## 2 Methodology and Data  
This analysis utilized data from 12 globally distributed MGEX stations (Figure 1 and Table 1), which collected multi-GNSS observations at 1 s intervals over a six-day period, from Day of Year (DoY) 223 to DoY 228 in 2024. These days were selected because real-time HAS product data were successfully collected for them. For each day, 8 three-hour sessions were analyzed, resulting in a total of 48 sessions per station across the six-day span. The computations were performed using the raPPpid software (version 3.1), which employs an Extended Kalman Filter (EKF), in combination with the conventional PPP model [53; 54]. The undifferenced ionosphere-free linear combinations for GPS and Galileo code and carrier-phase observations (in units of length) are expressed as  
\[ \begin{split}\mathrm{PR}_{\mathrm{IF,G}}&=\rho_{ \mathrm{r}}^{\mathrm{G}}+\mathrm{c}\left(\delta_{\mathrm{r,clock,G}}-\delta_{ \mathrm{clock}}^{\mathrm{G}}\right)+\mathrm{T}_{\mathrm{r}}^{\mathrm{G}}+ \epsilon_{\mathrm{IF}}\\ \Phi_{\mathrm{IF,G}}&=\rho_{\mathrm{r}}^{\mathrm{G}}+ \mathrm{c}\left(\delta_{\mathrm{r,clock,G}}-\delta_{\mathrm{clock}}^{\mathrm{G}} \right)+\mathrm{T}_{\mathrm{r}}^{\mathrm{G}}+\lambda_{\mathrm{FI}}^{\mathrm{G}} \mathrm{N}_{\mathrm{IF}}^{\mathrm{G}}+\epsilon_{\mathrm{IF}}\\ \mathrm{PR}_{\mathrm{IF,E}}&=\rho_{\mathrm{r}}^{ \mathrm{E}}+\mathrm{c}\left(\delta_{\mathrm{r,clock,E}}-\delta_{\mathrm{clock}}^{ \mathrm{E}}\right)+\mathrm{T}_{\mathrm{r}}^{\mathrm{E}}+\epsilon_{\mathrm{IF}} \\ \Phi_{\mathrm{IF,E}}&=\rho_{\mathrm{r}}^{\mathrm{E}}+ \mathrm{c}\left(\delta_{\mathrm{r,clock,E}}-\delta_{\mathrm{clock}}^{ \mathrm{E}}\right)+\mathrm{T}_{\mathrm{r}}^{\mathrm{E}}+\lambda_{\mathrm{IF}}^ {\mathrm{E}}\mathrm{N}_{\mathrm{IF}}^{\mathrm{E}}+\epsilon_{\mathrm{IF}}\end{split}  \tag{1}\]  
where  
* \(\mathrm{G}\), \(\mathrm{E}\) denote the GPS and Galileo systems, respectively;
* \(\mathrm{PR}_{\mathrm{IF}}\) and \(\Phi_{\mathrm{IF}}\) are ionosphere-free linear combination for code and carrier-phase observations, respectively [m]; \begin{table}
\begin{tabular}{c c c} \hline \hline
**Station** & **Receiver** & **Antenna** \\ \hline ALIC00 AUS & SEPT POLARX5 & TWIVC6050 NONE \\ CEBR00 ESP & SEPT POLARX5 TR & SEPCHOKE\_B3E6 NONE \\ CORDD0 ARG & SEPT POLARX5 & TPSCR\_G3 NONE \\ DAV100 ATA & SEPT POLARX5 & LEIAR25.R3 LEIT \\ GANP00 SVK & TRIMBLE ALLOY & TRM59800.00 SCIS \\ HOFN00 ISL & LEICA GR50 & LEIAR25.R4 LEIT \\ POHN00 FSM & SEPT POLARX5 & JAVRINGANT\_DM NONE \\ SASK00 CAN & JAVAD TRE\_G3 TH DELTA & NOV750.R4 NOVS \\ SOD300 FIN & JAVAD TRE\_3 DELTA & JAVRINGANT\_DM SCIS \\ URUM00 CHN & JAVAD TRE\_3 & JAVRINGANT\_G5T NONE \\ WIND00 NAM & JAVAD TRE\_3 & JAVRINGANT\_G5T NONE \\ YKRO00 CIV & JAVAD TRE\_3 DELTA & ASH701945C\_M NONE \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Equipment of the used IGS stations. Figure 1: Location of test stations. * \(\rho_{\rm T}^{\rm S}\) is the true geometric range between the satellite in the emission time and the receiver in the reception time [m];
* c is the speed of light [m/s];
* \(\delta_{\rm r,clock,G}\), \(\delta_{\rm r,clock,E}\) represent the receiver clock offsets in the GPS and Galileo system time, respectively [s]
* \(\delta_{\rm clock}^{\rm G}\), \(\delta_{\rm clock}^{\rm E}\) denote the satellite clock offsets for GPS and Galileo satellites, respectively [s];
* \(\rm T_{\rm T}^{\rm S}\) is the slant tropospheric delay [m];
* \(\lambda_{\rm IF}\) is the wavelength for the ionosphere-free linear combination [m];
* \(\rm N_{\rm IF}\) is the real value of the ambiguity ionosphere-free linear combination [cycles];
* \(\epsilon_{\rm IF}\), \(\epsilon_{\rm IF}\) are other errors, for example noise and multipath [m]. This model also requires the inclusion of errors such as receiver and satellite phase center corrections, relativistic correction for code and carrier-phase observations of the ionosphere-free linear combinations and carrier-phase wind-up for phase observations, and the use of site displacement effects, which are defined in the IERS conventions [55].