# Single-Baseline RTK Positioning Using Dual-Frequency GNSS Receivers Inside Smartphones
## 5 Experimental Results  
In this section, the obtained results are discussed while considering the two tested configurations separately. Generally, for each epoch it was possible to track 8 GPS, 8 GLONASS, 6 Galileo, and 11 BeiDou satellites, respectively, as shown in Figure 2, obtaining a maximum GDOP value equal to 1.3. These values refer to the average of the different sessions. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Characteristics** & **TORI CORS** & **Xiaomi Mi8** \\ \hline \multirow{6}{*}{GNSS signals} & GPS: C/A, L1, L2, L5, Doppler, S/N & GPS: C/A, L1, L5, Doppler, S/N \\  & GLONASS: L1, L2 & GLONASS: L1 \\  & Galileo: E1, E5 & Galileo: E1, E5 \\  & BeiDou: B1, B2a & BeiDou: B1, B2a \\ Cost [€] & 16000 & 800 \\ Receiver & LEICA GRX1200+ GNSS & Broadcom BCM47755 \\ Antenna & LEIAR25.R3 NONE & Microstrip patch antennas \\ Typical 3D positioning accuracy\({}^{*}\) & Less than 1 cm & \(\approx 10\)m \\ Applications & CORS & location-based applications and \\  & & services (LBS), navigation \\ \hline \hline \end{tabular}
\end{table} 
Table 1: GNSS receivers used as master stations. *accuracy provided for illustrative purposes [14; 18]. From a quality point of view of the signals, it is possible to note (Figures 3 and 4) that in some cases, the quality is not good, even if the cutoff angle has been chosen to be equal to \(10^{\circ}\). This happens when the signal to noise ratio (SNR) value is less than 25 dB-Hz, defining the satellite signal being as too noisy to be processed. In this context, only satellites with an SNR value greater than 28 dB-Hz and with an elevation greater than 15\({}^{\circ}\) are considered. Applying these filters, the number of available satellites decreases to 21: 7 GPS, 4 GLONASS, 3 Galileo, and 7 BeiDou. Figure 2: Skyplot of visible satellites in one of the selected epochs of measurements: green, red, blue and purple circles represent the GPS, GLONASS, Galileo, and BeiDou satellites, respectively. According to Table 2 and considering only satellites that provides SNR values greater than 28 dB-Hz, it is possible to affirm that the noise of signals is still quite high, so the expected result could be noisy. Figure 4: SNR values for tracked satellites - L5 frequency. No GLONASS satellites can track L5 frequency. Figure 3: Signal to noise ratio (SNR)values for tracked satellites - L1 frequency. As previously written, two different scenarios have been considered (Table 3) whose results are reported separately. All data are processed considering a modified version of RTKLIB 2.4.3 [28], while only using the \"continuous\" method for the integer ambiguity resolution and a tight combination for multi-GNSS RTK positioning. As described in reference [12], \"continuous\" means that integer ambiguities are continuously estimated and resolved. Moreover, the \"ratio test\" for the standard integer ambiguity validation strategy has been considered. This factor, that can be considered also as a threshold, means the ratio of the squared sum of the residuals with the second best integer vector to the the best integer vector, as shown in (5). \[\left(\sigma_{0}^{2}\right)_{2 nd}\!\!\!\!\!\!\!\!\! As shown from Figure 6, the average values between estimated and reference coordinates are not substantially changed, even if there is a strong improvement in terms of the precision of solutions. As shown from Table 4 the standard deviation (std) values decrease from about 14 cm and 52 cm in the case of FIX+FLOAT solutions up to 0.2 cm and 0.5 cm in the FLOAT-only case, considering the 2D and Up components, respectively. This means that the software is trying to fix the phase ambiguities but the quality of carrier-phase measurements is too bad for reaching a good \"FIX\" solution, as described in reference [12]. Although it is quite common to set the ratio threshold to be equal to 3 [20], in this case the variability of carrier-phase measurements allows the software to reach the fixing of the phase ambiguities with 15% (Figure 5) of epochs but in a wrong way.