Table 1 Feature development. Candidate features developed to describe the three biomechanical descriptors used in this study: posture (#1), movement intensity (#2 to #5), and movement periodicity (#6 to #9)

1.

Posture

meanRoll

Mean of data from roll axis

\( \frac{\Sigma_N{m}_{roll,w}}{N} \)

(1)

2.

Intensity

stdRoll

Standard deviation of data from roll axis

std(m_{roll, w})

(2)

3.

meanAbsDiffRoll

Mean of absolute values of time-differentiated roll data

\( \frac{\Sigma_N\left|\frac{d}{dt}\left({m}_{roll,w}\right)\right|}{N} \)

(3)

4.

axMaxMeanAbsDiff

Maximum, across axes, of mean of absolute values of time-differentiated data from each axis

\( \underset{\mathrm{A}\in \mathrm{roll},\mathrm{pitch},\mathrm{yaw}}{\max}\left(\frac{\Sigma_N\left|\frac{d}{dt}\left({m}_{A,w}\right)\right|}{N}\right) \)

(4)

5.

avgMeanAbsDiff

Mean, across axes, of mean of absolute values of time-differentiated data from each axis

\( \sum \limits_{A\in roll, pitch, yaw}\frac{\Sigma_N\left|\frac{d}{dt}\left({m}_{A,w}\right)\right|}{3N} \)

(5)

6.

Periodicity

rollFftPeakPower

Maximum squared coefficient

of Fourier transform of data from roll axis

\( \underset{\mathrm{i}\in 1\dots \mathrm{L}}{\max}\left({c}_{f_i, roll,w}^2\right) \)

(6)

7.

avgFftPeakPower

Mean, across axes, of maximum squared coefficient of Fourier transform of data from each axis

\( \underset{\mathrm{i}\in 1\dots \mathrm{L}}{\max}\left(\frac{c_{f_i, roll,w}^2+{c}_{f_i, pitch,w}^2+{c}_{f_i, yaw,w}^2}{3}\right) \)

(7)

8.

rollDiffFftPeakPower

Maximum squared coefficient of Fourier transform of time-differentiated roll data

\( \underset{\mathrm{i}\in 1\dots \mathrm{L}}{\max}\left({\delta}_{f_i, roll,w}^2\right) \)

(8)

9.

avgDiffFftPeakPower

Mean, across axes, of maximum squared coefficient of Fourier transform of time-differentiated data from each axis

\( \underset{\mathrm{i}\in 1\dots \mathrm{L}}{\max}\left(\frac{\delta_{f_i, roll,w}^2+{\delta}_{f_i, pitch,w}^2+{\delta}_{f_i, yaw,w}^2}{3}\right) \)

(9)