# Validation of a Wearable IMU System for Gait Analysis: Protocol and Application to a New System
## 2 Materials and Methods
### Specifications of the New Wearable System and Its Data to Be Validated
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameter** & \multicolumn{4}{c}{**Reliability Criteria**} \\ \hline  & **Excellent** & **Good** & **Sufficient** & **Not Acceptable** \\ \hline \multirow{2}{*}{Step length} & \(\varepsilon_{\%}\) \(<\) 5\% & 5\% \(\leq\)\(\varepsilon_{\%}\) \(<\) 10\% & 10\% \(\leq\)\(\varepsilon_{\%}\) \(<\) 20\% & \(\varepsilon_{\%}\)\(\geq\) 20\% \\  & (\(<\)3 cm) & (3 \(\leq\)\(\varepsilon_{\%}\) \(<\) 6 cm) & (6 \(\leq\)\(\varepsilon_{\%}\) \(<\) 12 cm) & (\(\geq\)12 cm) \\ \hline \multirow{2}{*}{Distance} & \(\varepsilon_{\%}\) \(<\) 5\% & 5\%\(\leq\)\(\varepsilon_{\%}\) \(<\) 10\% & 10\% \(\leq\)\(\varepsilon_{\%}\) \(<\) 20\% & \(\varepsilon_{\%}\)\(\geq\) 20\% \\  & (\(<\)0.35 m) & (0.35 \(\leq\)\(\varepsilon_{\%}\) \(<\) 0.70 m) & (0.70 \(\leq\)\(\varepsilon_{\%}\) \(<\) 1.40 m) & (\(\geq\)1.40 m) \\ \hline \multirow{2}{*}{Counting steps} & \(\varepsilon_{\%}\) \(<\) 2\% & 2\% \(\leq\)\(\varepsilon_{\%}\) \(<\) 4\% & 4\% \(\leq\)\(\varepsilon_{\%}\) \(<\) 6\% & \(\varepsilon_{\%}\)\(\geq\) 6\% \\  & (\(<\)1 steps) & (1 \(\leq\)\(\varepsilon_{\%}\) \(<\) 2 steps) & (2 \(\leq\)\(\varepsilon_{\%}\) \(<\) 3 steps) & (\(\geq\)3 steps) \\ \hline \multirow{2}{*}{Time} & \(\varepsilon_{\%}\) \(<\) 4\% & 4\% \(\leq\)\(\varepsilon_{\%}\) \(<\) 6\% & 6\% \(\leq\)\(\varepsilon_{\%}\) \(<\) 8\% & \(\varepsilon_{\%}\)\(\geq\) 8\% \\  & (\(<\)1.2 s) & (1.2 \(\leq\)\(\varepsilon_{\%}\) \(<\) 1.8 s) & (1.8 \(\leq\)\(\varepsilon_{\%}\) \(<\) 2.4 s) & (\(\geq\)2.4 s) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Reliability assessment grid for the analysis of wearable IMUs for GA. \(\varepsilon_{\%}\) is the mean absolute percentage error in accuracy. According to the pendulum and kinematic model [9; 10; 18; 23; 24], the length of the single step (S) is given by:  
\[\mathrm{S}=2\times\sqrt{2\times\mathrm{L}\times\mathrm{hCOM}-\mathrm{hCOM}^{2}} \tag{1}\]  
The length L of the lower limb is known for each subject through direct anthropometric measurement; hCOM is evaluated from the acceleration data measured with the device according to the harmonic oscillator model [23; 24], step by step, according to the following equation:  
\[\mathrm{hCOM}=2\times\mathrm{a_{V}}\times\left(\frac{\mathrm{T}}{2\pi}\right)^ {2} \tag{2}\]  
where \(\mathrm{a_{V}}\) is the measured maximum value of the vertical acceleration in the considered step and T is the measured period (=time between two consecutive acceleration peaks) of the considered step. For every walking cycle, by assessing hCOM amplitude using Formula (2), the step length S is computed using Formula (1). The incremental traveled distance is the incremental sum of these steps. The discussion about this biomechanical model and the method used for data analysis is explained in [23; 24] and it is briefly recalled here. The analysis processing raw accelerations is implemented in the Matlab(r) software suite. The detection of the peaks in raw acceleration signals corresponds to the steps. Then, different filters are applied according to the walking speed (high i.e., >1.4 m/s, normal i.e., 1.4 m/s < speed < 0.9 m/s, or low i.e., <0.9 m/s). At normal and high speed, the raw signal is processed with a fifth order low-pass Butterworth filter. Antero-Posterior, Vertical, and Medio-Lateral accelerations have the following cut-off frequencies, respectively: 1.8 Hz, 1.8 Hz, and 0.9 Hz. At low speed, the raw signal is processed with a fourth order low-pass Butterworth filter, and Antero-Posterior, Vertical, and Medio-Lateral accelerations have the following cut-off frequencies, respectively: 35 Hz, 5 Hz, and 3 Hz. Figure 3: Walking pattern of the sinusoidal oscillation of the COM (Center of Mass) projected onto the sagittal plane of a single gait cycle. L is the length of the rigid lower limb; \(\theta\) is the hip angle of the step. The maximum amplitude of COM oscillation is hCOM. Circles highlight COM maximum/minimum positions in the trajectory.