## 6 Effects of Multipath on GNSS Carrier Post-Fit Residuals  
In contrast to the pseudorange measurements, the multipath error on the carrier phase observations is limited to a quarter of the wavelength of the GNSS signal. [PERSON] [40] used the carrier phase post-fit residuals as a useful tool for examining the influence of multipath effects. The elevation dependence of the phase residuals, averaged across all azimuths, provides a useful metric of the phase modelling and multipath effects at each site. We compared the residuals of linear combinations of dual frequencies of GLONASS, Galileo and GPS carrier-phase measurements employing the ionospheric-free (LC) linear combination using GAMIT [59] and GIPSY [57] software packages.  
This results in post-fit residuals that contain multipath errors from individual signals and other unmodelled errors. We want to emphasise that we have applied an individually calibrated PCO and PCV antenna model, making its contributions to the total post-fit budget insignificant. The post-fit carrier phase residuals for station KBG1 as a function of elevation angle (between 3\({}^{\circ}\) and 90\({}^{\circ}\)) with Eccosorb material are shown in Figure 9a,c,d and similarly for site KBG2, without Eccosorb material, is shown in Figure 9b,e,f for all satellites from 1 March 2021. The residuals show large oscillations at low elevation angles to the satellite with respect to the local horizon, with a particular multipath error signature with higher magnitude and unmodelled atmospheric delay. For all the multi-GNSS ionospheric-free linear combinations, we formed for GPS using L1/L2, GLONASS G1/G2, and Galileo E1/E5a frequencies.  
Site KBG1 shows a lower RMS than the KBG2 station for all three multi-GNSSs considered. Figure 9a shows the residuals from the GAMIT solutions for Galileo, Figure 9c for GLONASS, and Figure 9d for GPS for the station KBG1. The RMS shows a clear demonstration that the Eccosorb material reduces the multipath error from 14.15  mm to 12.27  mm for Galileo, from 16.58 mm to 15.25  mm for GLONASS, and from 16.33  mm to 14.83  mm for GPS. Hence, there is a relative reduction in RMS 13% for Galileo and 9% for GLONASS and 10% for GPS. The Eccosorb material clearly shows a reduction in multipath signature but did not wholly eliminate the effect. [PERSON] [48] also shows an improvement using Eccosorb material but only slightly, likely due to the size of the Eccosorb that surrounds their GNSS antenna, which is nine times less than this study has used. We have also used the PPP solutions applying nearly identical products using the GipsyX software package to evaluate the post-fit residuals (not shown). The two software post-fit residuals are consistent with each other, again showing smaller multipath footprint for station KBG1 with the Eccosorb materials than KBG2 without.  
Figure 8: The number of cycle slips improved using the Eccosorb material with respect to not using the Eccosorb microwave-absorbing material. The improvement percentage is an average value for the period January 2021 until the 5 th of May 2021 using state-of-the-art Trimble Alloy reference receivers.  
Furthermore, we computed the RMS of the post-fit carrier phase residuals for a \(1^{\circ}\) bin width for an elevation angle between \(3^{\circ}\) and \(90^{\circ}\) for the KBG1 and KNG2 stations, as depicted in Figure 10. The RMS value decreases by approximately about \(1\) mm for elevation angles between \(3^{\circ}\) and \(35^{\circ}\); after that, the effect of the Eccosorb material becomes insignificant, and the two stations show similar RMS values.  
Figure 9: Post-fit LC carrier-phase residuals for individual GNSS constellations, i.e., Galileo (**a**), GLONASS (**c**) and GPS (**d**) for station KBG1 with Eccosorb and Galileo (**b**), GLONASS (**e**) and GPS (**f**) for station KBG2 without Eccosorb. The dataset was acquired on \(1\) March 2021.