Table 2 Processing (A) performed on raw acceleration data after applying a sliding window of five seconds prior to segmentation and summary statistics (features) calculated (B) for each window (two-, three-, and five-second windows) after segmentation
From: Identification of reindeer fine-scale foraging behaviour using tri-axial accelerometer data
A | Data processing | Term | Equation | Description |
|---|---|---|---|---|
|  | Static acceleration | sX, sY, sZ | \({\mathrm{sX}}_{\mathrm{i}}=\frac{1}{51}\sum_{\mathrm{i}-25}^{\mathrm{i}+25}{\mathrm{X}}_{\mathrm{i}}\) | Gravitational component of acceleration (9.81 m/s2 = 1 g) caused by gravitational force acting on the accelerometers [16, 17, 35] |
|  | Dynamic acceleration | dX, dY, dZ | \({\mathrm{dX}}_{\mathrm{i}}=\left|{\mathrm{X}}_{\mathrm{i}}-{\mathrm{sX}}_{\mathrm{i}}\right|\) | Dynamic acceleration measures acceleration caused by animal movements where the gravitational component is removed [e.g., 12, 23, 27] |
|  | Roll (φ) | roll | \(\mathrm{atan}2\left(\mathrm{sY},\mathrm{ sZ}\right)\) | Rotation around the X-axis (roll) given in Euler angles ranging between ± π radian (equivalent to ± 180º) using 2-argument arctangent function, implemented as atan2 in R |
|  | Pitch (θ) | pitch | \(-\mathrm{atan}(\frac{\mathrm{sX}}{\sqrt{{\mathrm{sY}}^{2}+{\mathrm{sZ}}^{2}}})\) | Rotation around the Y-axis (pitch) given in Euler angles ranging between ± π/2 rad (equivalent to ± 90º) using arctangent function, implemented as atan in R |
| Â | \(\ell^{2}\)-norm of raw accelerometer axes | Norm | \(\sqrt{{\mathrm{X}}^{2}+{\mathrm{Y}}^{2}+{\mathrm{Z}}^{2}}\) | Orientation-independent measure of acceleration magnitude [42, 62] |
| Â | Rotation matrix | Rx(\(\varphi\)) | \(\left[\begin{array}{ccc}1& 0& 0\\ 0& \mathrm{cos}\varphi & -\mathrm{sin}\varphi \\ 0& \mathrm{sin}\varphi & \mathrm{cos}\varphi \end{array}\right]\) | Rotation matrix around X-axis to adjust for rotations around the neck |
B | Summary statistics | Term | Description |
|---|---|---|---|
| Â | Mean | mean | Mean value for each axis in each window |
| Â | Minimum | min | Minimum value for each axis in each window |
| Â | Maximum | max | Maximum value for each axis in each window |
| Â | Median | m | Median for each axis in each window |
| Â | Interquartile range | IQR | Third quantile (Q3) subtracted by the first quantile (Q1) for each axis in each window |
| Â | Standard deviation | sd | Standard deviation for each axis in each window |