Animal-borne behaviour classification for sheep (Dohne Merino) and Rhinoceros ( Ceratotherium simum and Diceros bicornis )

Table 3 Features extracted from the compiled datasets

Feature	Equation
Average signal magnitude	\(\frac{1}{N}\sum\nolimits _{i=1}^{N}\sqrt{x_i^2 + y_i^2 + z_i^2}\)
Maximum value	\({\text {max}}({\mathbf {x}})\)
Minimum value	\({\text {min}}({\mathbf {x}})\)
Mean (\(\bar{x}\))	\(\frac{1}{N} \sum\nolimits _{i=1}^{N} x_i\)
Standard deviation (\(\sigma _x\))	\(\sqrt{ \frac{1}{N} \sum\nolimits _{i=1}^{N}(x_i - \bar{x})^2}\)
Variance	\(\sigma^2_x\)
Skewness	\(\frac{\frac{1}{N} \sum \nolimits_{i=1}^{N} (x_i - \bar{x})^3}{\sigma^3_x}\)
Kurtosis	\(\frac{\frac{1}{N} \sum\nolimits _{i=1}^{N} (x_i - \bar{x})^4}{\sigma^4_x}\)
Energy	\(\frac{1}{N} \sum\nolimits _{i=1}^{N} \|X_i\|^2\)
Spectral entropy	\(\sum\nolimits _{i=1}^{N} P(x_i) \log \frac{1}{P(x_i)}\)
Pairwise correlation between the axes	\(\frac{{\hbox {cov}}({{\mathbf {x}}}, {{\mathbf {y}}})}{\sigma_x \sigma_y}\)

Each frame consists of N sequential samples, and x denotes a vector of these samples for each accelerometer axis, x, y and z. The FFT of x is denoted by X and the normalised power spectrum of x by \(P({\mathbf {x}})\). Cross-correlation is calculated for each axis pair (x, y), (x, z), and (y, z). All features except average signal magnitude provide three values: one per axis