## 3 GNSS Data Collection with Android-Based Smartphones
### Stochastic Model Settings  
The stochastic model was then determined by fitting empirical 95 percent confidence ellipses/levels to the formal counterparts, as derived from the corresponding variance covariance (VCV) matrices of the positions. The empirical VCV-matrix is given by the positioning errors as derived by comparing the estimated positions to precise benchmark coordinates, whereas the formal VCV-matrix is given from the mean of all single-epoch formal VCV-matrices of the entire observation span [28]. Independent data were used to formulate the stochastic model for the data to be analysed in the following sections. By making use of a realistic stochastic model, we can assure that all baselines can achieve their best possible ambiguity resolution and positioning performance. Table 2 shows the undifferenced and zenith-referenced standard deviations (STDs) employed in the stochastic model, together with a description of all the used setup configurations in Figures 2-4. We make use of the same code and phase STDs for each individual frequency/GNSS and an elevation weighting function, as employed in RTKlib [24]. Figure 3: Short-baseline setup configurations with external antennas (**c,f**) in upright (**a,d**) and lying down (**b,e**) positions. Figure 2: Zero-baseline setup configurations for smartphones in (**a**) upright and (**b**) lying down positions. The re-radiating antenna receives the GNSS signals through the roof-top antenna in Figure 1.  
We further note that we make use of the upright position stochastic model settings also on that of the lying down positions (cf. Table 3). The dates of the data in Table 2 for the lying down positions are given within square brackets. It will become clear in the following sections that the stochastic model settings in Table 2 are indeed overly optimistic for the data when the smartphones are lying down, which implies that this likely is a suboptimal setup to use. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Baselines**} & **Phase STD** & **Code STD** & **Description** & **DOY, Hours of Data, hh:mm:ss** \\  & **(m)** & **(m)** & **Description** & **UTC** \\ \hline \multicolumn{5}{c}{Zero-baseline external antenna:} \\ \hline GPD1–GPD2 & 0.001 & 0.457 & \begin{tabular}{c} Smartphones in upright \\ (Figure 2a) and lying down \\ (Figure 2b) positions. \\ \end{tabular} & 2020 (12 h): \\ \hline SGD1–SGD2 & 0.001 & 0.175 & \begin{tabular}{c} Smartphones in upright \\ (Figure 2a) and lying down \\ \end{tabular} & 2035, 01:16:00–13:15:59 \\  & & \begin{tabular}{c} Smartphones in upright \\ (Figure 3a,d) and lying down \\ \end{tabular} & 2021 (8 h): \\ \hline SGD1–SGD2 & 0.003 & 0.485 & \begin{tabular}{c} Smartphones in upright \\ (Figure 3b,e) positions. \\ \end{tabular} & 2020 (12 s): \\ \hline \multicolumn{5}{c}{Short-baseline internal antennas:} \\ \hline GPD1-GPD2 & 0.004 & 5.997 & \
\begin{tabular}{c} Smartphones in upright \\ (Figure 4a,b) and lying down \\ \end{tabular} & 2020 (3.5 h): \\ \hline SGD1–SGD2 & 0.003 & 2.327 &
\begin{tabular}{c} Smartphones in upright \\ (Figure 4c,d) positions. \\ \end{tabular} & 2021 (3.5 h): \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The zenith-referenced and undifferenced code/phase STDs for zero- and short-baseline setup configurations, where we make use of the same STD for all frequencies (L1/L5/E1/E5a/B1) and GNSS for each smartphone setup. In the last column [within square brackets we depict the day of year (DOY) and Coordinated Universal Time (UTC) time for when the smartphones were in a lying down position]. Figure 4: Short-baseline setup configurations with smartphones internal antennas in upright (**a,b**) and lying down (**c,d**) positions. We note that for all datasets to be compared between the upright and lying down positions, we have taken the GPS and QZSS satellite constellation repeatability period of approximately 23 h and 56 min into account [29]. We also note that for the short-baseline external antenna experiment there is ten days between the datasets (cf.