## 2 Methodology and Data  
### Data and Solutions  
This analysis considered data from 13 global MGEX stations (Figure 1) which collected multi-GNSS observations with 30 s intervals, for one week from Day of Year (DoY) 38 to DoY 44, in 2021. For the chosen period, the condition of products used [53] and the ionosphere activity [54] was checked. In this period, there were no gross errors which allowed performing the analysis in normal observation conditions. For the calculations, PPPH software which uses the Extended Kalman Filter (EKF) and conventional PPP models [55; 56] was used. The code and carrier phase undifferenced ionosphere-free linear combinations for GPS and Galileo observations in units of length can be expressed by the following equations:  
\[ \begin{split}\text{PR}_{\text{IF,G}}=\rho_{\text{r}}^{\text{G}}+ \text{c}\Big{(}\delta_{\text{r,clock}}-\delta_{\text{clock}}^{\text{G}}\Big{)}+ \text{T}_{\text{r}}^{\text{G}}+\epsilon_{\text{IF}}\\ \Phi_{\text{IF,G}}=\rho_{\text{r}}^{\text{G}}+\text{c}\Big{(} \delta_{\text{r,clock}}-\delta_{\text{clock}}^{\text{G}}\Big{)}+\text{T}_{ \text{r}}^{\text{G}}+\text{A}_{\text{IF}}^{\text{G}}\text{N}_{\text{IF}}^{ \text{G}}+\epsilon_{\text{IF}}\\ \text{PR}_{\text{IF,E}}=\rho_{\text{r}}^{\text{E}}+\text{c}\Big{(} \delta_{\text{r,clock}}-\delta_{\text{clock}}^{\text{E}}\Big{)}+\text{T}_{ \text{r}}^{\text{E}}+\text{ISB}_{\text{GE}}+\epsilon_{\text{IF}}\\ \Phi_{\text{IF,E}}=\rho_{\text{r}}^{\text{E}}+\text{c}\Big{(} \delta_{\text{r,clock}}-\delta_{\text{clock}}^{\text{E}}\Big{)}+\text{T}_{ \text{r}}^{\text{E}}+\text{ISB}_{\text{GE}}+\lambda_{\text{IF}}^{\text{E}} \lambda_{\text{IF}}^{\text{E}}+\epsilon_{\text{IF}}\end{split}  \tag{1}\]  
where: G, E denote the GPS and Galileo systems, respectively; PR\({}_{\text{IF}}\) and \(\Phi_{\text{IF}}\) are ionosphere-free linear combination for code and carrier-phase observations, respectively; \(\rho_{\text{r}}^{\text{S}}\) is the true geometric range between the satellite in the emission time and the receiver in the reception time; c is the speed of light; \(\delta_{\text{r,clock}}\), \(\delta_{\text{clock}}^{\text{S}}\) are the receiver and the satellite clock offsets, respectively; T\({}_{\text{r}}^{\text{S}}\) is the slant tropospheric delay; \(\lambda_{\text{IF}}\) is the wavelength for the ionosphere-free linear combination; N\({}_{\text{IF}}\) is real value of the ambiguity ionosphere-free linear combination (cycle); ISB\({}_{\text{GE}}\) is the inter-system bias representing the offset between the time scale and hardware delay of GPS and Galileo systems; \(\epsilon_{\text{IF}}\), \(\epsilon_{\text{IF}}\) are other errors, for example: noise and multipath. This model also requires the inclusion of errors such as: receiver and satellite phase centers 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 the site displacement effects, which are defined in the IERS conventions [57]. In this way, the station coordinates, clock correction of the receiver, wet component of the tropospheric delay, real ambiguity values and ISB for multi-GNSS solutions was estimated. A list of used models and methods are shown in Table 1.  
Figure 1: Location of test stations.