# Native Smartphone Single- and Dual-Frequency GNSS-PPP/IMU Solution in Real-World Driving Scenarios
## 4 Results Analysis
### General Kinematic Performance Statistics  
Road tests are subject to a series of factors impacting positioning performance which cannot be controlled. These factors include various traffic conditions, passing of large vehicles, satellite availability, and tropospheric/ionospheric conditions at the time. Therefore, \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Processing Strategy** & **Std Dev (m)** & **Rms (m)** & **95 th Percentile Error (m)** & **Maximum Error (m)** \\ \hline
**SFDF-PPP** & 5.0 & 5.2 & 1.7 & 90.3 \\ \hline
**SFDF-PPP/IMU (MI8)** & 0.4 & 1.1 & 1.5 & 7.9 \\ \hline
**SFDF-PPP/IMU (Xsens)** & 0.3 & 1.0 & 1.5 & 4.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Horizontal errors with different sensor fusion combinations for single- and dual-frequency PPP processing. Figure 10: Horizontal error with respect to the reference trajectory and filter estimated precision comparison for single- and 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 c c c c} \hline \hline
**Elapsed Time (s)** & **917** & **918** & **919** & **920** & **921** & **922** & **923** & **924** & **925** \\ \hline
**SFDF-PPP Horizontal errors (m)** & 10.3 & 19.5 & 28.9 & 38.5 & 48.0 & 58.1 & 68.9 & 79.0 & 90.3 \\ \hline
**SFDF-PPP/IMU (MI8) horizontal errors (m)** & 0.9 & 1.3 & 1.7 & 2.2 & 2.8 & 3.6 & 4.7 & 6.2 & 7.9 \\ \hline
**SFDF-PPP/IMU (Xsens) horizontal errors (m)** & 0.8 & 0.9 & 1.1 & 1.3 & 1.5 & 1.7 & 2.0 & 2.3 & 2.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Horizontal errors growth with different sensor fusion combinations for single- and dual-frequency PPP over Outage B.  
this study summarises four more datasets based on three days of road tests, while also presenting additional performance results using a Samsung Galaxy S21+. The additional datasets are collected on identical routes (with identical buildings), but due to specific traffic levels and traffic lights they do not have identical duration. Table 9 summarising all five datasets. The collection of all five datasets illustrates the repeatability of the analyzed results and provides added confidence in the performance statistics. The following set of time series illustrates in Figure 11 shows the horizontal errors through each road test. Road test M3 was analyzed in Figures 7a, 8a and 10a, so its error analysis will not be repeated. Similarly, the SFDF-PPP solution (in green) shows the highest accuracy and stability by mitigating the majority of error peaks. In comparison to the S1 PPP solutions, inconsistent performance can be noticed for dual-frequency PPP-only processing for the S3 dataset (see Figure 11d) owing to insufficient dual-frequency satellites, which are reduced from, on average, 7.6 (S1) to 5.4 (S3). The inclusion of multiple datasets bring more challenges in smartphone native PPP/IMU solutions owing to the low-cost IMU hardware. Correspondingly, some smartphone PPP/IMU outliers can be observed such as jumps in M1 at elapsed time \(\sim\)8 min. In spite of these dataset variations, PPP/IMU solutions have more accurate performance compared to PPP GNSS-only solutions for most epochs. Figure 11: Horizontal error with respect to the reference trajectory comparison for different datasets processed by single-frequency, dual-frequency, single- and dual-frequency PPP and PPP/IMU strategies. (**a**) Horizontal position error for dataset M1. (**b**) Horizontal position error for dataset S1. (**c**) Horizontal position error for dataset M2. (**d**) Horizontal position error for dataset S3.