 3 Results and Discussion
### Results of GNSS/GPS Network Validation  
In the last, third, validation test within this research, an analysis at the GNSS/GPS network solution level was conducted. According to the experiment methodology (Section 2.3.3), a static GNSS survey on four stations (Figure 8) was conducted on 12 June 2023. Each of the four Trimble Zephyr 2 Geodetic GNSS antennas (I/L: Z1, Z2, Z3, Z4) was connected to a Trimble NetR5 infrastructure GNSS receiver, whereby only GPS carrier-phase observations was registered with an observation interval of 15 s and a standard elevation mask of 10\({}^{\circ}\). A summarized overview of the GNSS (GPS) survey is given in Table 10. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**PCC** & \multicolumn{3}{c}{**Baseline Accuracy \((\sigma)\) Per Component**} \\ \cline{2-4}
**Model** & **Height** & **2D** & **3D** \\ \hline IGS & 6.82 & 4.51 & 8.18 \\ LMMT & 2.62 & 1.87 & 3.21 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Short-baseline accuracy results in the height direction, 2D, and 3D per antenna PCC model applied to baseline processing (LMMT individual or IGS type-mean). All values are in millimeters. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Short-Baseline** & **Test** & **\(p\)-Value** & **Lower Critical** & **Upper Critical** & **Hypothesis** \\
**Component** & **Statistics** & **Value** & **Value** & **Accepted** \\ \hline Height & 6.793 & 0.014 & 0.226 & 4.433 & \(H_{\text{A}}\) \\
2D & 5.850 & 0.022 & 0.226 & 4.433 & \(H_{\text{A}}\) \\
3D & 6.475 & 0.016 & 0.226 & 4.433 & \(H_{\text{A}}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Key statistical parameters of the performed two-tailed \(F\)-test for equality of variances per short-baseline component. To estimate the influence of the receiver antenna PCC model (type-mean by IGS or individual by LMMT) on the GNSS/GPS network's local and global accuracy, the network solution was computed two times using identical input data and processing parameters, different only in the applied antenna PCC models. After the field survey, processing of GPS-only observations was performed using the WaSoft software package [43]. Baseline processing in the GNSS/GPS network was conducted in the standard dual-frequency mode by utilizing IGS precise (final) satellite orbits, IGS global ionospheric maps (GIMs), and tropospheric corrections (tropospheric zenith delay) based on the Saastamoinen model. The network was adjusted as a minimum constraint network and in a \"each-to-each\" approach by processing all six baselines between all four network stations. Furthermore, the non-standard approach without involvement of fixed stations was applied. The reasoning behind such an approach is that inclusion of reference points of higher order implies inclusion of antennas that have not been individually calibrated by the LMMT calibration system. This is contrary to the goals of this analysis. Furthermore, to support this research design approach, the primary focus of this analysis is not on station positions (coordinates), but rather on the achieved local and global network's accuracy. Results of GNSS/GPS network postprocessing and adjustment, per antenna model applied (type-mean by IGS or individual by LMMT), are presented in Table 11 (IGS PCC model) and Table 12 (LMMT PPC model). Furthermore, according to the elaborated validation methodology (Section 2.3.3), for both GNSS/GPS network realizations, the global accuracy of the network, defined by the standard deviation of point position according to Equation (5), is calculated: \begin{table}
\begin{tabular}{c c} \hline
**Date/DoY/Epoch** & 12 June 2023/163/2023.45 \\
**Time of survey (UTC)/Survey duration** & 6:20–13:00/6:40 \\
**Registration interval** & 15 s \\
**Elevation mask** & 10\({}^{\circ}\) \\
**Average number of GPS satellites** & 7 \\ \hline \end{tabular}
\end{table} 
Table 10: Recapitulation of basic information on the GPS survey of the GNSS/GPS network.