## 4 Calibration Impact on the Estimated Residuals  
To investigate the performance of the antennas after applying the corrections to the base and rover RINEX files, another PPK run over the same short baseline is performed using the same observation dates as in the calibration step. The only difference lies in applying the PCVs to the base and rover RINEX carrier phase observations (see Equation (2)). As a metric for the comparison, we use a robust estimator of the standard deviation, the Median Absolute Deviation (MAD):  
\[\text{MAD}=1.4826\cdot median(|x_{i}-\tilde{x}|). \tag{3}\]  
The variables \(x_{i}\) and \(\tilde{x}\) depict the observations and the median of the data. The scale factor of 1.4826 is constant and is multiplied by the median of the absolute deviations. The scale relates to the underlying assumption of normally distributed data. Compared to the standard deviation, the MAD is more resistant to outliers and, therefore, our preferred measure in this study. The MADs of the ambiguity fixed phase residuals before and after calibration are illustrated in Figure 2.  
The MADs of the ambiguity-fixed phase residuals are generally lower for the more expensive antennas and higher for the lower-cost antennas. The highest-quality antenna (LEIAR) results in the lowest phase residuals (MAD of 2.52 mm on \(L_{1}\) and 2.82 mm on \(L_{2}\)), which also remain unchanged after correcting the input data. It shows that the LEIAR antenna patterns of both base and rover are very similar so PCVs cancel out over a short baseline during the calibration step. Compared to LEIAR, which was also used by the base, the TRMS and GA530 have before correction an MAD on \(L_{1}\) that is 29% and 23% higher, and 36% higher on \(L_{2}\). After correction, the MAD on \(L_{1}\) is of the same level and just slightly above on \(L_{2}\). For the lower-cost antennas AV28 and ANN-MB with a circular ground plane, the MAD on \(L_{1}\) before correction is, respectively, 29% and 53% above the reference antenna, and on \(L_{2}\), respectively, 63% and 89%. After adjusting the phase data, these numbers are reduced to a difference of 12% and 35% on \(L_{1}\) and 16% and 52% on \(L_{2}\). The results with a rectangular adaptor demonstrate the highest deviations but also the highest improvements (from around 150% down to 60-100%). Though considerably improved, the performance is clearly below its counterparts utilizing a circular ground plane. Interestingly, the different resolutions of the applied PCV corrections only marginally affect the outcome. Compared to the results without calibrations and depending on the antenna type and ground plane, the residuals of the low-cost antennas were reduced by 11.4-34% on \(L_{1}\) and 19.5-38.7% on \(L_{2}\). The results suggest that, even after correction, noise is still present in the data, which could not be compensated by the mean of the stacked residuals. The random component of carrier-phase noise and model limitations are related to the finite bin size in azimuth and/or elevation. To further examine the effectiveness of the elevation-only averaging, we calculate the semivariance \(\hat{\gamma}\) (see, e.g., [17]) for each antenna before and after calibration over the full elevation and azimuth horizon to determine if only white noise is left in the residuals:  
\[\hat{\gamma}=\frac{1}{2N(d)}\sum_{||u_{i}-u_{j}||}(z(u_{i})-z(u_{j}))^{2}, \tag{4}\]  
where \(N(d)\) is the number of data pairs belonging to the data bin \(d\) and \(z\) are the paired observations at spatial locations u separated by the Euclidean distance \(||u_{i}-u_{j}||\). We conduct the grouping by separating the data points into bins of distinct distances using the \(1^{\circ}\) resolution averages. Figure 3 shows the 2D variogram maps of the antennas TRM5 and AV28 with a circular and rectangular adaptor using \(L_{1}\) observations before and after applying the corrections.