*3.2. Gait Analysis*

This Section is devoted to gather the results obtained when comparing the accelerations provided by each of the seven IMUs during the gait analysis described in Section 2.2, with the so-called virtual accelerations obtained from the optical motion capture. As explained in the mentioned Section, the trajectories of the markers recorded by the optical system should be processed by a motion reconstruction method, which includes filtering of the recorded data. Therefore, the results from each of the two reconstruction methods proposed in Section 2.2 are shown in what follows.

### 3.2.1. Vaughan's Method

The virtual accelerations obtained after the application of the forward-backward 2nd order Butterworth filter with different cutoff frequencies were compared with those directly measured by the IMUs. Figure 9 shows the three components of the accelerations at the seven segments analyzed for cutoff frequencies of 6, 12 and 40 Hz, while Figure 10 provides more detail for the left foot. Table 1 gathers the RMSE of the optical-system based accelerations, with cutoff frequencies ranging between 6 and 40 Hz, with respect to those directly measured by the inertial system.

**Figure 9.** Accelerations obtained from the optical system with Vaughan's method, for cutoff frequencies of 6 Hz (black), 12 Hz (blue) and 40 Hz (cyan), respectively, vs. accelerations measured by the IMUs (red).

**Figure 10.** Detail of accelerations at the left foot obtained from the optical system with Vaughan's method, for cutoff frequencies of 6 Hz (black), 12 Hz (blue) and 40 Hz (cyan), respectively, vs. accelerations measured by the IMUs (red).


**Table 1.** RMSE of the accelerations obtained from the optical system through Vaughan's method with different cutoff frequencies, with respect to the accelerations measured by the IMUs, taken as reference. The row with the lowest mean RMSE is highlighted in red.

> It can be seen that the influence of the filtering parameter is significant. For high cutoff frequencies (above 20 Hz), the accelerations were too noisy, with peak errors over 5 m/s2. Conversely, for low cutoff frequencies (below 8 Hz), the accelerations were too smooth, not reaching the experimental peak measurements of the inertial sensors. As opposed to the preliminary test, some acceleration peaks can be captured by the optical system at high cutoff frequencies, due to the softer contacting materials involved in this case, but at the cost of very noisy accelerations along the whole capture. The lowest errors were obtained for a cutoff frequency of 12 Hz, as highlighted in Table 1.
