Table 2.

Sensor-based features extracted from the QS test.

Feature	Sensor	Description
CF AP ML [55,56]	Accelerometer	Centroidal frequency; frequency at which spectral mass is concentrated. Spectral moments are needed for the estimate: $${\mu }_0={\displaystyle \sum }_{i=1}^{N}PS{D}_i=TP; {\mu }_2={\displaystyle \sum }_{i=1}^N f_i^2 PS{D}_i; CF=\sqrt{\frac{{\mu }_2}{{\mu }_0}}$$ where PSD is the Power Spectral Density of the signal, f is the frequency vector, and N is the total number of points of the PSD. Frequencies below 0.15 Hz are usually ignored.
EA DISPL [55,56]	Accelerometer, Displacement	The 95% confidence Ellipse Area is the area of the confidence ellipse enclosing 95% of the points on the sway trajectory. The accelerometer-based postural parameter can be defined by analogy with the parameter based on the displacement.
F50% AP ML [55,56]	Accelerometer	Median frequency; frequency below which 50% of total signal power (TP) is present. Starting from the Power Spectral Density (PSD) of the signal: $$g_n={\displaystyle \sum }_{i=1}^{n}PS{D}_i ; F_{50\%}=f_n ,{\min }_n:g_n \ge 50\%TP$$ where the second formula means that F50% is the frequency, f, corresponding to the nth index which is the smallest index such that g(n) is ≥50% of the total power. The total power is equal to g(N) where N is the total number of points of the PSD. Frequencies below 0.15 Hz are usually ignored.
F95% AP ML [55,56]	Accelerometer	Frequency below which 95% of total signal power (TP) is present. Starting from the Power Spectral Density (PSD) of the signal: $$g_n={\displaystyle \sum }_{i=1}^{n}PS{D}_i ; F_{95\%}=f_n ,{\min }_n:g_n \ge 95\%TP$$ where the second formula mean that F95% is the frequency, f, corresponding to the nth index which is the smallest index such that g(n) is ≥95% of the total power. The total power is equal to g(N) where N is the total number of points of the PSD. Frequencies below 0.15 Hz are usually ignored.
FD AP ML [55,56]	Accelerometer	Frequency dispersion; unitless measure of the variability of the power spectral density frequency content (zero for pure sinusoid; increases with spectral bandwidth to one). Spectral moments are needed for the estimate: $${\mu }_0={\displaystyle \sum }_{i=1}^{N}PS{D}_i=TP; {\mu }_1={\displaystyle \sum }_{i=1}^N{f}_i PS{D}_i ; {\mu }_2={\displaystyle \sum }_{i=1}^N{f}_i^2 PS{D}_i; FD=\sqrt{\frac{1-{\mu }_1^2}{{\mu }_0{\mu }_2}}$$ where PSD is the Power Spectral Density of the signal, f is the frequency vector, and N is the total number of points of the PSD. Frequencies below 0.15 Hz are usually ignored.
MV DISPL AP ML [55,56]	Accelerometer, Displacement	Mean Velocity of the postural sway computed as the median of the absolute value of the time series obtained integrating the acceleration: $$MV=median\left({{\displaystyle \int }}_{Tstart}^{Tend}a\left(t\right)dt\right)$$ where a is the acceleration component m/s2, Tend/Tstart are the end and the beginning of the observation time respectively. An alternative definition can be based upon the Sway Path (SP) of the displacement: $$MV=\left(\frac{SP}{T_{end}-T_{start}}\right)$$
NJS AP ML [35,54]	Accelerometer	Normalized Jerk Score of the acceleration: $$NJS=\sqrt{\frac{T^5}{2S{P}^2}}{{\displaystyle \int }}_{T_{start}}^{T_{end}}{\dot{\left(a\right)}}^{2}dt$$ where T is the duration (Tend − Tstart) of the considered component, a is the acceleration measured in m/s2, and SP is the Sway Path
Range AP ML	Accelerometer	Range of the signal
RMS AP ML	Accelerometer	Root Mean Square (RMS) of the signal, s (it is a measure of dispersion): $$RMS=\sqrt{\frac{1}{N}}{\displaystyle \sum }_{i=1}^N{\left(s_i -m\right)}^2$$ where N is the total number of points of the signal s, and m is the mean value $mean\left(s\right)$
SA DISPL [55,56]	Displacement	Sway Area (SA) estimated as the sum of the triangles formed by two consecutive points on the sway trajectory on the horizontal plane (sAP and sML) and the mean point (mAP and mML) on the plane: $$SA=\frac{1}{2}{\displaystyle \sum }_{i=1}^{N-1}\left|\left(s_{AP,i+1 }-m_{AP}\right)\left(s_{ML, i}-m_{ML}\right)-\left(s_{AP,i}-m_{AP}\right)\left(s_{ML, i+1}-m_{ML}\right)\right|$$ where s is a generic signal, sAP and sML are the two sway components on the horizontal plane. N is the total number of points of the signal time series. The accelerometer-based postural parameter can be defined by analogy with the parameter based on the displacement.
SE AP ML [55,56]	Accelerometer	Spectral Entropy Power spectrum entropy of acceleration (unitless).
SP AP ML DISPL SP Planar DISPL [55,56]	Accelerometer, Displacement	Sway Path, the total length of the sway trajectory, computed as the sum of the distances between consecutive points in the time series. When considering a single direction of the sway: $$P={\displaystyle \sum }_{i=1}^{N-1}\left(s_{i+1}-s_i\right)$$ When considering the sway path on the horizontal plane: $$SP=\frac{1}{2}{\displaystyle \sum }_{i=1}^{N-1}{\left(s_{AP, i+1}-s_{AP, i}\right)}^2+{\left(s_{ML,i+1}-s_{ML, i}\right)}^2$$ where s is a generic signal, sAP and sML are the two sway components on the horizontal plane. N is the total number of points of the signal time series. The accelerometer-based postural parameter can be defined by analogy with the parameter based on the displacement

ACRONYMS: AP: Antero-Posterior; CF: Centroidal Frequency; EA: Ellipse Area; F_50%: Median Frequency; F_95%: Frequency below 95% of total signal power; FD: Frequency Dispersion; ML: Medio-Lateral; MV: Mean Velocity; NJS: Normalized Jerk Score; RMS: Root Mean Square; SA: Sway Area; SE: Spectral Entropy; SP: Sway Path; V: Vertical.