A right-handed rotation ( \(C\)) about the y-axis at \(F_{1}\), through angle θ (Eq. 5), to get to the second intermediate frame ( \(F_{2}\)). Alaimo A, Artale V, Milazzo C, Ricciardello A. Comparison between Euler and quaternion parametrization in UAV dynamics. AIP Conf Proc. 2013;1558(1):1228–31. Adachi T, Costa DP, Robinson PW, Peterson SH, Yamamichi M, Naito Y, Takahashi A. Searching for prey in a three-dimensional environment: hierarchical movements enhance foraging success in northern elephant seals. Funct Ecol. 2017;31(2):361–9.

We already have nice dataframe now with all the information available in the GPX file for each position. Each position is defined by the latitude and longitude and we also have the elevation (altitude) available. Note, that the altitude ist quite noisy with GPS, we will see this in a minute. where h refers to the vector containing the heading data. Should the user not correct for axis alignment between the device and animal body frame (cf. Eqs. 4– 12, R 11:22) then a reasonable post-correction for small discrepancies about the yaw axis would be to subtract the difference to h values at this point. Department of Veterinary Tropical Diseases, Faculty of Veterinary Science, University of Pretoria, Onderstepoort, 0110, South Africa Feng K, Li J, Zhang X, Shen C, Bi Y, Zheng T, Liu J. A new quaternion-based Kalman filter for real-time attitude estimation using the two-step geometrically-intuitive correction algorithm. Sensors. 2017;17(9):2146.Shamoun-Baranes J, Bom R, van Loon EE, Ens BJ, Oosterbeek K, Bouten W. From sensor data to animal behaviour: an oystercatcher example. PLoS ONE. 2012;7(5):e37997. In R, the formulae to calculate the great-circle distance and great circular bearing are saved within the disty (R 61) and beary (R 62) functions, respectively, where lon1, lat1, long2 and lat2 represent longitude and latitude positions (decimal format) at \(t_{i}\) and \(t_{i + 1}\), ( \(t\) representing time). Dividing the number of steps detected within a given rolling window length (cf. R 1:4), by the window length ( s) gives an estimated step count per second. This can be converted to speed by multiplying by a distance per step estimate (assuming constant distance travelled between step gaits). We review this further in Additional file 1: Text S4, including a simple peak finder function— Gundog.Peaks (Additonal file 3) that locates peaks based on local signal maxima, using a given rolling window, with each candidate peak filtered according to whether it surpassed a threshold height (in conjunction with other potential user-defined thresholds). Note, this method can equally be applied to non-terrestrial species, using flipper/tail beats instead, where appropriate. School of Biological Sciences, Queen’s University Belfast, Belfast, 19 Chlorine Gardens, Belfast, BT9 5DL, Northern Ireland, UK

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Schlägel UE, Signer J, Herde A, Eden S, Jeltsch F, Eccard JA, Dammhahn M. Estimating interactions between individuals from concurrent animal movements. Methods Ecol Evol. 2019;10(8):1234–45.