# Experimental Validation of a GNSS Receiver Antenna Absolute Field Calibration System
## 3 Results and Discussion
### Results of Validation with Geo++ GmbH  
To experimentally validate the LMMT GNSS receiver antenna calibration facility and its calibration results, a comparative analysis was conducted with independent calibrations obtained by Geo++ GmbH. Dual-frequency calibration results for the TRM57971.00 NONE antenna (S/N: 30739001, I/L: Z1) were compared at the pattern level. PCC difference patterns \(\Delta\)_PCC_, per frequency (G01 and G02), were calculated and are illustrated in Figure 12. PCC difference values were calculated for the entire upper antenna hemisphere, i.e., \(\alpha=[0^{\circ},360^{\circ}]\) and \(z=[0^{\circ},90^{\circ}]\), using an angular grid defined by azimuthal and zenithal increments of \(5^{\circ}\). To quantitatively assess the accuracy of the LMMT calibrations, scalar metrics were derived from the calculated PCC difference patterns. These metrics are presented, per frequency, in Table 4.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{3}{*}{**Calibration Frequency**} & \multicolumn{4}{c}{**Full Antenna Hemisphere**} & \multicolumn{4}{c}{**Reduced Antenna Hemisphere**} \\  & \multicolumn{4}{c}{**(\(0^{\circ}\) Elevation Cut-Off)**} & \multicolumn{4}{c}{**(10\({}^{\circ}\) Elevation Cut-Off)**} \\ \cline{2-11}  & **Min.** & **Max.** & **RMS** & **Range** & **IQR** & **Min.** & **Max.** & **RMS** & **Range** & **IQR** \\ \hline GPS L1 (G01) & \(-1.85\) & \(0.61\) & \(0.36\) & \(2.46\) & \(0.41\) & \(-1.13\) & \(0.61\) & \(0.31\) & \(1.74\) & \(0.38\) \\ GPS L2 (G02) & \(-2.15\) & \(1.01\) & \(0.54\) & \(3.16\) & \(0.67\) & \(-1.26\) & \(0.85\) & \(0.47\) & \(2.11\) & \(0.54\) \\ \hline \hline \end{tabular}
\end{table}
Table 4: Scalar metrics characterizing the difference between individual absolute calibrations from Geo++ GmbH and LMMT.  
Figure 11: TPSPG_A1 NONE antenna (S/N: 308-1874, I/L: TP) LMMT individual calibration results (PCO vector and PCVs) for GPS L1 (G01) and GPS L2 (G02).  
Analyzing the full receiver antenna hemisphere, Geo++ and LMMT PCC differences are within a range of 2.46 mm for G01 and 3.16 mm for G02. The middle half of PCC differences are within 0.41 mm for G01 and 0.67 mm for G02. The overall agreement between the individual PCC patterns of Geo++ and LMMT, quantified by the root-mean-square (RMS) deviation, per frequency, is:  
\[\begin{split}\text{RMS}_{\text{G01}}=0.36\text{ mm},\\ \text{RMS}_{\text{G02}}=0.54\text{ mm}.\end{split} \tag{6}\]  
The GPS L1 calibration results show slightly better agreement with Geo++ GmbH reference values than GPS L2 results. However, as the G01 and G02 metrics differences are in the order of tenths of a millimeter, their potential impact on practical applications remains to be thoroughly analyzed. Furthermore, by analyzing scalar metrics for the elevation-reduced antenna hemisphere, a higher calibration accuracy is evident. However, this is to be expected because such an analysis does not include the antenna's PCC model near the horizon (below 10\({}^{\circ}\) of elevation in the AF) which will, in general, always be of lower accuracy due to SH expansion properties and the fact that few or no observations are available below the antenna's horizon.  
In line with the obtained experimental validation results, it is evident that the developed GNSS receiver antenna absolute field calibration system is in agreement with Geo++ GmbH within 0.54 mm for dual-frequency GPS (L1 and L2) calibrations.