## 3 Calibration Methodology
However, if users prefer to not modify the code, but apply the DD to SD correction manually, the following formula (after [15]), assuming a zero-mean condition, can be used:  
\[SD_{i}=DD_{i}-mean(DD_{0...n}), \tag{1}\]  
with \(i\) being the satellite at the specified epoch and frequency and \(n\) being the number of DDs on that frequency and epoch. We use GPS \(L_{1}\) and \(L_{2}\) observations exclusively to keep it simple and because most existing antenna calibrations to date (which are used for validation of the method) are available for these frequencies. However, the method can easily be extended to different frequencies and systems. The ambiguity-fixed residuals over three full observation days for all antennas, except ANN-MB with a circular adaptor, which uses only two full days, were selected and stacked over 0.1\({}^{\circ}\) elevation and azimuth bins. The days were manually selected based on a visual inspection of the ambiguity-fixed phase residuals. To investigate the effect of different averaging widths, the mean of the stacked residuals was applied to obtain elevation-only averages in the resolutions 0.1\({}^{\circ}\), 1\({}^{\circ}\), and 5\({}^{\circ}\). The elevation-only approach was preferred over an azimuth- and elevation-dependent approach since the observation period was short and no antenna rotation was performed to cover all parts of the antenna. A previously conducted test with both methods also revealed a slight performance decrease in the ZTD estimation [16] using the latter. A figure illustrating the elevation-only phase residuals can be found in the Appendix A. To apply the antenna corrections, the mean of the stacked SD residuals could be added directly to the rover observations. However, this would limit the application to the analyzedbaseline and could not be applied to other locations. To obtain PCVs independent of the analyzed baseline, absolute PCVs of the rover antenna are needed. We achieve this by adding the absolute PCVs from the base station antenna (LEIAR25.R3 LEIT) to the stacked relative residuals between base and rover. We use the base station antenna entry from the IGS type mean ANTEX file (I14.ATX) for this purpose. This creates PCVs for each investigated rover antenna for each frequency. Since three different resolutions (0.1\({}^{\circ}\), 1\({}^{\circ}\), and 5\({}^{\circ}\)) are investigated, a new ANTEX file is created for each of them. To further generalize the presented method and since not all processing engines allow us to supply our own ANTEX files to their processing chain, the base and rover RINEX files are manipulated according to the PCVs of their respective antennas. We adjust the phase data using the following formula:  
\[\bar{L}_{i}=L_{i}-\frac{\phi_{i}^{r}(el,az)}{\lambda_{i}}, \tag{2}\]  
with (\(\bar{L}_{i}\)) being the corrected phase data on frequency \(i\) and \(L_{i}\) the original RINEX phase observation in cycles. The azimuth- and elevation-dependent ANTEX PCV correction \(\phi_{i}^{r}(el,az)\) is scaled by the wavelength \(\lambda_{i}\). The following section describes the impact of the calibration step on the estimated residuals. Positioning results can be found in Section 6.