## 3 Experiments and Result
### Result
#### 3.2.2 Gait Parameters  
The gait parameters can be computed using the Doppler envelope extracted by the proposed method, as outlined in (19)-(23). Figure 13 shows the range envelope and Doppler envelope for each subject, with the steps marked on the graphs. \[\text{Speed}=\text{mean}(\text{velocity}(S_{i})) \tag{19}\]  
\[\text{Step time}=\text{mean}\left(\sum_{i}(\text{time}(S_{i+1})-\text{time}(S_ {i}))\right) \tag{20}\]  
\[\text{Step length}=\text{mean}\left(\sum_{i}(\text{range}(S_{i+1})-\text{ range}(S_{i}))\right) \tag{21}\]  
\[\text{Stride time}=\text{mean}\left(\sum_{i}(\text{time}(S_{i+2})-\text{time}(S_ {i}))\right) \tag{22}\]  
\[\text{Stride length}=\text{mean}\left(\sum_{i}(\text{range}(S_{i+2})-\text{ range}(S_{i}))\right) \tag{23}\]  
Speed refers to the walking speed, Step time is the time it takes to take one step, Step length is the distance of one step, Stride time is the time it takes to take two steps, and Stride length is the distance of two steps. Figure 14 presents a subject-wise comparison of the speed values estimated by the conventional method, the proposed method, and the ground truth for each body part (Spine, Leg, Foot). This figure allows for direct visual comparison of the actual estimated values. It can be observed that the proposed method consistently provides speed values closer to the ground truth compared to the conventional method, especially for the Spine and Leg. Figure 15 illustrates the distribution of relative errors (%) in five gait parameters--Speed, Step Time, Step Length, Stride Time, and Stride Length--across the Foot, Leg, and Spine regions. The blue and orange boxes represent the conventional percentile-based method and the proposed contour-based method, respectively. Figure 13: Range and Doppler envelopes of Subject 3 with walking steps marked. (**a**) Range envelope, (**b**) Doppler envelopes of Spine, Leg, and Foot. The relative error for each parameter was computed as:  
\[\text{Relative Error (\%)}=\frac{\left|\text{Estimated value}-\text{ Ground Truth}\right|}{\left|\text{Ground Truth}\right|}\times 100\]  
This metric quantifies the percentage deviation of the radar-estimated value from the ground truth provided by the motion capture system. In general, both methods demonstrate comparable levels of accuracy, with the proposed method showing slightly reduced variability in several parameters. Notably, the proposed approach exhibits more compact error distributions for Foot Speed, Leg Speed, and Foot Stride Length, while a few parameters such as Leg Step Length and Spine Stride Time show wider spreads, indicating the presence of occasional outliers. Figure 14: Comparison of speed values for each subject using three methods: conventional (blue), proposed (red), and ground truth (yellow). (**a**) Spine, (**b**) Leg, (**c**) Foot. To provide a quantitative summary of these distributions, Table 4 reports the mean and standard deviation of the relative errors for each gait parameter and body region. Table 4 presents the mean and standard deviation of the relative errors (%) for each gait parameter and body region. The results indicate that the proposed method achieves similar or slightly improved accuracy compared to the conventional method in most cases. Although the average relative error for some parameters exceeds the often-cited clinical threshold of 5%, key metrics such as Foot Speed (5.10% \(\pm\) 4.52%), Leg Speed (1.28% \(\pm\) 1.96%), and Foot Stride Length (2.29% \(\pm\) 1.35%) remain well within acceptable ranges. When interpreted together, the figure and table offer complementary insights; the boxplots highlight the typical distribution and spread of errors, showing that the proposed  
Figure 15: Boxplots showing the relative errors between estimated values and ground truth across 5 subjects, categorized by body part (Spine, Leg, Foot) and gait parameter (Speed, Step Time, Step Length, Stride Time, Stride Length) for both the conventional and proposed methods. (**a**) Spine, (**b**) Leg, (**c**) Foot.