# A Novel AHRS Inertial Sensor-Based Algorithm for Wheelchair Propulsion Performance Analysis
## 3 Results  
After post-processing the data, it was clear that there were two large magnetic disturbances running parallel to the court that affected all trials. The disturbance was located approximately 75 cm into the trial. The results of the 14 m straight line test were tabulated, shown below in Table 1.  
Table 1 provides evidence that the laser is an accurate reference of the linear velocity profile, in terms of the distance covered over a specific period of time. This allowed for the visual comparison of \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Test** & **Laser** & **R1** & **R2** & **L1** & **L2** & **Mean** & **SD** & **\% Error** \\ \hline
1 & 13.96 & 14.06 & 14.23 & 14.49 & 14.30 & 14.27 & 0.16 & 1.92 \\
2 & 13.93 & 14.18 & 14.32 & 14.48 & 14.33 & 14.325 & 0.105 & 2.323 \\
3 & 14.02 & 14.15 & 14.31 & 14.52 & 14.34 & 14.330 & 0.130 & 2.354 \\
4 & 13.94 & 14.08 & 14.25 & 14.62 & 14.40 & 14.334 & 0.200 & 2.386 \\
5 & 13.96 & 14.11 & 14.26 & 14.49 & 14.30 & 14.290 & 0.134 & 2.068 \\ Mean & 13.96 & 14.12 & 14.27 & 14.52 & 14.33 & - & - & - \\ SD & 0.03 & 0.04 & 0.04 & 0.05 & 0.03 & - & - & - \\ \% Error & 0.28 & 0.81 & 1.90 & 3.57 & 2.33 & - & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Fourteen meter straight line distance test results. Comparing the distance from the laser, and the independently found distance from each of the four wheel sensors (R1, R2, L1, L2) to the known 14 m distance from the court markings. Figure 2: IMU sensor placement. Right wheel 1 and 2 (RW1 + RW2) and Left wheel 1 and 2 (LW1 + LW2) oriented +x wheel rotation direction and +z into the wheel. Centered frame (Cf) sensor oriented +x forward, +y right, +z down. (**A**) photo of sensor placement, with blue squares overlaid on sensors to increase visual prominence; (**B**) schematic of the sensor location with additional componentry removed; and (**C**) court testing dimensions. velocity from the four inertial sensors against this reference. One trial example--trial one of the 14 m test--is shown below in Figure 3.  
The results of the halfway to baseline test are shown below in Table 2.  
Tables 3 and 4 show the results from the half court laps performed both clockwise and then anticlockwise. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Test** & **Laser** & **R1** & **R2** & **L1** & **L2** & **Mean** & **SD** & **\% Error** \\ \hline
1 & 15.87 & 16.04 & 16.03 & 16.51 & 16.37 & 16.24 & 0.21 & 2.23 \\
2 & 15.87 & 16.04 & 16.13 & 16.54 & 16.42 & 16.28 & 0.21 & 2.51 \\
3 & 15.82 & 16.07 & 16.09 & 16.45 & 16.32 & 16.23 & 0.16 & 2.20 \\
4 & 15.91 & 16.12 & 16.21 & 16.73 & 16.58 & 16.41 & 0.25 & 3.32 \\
5 & 15.85 & 16.13 & 16.22 & 16.45 & 16.33 & 16.28 & 0.12 & 2.52 \\ Mean & 15.86 & 16.08 & 16.14 & 16.53 & 16.40 & - & - & - \\ SD & 0.03 & 0.04 & 0.07 & 0.10 & 0.09 & - & - & - \\ \% Error & 0.10 & 1.22 & 1.57 & 3.94 & 3.18 & - & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Range test, 15.88 m straight line. Comparing the distance found by the laser, the distance found independently for each of the four wheels (R1, R2, L1, L2), and the known distance from the court markings. Figure 3: Velocity profile comparison of the four sensors used in trial 1, 14 m.  
To visualise the information given in Tables 3 and 4, the trajectory was plotted for each half court loop. Figure 4 shows one example plot, depicting the four independent wheel measures starting from the origin (0, 0), with the error visually highlighted by the incompleteness of the loop.