**4. Results**

The difference in heights between KRAW, KRA1, KR01, and KR02 was calculated by post-processing of the observations. Due to the KRAW Ashtech UZ-12 receiver capability, only the GPS system was used. Post-processing was based on the final IGS orbits, the igs08.atx antenna corrections model, and a zero-elevation mask. Height differences obtained from precise levelling were compared with those derived from EPN-combined solutions, PPP calculated with Bernese GNSS Software (BGS) [30], Nevada Geodetic Laboratory (NGL, [31]), a network solution, a single baseline solution (GNSS Solutions 3.80.8, Trimble Business Centre 3.50), and other archive materials. In GNSS Solutions, only the elevation-dependent PCV version of the antenna characteristics was used.

Height differences obtained from precise levelling and GNSS solutions showed several discrepancies. Height differences between the KRA1 antenna reference point and the three other measured stations (KRAW, KR01, and KR02) from GNSS post-processing are affected by the inaccuracy of the antenna PCO and PCV. The analysis shows that the height of the KRAW station antenna (ASH70195C\_M SNOW) from GNSS processing (EPN combined and PPP solutions) is 16 mm too high in comparison to the levelling results (Figure 6). This may indicate the inadequacy of the ASH70195C\_M SNOW calibration data. A lower disagreement was obtained in the case of the TRM57971.00 NONE antenna (KR01 and KR02 stations). This discrepancy was about 5 mm for PPP solutions and 2 mm for network solutions. The differences obtained by single baseline solutions using the Trimble Business Centre (TBC) and GNSS Solution engineering software show far fewer discrepancies, not exceeding 0.4 mm. This is due to the very short baseline between the measured points.

The height difference of KRAW–KRA1 was calculated based on the EPN weekly combined SINEX (Software INdependent Exchange format) solutions from 2010 to 2016 (1564 to 1877 GPS weeks, Figure 7). During weeks when igs08 and igb08 were in use, there were some inaccurate solutions, which may be treated as gross errors. Despite that, clearly visible is the change in ellipsoidal height difference after the introduction of the IGS14 system (after GPS week 1933 [33]). The offset is up to about 8 mm (Figure 7). It is surprising that, during the short time between the introduction of the IGS14 system and individual phase corrections for the KRA1 antenna (week 1986), the height difference was closest to levelling (−0.5 mm) from any network calculation.

**Figure 7.** The time series for the height difference between KRAW–KRA1 calculated by EPN on the basis of several antenna correction catalogues (IGS ATX files) [32].

Alternatively, an independent PPP calculation was used—the Nevada Geodetic Laboratory (NGL). The facility provides permanent, fully, and freely available PPP results based on globally distributed permanent GNSS station data. Based on these data, the ellipsoidal height differences between station KRAW and KRA1 for the period 2009.7–2022.0 GPS weeks 1569–2190) were analysed (Figure 8). The results showed a mean difference +1.83 mm (green line) and were compared to precise geometric levelling −6.2 mm (red line). Both data provided inaccurate results, which was not a surprise, as they were based on the different antenna characteristics (IGS Antex files) of the KRAW antenna.

**Figure 8.** Height difference between KRA1–KRAW from NGL–PPP (navy dots), systematic difference from levelling −6.2 mm (red line), and mean difference 1.83 mm (green line) [31].

The archival materials regarding the height differences between the KRAW–KRA1 stations consist of: two independent sets of post-processing results from 2008 to 2011 calculated during the Polish integration of the base geodetic network with reference permanent

stations ASG-EUPOS (BGS), EPN combined solutions 2013–2014, PPP (BGS) 2012–2014, and the post-processing of various short GPS observations (Trimble Business Centre 3.50— TBC) 2011–2016 (Table 1). The short GPS observations consist of various 4-h, 8-h, and 12-h sessions, the calculations of which were also checked in GNSS Solutions 3.80.3 and Geonet 2006 software [29]. The differences between them are negligible, which allows us to show a single (mean) value achieved by the most often-used software. The compatibility of the short observation post-processing (TBC, GNSS Solutions, or Geonet 2006) and spirit levelling (−6.2 mm) results is noticeable when the more sophisticated solutions (e.g., PPP network solutions) give opposite values. The most contrary are values from PPP (BGS) 2012–14; the differences in the levelling result were as much as 20 mm. All of them used IGS08 antenna characteristics or only the elevation-dependent PCV model (GNSS Solutions). Surprisingly, such popular "engineering" software (e.g., TBC) achieved better results, comparable to spirit levelling, than the BGS (both short baseline calculations and PPP). The origin of the advantage of this type of software is not clear. It is probably that, for very close stations, the single baseline solutions, based only on the L1 frequency, give better results.

**Table 1.** Archive values of differences between the KRA1–KRAW stations.


\* Military University of Technology Analysis Coordination Centre.

Finally, the results of the height difference between the KRAW–KRA1 station were estimated by geometrical levelling, using a series of observations from 2011 to 2022 (Figure 9). Its most probable value is −6.2 mm ± 0.2 mm (Figure 10).

**Figure 9.** Height difference between KRA1 and KRAW from the levelling from 2011 to 2022.

**Figure 10.** Height difference (m) between the KRAW and KRA1 antenna reference points from precise levelling.

#### **5. Discussion**

Modern manufactured antennas are of better repeatability than older models, i.e., exhibiting less deviation from the pattern (average) in antex files. This is the case for, e.g., the Trimble Zephyr Geodetic 2 (TRM57971.00 NONE) antenna used in the experiment. In selected stations (e.g., KRAW and BOGI), antennas are still being used that date back to the 1990s. Their characteristics may differ from the accepted standards. Therefore, it can be postulated that individual characteristics should be developed for them, so that they do not introduce errors to the network in which they work (IGS, EPN, etc.). However, their individual calibrations are a matter of debate due to costs.

We checked the KRAW station based on a KRA1–KRAW overpass survey and the additional temporary stations KR01 and KR02. Archival materials from various authors were also collected. As a result of the analysis of these materials, it can be stated that the antenna (Ashtech ASH70195C\_M SNOW) of the KRAW station has different characteristics from those revealed in the IGS files of the subsequent versions. Azimuth elevation is mostly dependent on the lowest-over-horizon satellites [4,37], which have the smallest weights in processing. Thus, this aspect has the smallest impact. PPP processing shows a systematic shift in the KRAW–KRA1 height difference at the level of +1.8 mm, while measurements directly from levelling show a −6.2-mm difference. This may result in incorrect altitude results and have an adverse effect on, e.g., fitting the global geopotential model into the national height frame. Therefore, old stations that are included in the national (or transnational) permanent network need individual PCC. The tested network solutions, both PPP and baseline solutions [34,35], were not resistant to the impact of real KRAW antenna characteristics, different from any analysed ATX catalogue. As a result, the permanent stations' ellipsoid heights in network solutions may be subject to systematic errors. Even using advanced and renowned software (Bernese GNSS Solutions), such errors cannot be detected. The analysis showed that a calculation strategy based on a short baseline L1-only solution may detect the error, even if the popular "engineering" software is used (Trimble Business Centres, GNSS Solutions, Geonet).

The question arises as to what the optimal solution for old antennas is—the determination of individual characteristics (PCC) or replacement with a new antenna (also with

individual PCC). In other words, should the old stations be partially or fully modernized? For the analysed station KRAW (antenna ASH70195C\_M SNOW), a full upgrade had the advantage of introducing four GNSS systems compared to the existing GPS-only. Especially, introduction of the Galileo system may benefit the station solution [38,39], e.g., decreasing the positioning error statistics for GPS + Galileo combinations [40] despite Galileo still not providing the same satellite availability as GPS [41]. Concluding the results and achievements in the investigation of PCC by other authors [16,19,21,24], we are inclined to say that the time of antennas from the 1990s should be completed and full modernization carried out, despite the higher costs.

**Author Contributions:** Conceptualization, L.B.; methodology, L.B. and J.K.; software, L.B. and J.K.; validation, L.B., J.K. and K.M.; formal analysis, L.B., J.K. and K.M.; investigation, L.B., J.K. and K.M.; resources, L.B. and J.K.; data curation, L.B. and J.K.; writing—original draft preparation, L.B., J.K. and K.M.; writing—review and editing, L.B., J.K., K.M., M.S. and B.K.; visualization, L.B., J.K., B.K. and K.M.; supervision, L.B., J.K., K.M. and M.S.; project administration, L.B.; and funding acquisition, L.B., J.K., M.S., B.K. and K.M. Percentage contributions: L.B., 60%; J.K., 15%; B.K., 5%; M.S., 5%; and K.M., 15%. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was funded by the Initiative for Excellence Research University grant from the AGH University of Science and Technology, by research subvention no. 16.16.150.545, and by the National Science Centre as part of MINIATURA 5, application no. 2021/05/X/ST10/00058. This work was supported by the grant VEGA 1/0736/21 of the Scientific Grant Agency of the Ministry of Education Science Research and Sport of the Slovak Republic and the Slovak Academy of Sciences.

**Data Availability Statement:** Not applicable.

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

### **References**

