# Native Smartphone Single- and Dual-Frequency GNSS-PPP/IMU Solution in Real-World Driving Scenarios
## 4 Results Analysis
### General Kinematic Performance Statistics
To better appreciate the benefit of this combination strategy, metrics such as the number of satellites and observations, as well as PDOP (position dilution of precision) are compared for the three chosen PPP processing strategies. The kinematic dataset M3 collected on 30 November 2021 (DOY 331) with the MI 8 is used for the analysis (see Figure 13). As illustrated in Figure 13, it is expected that the number of processed satellites of SF (16.6), and SFDF (16.1) strategies far outweigh the DF (6.1) processing. Accordingly, the SF-PPP PDOP (1.7) is almost identical to the PDOP for SFDF-PPP (1.7), as opposed to the DF-PPP PDOP (4.7) owing to the limited number of tracked satellites. The SFDF method, nevertheless, is able to track an average of 43.6 observations including phase and code measurements, which is significantly larger than the other two approaches, leading to better positioning performance. From Figure 13c,d, the number of observations and PDOP  
Figure 13: Time series of the number of satellites, observations, and PDOP in three processing strategies. (**a**) Time series of the number of satellites and observations in SF processing. (**b**) Time series of PDOP in SF processing. (**c**) Time series of the number of satellites and observations in DF processing. (**d**) Time series of PDOP in DF processing. (**e**) Time series of the number of satellites and observations in SFDF processing. (**f**) Time series of PDOP in SFDF processing. fluctuate significantly not only at the outages A and B, but in some scenarios where the dual-frequency satellites are not sufficient owing to buildings or trucks blockage, such as C (marked by the black rectangle), indicating that the DF-PPP is more sensitive and vulnerable to multipath effects and signal outages, particularly in challenging environments. The impact on horizontal errors from the number of observations and PDOP can be seen in Figure 14. Figure 14a shows the correlation between horizontal errors and the number of observations based on all datasets for SFDF-PPP processing, and by increasing the number of observations that the filter can draw on, a negative correlation (\(-0.37\)) is observed with horizontal positioning accuracy. However, excessive observations (more than 40) only provide marginal improvement on positioning, due mainly to the limitation of satellite geometry. Meanwhile, a positive but relatively low correlation coefficient of 0.28 is observed between PDOP and positioning accuracy in Figure 14b, which suggests PDOP may not serve as an ideal indicator for smartphone PPP performance. It is worth mentioning that the scenarios where insufficient or no satellites observed are excluded from this correlation analysis. Table 11 compares the pre-fit and post-fit residuals for L1/E1/B1 (GREC) and L5/E5a (GE) signals in SFDF-PPP processing strategy and interestingly, both the pre-fit pseudorange and carrier-phase residuals exceed 10 m. The L5/E5a residuals are significantly lower than for L1/E1/B1, namely 3.7 cm and 2.7 cm of post-fit carrier-phase residual rms can be observed for L1/E1/B1 and L5/E5a signals, respectively. The aforementioned correlation and residual rms analysis provide insight into how SFDF-PPP solutions benefit from the extra observations with more accurate L5/E5a frequencies. To explore the reason behind the unexpected magnitude of pre-fit residual rms, Figure 15 illustrates the time series of estimated GPS clock offset and clock difference of two adjacent epochs. Some fluctuations in smartphone estimated GPS receiver clock offset are due to their very low-cost oscillators compared to, e.g., geodetic GNSS receivers embedded with voltage-control or more stable oscillators. Such unstable estimated clock offsets lead to the same variations of their clock difference. In other words, the relatively large rms of pre-fit residuals is caused by the inaccurate EKF prediction utilizing the estimated receiver clock offset from the previous epoch, which cannot reflect the current or true estimated clock offset.