## 6 Effects of Multipath on GNSS Carrier Post-Fit Residuals
### Measurement of SNR Frequency Content Using the Wavelet Transform
In the 80-120 period band, the power of KBG2 (with no microwave-absorbing material attached to it) shows a higher power than KBG1 for both DoYs. A similar wavelet power is also manifested for period bands 40-80 again for station KBG2 for the time series between 61,000 to 61,200 s and then back again to a diminished power for the time series between 62,000 to 62,850 s (for 850 s). Slightly higher power is shown for the period band 20-40, which is fairly short-lived and stays for 200 s. For the period band between 2 and 20, KBG2, in general, show a higher power but is very short-lived, mostly appearing at the end of the time series. Similarly, KBG1 also showed some power at the end of the time series for the period band 2-20. What is also evident for station KBG2 is that near-identical higher wavelet power is manifested from the two consecutive DoYs. The wavelet power appeared approximately 240 s earlier for DoY 61, confirming the sidereal repeatability nature of the multipath, and which is associated with the location of the KBG2 antenna in relation to the reflecting surfaces. \[\psi(x)=\pi^{-1/4}e^{i\omega_{o}x}e^{(-x^{2})/2} \tag{8}\]0 The Morlet wavelet analysis of \(\delta SNR\) for an ascending arc of GPS satellite PRN27 on 1 March 2021. **(a,b)**\(\delta SNR\) time series (solid light green line) for station KBG1 for days of the year (DoYs) 60 and 61, respectively. **(c,d)**\(\delta SNR\) time series (solid light red line) for station KBG2 for doYs 60 and 61, respectively. **(e,f)** Scaled averaged wavelet power \(\left(\frac{|\left[W_{s}(s)\right]|^{2}}{s}\right)\) for all scales, which appears in the 20–40 s period band for stations KBG1 and KBG2 for DoYs 60 and 61, respectively. **(g,h)** Scaled averaged wavelet power for all scales, which appears for the period 40–80 s for both stations during DoYs 60 and 61, respectively. The maximum powers for station KBG2 appear at 61,118 s and 60,872 s for DoYs 60 and 61, respectively. A second peak with diminished power also appears for KBG2. For KBG1, the maximum powers appear at 62,786 and 61,754 s for the DoYs 60 and 61, respectively, with much-reduced power compared to KBG2. **(i,j)** Scaled averaged wavelet power for all scales, which appear in the 80–120 s band for both stations and for the DoYs 60 and 61, respectively. For KBG2, the maximum power occurs at 62,152 s for DoY 060 and 61,930 s for DoY 61. Figure 15 shows the spectrum of the Morlet wavelet transform on the \(\delta SNR\) time series on 1 March 2021 (DoY 60) on the left from station KBG1 and to the right from the same date for station KBG2. For this study, we chose GPS satellite PRN27 as the satellite that ascends a subtending angle between 255\({}^{\circ}\) and 275\({}^{\circ}\) in azimuth from elevation angles 2\({}^{\circ}\)-30\({}^{\circ}\). For station KBG1, a significant power was observed for a period of 60-100 s but manifested for 260 s. During this, the satellite moved one degree in azimuth (from 265\({}^{\circ}\) to 266\({}^{\circ}\)) and ascended from \(\sim\)16\({}^{\circ}\) to 18\({}^{\circ}\) in its elevation angle. For station KBG2, the same satellite shows a significant spectral power for the period 30-64 s spanning \(\sim\)100 s. During this, the satellite moved one degree in azimuth (from 258\({}^{\circ}\) to 259\({}^{\circ}\)) and ascended from 7 to 7.5\({}^{\circ}\). Again, KBG2 shows a significant power for the period 64-128 s but spans much longer (for \(\sim\)850 s), though at half the power of earlier. Its power was concentrated between 12.5\({}^{\circ}\) and 17.7\({}^{\circ}\). At this stage, the satellite moved further to the south-southwest. The significant \(\delta SNR\) power occurring at periods 0-128 s does not correspond to the ideal horizontal reflecting the infinite extent surface that corresponds to the height of the antenna at 3.5 m above the ground. Therefore, the various structures on the roof of the building further from the GNSS antenna contribute to the multipath budget, more adversely affecting station KBG2 without the Eccosorb material.