## 7 Conclusions  
In this work, we introduce a cost-efficient antenna calibration method that improves the performance of low-cost GNSS receiver antennas up to the level of traditional, high-end GNSS equipment. The calibration procedure can be applied directly in the field and is made available online as a web service ([[https://gnss-antcal.citig.tudelft.nl](https://gnss-antcal.citig.tudelft.nl)]([https://gnss-antcal.citig.tudelft.nl](https://gnss-antcal.citig.tudelft.nl)), accessed on 9 February 2022). This paves the way for PCO and PCV estimation for high-precision positioning and meteorological and other applications with low-cost equipment. The quality and remaining residuals in the antenna calibration procedure are assessed and positioning performance is demonstrated in PPP and PPK applications with five antennas of different quality and price. The analysis of the ambiguity-fixed phase residuals before and after the conducted calibration demonstrates a clear reduction in the MAD for all antennas. Comparing the residuals before calibration to the results of our reference antenna LEIAR25.R3 LEIT, the lower-priced antenna, AV28, was, on average, off by 0.74 mm (29%) on \(L_{1}\) and 1.78 mm (63%) on \(L_{2}\). For ANN-MB, these values are 1.33 mm (53%) on \(L_{1}\) and 2.52 mm (89%) on \(L_{2}\). After calibration, the AV28 residuals could be reduced to a difference of 0.3 mm (12%) on \(L_{1}\) and 0.44 mm (16%) on \(L_{2}\). For ANN-MB, these values were 0.89 mm (35%) on \(L_{1}\) and 1.48 mm (52%) on \(L_{2}\). In comparison, the higher-grade antennas, TRM5 and GA530, were off by 0.74 mm (29%) and 0.59 mm (23%) on \(L_{1}\) and 1.03 mm (36%) on \(L_{2}\) before application of the calibration procedure and could be reduced to the same level of the reference antenna on \(L_{1}\) and close to 0.29 mm (10%) on \(L_{2}\). With the implemented elevation-based residual averaging method, the phase pattern could be captured for a great part for all antennas. However, some distinctions can be made. It occurs that the TRM5 and GA530 are characterized by an almost circular phase pattern over the full horizon, whilst the lower-priced antennas, AV28 and ANN-MB, indicate a greater azimuthal dependency. The calibration efficiency of all antennas is demonstrated by evaluating the positioning stability and offsets. First, we investigated the PCV influence and estimated the positioning offsets on the ionosphere-free linear combination phase center in PPP. A height offset of 92 and 66 mm was observed for the lower-priced antennas, AV28 and ANN-MB, before calibration. After calibration, the offsets were reduced to approximately 40 and 27 mm, respectively. Interestingly, the same antennas on a rectangular adaptor that yielded height offsets of \(-\)76 and \(-\)70 mm before calibration were transformed to similar positive offsetsof approximately 30 and 27 mm after calibration. Second, the kinematic positioning stability was analyzed over a short baseline in PPK. Similar to the residual performance, we observed the best positioning stability performance for the highest-quality antennas. Comparably, the lower-priced antennas demonstrated higher variance but improved significantly after the calibration. The MADs in the vertical direction of the low-cost antennas were reduced by 20.4-23.9%. For the AV28 antenna, they were lowered from 5.6 to 3.8 mm. For ANN-MB-00, they were brought from 5.2 to 4 mm. It brings them to a level close to the performance of the antennas LEIAR, TRM5, and GA530, which are characterized by MADs of 3.3, 4.1, and 3.8 mm before and 3.3, 3.6, and 3.4 mm after calibration. The special case scenario consisting of the antennas AV28 and ANN-MB with a metallic rectangular adaptor demonstrated the highest deviations, the strongest azimuthal dependency, but also the greatest improvements in all cases.