# Native Smartphone Single- and Dual-Frequency GNSS-PPP/IMU Solution in Real-World Driving Scenarios
## 4 Results Analysis
### General Kinematic Performance Statistics
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Road Test \#** & **Phone Model** & **GPS Date of Collection (2021)** & **Duration** \\ \hline
**M1** & M1 8 & 8 August & 01:52–02:18 \\ \hline
**S1** & S21+ & 8 August & 01:52–02:18 \\ \hline
**M2** & M1 8 & 12 October & 00:44–01:00 \\ \hline
**S3** & S21+ & 30 November & 02:04–02:28 \\ \hline
**M3** & M1 8 & 30 November & 02:04–02:28 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Summary of all road tests. To generalise the findings from all collected datasets in comparing the three PPP-processing strategies and the impact of IMU fusion, the horizontal rms errors are concluded in Figure 12a and 95 th percentile errors are concluded in Figure 12b. Statistically, all six combinations of the processing strategies are presented in Table 10. Figure 12a emphasizes the effect from IMU fusion through all epochs during the road tests, thus covering various error peaks and the corner cases encountered. There is a reduction of standard deviation (of horizontal errors) from 6.5 m to 1.0 m, and 6.8 m to 1.9 m of rms with SFDF-PPP processing. Similar observations can be made for SF-PPP and DF-PPP processing. The results show a potential key role of IMU fusion in generating a more stable smartphone navigation solution in real-world scenarios. For higher-cost GNSS receiver/IMU combinations, the result is well expected. However, as the results are produced from ultra-low-cost smartphone hardware, this results demonstrate the sense of necessity of sensor fusion to achieve more demanding user requirements with given cost constraints. Figure 12b emphasizes the majority case for all road tests, showing 95 th percentile horizontal error. As in Figure 12a, the fusion with the native IMU shows improvement over PPP-only solutions, despite being less significant in SF and SFDF-PPP processing. As expected, without IMU fusion, DF-PPP displays lower solution quality compared to SF-PPP and SFDF-PPP due to inconsistencies in tracking dual-frequency satellites from the vehicle dashboard. However, by fusing GNSS measurements with IMU measurements, DF-PPP/IMU combination shows a reduction of 95 th percentile error from 4.3 m to 3.4 m compared to SF-PPP/IMU in contrast to PPP-only processing where there is an increase from 4.4 m to 6.6 m, indicating that though DF-PPP on smartphones suffer from inconsistent measurements, it can still provide better solutions than SF-PPP when inertial sensors are used. The SFDF-PPP strategy shows the most robust accuracy among all three PPP processing strategies. In addition, compared to the existing literature, such as [28] which achieved approximately 0.85 m horizontal rms in open-sky walking environments, the smartphone native SFDF-PPP/IMU solutions are capable of providing comparable positioning performance in real-world driving scenarios, showing great potential for vehicle and other smartphone-based applications. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Processing Strategy** & **Std Dev (m)** & **Rms (m)** & **95 th Percentile Error** & **Maximum Error (m)** \\ \hline
**SF-PPP** & 7.3 & 7.8 & 4.4 & 175.5 \\ \hline
**SF-PPP/IMU** & 2.2 & 3.2 & 4.3 & 70.6 \\ \hline
**DF-PPP** & 6.6 & 7.3 & 6.6 & 139.2 \\ \hline
**DF-PPP/IMU** & 1.5 & 2.5 & 3.4 & 57.5 \\ \hline
**SFDF-PPP** & 6.5 & 6.8 & 3.2 & 138.6 \\ \hline
**SFDF-PPP/IMU** & 1.0 & 1.9 & 2.9 & 19.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Overall statistics for different processing strategies. Figure 12: Overall horizontal errors from different processing strategies. (**a**) Overall horizontal rms comparison. (**b**) 95 th percentile horizontal errors comparison. Correlation Analysis of Single- and Dual-Frequency PPP Horizontal Accuracy under Different Environments  
The previous results have highlighted the importance of PPP processing with SFDF observations.