**5. Conclusions**

In this paper we investigated the PPP ZTD performance of a recently introduced low-cost dual-frequency receiver (U-blox ZED F9P) in combination with different antennas, ranging from geodetic to mass-market devices, with and without applying relative antenna calibrations. The conducted experiments demonstrated that the U-blox ZED-F9P dual-frequency receiver is very well capable to produce high-quality results, with the limiting factor being the quality of the receiving antenna. However, our results show that, using a simple-to-apply method to correct for the PCV

of cost-efficient receiver antennas, high quality results are achievable even for low-cost antenna. This is demonstrated by a field experiment, resulting in ZTD estimations of similar quality as with high-grade antennas.

The phase residuals with different antenna types were analyzed over a short baseline. The aim was to do a relative antenna calibration. The absolute antenna calibration pattern can then be computed from the absolute antenna calibration of the reference antenna and the relative calibration result from the short baseline experiment. For two of the tested antennas, the AV28 and ANN-MB-00 antennas, when used with a rectangular bracket as mounting point, very prominent elevation-based patterns were found (see Figure 5). These cases result in the highest RMSE phase residuals when compared to other antennas. Figure 6 indicates azimuth dependent patterns with strongly fluctuating amplitudes. The rectangular bracket presumably caused high residuals for L2 close to the horizon, but also in East and West direction for L1. Smaller residuals were obtained after repeating the experiment with a circular ground plane. These results showed that our approach is working, regardless of the size of the residual patterns. This suggests that our approach is feasible for even more challenging, multipath-prone environments. Additional uncertainty may be introduced by the smoothing technique we used to obtain PCVs in the 5-degree bin size required by the ANTEX standard. A lower binning size may further improve the results. Considering that only three days of data were used for the calibration, and that the antenna was not rotated, many of the azimuth-elevation bins were without data or had only few observations. For this reason the elevation-only based calibration is preferred over the azimuth-elevation based calibration.

The impact of the different antenna PCV corrections on PPP ZTD estimations has been analyzed for the tested antennas. Our results confirm that antenna pattern corrections are essential for PPP ZTD estimations. Applying satellite PCO/PCV corrections significantly decreases the standard deviation in the ZTD error compared to using no ANTEX corrections at all. Without applying receiver antenna corrections, the ANN-MB-00 and Trimble AV28 antennas with a rectangular bracket, resulted in a ZTD bias between −20 and −24 mm and similar standard deviations. With a circular plane the effect could be partially mitigated, but biases in the order of about 9.5 mm and 5.3 mm remained. The results suggest that a phase pattern is present for the low-cost antennas which we address by applying a relative antenna calibration. Applying elevation or azimuth-elevation dependent corrections to the data reduced the ZTD bias significantly and lowered the standard deviation. For example, when using the azimuth-elevation dependent corrections on the ANN-MB-00 antenna, the bias in the ZTD was reduced to −0.52 mm and an RMSE to only 3.77 mm. Results for the other antennas, and using elevation only patterns, were similar. This shows that the ZTD estimations achieve an error level that is comparable to high-grade antennas. Though the biases for ANN-MB-00 (rectangular bracket), AV28 (circular plane) and AV28 (rectangular bracket) could not be completely removed, they were reduced significantly to a level that makes the observations useful for tropospheric analysis.

The ionosphere-free linear combination used by the PPP solutions is very noisy. The noise in the L1 and L2 data, including the errors in the relative calibration, is basically tripled. For this reason we also looked at only using the L1 data in combination with the SEID algorithm to generate L2 data from an existing network of geodetic-grade receivers. In case no PCV correction is done for the receiving antenna, the bias and standard deviation in ZTD for the GA530, AV28 and ANN-MB-00 antennas, were smaller using L1 with SEID generated L2 data, than for the original dual-frequency data. This is a clear indication that the ionosphere-free linear combination on the original L1 + L2 data is considerably amplifying the noise present in the datasets. Using SEID in combination with the elevation or azimuth-elevation based L1 corrected data removed the biases almost entirely. The results are of comparable quality to ZTD estimations derived from the dual-frequency results.

This experiment uses exclusively GPS observations. As many of the low-cost receivers can track multiple GNSS systems, expanding the antenna calibrations to include multi-GNSS may further increase the application of the presented approach. Another interesting experiment would be to perform an absolute antenna calibration by a specialized company on low-cost antennas and compare their calibrations to our results. Further work is needed to investigate, if the observed pattern is reproduced (or differs) from other antennas of the same model, so that the observed elevation-based phase pattern of an antenna can be applied to other antennas of the same model. This will be subject of future experiments.

**Supplementary Materials:** The following are available online at http://www.mdpi.com/2072-4292/12/9/1393/s1. The utilized IGS I14.ATX ANTEX file appended with the elevation-only calibrations (without PCO estimations) for the antennas LEIAR25.R3 LEIT, TRM55971.00 NONE, Trimble GA530 and Trimble AV28 and U-blox ANN-MB-00 using a circular plane. The file (file extension .ATX) is a plain text file and a standard convention for GNSS antenna calibrations. The format description can be found on the website of the IGS [35]. The file can be opened in every classical text editor.

**Author Contributions:** Conceptualization, A.K., H.v.d.M., M.-C.t.V. and N.v.d.G.; methodology, A.K., H.v.d.M. and M.-C.t.V.; software, A.K. and H.v.d.M.; formal analysis, A.K., H.v.d.M., M.-C.t.V. and N.v.d.G.; data curation, A.K. and H.v.d.M.; writing—original draft preparation, A.K.; writing—review and editing, A.K., H.v.d.M., M.-C.t.V. and N.v.d.G.; visualization, A.K.; supervision, H.v.d.M., M.C.t.V. and N.v.d.G.; funding acquisition, M.-C.t.V. and N.v.d.G. All authors have read and agreed to the published version of the manuscript.

**Funding:** The work received funding from the European Community's Horizon 2020 Programme (2014–2020) under grant agreement No. 776691 (TWIGA). This project has also received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No. 700699 (BRIGAID).

**Acknowledgments:** We like to thank Christian Tiberius for providing the U-blox ZED F9P engineering sample. A special thanks goes to Sander Terwee from Geometius (www.geometius.nl) for donating the antennas Trimble Zephyr 2 Geodetic and GA530 for educational and scientific purposes to the Faculty of Civil Engineering.

**Conflicts of Interest:** The authors declare no conflict of interest.
