Step by step: reconstruction of terrestrial animal movement paths by dead-reckoning
© Bidder et al. 2015
Received: 21 January 2015
Accepted: 6 September 2015
Published: 15 September 2015
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.
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.
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.
Animal movement interests animal biologists because, inter alia, it determines the success of individuals in obtaining resources, avoiding predation, maximising fitness and managing energetic profitability [1–3]. The success of individuals modulates populations and drives evolution and the diversity of life . There are also numerous practical benefits to understanding animal movement, such as predicting the impact of land use changes, control of invasive and pest species, conservation of endangered species and foreseeing the spread of zoonotic diseases [5–8].
Obtaining the required information on animal movements is far from trivial, however, as many species operate in environments that preclude them from being observed (e.g. [9, 10]). Many biotelemetry methods deal with this  because they obviate the need for visual contact between researcher and study animal. The two methods most frequently applied in terrestrial environments for obtaining animal location data are VHF and GPS telemetry [12, 13]. Both however, have their limitations ; VHF is an established method, but requires significant field effort to implement  while GPS telemetry is considered to be ‘accurate’  but prone to bias according to the environment [17, 18], particularly with regard to vegetation  and landscape topography . In addition, the high current drain of GPS systems necessitate large batteries when recording at high sampling rates, which limits use on smaller species [21–23], or restricts researchers to deployments of shorter duration . Analysis of data obtained by both methods assumes straight line travel between temporally infrequent positions  even though much animal movement is known to be highly tortuous . Clearly, there is a need for fine-scale animal movement data in both space and time so that animal movement models can better reflect the true nature of animal movement (c.f. ).
In fact, the only biotelemetric method purported to produce fine scale (i.e. >1 Hz) terrestrial animal movement data is dead-reckoning [28–30] which may resolve movement so finely that it can even be used to infer behaviour . Dead-reckoning calculates the travel vector for a given time interval using information on heading, speed and change in the vertical axis . Once this is achieved, the three dimensional movement path can be reconstructed by integrating the vectors in sequence [33–35]. Because data are recorded by sensors on board an archival logger, its efficacy is unaffected by the permissiveness of the environment [17, 18] which is important for obtaining accurate, unbiased data [36, 37]. In addition, archival loggers require considerably less power than GPS systems. Typically, a GPS running at 1 Hz may require between 30 and 50 mA of current, where as a modern iteration of the daily diary recording tri-axial acceleration and magnetometer data at 40 Hz requires only 5–10 mA of current (Holton, pers. comm.)
Dead-reckoning has been employed for tracking aquatic species [30, 33, 35, 38–40] but is yet to be used for species that utilise terrestrial locomotion. This is partly because of the difficulty for determining the speed of terrestrial animals , a process which is simpler underwater where mechanical methods can be used due to the density and viscosity of water [42–50]. However, an ability to estimate speed reliably for land animals should, in fact, make terrestrial dead-reckoning more straightforward than for aquatic or volant species  because terrestrial movement is not subject to drift due to air flow  or ocean currents . Thus, the primary difficulty for terrestrial dead-reckoning may simply be the measurement of speed, and, were this to be provided, that this approach should provide a means to determine latent positions of animals between less frequent location data obtain by other means of telemetry .
Recently though, Bidder et al.  have shown that dynamic acceleration, as measured by animal borne inertial sensors, provides a means to estimate speed by proxy. Although the relationship between speed and dynamic acceleration can be perturbed by variations in substrate and incline , potential cumulative errors such as these [31, 38] could be corrected by periodic ground-truthing by a secondary means of telemetry. Indeed, this remains the most workable theoretical solution for terrestrial dead-reckoning, with the additional benefit that the use of accelerometers also enables behavioural analysis [54–56]. However, the terrestrial dead-reckoning method and the procedure for correcting tracks to verified positions has yet to be illustrated explicitly.
The present study details how terrestrial dead reckoning can be achieved using a novel correction method that couples accelerometer and magnetometer data to periodic ground-truths, obtained by a secondary means such as GPS telemetry.
The dead-reckoning procedure for terrestrial animals
Computing acceleration components
This metric is used as a proxy for speed , below, while the static acceleration values are used to help calculate the attitude or pitch and roll of the device. Note that VeDBA values are the instantaneous measurements of dynamic acceleration for any given sample.
Computing pitch and roll from accelerometers
This proposed method calculates pitch and roll based on derivation of static acceleration using low-pass filtering based on a running mean, and is therefore prone to inaccuracies when animal movement is highly variable or sudden [61–64]. However, attitude is often measured using combined accelerometers and gyroscopes [59, 65–67] and certainly gyroscopes calculate attitude more accurately than accelerometers alone [62–64]. The question is whether this makes a real difference in dead-reckoning studies. Certainly, the limited difference in derived attitudes from accelerometers versus gyroscopes in wild animal studies [62–64] would imply not, especially since accelerometers alone reliably estimate attitude during periods of steady locomotory activity . In addition, gyroscopes must record at very high sampling rates (>100 Hz), and have substantive power and memory requirements [63, 64] which precludes their use on many free-living animals with realistic package sizes and deployment periods [63, 64]. Indeed, it has been claimed that such inertial reference systems have weight, power requirement and costs that are tenfold those of simple accelerometer systems . Other methods of deriving static acceleration from accelerometers without the need for gyroscopes exist, such as using a combination of Fast-Fourier transformation and low-pass finite impulse response filters [59, 69], or various other low-pass filters and approaches [44, 58, 70, 71]. We used the running mean method because it was already required to calculate the metric for dynamic acceleration, VeDBA  and because it has been demonstrably successful. Importantly though, the calculated static acceleration is only obtained to inform the orientation calculations, and the correction method for dead-reckoned tracks (see below) should filter any minor differences generated by using different static acceleration values in this stage of analysis.
Hard and Soft iron corrections for magnetometers
The earth’s magnetic field can be distorted by the presence of ferrous materials or sources of magnetism near the magnetometer and this can result in errors in heading derivation due to the magnetometer’s susceptibility to magnetic distortions . Few papers in the biological literature for dead-reckoning give explicit consideration to magnetic deviation in this manner [29–31, 33, 38], despite there being considerable discussion of its impacts within the engineering literature [73–76]. There are two primary sources of error in heading calculation from digital magnetometers; soft iron and hard iron magnetic distortions . In the absence of magnetic distortions and after normalising the compass data for each axis, rotating the magnetometer through all possible orientations should produce a sphere when the data are plotted in a 3-dimensional scatterplot. This is because the magnetic field detected on each axis is the trigonometric product of the vector angle (i.e. heading) between them .
Normalizing compass data
Rotating axes according to pitch and roll
Derivation of heading
Calculation of speed from VeDBA
Verification of calculated paths
Results and Discussion
Validation of terrestrial dead-reckoning
Example studies on animals
The viability of the dead-reckoning procedure will be dependent on a large number of particularities (such as the terrain and the quality and frequency of the GPS fixes etc.) associated with the study animal in question. Thus, we present example results of dead-reckoning systems, deployed largely on domestic animals so as to be able to derive errors more readily, to give a general idea of the suitability of this procedure to determine terrestrial animal movements.
‘Daily Diary’ accelerometer loggers (wildbyte-technologies, Swansea, UK) and ‘i-gotU’ GPS data loggers (Mobile Action, Taipei City, Taiwan) were used to record both location and movement in a domestic dog (Canis lupus familiaris), horse (Equus ferus caballus), cow (Bos Taurus) and a badger (Meles meles) in deployment periods that lasted up to approximately 24 h. Loggers were attached using a leather neck collar to the badger and dog, to the saddle pad of the horse and by a surcingle-belt to the cow. Daily diaries recorded at 40Hz. GPS loggers recorded every 5 s for horse and dogs, 20s for cattle and every 60 min for badgers. Daily diaries weighed 28.0 g and had dimensions 46 × 19 × 39 mm. GPS loggers weighed 21.2 g and had dimensions 13 × 43 × 27 mm. The battery longevity for both the accelerometers and the GPS loggers was approximately 10 days.
Dead-reckoning versus GPS
Details for accordance between GPS and dead-reckoned positions prior to and post correction procedure for data derived from animals using DDs recording tri-axial acceleration and tri-axial magnetic field strength, with 12-bit resolution, at a sampling frequency of 20 Hz with GPS loggers (iGotU GT-120, Mobile Action Technology) recording at 0.2 Hz. Devices (61 g) were collar-mounted in the dogs, and placed on the saddle pad above the withers in the horse
Mean Error before correction (m)
Mean Error after correction (m)
Summary of track length estimations according to GPS telemetry and dead-reckoning for data presented in Table 1. The tortuosity was calculated as average change in heading between measurements (at 40 Hz)
GPS Length (km)
Dead Reckoning Length (km)
In particular, although there was relatively little variation in the speed correction factor over time, the heading correction was, at times, radically different from that initially computed using the acceleration- and magnetometry-derived data (Fig. 12). The cause for this is due, in part to the high frequency of GPS fixes, the error in those fixes and the speed of the animal. Another possible source of errors may be associated with the estimation of static acceleration (used in the orientation correction of magnetometer data) via smoothing of the data. Further studies should be able to assess this by using more than one method to estimate static acceleration and monitoring if heading estimations differ.
This highlights why temporally finely resolved GPS positional estimates require such radical heading corrections in headings derived using dead-reckoning. In slow-moving animals such as cows (Fig. 13), GPS fixes can be calculated as being several metres in front of the true position and several metres behind in an animal that is moving slowly in one direction. In such a case, corrected dead-reckoned tracks will, at times, have to use a heading that is the exact opposite of that derived using the magnetometry data. This problem will presumably diminish as GPS fixes become less frequent and as the speed of the animal increases.
Potential and pitfalls in ground-truthed terrestrial dead-reckoning
This exploratory work suggests that dead-reckoning is a viable means to track terrestrial animal movements on a fine scale. One notable advantage of terrestrial, compared to fluid-based dead-reckoning, is that there is no drift due to horizontal vectors such as wind or currents . However, dead-reckoned data must be periodically ground-truthed because system errors, such as imperfect tag orientation on the animal and terrain effects [52, 53], cause the track to become uncoupled from the environment. The appropriate frequency and quality of such ground-truthed points is complex. GPS loggers used on wild animals typically record at fix at periods ranging over seconds [87–89], hours [90, 91], days  or even months  and have errors that depend on the permissiveness of the environment [18–20, 85] so a clear next stage in this work is to derive a rule book for maximizing the value of both GPS and dead-reckoned data according to the questions being asked. In environments in which accurate GPS locations are not possible (e.g. under dense canopy cover [17, 20, 94–98]) ground-truthing may be more reliably achieved using Radio Frequency Identification (RFID) stations or camera traps at known locations.
Implications of dead-reckoned tracks for understanding movement ecology
While the advantages of GPS-derived data are clear, those of dead-reckoned data have received less attention, perhaps because of the limited number of users. Importantly though, dead-reckoned data show relative movement with very fine resolution, with better coherence of these data the closer they are in time to each other. With the advent of novel open-source analysis software (see , in this volume), dead-reckoning may also be implemented with little computational acumen or programming skill. Thus, we expect researchers to be able to use movement defined by dead-reckoned tracks over seconds to be able to resolve behaviours, examining 2- or 3-d space use as a template in the same manner as accelerometry data .
Currently, the majority of studies of animal movement are based on infrequent positional fixes obtained via transmission telemetry, calculating distance by assuming straight line travel between fixes . The assumption of such straight line paths ignores sub-fix tortuosity in animal paths  and leads to obvious underestimations of animal travel distance, both theoretically (Fig. 2; [102–104]) and practically [100, 105–107]. Such issues become critical for examining models such as Lévy Walk, where animal movement should be scale-independent (see  and references therein) and needs to be examined as such [85, 109]. Solutions require sampling animal position with higher temporal resolution [110–112], which may be possible for larger animals [86, 109] with improvements in GPS technology  but, ultimately, fixes need to resolve the minimum radius tortuosity .
The GPS-enabled dead-reckoning method described in the current study is the only method by which distance and animal tortuosity can be measured accurately independent of any bias due to scale [31, 38]. Not only should this method provide new information on the habits of animals, but it offers a means for acquiring data on, and testing recent theoretical developments in movement ecology such as Correlated Random Walks, Levy Flights and State-space models (c.f. [114–122]). Given that tortuosity and movement patterns are likely to vary between species, populations and individuals, this new tool available to animal ecologists may be the only means to measure this variation properly, and should be considered a significant development in the understanding of movement ecology [100, 123].
Dead-reckoning has the potential to record the fine scale movement of terrestrial animals. To obtain the same level of detail from GPS telemetry alone, devices would require large amounts of power and could induce bias at small scales. Despite dead-reckoning having been employed on aquatic species, numerous methodological barriers restricted its use on terrestrial species. This study is the first explicit demonstration of terrestrial dead-reckoning and should provide adequate information to be used by those researchers of terrestrial species that are currently limited to temporally sparse GPS telemetry. These continuous, fine scale dead-reckoned tracks should record animal movement on a step by step basis, providing a complete account of animal location and movement. Initially, estimation of speed for integration in dead-reckoning calculations was problematic for terrestrial animals, but this issue has been largely overcome by use of accelerometers and a novel correction method that makes use of secondary ground truth positions. This technique has the potential to develop our understanding of animal movement ecology, and inform movement models that better reflect the true nature of animal movement patterns.
Availability of supporting data
A video detailing the dead reckoning validation experiment and illustration of results depending on different correction regimes is available in Additional File 1.
OB was funded by a KESS PhD studentship and an Alexander von Humboldt Post-Doctoral Fellowship. JSW was funded by an EPSRC doctoral training grant. IEM and EAM were funded by PhD studentships from the Department of Employment and Learning (DEL) and the Department of Agriculture and Rural Development (DARD), Northern Ireland, respectively. Thanks go to Megan Woodhouse for her assistance in data collection on the horse.
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