# Native Smartphone Single- and Dual-Frequency GNSS-PPP/IMU Solution in Real-World Driving Scenarios
## 4 Results Analysis
### Kinematic Performance Assessment with Different Processing Strategies
#### 4.2.2 Dual-Frequency PPP-IC/IMU Processing  
Similarly, Figure 8 shows the time series of horizontal errors and EKF estimated precision when processing DF-PPP (GE) with different IMU sensors. It is anticipated that the DF-PPP performance is not as stable as SF-PPP due mainly to the limited number of tracked dual-frequency constellations and satellites. Thus, numerous fluctuations occurred not only during the two outages A and B, but also in some unexpected scenarios such as C on a highway, which may be owing to dual-frequency signal blockage by passing trucks.  
In spite of the lack of dual-frequency signals, it is somewhat surprising that with the aid of an IMU, the standard deviation of horizontal errors are improved from 6.0 m to the  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Elapsed Time (s)** & **917** & **918** & **919** & **920** & **921** & **922** & **923** & **924** & **925** \\ \hline
**SF-PPP Horizontal errors (m)** & 13.3 & 25.6 & 37.4 & 48.5 & 59.9 & 71.9 & 81.9 & 95.6 & 104.1 \\ \hline
**SF-PPP/IMU (MIS) horizontal errors (m)** & 1.8 & 2.3 & 2.9 & 3.8 & 4.5 & 4.8 & 4.9 & 5.1 & 5.8 \\ \hline
**SF-PPP/IMU (Xsens) horizontal errors (m)** & 1.3 & 1.4 & 1.4 & 1.5 & 1.6 & 1.7 & 1.8 & 2.0 & 2.4 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Horizontal errors growth with different sensor fusion combinations for single-frequency PPP over Outage B.  
Figure 8: Horizontal error with respect to the reference trajectory and filter estimated precision comparison for dual-frequency PPP processing using smartphone GNSS measurements, GNSS+IMU measurements, and GNSS and Xsens IMU measurements. (**a**) Horizontal position error. (**b**) Horizontal precision estimate.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Processing Strategy** & **Std Dev (m)** & **Rms (m)** & **95 th Percentile Error (m)** & **Maximum Error (m)** \\ \hline
**SF-PPP** & 6.0 & 6.3 & 2.7 & 104.1 \\ \hline
**SF-PPP/IMU (MI8)** & 0.7 & 1.7 & 2.6 & 5.8 \\ \hline
**SF-PPP/IMU (Xsens)** & 0.6 & 1.6 & 2.6 & 3.8 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Horizontal errors with different sensor fusion combinations for single-frequency PPP processing.  
sub-metre level, and the horizontal positioning error is mitigated from 8.3 m to 2.4 m and 2.3 m with MI8 and Xsens IMU, respectively (see Table 5). Similarly, Table 6 shows the horizontal error growth for dual-frequency PPP over Outage B. Furthermore, by leaving out the largest 5% of position outliers, the 95 th percentile level of horizontal error indicates that the DF-PPP/IMU combination is capable of providing almost the same level of positioning accuracy as the SF-PPP/IMU solution, showing the benefits of the sensor fusion.  
To explicitly appreciate the benefits of added L5/E5a signals, Figure 9 compares the smartphone horizontal positioning performance produced from single-frequency PPP (red line) and dual-frequency PPP (blue line) processing with same dual-frequency satellites. Dual-frequency PPP outperforms single-frequency PPP, and the latter approach cannot provide stable positioning performance with accuracy lower than 20 m during the elapsed time between 15 and 20 min, owing to insufficient and inaccurate single-frequency measurements.  
The solution shows the kinematic DF-PPP accuracy without sensor fusion is improved by 1-2 m as per the literature in similar experimental settings [26]. The pattern of higher DF-PPP errors than SF-PPP errors due to the lack of dual-frequency signals is also found in existing literature [25]. The solution shows accuracy degradation of DF-PPP solution of about 3 m compared to similar settings with phones on top of vehicle, whereas the discrepancy in fused horizontal accuracy is within \(\pm\)1 m [35].