Elsevier

Journal of Biomechanics

Volume 37, Issue 12, December 2004, Pages 1891-1898
Journal of Biomechanics

Accuracy of non-differential GPS for the determination of speed over ground

https://doi.org/10.1016/j.jbiomech.2004.02.031Get rights and content

Abstract

Accurate determination of speed is important in many studies of human and animal locomotion. Some global positioning system (GPS) receivers can data log instantaneous speed. The speed accuracy of these systems is, however, unclear with manufacturers reporting velocity accuracies of 0.1–0.2 ms−1. This study set out to trial non-differential GPS as a means of determining speed under real-life conditions.

A bicycle was ridden around a running track and a custom-made bicycle speedometer was calibrated. Additional experiments were performed around circular tracks of known circumference and along a straight road. Instantaneous speed was determined simultaneously by the custom speedometer and a data logging helmet-mounted GPS receiver. GPS speed was compared to speedometer speed. The effect on speed accuracy of satellite number; changing satellite geometry, achieved through shielding the GPS antenna; speed; horizontal dilution of precision and cyclist position on a straight or a bend, was evaluated. The relative contribution of each variable to overall speed accuracy was determined by ANOVA. The speed determined by the GPS receiver was within 0.2 ms−1 of the true speed measured for 45% of the values with a further 19% lying within 0.4 ms−1 (n=5060). The accuracy of speed determination was preserved even when the positional data were degraded due to poor satellite number or geometry. GPS data loggers are therefore accurate for the determination of speed over-ground in biomechanical and energetic studies performed on relatively straight courses. Errors increase on circular paths, especially those with small radii of curvature, due to a tendency to underestimate speed.

Introduction

Accurate determination of an individual's speed is fundamental to many studies of human and animal locomotion. Speed is the rate of change of position and its determination requires measurements of distance and time components, which can be achieved directly or indirectly. Most commonly used methods for determining an individual's speed require direct measurement of both distance and time. Chronometry over a known distance using a simple stopwatch (Sharp, 1997) or by more accurate means such as light gates is limited to use under controlled conditions, on a pre-defined track. In addition, chronometry only determines average speed over the course; fluctuations of speed or route taken are ignored. Alexander used the time taken to pass a defined landmark on video film of free-running ungulates to calculate speed, but recognised the limited accuracy of the method due to the frame rate of the camera (Alexander et al., 1977) and parallax effects. High-speed video motion analysis and differentiation with respect to time of the position of a fixed marker can provide speed data many times per second, however, such systems are expensive, only effective within a limited volume and usually rely on infrared light, which limits their application outdoors. Indirect methods of predicting speed include foot-mounted pedometers (Saris and Binkhorst, 1977) or measurement of stance time via accelerometers (Weyand et al., 2001). Laser speed guns, which rely on the principle of Doppler shift, are commonly employed for the determination of vehicular speed, the velocity of ballistics and the speed of movement of small mammals (Marsden and King, 1979). However, these techniques are limited to single point, instantaneous measurements. Integration of body-mounted accelerometer signals is possible but error handling during integration is difficult (Perrin et al., 2000; Herren et al., 1999).

An increasingly popular method of determining an individual's position is the Global Positioning System (GPS). GPS was originally developed as a military tool. It comprises a network of ground-station controlled satellites, which emit low power radio signals containing atomic clock time data. Transit-time delays in these time signals are used by the ground-based GPS receiver to triangulate position. In order to limit the potential accuracy of the system, small random errors were introduced into the satellite clock signals by the US government (termed selective availability, or SA). This spurred the development of several approaches to enhance the accuracy of GPS. Differential GPS (dGPS) compares the known position of a fixed receiver with that determined by satellite triangulation. The difference is then used to correct the transit time of individual satellite signals either in real time via a radio link or, less commonly, in a collected data set during subsequent analysis. It is currently not clear, however, whether the improved positional accuracies of dGPS are mirrored by enhancements in the accuracy of speed determination, since GPS speed determination does not rely solely on differentiation of position data over time but also depends on Doppler shift of the carrier wave.

Further increases in positional accuracy can be achieved by determining the phase difference in the carrier wave signal from a satellite as seen by two neighbouring receivers (carrier wave differentiation). Sub-centimetre accuracies have been reported for this system (Leick, 1995) and it has been employed in studies for the measurement of both trunk position (Terrier et al (2000), Terrier et al (2001)) and speed (Larsson and Henriksson-Larsén, 2001). Schutz and Herren (2000) report accuracies with a standard deviation of 0.03 m s−1 for running with this system. The equipment is however both costly and bulky since units weigh 2 kg or more (Leica System 500, Leica Geosystems, Heerburg, Switzerland) and are therefore of limited potential for many studies of field locomotion. Further, the discontinuation of SA in May 2000 has meant that the accuracy of standard, non-differential GPS systems is improved for position and possibly for speed determination. The development of satellite-based differential systems such as Wide Angle Augmentation System (WAAS) and European Geostationary Navigation Overlay Service (EGNOS), which transmit correction data via satellite rather than land-based radio beacons, may mean that, in future, units the size of current non-differential units but with the accuracy of basic differential GPS will be available.

Improvements in technology, including reduced time-to-fix (TTF), as well as miniaturisation of GPS receivers for implementation in automobiles and mobile phones (7 g OEM modules are now available), has stimulated interest in GPS for applications in animal tracking (Steiner et al., 2000; von Hünerbein et al., 2000). Battery requirements are still a constraint, however, due to the high power consumption of GPS receivers. Low power duty cycling can be undertaken for studies in animal tracking; however, continuous data are often required for applications involving speed measurement. The positional accuracy of GPS systems since SA removal has been determined (Adrados et al., 2002) but validation of non-differential GPS for velocity determination has not been undertaken. Manufacturers quote accuracies in the region of 0.1–0.2 m s−1, with the specific algorithm employed being the variable which most influences accuracy between manufacturers. However, due to commercial confidentiality further information on how the system calculates speed and the limitations of the system are not forthcoming.

The accuracy of the Global Positioning System is influenced by several variables. The number of satellites available to the receiver is clearly important and a theoretical minimum of four satellites is required to obtain a 3D position fix. In addition, the geometrical arrangement of the satellites relative to each other and the receiver affects the quality of the triangulation for position. This is quantified in a measurement known as dilution of precision (DOP), which is inversely proportional to the volume of a cone delineated by the position of the satellites and the receiver. An ideal DOP of 1, i.e. the greatest predicted accuracy of triangulation, will be seen when one satellite is directly overhead and the remainder are equally spaced around the horizon. In contrast, higher DOP values will be seen if the satellites are tightly clustered overhead and the maximum value of 50 means that the fix is unreliable. Clearly, the orientation of the satellites and the identity of the satellites used changes over time and thus experimental conditions cannot be wholly standardised. The response of the GPS system to changing satellite availability is of interest for potential application of the system in conditions of less than ideal sky-view.

This study was designed to test the hypothesis that non-differential GPS is an accurate and reliable method for the determination of speed over ground.

Section snippets

Materials and methods

The speed of a cyclist was determined simultaneously by GPS and by a custom designed bicycle speedometer during a series of trials under varying conditions. These data were used to determine GPS accuracy during cycling at constant speed around a running track, on curves of two different radii, on a straight road and during rapid acceleration/deceleration.

A road-racing bicycle was instrumented with a Hall-effect proximity switch (RS Components Ltd., part no. 307–466, Northamptonshire, UK), which

Experiment 1

A total of 5060 GPS speed values were recorded during the track study. The actual speeds achieved by the cyclist ranged from 2.1 to 10.8 m s−1. The cyclist consistently failed to achieve the highest target speed of 35 km h−1, dropping as low as 25% below it.

The speed determined by the GPS receiver was within 0.2 m s−1 of the true speed measured for 45% of the values (Fig. 2) with a further 19% lying within 0.4 m s−1. A negative error (i.e. GPS underestimation of speed) of greater than 1.0 m s−1 was seen

Discussion

The hypothesis of this study was that GPS is an accurate and reliable method for the determination of speed over ground. The results show that GPS is generally accurate for speed determination under all conditions where a position fix is obtained although some erroneous values are generated.

The accuracy of the wheel speedometer is critical to the results of the study. Wheel diameter was determined from the running track experiments using the lap distance and the total number of revolutions over

Conclusion

The GPS is accurate for the determination of speed over ground (about 10 times more accurate than a car odometer) when moving at relatively constant speed in straight lines and is competent at determining speed on curved paths, although some overshoot does occur during transitions. Absolute error increases slightly at higher speeds but in percentage terms is less. In addition, when the system is tested under conditions of sudden changes in speed some inadequacies become evident. The system

Acknowledgements

We thank the Horserace Betting Levy Board for funding THW and the BBSRC for contributing to the work carried out here.

References (16)

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