# Experimental Validation of a GNSS Receiver Antenna Absolute Field Calibration System
## 3 Results and Discussion
### Results of Short-Baseline Validation
The goal of such an analysis is to evaluate if the application of different antenna PCC models has a different impact on baseline determination in the height direction, horizontal direction, and spatial direction. Therefore, in line with this analysis, based on the determined short-baseline errors (Table 7) and Equation (7), the accuracies of short-baselines were calculated and are presented in Table 8. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline
**Short** & **PCC** & **\(\varepsilon_{X}\)** & \(\varepsilon_{Y}\) & \(\varepsilon_{Z}\) & \(\varepsilon_{e}\) & \(\varepsilon_{n}\) & \(\varepsilon_{u}\) & \(\varepsilon_{2\text{D}}\) & \(\varepsilon_{3\text{D}}\) \\
**Baseline** & **Freq.** & **Model** & \([\mathbf{mm}]\) & \([\mathbf{mm}]\) & \([\mathbf{mm}]\) & \([\mathbf{mm}]\) & \([\mathbf{mm}]\) & \([\mathbf{mm}]\) & \([\mathbf{mm}]\) & \([\mathbf{mm}]\) & \([\mathbf{mm}]\) & \([\mathbf{mm}]\) \\ \hline T-R & L1 & IGS & \(-\)0.2 & 2.0 & 0.9 & 2.0 & 0.4 & 0.9 & 2.0 & 2.2 \\  & LMMT & \(-\)0.1 & 1.0 & \(-\)0.8 & 1.0 & \(-\)0.7 & \(-\)0.4 & 1.2 & 1.3 \\  & L2 & IGS & 9.0 & 0.4 & 7.2 & \(-\)2.1 & \(-\)1.2 & 11.3 & 2.4 & 11.5 \\  & LMMT & \(-\)2.3 & \(-\)0.2 & \(-\)2.8 & 0.4 & \(-\)0.3 & \(-\)3.6 & 0.6 & 3.6 \\  & L0 & IGS & \(-\)15.0 & 5.0 & \(-\)10.2 & 8.9 & 2.2 & \(-\)16.4 & 9.2 & 18.8 \\  & LMMT & 2.5 & 3.1 & 0.5 & 2.3 & \(-\)2.0 & 2.6 & 3.0 & 4.0 \\ \hline T-A & L1 & IGS & 0.4 & 0.8 & 2.4 & 0.7 & 1.2 & 2.1 & 1.4 & 2.6 \\  & LMMT & \(-\)1.2 & 1.0 & \(-\)1.0 & 1.3 & \(-\)0.1 & \(-\)1.3 & 1.3 & 1.9 \\  & L2 & IGS & 1.9 & 0.6 & \(-\)1.9 & 0.1 & \(-\)2.8 & 0.0 & 2.8 & 2.8 \\  & LMMT & 0.7 & 1.4 & \(-\)1.1 & 1.2 & \(-\)1.5 & 0.0 & 1.9 & 1.9 \\  & L0 & IGS & \(-\)3.7 & 1.2 & 6.8 & 2.2 & 7.1 & 2.6 & 7.4 & 7.8 \\  & LMMT & \(-\)5.6 & 0.4 & \(-\)2.9 & 1.9 & 1.7 & \(-\)5.8 & 2.6 & 6.3 \\ \hline T-ST & L1 & IGS & \(-\)0.6 & 0.7 & \(-\)1.4 & 0.8 & \(-\)0.7 & \(-\)1.3 & 1.1 & 1.7 \\  & LMMT & \(-\)0.1 & 0.7 & \(-\)1.5 & 0.7 & \(-\)1.1 & \(-\)1.0 & 1.3 & 1.7 \\  & L2 & IGS & \(-\)2.6 & 2.0 & \(-\)0.9 & 2.6 & 0.8 & \(-\)2.0 & 2.7 & 3.4 \\  & LMMT & \(-\)0.8 & 1.5 & \(-\)2.6 & 1.7 & \(-\)1.6 & \(-\)2.1 & 2.3 & 3.1 \\  & L0 & IGS & 1.5 & \(-\)1.1 & \(-\)4.1 & \(-\)1.5 & \(-\)3.7 & \(-\)2.1 & 4.0 & 4.5 \\  & LMMT & 0.1 & \(-\)0.2 & \(-\)1.6 & \(-\)0.2 & \(-\)1.1 & \(-\)1.1 & 1.2 & 1.6 \\ \hline \end{tabular}
\end{table} 
Table 7: Short-baseline errors expressed along each coordinate axis individually, as well as in terms of the horizontal (2D) and total spatial (3D) errors, 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). The obtained short-baseline accuracy results imply a higher achieved accuracy based on the application of LMMT individual antenna phase center models. Therefore, to test the hypothesis of equality of the gained accuracies, a two-tailed \(F\)-test was performed. The corresponding null hypothesis \(H_{0}\) and alternative hypothesis \(H_{\text{A}}\) were set:  
\[ \begin{split} H_{0}:\ \sigma_{\text{IGS}}=\sigma_{\text{ LMMT}},\\ H_{\text{A}}:\ \sigma_{\text{IGS}}\
eq\sigma_{\text{ LMMT}}.\end{split}  \tag{8}\]  
The tests were performed at a significance level of \(\alpha=0.05\), with the numerator and denominator degrees of freedom \(f_{\text{IGS}}=f_{\text{LMMT}}=8\). Key statistical parameters for the analysis are summarized in Table 9.  
Results of the performed two-tailed \(F\)-tests provide strong evidence to reject the null hypothesis. With a probability of 0.95, it can be concluded that empirical accuracies (standard deviations) of the two independent experimental data sets are significantly different. A significant difference in short-baseline accuracies with respect to the antenna phase center models used (individual by LMMT and type-mean by IGS) was achieved.