# Stochastic Modeling of Smartphones GNSS Observations Using LS-VCE and Application to Samsung S20
## 4 Experimental Results
### Noise Assessment of Samsung S20
The DD code and phase observations for all visible satellites on the L1 frequency for both constellations are presented in Figure 6. Table 4 provides the mean and RMS of the DD code observations for GPS and GLONASS on the L1 frequency. Based on the results, the quality of the GLONASS code observations on the L1 frequency is worse than the other two systems. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Observation Type** & **Parameter** & **GPS** & **GLONASS** \\ \hline \multirow{2}{*}{Code} & Mean & 0.126 & 0.001 \\  & RMS & 3.408 & 13.596 \\ \hline \multirow{2}{*}{Phase} & Mean & 0.001 & 0.001 \\  & RMS & 0.01 & 0.009 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Mean and RMS of the DD code and phase observations on L1 frequency (in meters). Figure 5: Sky plot for Samsung S20B (red: GPS satellites with L5 signals observed). Figure 6: DD observations of GPS and GLONASS for all visible satellites: (**left**) code and (**right**) phase observations. We now employ the LS-VCE method on the DD code and phase observations on the L1 frequency. First, the entire time span of the smartphone observations (10,800 epochs) is divided into 45 groups, each consisting of 240 consecutive epochs (4 min). The unknown (co)variance parameters \(\sigma=\left[a_{code}^{GPS}\quad a_{phase}^{GPS}\quad\rho^{GPS}\quad a_{code}^{ CLO}\quad a_{phase}^{GLO}\quad\rho^{GLO}\right]^{T}\) can then be separately estimated for each group. The final solution will be the average over all groups. Figure 7 shows the groupwise estimates of \(a_{type}^{sys}\) for the code/phase observations of GPS and GLONASS on the first frequency as well as estimated correlations among the code and phase observations of each constellation (i.e., \(\rho^{GPS}\) and \(\rho^{GLO}\)). The final estimates are just the arithmetic mean of the individual estimates over the 45 groups. Table 5 presents the mean value of the estimated coefficients (\(a_{type}^{sys}\) where _sys_ refers to GPS and GLONASS and _type_ denotes the observation type, i.e., code and phase) on L1 frequency as well as the correlation between code and carrier phase observations. The results indicate that there is no significant correlation between the code and carrier phase observations of GPS and GLONASS. Considering \(a_{code}^{GPS}=0.35\times 10^{5}\) and \(a_{code}^{GLO}=1.08\times 10^{5}\), the standard deviation (STD) of the code observations for GPS and GLONASS on the first frequency can be observed in Figure 8 as a function of the C/N0 value and elevation angle. [PERSON] et al. [34] also investigated the noise characteristics of the Samsung S20 and Google Pixel 4 smartphones by fitting empirical 95% confidence ellipses/levels to the formal counterparts, as derived from the corresponding variance-covariance (VCV) matrices of the positions. The empirical VCV-matrix was obtained by comparing estimated positions to precise benchmark coordinates, while the formal VCV-matrix was obtained from the means of all single-epoch formal VCV-matrices over the observation span. The study obtained the undifferenced and zenith-referenced STDs in three different setup configurations: zero-baseline external antennas, short-baseline external antennas, and short-baseline internal antennas. The authors assumed the same code and phase STDs for all frequencies (L1, L5,  
Figure 7: Groupwise estimate of coefficient (\(a_{type}^{sys}\); _sys_: GPS and GLONASS and _type_: code and phase) on L1 frequency as well as correlations among code and phase observations of each constellation (i.e., \(\rho^{GPS}\) and \(\rho^{GLO}\) ). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Constellation** & \(a_{code}^{sys}\) & \(a_{phase}^{sys}\) & \(\hat{\rho}^{\wedge}\) \\ \hline GPS & \(0.35\times 10^{5}\) & \(0.04\times 10^{5}\) & \(0.04\) \\ GLONASS & \(1.08\times 10^{5}\) & \(0.04\times 10^{5}\) & \(0.03\) \\ \hline \hline \end{tabular}
\end{table}