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.
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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.
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.
There are a number of stages required to obtain animal travel paths using dead-reckoning (Fig. 1), which require concurrent data from an animal-attached tag containing accelerometers and magnetometers with tri-axial orthogonal sensors recording at infra-second rates (e.g. typically >10 Hz). The stages are treated sequentially in detail below with brief discussion on potential system errors before the approach is trialled on animals to demonstrate performance.
where m is the constant of proportionality and c is a constant. During the dead-reckoning process (see below), the value for m can be changed iteratively until dead-reckoned paths and ground truth positions accord. In turn, speed (s) can be used to calculate distance, d, according to the time period length, t, as;
where the distance between the two coordinates is given in km. If the coordinates do not accord, the dead-reckoned track can be corrected according to the following procedure; For any time period, the distance between consecutive GPS positions is first calculated. This distance is then divided by the corresponding distance for the same time period calculated by dead-reckoning, providing a correction factor by which dead-reckoning over- or underestimates speed. Subsequently, all speed values (s) for this time period can be multiplied by the correction factor (Fig. 6).
Non-accordance of the two tracks after this is indicative of a heading error, most likely due to the long axis of the tag imperfectly representing the longitudinal axis of the animal. To correct for this, the heading between the two ground-truthed positions that start and finish the relevant time period is calculated, as is the heading between the start and end positions of the dead-reckoned track. Then, in a manner similar to the correction of speed, the heading for the ground-truthed positions is divided by the heading for the dead-reckoned track to provide the heading correction factor (Fig. 7). This factor is applied to the heading data used in all intermediate dead-reckoning calculations and the dead-reckoned track then recalculated. This procedure of correcting distance and heading continues iteratively until dead-reckoned tracks and ground-truthed positions align.
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.
Dead-reckoning- and GPS-derived positions are fundamentally different but give superficially similar results (Fig. 10). GPS-derived positional data show excellent spatial coherence at scales over 10 m and are independent of time. Dead-reckoned tracks replicate the major features shown by GPS-derived tracks but, when they have no ground-truthed points along them, are uncoupled from the environment and generally show decreasing coherence with respect to themselves over time (Fig. 10). Nevertheless, over small time and scale intervals, dead-reckoned data show features in movement that are often lost in GPS-derived positions. For example, during data acquisition used for Fig. 8, the horse was directed to move in tight circles, which are much better resolved than the GPS data.
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
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.
All this emphasises the value of dead-reckoning per se, in helping define very fine animal movements (Fig. 14), where such definition may even help identify animal behaviours although such data may not be in perfect spatial placement. Otherwise, dead-reckoning is clearly useful for filling in likely trajectories for animals where positional information via GPS is only gained infrequently although the errors will require much more work to formalise. However, this work points to appreciable problems that will need to be resolved when GPS-based positional information is acquired at high frequencies and dead-reckoning is to be used to derive a trajectory. One approach is to filter GPS point accuracy according to the number of satellites used to derive the positional fix, or similar metrics such as minimum distance or motion sensor threshold [86]. However, even this will never give perfect spatial resolution. A better way forward may be to combine such metrics with an error circle and consider the extent to which the dead-reckoned path may pass through it.
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 [99], 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 [56].
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.
Abstract:This paper proposes a pedestrian dead reckoning (PDR) algorithm based on the strap-down inertial navigation system (SINS) using the gyros, accelerometers, and magnetometers on smartphones. In addition to using a gravity vector, magnetic field vector, and quasi-static attitude, this algorithm employs a gait model and motion constraint to provide pseudo-measurements (i.e., three-dimensional velocity and two-dimensional position increment) instead of using only pseudo-velocity measurement for a more robust PDR algorithm. Several walking tests show that the advanced algorithm can maintain good position estimation compare to the existing SINS-based PDR method in the four basic smartphone positions, i.e., handheld, calling near the ear, swaying in the hand, and in a pants pocket. In addition, we analyze the navigation performance difference between the advanced algorithm and the existing gait-model-based PDR algorithm from three aspects, i.e., heading estimation, position estimation, and step detection failure, in the four basic phone positions. Test results show that the proposed algorithm achieves better position estimation when a pedestrian holds a smartphone in a swaying hand and step detection is unsuccessful.Keywords: SINS; PDR; MEMS-IMU; mobile devices; indoor positioning 2ff7e9595c
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