## 5 Conclusions and Remark  
In this study, we conducted a comprehensive and detailed analysis of GNSS signal characteristics from the aspects of duty cycle, carrier-to-noise ratio, cycle slip, gradual accumulation of phase error, and pseudorange residual on a smartphone. The main conclusions are summarized as follows:  
1. The duty cycle can seriously affect the carrier phase observation data logging on some early smartphones, such as the Huawei Mate9, but it has little effect on some new smartphones such as the Huawei Mate30 and Huawei P30. 2. Unlike the geodetic receiver, the GNSS satellites with high elevation do not necessarily bring the high carrier-to-noise ratio on the smartphone. The rate of GNSS carrier phase cycle slip on the Huawei Mate30 is inversely related to the carrier-to-noise ratio, and the most cycle slips are largely concentrated in the carrier-to-noise ratio below 30 dB-Hz. This means that the conventional stochastic model depending on elevation is difficult to accurately reflect the GNSS observation quality of the smartphone. 3. In the phase-code differences experiment, the gradual accumulation of phase errors is most marked in BDS on the Huawei Mate30, and the trends correspond to a change of about \(-1.401\) cm/s for BDS. Meanwhile, some extra cycle slips in BDS can be detected by MPF when the difference value between the carrier phase observations (in meters) and the pseudorange observations reached the threshold of 50 m. Moreover, the L5 band of GPS is also affected by the gradual accumulation of phase errors, but the trends are hard to draw. 4. The comparison results of GNSS pseudorange residuals show that the RMS of GLONASS pseudorange residuals on the Huawei Mate30 is lower than that of GPS and BDS. Moreover, as the \(\mathcal{C}\)/\(N_{0}\) value increased, the RMS of GPS, BDS, and GLONASS pseudorange residuals all decreased significantly. In view of the GNSS signal characteristics of smartphones and to optimize the performance of multi-GNSS PPP, we propose a PPP mathematic method. The proposed undifferenced and uncombined multi-GNSS PPP model with single frequency and dual frequency observations is more suitable for these types of observations on smartphones. Unlike the geodetic receiver, there are significant differences between the gross measurement noises of GPS, BDS, and GLONASS observations from the smartphone. Therefore, we establish separately the \(\mathcal{C}\)/\(N_{0}\)-dependent stochastic model with step function variance according to the statistical data on variance of GPS, BDS, and GLONASS observations, and the appropriate weight matrix is set to improve the multi-GNSS positioning performance of \begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**Direction**} & \multicolumn{6}{c}{**Kinematic Precise Point Positioning Error RMS (m)**} \\ \cline{2-7}  & **G(EK)** & **G(CR)** & **G + B(EK)** & **G + B(CR)** & **G + B + R(EK)** & **G + B +R(CR)** \\ \hline E & 0.962 & 0.763 & 0.866 & 0.897 & 1.257 & 0.928 \\ N & 0.857 & 0.707 & 0.754 & 0.640 & 0.778 & 0.624 \\ U & 4.162 & 2.235 & 3.621 & 2.062 & 2.722 & 2.167 \\ Max & 35.991 & 17.442 & 17.298 & 11.083 & 16.543 & 10.317 \\ \hline \end{tabular}
\end{table} 
Table 3: RMS of GPS, BDS, and GLONASS kinematic PPP errors in three directions within 100 min. MAX denotes maximum three-dimensional error. smartphones. Moreover, the robust Kalman filter is used in parameter estimation, the equivalent variance matrix balances the contribution of the normal and abnormal observations. The experimental results show that the proposed PPP method converges more quickly than the conventional PPP method, depending on elevation under static conditions both the RMS and the maximum of multi-GNSS positioning errors decrease in kinematic tests.