# Table 3 Set of features extracted to test the proposed scheme performance

DomainFeatureEquation*
TimeArithmetic mean$$\bar{s} = \frac{1}{N}\mathop \sum \limits_{i = 1}^{N} s_{i}$$
TimeMinimum amplitude$$s_{min} = min\left( {s_{i} } \right)$$
TimeMaximum amplitude$$s_{max} = max\left( {s_{i} } \right)$$
TimeStandard deviation$$std\left( s \right) = \sigma = \sqrt {\frac{1}{N}\mathop \sum \limits_{i = 1}^{N} \left( {s_{i} - \overline{s} } \right)^{2} }$$
Timekurtosis$$kurtosis\left( s \right) = \mathop \sum \limits_{i}^{N} \frac{{\left( {s_{i} - \overline{s} } \right)^{4} }}{{N\sigma^{4} }}$$
TimeSkewness$$skewness\left( s \right) = \mathop \sum \limits_{i}^{N} \frac{{\left( {s_{i} - \overline{s} } \right)^{3} }}{{N\sigma^{3} }}$$
TimeSignal magnitude area$$sma\left( s \right) = \frac{1}{3}\mathop \sum \limits_{i = 1}^{3} \mathop \sum \limits_{j = 1}^{N} \left| {s_{i,j} } \right|$$
TimeMedian absolute deviation$$mad\left( s \right) = median_{i} \left( {\left| {s_{i} - median_{{j\left( {s_{j} } \right)}} } \right|} \right)$$
TimeInterquartile range$$iqr\left( s \right) = Q3\left( s \right) - Q1\left( s \right)$$
TimeAutoregression$$a=arburg\left( s,4 \right), \, \!\! \!\! \, a\epsilon {{\mathbb{R}}^{4}}$$
TimeSum vector magnitude$$\left| s \right| = \sqrt {s_{i, x}^{2} + s_{i, y}^{2} + s_{i, z}^{2} }$$
TimeAngle between z-axis and vertical$$\theta 1 = atan2\left( {\sqrt {s_{i,x}^{2} + s_{i,y}^{2} } ,s_{i, z} } \right)$$
TimeOrientation of a person’s trunk$$\theta 2 = {\text{atan}}\left( {\sqrt {s_{i, x}^{2} + s_{i, y}^{2} } /s_{i, z} } \right)$$
TimeAngle between device and ground$$\theta 3 = \sin \left( s \right)$$
FrequencyMaximum frequency index$$maxFreqInd\left( S \right) = arg \,max_{i} \left( {S_{i} } \right)$$
FrequencyMean frequency$$mean\,freq\left( S \right) = \mathop \sum \limits_{i = 1}^{N} \left( {iS_{i} } \right)/\mathop \sum \limits_{j = 1}^{N} S_{j}$$
FrequencyEnergy$$E_{f} = \sum \left| {S\left( f \right)} \right|^{2}$$
FrequencyEntropy$$H\left( {S\left( f \right)} \right) = - \mathop \sum \limits_{i = 1}^{N} p_{i} \left( {S\left( f \right)} \right) \log_{2} p_{i} \left( {S\left( f \right)} \right)$$
1. *Here $$s$$. represents a 3D signal, $$i$$ and $$j$$ signify the signal index, $$s_{i, x}$$., $$s_{i, y}$$, and $$s_{i, z}$$ denote the signal value along x, y, and z-axis of the sensor, respectively,$$Q1$$ and $$Q3$$ represent the first and third signal quartile, $$N$$ is the total number of samples in a data chunk, $$S$$ is the Fourier transform of signal $$s$$, and $$p$$ is the probability