2.2.3. Acceleration

The *Acceleration* method introduced in [6] uses only acceleration data for step segmentation and the computation of stride length and stride velocity. The method correlates the velocity of the foot (and thus, the subject) with the acceleration during the swing phase of the foot. It consists of three different algorithmic steps: (1) a continuous calculation of an integration value with a strong correlation to the movement velocity, (2) a stride segmentation based on initial ground contacts to determine the swing phase of the foot, and (3) a regression model to translate the continuous integration value to the velocity value.

We used the step segmentation algorithm from the cited publication due its applicability to movements other than running [6]. The inputs to the processing pipeline were the sampled triaxial acceleration signals from the foot sensor *ax*, *ay*, and *az*. After smoothing the input signals using a sliding window filter, the integration value *ι* was calculated as a multi-step absolute averaging across all directional components with:

$$\ln[n] = \frac{1}{L+1} \sum\_{i=0}^{L} \sum\_{d=\mathbf{x}, \mathbf{y}, z} |\mathbf{s}\_d[n-i]|\,, \tag{7}$$

where *L* is the window length, which is expected to be the same as the duration of the foot swing phase.

Individual strides were determined in the smoothed dorsoventral acceleration signal *sy* using a peak detection process in combination with two knowledge-based parameter thresholds. The goal was to detect and isolate the high impact response of initial ground contact in the smoothed signal [6]. Each time a valid stride was detected by the stride segmentation algorithm, the average velocity per stride *vstride* was determined based on a second degree polynomial regression function:

$$
\sigma\_{stride} = A + B \cdot \iota[n\_{IC}] + \mathcal{C} \cdot \iota[n\_{IC}]^2,\tag{8}
$$

where the constants *A*, *B*, and *C* are derived during a regression model training phase where known reference velocity observations are matched to velocity integration values using parametric regression analysis. A trained regression model can be observed in Figure 3.

**Figure 3.** Polynomial function of second degree (red line) that relates the velocity integration value *ι* to the reference velocity values *vstride* (grey dots).
