# S-PDR: SBAUPT-Based Pedestrian Dead Reckoning Algorithm for Free-Moving Handheld Devices
## 5 Results and Discussion
### Outdoor Test  
The trajectory for this test was planned outdoor over a small, squared park found between the CCIT, END, and ENG buildings at the University of Calgary. The small park is surrounded by metal and glass structures. The glass structures contribute heavily to errors in GNSS navigation systems and would benefit from aiding by an alternative system, while the metal structures make relying on the magnetometer solely for estimating the azimuth nearly impossible due to high magnetic interference. A sample of the results from S-PDR and Xsens for the planned trajectory is shown in Figure 23. The trajectory is approximately 235 m long and on average took 340 steps to cover with an average step length of approximately 0.7 m for regular walking, and 295 steps with an average step length of approximately 0.8 for fast walking.  
The results from the shown outdoor test sample show a final positional error of 2.5 m for the S-PDR, while the Xsens reconstructed trajectory had a positional error of 38.32 m. The test was carried out 20 times using the same configuration as that of the indoor test and the results are shown in Table 3.  
Figure 23: Outdoor reference trajectory and reconstructed trajectory using S-PDR and Xsens.  
Figure 22: Boxplot of the errors of S-PDR vs. Xsens for indoor test.  
Similar to the indoor test, the Xsens suffered from quick and high drift in attitudes that resulted in a high positional error. In this scenario, the magnetic interference was higher due to the large buildings metal structures surrounding the area where the tests were carried out. The attitudes derived from the Xsens on-board sensor fusion algorithm suffered from high drift resulting in poor tracking. On the other hand, the results show that S-PDR was once more consistent even with the magnetic interference due to the rejection criteria and the adaptive fusion technique it utilizes for azimuth estimation. The analysis of the results presented in Table 3 is shown as boxplots in Figure 24.  
For the case of S-PDR all the tests had a final positional error ranging between 1.59 and 4.58 m, with one sigma confidence interval in the 2.1 to 3.86 m of error range. The average duration of this test was 2 min with an average trajectory length of 230 m, hence the relative final position error is found to be ranging between 0.5% to 2.17% of the trajectory. Although the errors are lower than the indoor case, they are consistent as this trajectory was shorter and the errors increase at a higher rate as the duration of the navigation is prolonged. The findings of this test are crucial for the case of urban canyons where GNSS signals are hindered, and AHRS-based tracking suffers from magnetic interference and results in a high positional error. The S-PDR system developed was able to track the position while reducing the attitude drift and positional error, and being resisit  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Test \#**} & \multicolumn{2}{c}{**Final Positional Error (m)**} & \multicolumn{2}{c}{**Average Position Error across Trajectory**} \\ \cline{2-4}  & **S-PDR** & **Xsens MTi G-710** & **S-PDR** & **Xsens MTi G-710** \\ \hline
1 & 1.59 & 37.12 & 0.87 & 20.32 \\ \hline
2 & 4.31 & 45.94 & 2.95 & 14.49 \\ \hline
3 & 2.50 & 38.32 & 1.42 & 27.91 \\ \hline
4 & 2.91 & 29.73 & 1.