Step by step: reconstruction of terrestrial animal movement paths by dead-reckoning

Abstract

Background: Research on wild animal ecology is increasingly employing GPS telemetry in order to determine animal movement. However, GPS systems record position intermittently, providing no information on latent position or track tortuosity. High frequency GPS have high power requirements, which necessitates large batteries (often effectively precluding their use on small animals) or reduced deployment duration. Dead-reckoning is an alternative approach which has the potential to 'fill in the gaps' between less resolute forms of telemetry without incurring the power costs. However, although this method has been used in aquatic environments, no explicit demonstration of terrestrial dead-reckoning has been presented.

Results: We perform a simple validation experiment to assess the rate of error accumulation in terrestrial dead-reckoning. In addition, examples of successful implementation of dead-reckoning are given using data from the domestic dog Canus lupus, horse Equus ferus, cow Bos taurus and wild badger Meles meles.

Conclusions: This study documents how terrestrial dead-reckoning can be undertaken, describing derivation of heading from tri-axial accelerometer and tri-axial magnetometer data, correction for hard and soft iron distortions on the magnetometer output, and presenting a novel correction procedure to marry dead-reckoned paths to ground-truthed positions. This study is the first explicit demonstration of terrestrial dead-reckoning, which provides a workable method of deriving the paths of animals on a step-by-step scale. The wider implications of this method for the understanding of animal movement ecology are discussed.

Keywords: GPS; Step length; animal movement; dead reckoning; terrestrial.

Fig. 1

Flow diagram showing the process required to perform dead-reckoning

Fig. 2

Idealised illustration of how static acceleration (S_i) is calculated using a moving average of window size w. The locomotion of the animal produces a charicteristic waveform, which oscillates around the static acceleration S_i

Fig. 3

Illustration of how changes in body orientation, i.e. a Roll (γ), b Pitch (β), produce changes in static acceleration. S_x represents the Heave axis (dorso-ventral), S_y represents the Surge axis (anterior-posterior), and S_z represents the Sway axis (lateral)

Fig. 4

Visualisation of magnetometer data where distortions in the magnetic field due to soft iron sources near to the sensors may change the expected outputs on the various axes (two of three shown for simplicity). This can be corrected by appropriate normalising procedure (see text)

Fig. 5

Visualisation of displacement correction for the magnetometer output in two axes. The red circle represents data for a 360° rotation from two magnetometer axes that are subject to displacement from the true point of origin (black circle) by hard iron distortion

Fig. 6

Illustration of how the distance correction factor is calculated. The correction factor is then applied to all distance calculations so that dead-reckoned and ground-truthed positions accord

Fig. 7

When distances between two time-synchronized positions derived from both GPS and dead-reckoned are equal but there is displacement between dead-reckoned and GPS-derived positions, a heading error is likely to have occurred but can be corrected (see text)

Fig. 8

2D paths of the human participant as determined by a Video Recording, b GPS, c Dead-Reckoning without correction, d Dead-Reckoning with correction every 2 s, e Dead-Reckoning with correction every 5 s, f Dead-Reckoning with correction every 10 s

Fig. 9

Mean Distance Error (m) at each of the ground-truthing regimes. Error bars represent Standard Deviation of the Mean

Fig. 10

The movements of a rider-directed horse Equus ferus caballus, starting and ending in the top left corner, as elucidated by GPS (at 1 Hz - black track) and dead-reckoning (at 20 Hz) without any ground-truthed points (red track). Note that the dead-reckoned trace has no scale since the distance moved is derived from the speed and this is assumed to be linearly related to VeDBA, with a nominal relationship until ground-truthed (see text). The two dashed squares show a period when the horse was directed to move in tight circles. For scale, the total track length according to the GPS (black track) was 10.127 km

Fig. 11

Movement path of a domestic dog. The purple track displays the GPS data (at 0.2 Hz) while the green shows the dead-reckoned path (at 40 Hz). For scale, the total track length according to the GPS was 3.040 km. Note the additional track tortuosity of the dead-reckoned track

Fig. 12

Changes in speed and heading correction factors necessary to tie dead-reckoned tracks into those acquired by GPS during deployment of a GPS-enabled DD on a) dog 1, b) dog 2, c) dog 3 and d) a horse. Note that the speed correction value changes relatively little but the heading estimates sometimes varied considerably

Fig. 13

GPS-enabled dead-reckoned tracks (DD sampling rate 40 Hz, GPS sampling rate 0.1 Hz) from a domestic cow Bos taurus in an enclosed field (light grey area) over 2 h. The yellow track shows the calculated trajectory using all GPS points (at 20 s intervals) while the blue track shows the calculated trajectory omitting all unrealistic GPS points (based on speed and estimates outside the peripheral fence). Note that various elements of the GPS, such as the Kahlmann filter, may give highly credible loops within the track that do not correspond to the real trajectory of the animal (cf. yellow lines outside the field periphery)

Fig. 14

GPS-corrected (30 min intervals,) dead-reckoned (40 Hz) track of a wild badger Meles meles over 200 mins during which time the animal was calculated to have moved to a distance of 670 m from its sett. The boxes show zoomed sections of the track to illustrate the effective maintenance of resolution over even short time intervals