# Estimation of Stride Length, Foot Clearance, and Foot Progression Angle Using UWB Sensors
## 3 Results
### Results for Gait Parameters  
Figure 6 shows the UWB data acquired from participant #3 of the gait experiment and the 3D trajectory of the right foot determined using Equations (8)-(10). The foot trajectory estimated using UWB is shown in Figure 6a. Here, a closed curve is drawn using the combined trajectory of the foot when the tag is in the swing and stance phases. Herein, after the heel strike point, when the foot is in a swing state and higher than the opposite foot, the z-direction location value reverses as the opposite foot lifts from the ground. Therefore, the foot's trajectory at a wholesome swing phase could be illustrated only if the data with the z value of the anchor of the opposite foot is higher than the z value data of the tag location installed on the stepping foot in the stance phase. This is illustrated in Figure 6b.  
Figure 7 shows the Bland-Altman plot that assesses SL, FC, and FPA using the 3D trajectory data of the foot during the swing phase. It shows the data acquired from all participants. The x-axis represents the average of the values measured by the MSC (or optical reference) and the UWB system, and the y-axis represents the difference between the two measured values (MCS (or optical reference)--UWB).  
It can be seen that the SL data in Figure 7a is divided into two groups, and the average SL values of each group are 719 mm and 874 mm, respectively. The data near SL = 719 mm, were mainly obtained from a group of female participants with heights < 170 cm. The data near SL = 874 mm were mainly from a mixed group of participants with heights \(\geq\) 170 cm. Figure 7 shows that the obtained data were mostly within 95% confidence interval. Therefore, the foot trajectory data estimated using UWB could be considered to be in good agreement with the data measured using MCS.  
The data in Figure 7 were analyzed and are presented in Table 2. The differences in SL at speeds of 2, 3, and 4 km/h were 45.13, 46.99, and 45.40 mm, respectively. Furthermore, the average difference in the entire gait speed section was 45.84 mm. The differences in FC at speeds of 2, 3, and 4 km/h were 7.80, 7.45, and 7.54 mm, respectively, and the average difference for the entire gait speed section was 7.60 mm. The differences in the FPA for the same speeds were 2.53\({}^{\circ}\), 2.86\({}^{\circ}\), and 3.12\({}^{\circ}\), respectively, and the average difference for the entire gait speed section was 2.82\({}^{\circ}\). In Figure 8, the average SL, FC, and FPA were measured for each gait speed. Moreover, a 95% confidence interval was identified. Overall, the difference in SL was trivially impacted by the variation in gait speed. In addition, the difference in FC was relatively large when the gait speed was low and tended to converge to a certain value as the gait speed increased. The difference in FPA increased continuously as the gait speed increased, although the amount of variation was marginal.  
Figure 6: Foot trajectory estimation using UWB sensors: (**a**) All the foot trajectory results; (**b**) Only the results estimated in the swing phase.  
Figure 7: Bland–Altman graphs for gait parameter values determined using UWB and motion capture system: (**a**) Stride length; (**b**) Foot clearance; (**c**) Foot progression angle.  
The estimated gait parameters from UWB and MCS were compared: they show good correlation coefficients (r\({}^{2}\) > 0.7) of 0.898 in SL, 0.761 in CL, and 0.743 in FPA.