## 3 Materials and Methods
### Data Processing  
The data were acquired on different days in order to obtain more datasets in different satellite configurations. The first dataset consists of the observations obtained in the first 5 min of each hour of observation; the second dataset consists of the first 10 min of each hour; the third dataset consists of the first 15 min of each hour; the fourth dataset consists of the first 30 min,; and the fifth dataset consists of 60 min of complete observation. Each observation was processed with RTKPOST and CSRS-PPP. Static differential positioning with pseudorange measurements was performed by RTKPOST, using the permanent TARA GNSS station as a reference (base). CSRS-PPP was used to perform Single Point Positioning. The SPP was performed on single-frequency code observations and the data were mainly processed with a rapid ephemeris; the final ephemeris was used, if available. At the end of all processing, for each observation, the coordinates were obtained of the positioning of Xiaomi Mi 10 in Eastings (\(\overline{\text{E}}_{\text{Xiaomi MI10,i}}\)) and Northing (\(\overline{\text{N}}_{\text{Xiaomi MI10,i}}\)) in the WGS84-UTM system, and the ellipsoidal height Up (\(\overline{\text{U}}_{\text{Xiaomi MI10,i}}\)) with their respective standard deviations (\(\overline{\text{SDE}}_{\text{Xiaomi MI10,i}}\), \(\overline{\text{SDN}}_{\text{Xiaomi MI10,i}}\) and \(\overline{\text{SDU}}_{\text{Xiaomi MI10,i}}\)). Following, the sub-datasets are shown for 5, 10, 15, 30 and 60 min:  
\[\text{E} = \left\{\overline{\text{E}}_{\text{Xiaomi MI10,1}},\;\ldots, \overline{\text{E}}_{\text{Xiaomi MI10,n}}\right\} \tag{1}\] \[\text{N} = \left\{\overline{\text{N}}_{\text{Xiaomi MI10,1}},\;\ldots, \overline{\text{N}}_{\text{Xiaomi MI10,n}}\right\}\] (2) \[\text{U} = \left\{\overline{\text{U}}_{\text{Xiaomi MI10,1}},\;\ldots, \overline{\text{U}}_{\text{Xiaomi MI10,n}}\right\}\] (3) \[\text{SDE} = \left\{\overline{\text{SDE}}_{\text{Xiaomi MI10,1}},\;\ldots, \overline{\text{SDE}}_{\text{Xiaomi MI10,n}}\right\}\] (4) \[\text{SDN} = \left\{\overline{\text{SDN}}_{\text{Xiaomi MI10,1}},\;\ldots, \overline{\text{SDN}}_{\text{Xiaomi MI10,n}}\right\}\] (5) \[\text{SDU} = \left\{\overline{\text{SDU}}_{\text{Xiaomi MI10,1}},\;\ldots, \overline{\text{SDU}}_{\text{Xiaomi MI10,n}}\right\} \tag{6}\]  
Considering, as reference, the coordinates of the FATA (\(\text{E}_{\text{FATA}}\), \(\text{N}_{\text{FATA}}\), and \(\text{U}_{\text{FATA}}\)), the positioning errors \(\Delta\text{E}_{\text{i}}\), \(\Delta\text{N}_{\text{i}}\), \(\Delta\text{U}_{\text{i}}\) of the Xiaomi Mi 10 were calculated with the following formulas:  
\[\Delta\text{E}_{\text{i}} = \left|\overline{\text{E}}_{\text{Xiaomi MI10,i}}-\overline{\text{E }}_{\text{FATA}}\right| \tag{7}\] \[\Delta\text{N}_{\text{i}} = \left|\overline{\text{N}}_{\text{Xiaomi MI10,i}}-\overline{\text{N }}_{\text{FATA}}\right|\] (8) \[\Delta\text{U}_{\text{i}} = \left|\overline{\text{U}}_{\text{Xiaomi MI10,i}}-\overline{\text{U }}_{\text{FATA}}\right| \tag{9}\]  
The sub-datasets created, \(\Delta\text{E}\), \(\Delta\text{N}\), \(\Delta\text{U}\), take the following form:  
\[\Delta\text{E} = \left\{\Delta\text{E}_{\text{1}},\;\ldots,\Delta\text{E}_{\text{n }}\right\} \tag{10}\] \[\text{N} = \left\{\overline{\text{N}}_{\text{Xiaomi MI10,1}},\;\ldots, \overline{\text{N}}_{\text{Xiaomi MI10,n}}\right\}\]0 (11) \[\text{N} = \left\{\overline{\text{N}}_{\text{Xiaomi MI10,1}},\;\ldots, \overline{\text{N}}_{\text{Xiaomi MI10,n}}\right\}\]1  
where:  
* \(\text{i}=1,\ldots,\text{n}\);
* \(\text{n}\) is equal to the number of observations for 5, 10, 15, 30 and 60 min: n = 9 for the 5, 10 and 15 min datasets; n = 7 for the 30 and 60 min datasets. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Station** & **X (m)** & **Y (m)** & **Z (m)** \\ \hline FATA & 4,635,800.173 & 1,442,401.642 & 4,122,685.780 \\ TARA & 4,635,794.786 & 1,442,422.405 & 4,122,684.175 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Coordinates of FATA (smartphone position) and TARA in the ITRF14 system.