# A Novel AHRS Inertial Sensor-Based Algorithm for Wheelchair Propulsion Performance Analysis
## 4 Discussion  
Magnetometer data showed two large magnetic disturbances on the basketball court which affected the sensor heading angle, occurring 1.81 \(\pm\) 0.09 s into the 14 m trial. The cause of this disturbance was determined to be high voltage power and telecommunications lines for the adjoining sports stadium that ran underneath the court. This heading angle error due to the magnetic disturbance shaped the decision to utilise only the IMU AHRS implementation for all calculations. The 14 m straight line trial (shown in Table 1) indicated that the proposed algorithm gives accurate, less than \(\pm\)5% error, distance calculations when compared to the known 14 m track length. The mean value was 14.31 \(\pm\) 0.15 m, overestimating distance for the trial by an average error of 2.21%. The inter-sensor error was also very low, with an average 0.77% distance error between the five trials with the average range of 0.11 \(\pm\) 0.03 m. The laser measurement gave a mean result of 13.96 \(\pm\) 0.03 m, demonstrating its use as a velocity reference. When comparing the gradient of the velocity curve between the four wheel sensors and the laser shown in Figure 2, it is apparent that the velocity estimation based on distance and time is an accurate reflection of the true velocity. The halfway centre court position to the baseline corner was chosen as the second measure of distance, shown in Figure 2C. The rationale was that if the wheel was pushed in a slightly non-linear trajectory, the left outside wheel would show a greater travelled distance. The laser again proved to be an accurate measure, estimating the distance at an average of 15.864 \(\pm\) 0.032 m. The IMU sensors also provided an accurate distance measurement when compared to the known distance 16.288 \(\pm\) 0.205 m, with a mean distance error percentage of 2.57%. A left wheel distance dominance was seen, with a mean increase in distance of 0.362 m, indicating that the wheelchair was not pushed directly straight and rather had a slightly curved trajectory. Three half court laps were performed in each direction. As the wheelchair was walked along the centre line, the internal wheel distance should equate to 56.25 m, and the external wheel should travel 61.72 m. The mean distance travelled for the internal wheel 57.27 \(\pm\) 0.70 m, and the external wheel 60.85 \(\pm\) 0.46 m, with an average internal wheel over-estimation error of 1.79% and an average outside wheel under-estimation of 1.42%. The tracking accuracy using the orientation from the rigidly-mounted chair sensor was also very good, with a radial distance error mean of 0.71 \(\pm\) 0.17 m. If the MARG AHRS system was used, it could be assumed that this error would be further reduced, as a more accurate heading could be attained. In addition to the computational efficiency and accuracy of the measurement algorithm, the algorithmic implementation also benefits, as it is both placement and camber agnostic. This is a substantial benefit in comparison to pre-existing algorithms, reducing setup time and enhancing useability. The algorithm in its current form has a few limitations. The algorithm did not include wheel skid correction factors, as the testing did not encompass any skid moments. For in-game distance and trajectory, a modification of [PERSON] et al. 's [PERSON] et al. (2014) correction algorithm will be integrated, as skidding is likely to occur. The implemented algorithm also requires an accurate wheel radius measurement, and this radius will vary with tire pressure and deformation due to player loading. Therefore, to ensure measurement accuracy for tire radius measurements, [PERSON] et al. 's [PERSON] et al. (2016) wheel radius measurement protocol will be adopted for testing with athletes. Furthermore, due to the ferromagnetic disturbance, MARG AHRS was not utilised. If possible, it should be used; however, as the magnetometer was affected, a more accurate trajectory could not be ascertained.