# Real-Time Kinematic Positioning Using Multi-Frequency Smartphone Measurements +
## 3 Static Tests  
To understand the impact of the antenna on the quality of the smartphone measurements, we compared the mean Carrier-to-Noise Ratio (C/N\({}_{0}\)) versus the satellite elevation for the GPS L1 case using the external antennas and the smartphone's internal antenna. The mean was computed over five-degree elevation bins and considering all satellites jointly. When the survey grade PG-F1 antenna was used (Figure 4), the maximum C/N\({}_{0}\) was around 50 dB-Hz, while, when a patch antenna was used (Figure 5), the maximum C/N\({}_{0}\) was around 45 dB-Hz and the signal fluctuations due to multipath were more evident. As expected, in both cases, the signal power increases for higher satellite elevations. Figure 4: Mean C/N\({}_{0}\) versus elevation for the test with the survey grade Topcon PG-F1 antenna. Figure 5: Mean C/N\({}_{0}\) versus elevation for the test with the survey grade Taoglass patch antenna. Figure 3: (**a**) Set-up used for the kinematic test with the car and the smartphone inside the car; (**b**) set-up used for the kinematic test with the tractor. The same analysis was repeated using the smartphone without any external antenna (Figure 6). In this case, the signal fluctuations due to multipath are evident even for higher satellite elevations. Moreover, the increase in C/N\({}_{0}\) with respect to the satellite elevation was less significant than in the previous two cases. In the following, the statistics are reported for the different static tests to showcase the results that can be achieved with the GNSS measurements from a smartphone and RTK positioning with different baseline lengths. Specifically, in Table 1, the results obtained with the PG-F1 antenna are summarised. The test lasted about eight hours and samples were collected at 1 Hz. With the increase in the baseline length, an increase in the TTFF can be observed. However, the percentage of fix solutions is above 99% for all cases. As expected, a slight degradation in the root mean squared (rms) of the position accuracy and precision can be observed with the increase in the baseline length. In Table 2, the results obtained with the patch antenna are also summarised. Also, in this case, the increase in the baseline length affects the TTFF. Moreover, for the baseline of 25 km, a decrease in the percentage of fix solutions can also be observed. Finally, in Table 3, the results obtained with the smartphone's antenna are reported. In this case, the test was shorter, since it lasted around 2.5 h. In this case, the percentage of fix solutions is above 91% for all cases, also when the baseline length is 25 km. For this test, we report the horizontal and vertical precision instead of the accuracy since it was not possible to survey the exact position of the smartphone in an accurate way. A degradation in the solution precision can be observed with the increase in the baseline length. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Base**} & \multirow{2}{*}{**Samples**} & \multirow{2}{*}{**TTFF** [s]**} & \multirow{2}{*}{**Fix \%**} & \multicolumn{2}{c}{**Horizontal** **Accuracy [m]**} & \multicolumn{2}{c}{**Vertical**} & \multicolumn{2}{c}{**Horizontal**} & \multicolumn{2}{c}{**Vertical**} \\  & & & **Accuracy [m]** & **Accuracy [m]** & **Precision [m]** & **Precision [m]** \\ \hline CN09 & 28,571 & 12 & 99.9 & 0.010 & 0.011 & 0.006 & 0.006 \\ \hline CGU2 & 28,571 & 14 & 99.9 & 0.013 & 0.014 & 0.009 & 0.010 \\ \hline GUAS & 28,571 & 64 & 99.7 & 0.040 & 0.034 & 0.016 & 0.034 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: PG-F1 antenna (CN09: 1 km, CGU2: 5 km, GUAS: 25 km).