# Experimental Validation of a GNSS Receiver Antenna Absolute Field Calibration System
## 2 Materials and Methods
### Validation Methodology
#### 2.3.2 Short-Baseline Validation  
The second experimental validation was conducted in a short-baseline setup. Four GNSS receiver antennas (I/L: Z1, TP, LG, Z2) were utilized for the validation test, forming three short-baselines of approximate lengths: 5 meres (baseline T-R), 10 m (baseline T-A), and 20 m (baseline T-ST). The short-baseline validation setup is depicted in Figure 7.  
Figure 6: Individual calibration results (PCO/PCVs) by Geo++ GmbH for the TRM57971.00 NONE (S/N: 30739001) GNSS receiver antenna at G01 and G02 frequencies.  
Such a short-baseline validation test is based on the evaluation of the developed antenna calibration system in the spatial domain and on the product level, i.e., antenna PCC model. The accuracy of GNSS-derived short-baseline solutions is determined by comparison with reference values of baseline components that have been predetermined with independent methods of significantly higher accuracy. The short-baseline approach is applied because GNSS carrier-phase data can be processed in a single-frequency mode, and thus PCC models can be evaluated per calibrated frequency.  
Within this experimental validation, short-baseline processing was performed multiple times with two distinct antenna calibrations: type-mean from IGS and individual from LMMT. Furthermore, processing was performed in a single-frequency mode independently for GPS L1 frequency (G01), GPS L2 frequency (G02), and, lastly, in a dual-frequency mode by using the well-known ionosphere-free linear combination GPS L0 [41] of GPS L1 and GPS L2. Therefore, the main goals of this experimental validation test are to determine how the application of different PCC models transfers to the spatial domain and subsequently impacts geodetic-grade positioning in relative positioning mode and to evaluate if individual antenna calibration at the LMMT calibration facility results in higher baseline accuracy when compared to IGS type-mean antenna PCC models. A two-tailed \(F\)-test was conducted to objectively evaluate the equivalence of the obtained IGS and LMMT short-baseline accuracy results.  
The realization in the test field, i.e., the determination of reference values of short-baseline components, was performed through an independent measurement campaign, which included a GNSS survey and a high-precision terrestrial survey of a micro-network using a total station and precise leveling. Precise coordinates of stations T, R, A, and ST were determined with submillimeter accuracy at a level of 0.1-0.2 mm [32]. Using these coordinates, reference values of short-baseline components were derived and are presented in Table 3.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Short-Baseline** & \(\Delta X\) & \(\Delta Y\) & \(\Delta Z\) & \(\Delta e\) & \(\Delta n\) & \(\Delta u\) \\  & \([\mathbf{m}]\) & \([\mathbf{m}]\) & \([\mathbf{m}]\) & \([\mathbf{m}]\) & \([\mathbf{m}]\) & \([\mathbf{m}]\) \\ \hline T–R & 0.1785 & \(-\)4.8749 & 1.1078 & \(-\)4.7350 & 1.6132 & \(-\)0.0262 \\ T–A & 0.3986 & \(-\)9.7471 & 2.2109 & \(-\)9.4789 & 3.1940 & \(-\)0.0274 \\ T–ST & 0.8633 & \(-\)19.4700 & 4.4171 & \(-\)18.9529 & 6.3345 & \(-\)0.0091 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Reference values of short-baseline components in ITRF2020 and topocentric frame (TF), i.e., local-level frame, predetermined by an independent measurement campaign.  
Figure 7: Four GNSS receiver antennas in a short-baseline setup as part of the experimental validation survey; station T—TRM57971.00 NONE antenna (I/L: Z1); station R—TPSPG_A1 NONE antenna (I/L: TP); station A—LEIAX1202 GG NONE antenna (I/L: LG); station ST—TRM57971.00 NONE antenna (I/L: Z2).