**2. Methods**

The paper is focused on the changes of the ellipsoid height, which are measured to the ARP. The height and the horizontal component are revealed in the current international terrestrial reference frame (ITRF2014). Along with the reference frame change, GNSS receiver antenna calibration models are also changed to be consistent with the current realisation of the frame. In the epoch under analysis, the International GNSS Service (IGS) provided data on 316 GNSS permanent stations. After the introduction of the ITRF2014, 113 of these changed their reported heights due to the antenna calibration parameter changes. The values of the estimated height offset are shown in Figure 2, which are based on IGS data.

**Figure 2.** Height offset due to antenna model changes; red marks indicate positive height changes, blue marks indicate negative changes, and white indicates that no changes occurred. The 'whiskers' show the amount of height offset.

As an example, the difference between the I08.ATX and I14.ATX calibration models for the TRM57971.00 NONE antenna is shown in Figure 3. The −1.8-mm PCO difference for the G01 (GPS L1) frequency and high PCV elevation dependent differences for the R01 (GLONASS L1) frequency are clearly seen.

Figure 4 shows PCV variations of the TRM57971.00 NONE antenna between the ATX08 and ATX14 antenna models for two (G01 and G02) GPS signal frequencies. Azimuth elevation differences vary from −1.5 mm to 1.5 mm. The largest differences are in the northwest vs. southeast directions, which are up to 1.5 mm, while, in the perpendicular direction (northeast vs. southwest), the situation is the opposite, with a difference of up to −1.5 mm. Such maximum differences appear only for the nearest-to-horizon satellites, which have the smallest impact on the GNSS processing due to weighting. Differences for satellites with the highest elevation (located in the centre of the circles) are close to 0.

**Figure 3.** PCO and PCV difference between I08.ATX and I14.ATX calibration data for the TRM57971.00 NONE antenna.

**Figure 4.** PCV variations between ATX08 and ATX14 for two GPS signal frequencies for the TRM57971.00 NONE antenna.

In general, changes in the station heights mean that the antenna model changes or suggests an inaccurate calibration model of the antenna's PCO or/and PCV. Detailed research has been performed for the ASH701945\_C antenna. This type of the antenna, with various domes, is still used at stations including IENG, KELY (NONE), BOGI, KRAW (SNOW), and SKEO (OSOD). The ASH701945C\_M SNOW antenna was calibrated by Geo++ GmbH on 25 March 2011 with the use of a single antenna [4]. Six others had individual calibrations, not KRAW or BOGI. It is possible that the antenna used at the KRAW station has distinctive characteristics other than those determined by Geo++. To check on this, an experiment on the KRAW antenna was conducted. In contrast to robot or anechoic chamber experiments, the authors used an analysis of the short baselines between the different permanent (KRAW and KRA1) and auxiliary stations (KR01 and KR02).

#### **3. KRAW and KRA1 Stations**

The pair of antennas KRAW and KRA1 are located on a five-storey university building about 3.5 m away from each other. This is an unusual circumstance, which is beneficial for GNSS networks [25], but very few permanent reference stations are located in this way. The oldest station KRAW has continuously collected data since the end of 2002, while the younger KRA1 has been collecting data since 2010 [26]. In 2005, the characteristics of the gravity field (acceleration and gradient) were measured for the KRAW station, and a station normal height was determined [27]. Up to 2018 to 2019, the station's equipment did not change (brand and model). The KRAW used an Ashtech UZ-12 receiver with an ASH70195C\_M SNOW antenna. In 2019, a new receiver was introduced, a LEICA RX1200 GGPRO (without changing the antenna). The KRA1 uses a Trimble NETR5 receiver with a TRM57971.00 NONE antenna. In 2018, the KRA1 antenna was replaced by another TRM57971.00 NONE model with individual PCC. For the KRAW station, the ASH70195C\_M SNOW antenna was not calibrated individually.

During the experiments on quasi-geoid modelling, it was found that the antenna's calibrations might be inaccurate [28]. It was suspected that the ellipsoidal height difference between the stations is of the opposite sign to their coordinates in the EPN network [29]. To verify this situation, a test survey was organised. It was based on a comparison of the height differences between the stations (KRAW and KRA1) and temporary stations KR01 and KR02 (with TRM57971.00 NONE antennas), as well as an analysis of the archival data. The Trimble antennas at KR01 and KR02 are commonly used in GNSS permanent networks. Exactly the same type was tested at Wuhan University by the absolute method (the field robot); the test showed the high repeatability of the obtained calibrations: σ<sup>N</sup> = 0.17 mm, σ<sup>E</sup> = 0.12 mm, and σ<sup>U</sup> = 0.30 mm [12]. The same model of antennas on KRA1, KR01, and KR02 guaranteed that the impact of the differences between the antennas would not be significant. The only difference was the power supply system (different model). The antennas were located at similar height levels, with a distance of about 3.5 m from each other (Figure 5).

**Figure 5.** Location of the KRAW and KRA1 permanent stations on the roof of the AGH-UST buildings with the temporary KR01 and KR02 stations.

The observation sessions took place over 12 days in December 2016. The precise differences in height were defined by GPS post-processing. As the height difference reference value, the results of geometric levelling (Zeiss KoNi 007) were used. The levelling was conducted both at the beginning and the end of the GPS session.
