# Early Results on GNSS Receiver Antenna Calibration System Development +
## 3 Results and Discussion  
To test the antenna calibration system at LMMT and to validate the calibration results with Geo++ GmbH, an IGS approved calibration institution, from April to June of 2023, four calibration campaigns of the same GNSS antenna Trimble Zephyr 2 Geodetic (TRMS7971.00 NONE, S/N: 30739001) for the GPS L1 frequency were conducted. Figure 3 visualizes the main benefit of using a robot for antenna calibration, i.e., a full coverage of the entire antenna hemisphere, even after only approx. 2 h of calibration. Figure 3: Satellite azimuth and zenith angle plot (sky-plot) during antenna calibration at LMMT: (**a**) topocentric frame (TF); (**b**) antenna frame (AF). Figure 2: GNSS antenna calibration system at the Laboratory for Measurements and Measuring Technique (LMMT) of the Faculty of Geodesy of the University of Zagreb in Croatia; REF—reference antenna (TRM57971.00 NONE); AUT—antenna-under-test (LEIAX1202 GG NONE). The calibration field consists of two 5-m-spaced pillars, which are part of the Calibration Baseline of the Faculty of Geodesy of the University of Zagreb [17]. To validate the LMMT antenna calibration results, a comparison with an independent calibration was conducted. For that purpose, the investigated antenna was calibrated individually by Geo++ GmbH, an IGS approved institution, on 5 August 2022. According to the new calibration method at LMMT, PCCs have been estimated for every conducted antenna calibration campaign. Lastly, to obtain a final solution, calibration results have been averaged, and the final PCO and PVC grids were exported to ANTEX. Table 1 summarizes the LMMT and Geo++ GmbH estimated PCOs. The PCO differences between the LMMT and Geo++ GmbH calibrations are on the sub-millimeter level. The PCVs of the investigated antenna for the GPS L1 frequency, per calibration institution, are depicted in Figure 4. Both individual calibration results show similar PCV behaviors over the entire antenna hemisphere, with noticeable larger values at the antenna horizon for the Geo++ calibrations. Also, for both calibration results (LMMT and Geo++ GmbH), small azimuthal variations are noticeable. To estimate the accuracy of LMMT individual antenna calibration results, the Geo++ GmbH calibration results are taken as reference values. The PCC differences \(\Delta\)_PCC_ of antenna TRM57971.00 NONE (S/N: 30739001) for GPS L1 (G01) frequency, over the entire antenna hemisphere, are calculated, and they are depicted in Figure 5. By a simple visualization of the gained difference pattern, it is evident that values around zero prevail with larger values mainly located at low antenna elevations, e.g., for an azimuth of approx. 300\({}^{\circ}\). To obtain a quantitative accuracy estimation of LMMT calibration results, the following scalar measures of the PCC difference pattern are calculated: minimum and maximum \(\Delta\)_PCC_, root-mean-square (RMS) deviation of \(\Delta\)_PCC_, range of the \(\Delta\)_PCC_, and the interquartile range (IQR) of the \(\Delta\)_PCC_. All calculated values are given in Table 2. Furthermore, because during the majority of GNSS applications, a standard elevation mask of a minimum of 10\({}^{\circ}\) is used, a 10\({}^{\circ}\) elevation-reduced antenna hemisphere analysis is justified. All accuracy measures were determined accordingly and are given in Table 2. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Calibration** & \multicolumn{3}{c}{**Phase Center Offset (PCO)**} \\ \cline{2-4}
**Institution** & **North** & **East** & **Up** \\ \hline Geo++ GmbH & 0.79 & 0.32 & 66.96 \\ LMMT & 1.24 & 0.11 & 67.24 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: PCO vector components of antenna TRM57971.00 NONE (S/N: 30739001) of GPS L1 (G01) frequency per calibration institution. All values are in millimeters (mm). Figure 4: (a) Geo++ GmbH and (b) LMMT phase center variations (PCVs) of antenna TRM57971.00 NONE (S/N: 30739001) for GPS L1 (G01) frequency.