## 6 Positioning Analysis
### RTKLIB PPK Results  
Post Processed Kinematic (PPK) positioning results, with and without antenna PCV corrections, are obtained using RTKLIB. The correction is performed by modifying both base and rover RINEX datasets with the absolute PCVs. However, the same effect can be achieved by correcting the rover data with the mean of the stacked SD residuals from which the absolute PCV values are derived. We provide results after correcting the RINEX files according to the different PCV averaging widths obtained from the calibration procedure (0.1\({}^{\circ}\), 1\({}^{\circ}\), and 5\({}^{\circ}\)). One full day is processed for each antenna and only ambiguity-fixed estimations are used. As with the calibration step, the IGS station DLF1 is used as the base station. Errors caused by the troposphere or ionosphere are assumed equal and eliminated in the process. Other parameters, i.e., positioning components and clock errors, are estimated in the Kalman filter as parameters. One of the main goals of antenna calibration is to increase the repeatability of kinematic position solutions. We therefore analyze the positioning performance by computing the MAD of the kinematic North, East, and Up  
Figure 5: PPP height differences regarding the reference height before and after applying the PCV corrections. The abbreviations (c) and (r) in the antenna names correspond to the utilized mounting brackets (circular plane and rectangular bracket). (NEU) components, with the results for the vertical component given in Figure 6. For each run, also the median offset in the NEU components is reported, using the \(L_{1}+L_{2}\) RTKLIB solution with results for the vertical component given in Figure A3. These provide estimates of the \"\(L_{1}+L_{2}\)\" PCO. Processing in RTKLIB can be done with \(L_{1}\) only, or \(L_{1}+L_{2}\) combined. To use all observations, the \(L_{1}+L_{2}\) option is used, but this results in a single \(L_{1}+L_{2}\) position estimate (likewise, for the calibration itself, \(L_{1}+L_{2}\) processing is used to obtain residuals for both \(L_{1}\) and \(L_{2}\)). In the ANTEX files, only separate \(L_{1}\) and \(L_{2}\) PCOs are available, and the combined PCO for \(L_{1}+L_{2}\), which depends on the weighting applied in RTKLIB, is not available. However, this does not matter here, as, in our calibration procedure, the PCVs are given with respect to the combined \(L_{1}+L_{2}\) PCO, and there is no reason that the \(L_{1}\) and \(L_{2}\) PCO cannot be the same as long as it is consistent with the provided PCV for each frequency. Another useful observation to make here is that the positioning results are not sensitive to a constant shift in the PCV: any constant that is added to the PCV is absorbed by the clock estimate in the positioning estimate. This means that we can have PCO/PCV calibrations for which not only the \(L_{1}\) and \(L_{2}\) PCO is the same, but also the \(L_{1}\) and \(L_{2}\) PCV at zenith is zero, as is the case in our calibrations. The MAD for the kinematic Up component from the \(L_{1}+L_{2}\) solution is illustrated in Figure 6. Results containing the horizontal components and \(L_{1}\)-only results can be found in Tables A2-A4 in the Appendix A. For the results without antenna phase center corrections, the highest-cost antennas (LEIAR, TRM5, and GA530) have the smallest vertical MADs. They vary around 3 to 4 mm. This is rather unsurprising for the LEIAR antenna because the phase effects largely cancel out over the short baseline, yet similar performance is found for the TRM5 and GA530 antennas. The AV28 and ANN-MB antennas yield 5.6 and 5.2 mm, respectively. More importantly, after applying the corrections to the data, the precision always increased (or remained equal as in the reference LEIAR case). After correcting, the MAD for the higher-cost TRM5 and GA530 antennas was reduced to 3.6 and 3.4 mm, approaching the LEIAR result (3.3 mm).