# Experimental Validation of a GNSS Receiver Antenna Absolute Field Calibration System
## 3 Results and Discussion
### Results of Short-Baseline Validation
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Short** & **PCC** & **\(\Delta\mathbf{X}\)** & **\(\Delta\mathbf{Y}\)** & **\(\Delta\mathbf{Z}\)** & **\(\Delta\mathbf{e}\)** & **\(\Delta\mathbf{m}\)** & **\(\Delta\mathbf{u}\)** \\
**Baseline** & **Freq.** & **Model** & \([\mathbf{\mathbf{m}}]\) & \([\mathbf{\mathbf{m}}]\) & \([\mathbf{\mathbf{m}}]\) & \([\mathbf{\mathbf{m}}]\) & \([\mathbf{\mathbf{m}}]\) & \([\mathbf{\mathbf{m}}]\) \\ \hline T-R & L1 & IGS & 0.1787 & \(-\)4.8769 & 1.1069 & \(-\)4.7370 & 1.6129 & \(-\)0.0271 \\  & & LMMT & 0.1786 & \(-\)4.8759 & 1.1086 & \(-\)4.7360 & 1.6139 & \(-\)0.0258 \\  & & IGS & 0.1695 & \(-\)4.8753 & 1.1006 & \(-\)4.7329 & 1.6145 & \(-\)0.0375 \\  & & LMMT & 0.1808 & \(-\)4.8747 & 1.1106 & \(-\)4.7355 & 1.6136 & \(-\)0.0226 \\  & & IGS & 0.1935 & \(-\)4.8799 & 1.1180 & \(-\)4.7440 & 1.6110 & \(-\)0.0098 \\  & & LMMT & 0.1760 & \(-\)4.8780 & 1.1073 & \(-\)4.7373 & 1.6152 & \(-\)0.0289 \\ \hline T-A & L1 & IGS & 0.3982 & \(-\)9.7479 & 2.2085 & \(-\)9.4796 & 3.1928 & \(-\)0.0295 \\  & & LMMT & 0.3998 & \(-\)9.7481 & 2.2119 & \(-\)9.4802 & 3.1941 & \(-\)0.0260 \\  & & IGS & 0.3967 & \(-\)9.7477 & 2.2128 & \(-\)9.4790 & 3.1968 & \(-\)0.0274 \\  & & LMMT & 0.3979 & \(-\)9.7485 & 2.2120 & \(-\)9.4801 & 3.1956 & \(-\)0.0273 \\  & & IGS & 0.4023 & \(-\)9.7483 & 2.2041 & \(-\)9.4811 & 3.1870 & \(-\)0.0300 \\  & & LMMT & 0.4042 & \(-\)9.7475 & 2.2138 & \(-\)9.4809 & 3.1923 & \(-\)0.0216 \\ \hline T-ST & L1 & IGS & 0.8639 & \(-\)19.4707 & 4.4185 & \(-\)18.9537 & 6.3352 & \(-\)0.0078 \\  & & LMMT & 0.8634 & \(-\)19.4707 & 4.4186 & \(-\)18.9536 & 6.3356 & \(-\)0.0081 \\  & & IGS & 0.8659 & \(-\)19.4720 & 4.4180 & \(-\)18.9555 & 6.3337 & \(-\)0.0071 \\  & & LMMT & 0.8641 & \(-\)19.4715 & 4.4197 & \(-\)18.9545 & 6.3361 & \(-\)0.0070 \\  & & IGS & 0.8618 & \(-\)19.4689 & 4.4212 & \(-\)18.9514 & 6.3382 & \(-\)0.0069 \\  & & LMMT & 0.8632 & \(-\)19.4698 & 4.4187 & \(-\)18.9526 & 6.3357 & \(-\)0.0080 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Short-baseline solutions, i.e., geocentric (ITRF2020) and topocentric coordinate differences, per frequency (GPS L1, GPS L2, and ionosphere-free linear combination L0 of L1 and L2) and per receiver antenna model (LMMT individual and IGS type-mean). \begin{table}
\begin{tabular}{c c} \hline
**Date/DoY/Epoch.** & 7 June 2023/158/2023.43 \\
**Time of survey (UTC)/Survey duration** & 6:45-12:45/6:00 \\
**Observation interval** & 1 s \\
**Elevation mask** & 10\({}^{\circ}\) \\
**Average number of GPS satellites** & 9 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Recapitulation of basic information on the GNSS (GPS) survey of short-baselines. From a simple overview of the resulting short-baseline errors, consistently lower values obtained with the application of LMMT individual PCC models are evident. Furthermore, short-baseline errors derived by forming the ionosphere-free linear combination GPS L0 of GPS L1 and GPS L2 show a change correlated with the ionosphere-free linear combination's coefficients, i.e., approximately 2.54 for G01 (GPS L1) and \(-\)1.54 for G02 (GPS L2). This results in a significant amplification of short-baseline errors based on the application of IGS type-mean PCC models. To objectively evaluate the equivalence of the obtained short-baseline accuracies with respect to the antenna phase center model used (LMMT individual or IGS type-mean) all short-baseline validation results were considered, regardless of processing frequency, and a two-tailed \(F\)-test was conducted. The general formula to calculate baseline accuracy \(\sigma\) is given by the following expression:  
\[\sigma=\sqrt{\frac{1}{n}\sum_{i=1}^{n}\varepsilon_{i}^{2}} \tag{7}\]  
Short-baseline accuracy was quantified in 1D (height or equivalent to the PCO Up component), 2D (horizontal component), and 3D (spatial component) per antenna model (LMMT individual or IGS type-mean).