The validity of a non-differential global positioning system for assessing player movement patterns in field hockey

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1 Journal of Sports Sciences, January 15th 2009; 27(2): The validity of a non-differential global positioning system for assessing player movement patterns in field hockey HANNAH MACLEOD 1, JOHN MORRIS 2, ALAN NEVILL 3, & CAROLINE SUNDERLAND 1 1 School of Science and Technology, Nottingham Trent University, Nottingham, 2 School of Sport and Exercise Sciences, Loughborough University, Loughborough and 3 School of Sport, Performing Arts and Leisure, University of Wolverhampton, Walsall Campus, Walsall, UK (Accepted 20 August 2008) Abstract Nine games players (mean age 23.3 years, s ¼ 2.8; height 1.73 m, s ¼ 0.08; body mass 70.0 kg, s ¼ 12.7) completed 14 laps of a measured circuit that incorporated intermittent running and directional changes, representative of the movements made by field hockey players during match-play. The distances and speeds recorded by a global positioning satellite (GPS) system (Spi Elite TM ) were compared statistically with speed measurements made using timing gates and distances measured using a calibrated trundle wheel, to establish the criterion validity of the GPS system. A validation of the speed of movement of each participant separately was also made, using data from each timing gate, over a range of speeds. The mean distance recorded by the GPS system was 6821 m (s ¼ 7) and the mean speed was 7.0 km h 71 (s ¼ 1.9), compared with the actual distance of 6818 m and recorded mean speed of 7.0 km h 71 (s ¼ 1.9). Pearson correlations (r) among timing gate speed and GPS speed were 0.99 (P ) and the mean difference and 95% limits of agreement were km h 71. These results suggest that a GPS system (Spi Elite TM ) offers a valid tool for measuring speed and distance during match-play, and can quickly provide the scientist, coach, and player with objective information about certain movement patterns during competitive games. Keywords: Team sports, performance analysis, match analysis, satellite positioning Introduction The greater the understanding of the specific demands imposed upon sports performers by match-play and training, the more likely it is that appropriate training and recovery programmes will be developed and employed, which may lead to enhanced performance and perhaps even a reduced risk of injury or ill health. A variety of methods have been used to evaluate the physiological strain and movement patterns associated with a variety of sporting and physical activities, including assessment of heart rate response (Lothian & Farrally, 1992), lactate accumulation (Bangsbo, Norregaard, & Thorso, 1991), and distances covered, via motion analysis and digitization (Di Salvo, Collins, McNeill, & Cardinale, 2006; Duthie, Pyne, & Hooper, 2005; Pers, Bon, Kovacic, Sibila, & Dezman, 2002; Reilly & Thomas, 1976; Roberts, Trewartha, & Stokes, 2006). All of these methods have limitations, including expense, the time required to analyse the raw data, obscured views, and potential problems arising from operator, hardware, and software errors. Global positioning satellite (GPS) systems are a recent technology that offer another method of assessing movement patterns in sports performers and others, and hence have the potential to contribute to a better understanding of the physiological and movement challenges they have to overcome. Global positioning satellite-based systems typically utilize a network of 24 satellites in orbit around the Earth. Each satellite is equipped with an atomic clock that emits, at the speed of light, the exact time and the position of the satellite. The GPS receiver compares the time emitted by each satellite signal. The lag time, measured by the receiver, is translated into distance by trigonometry. By calculating the distance to at least four satellites, the exact position and altitude of the receiver on the Earth s surface can be determined (Townshend, Worringham, & Stewart, 2008). Originally, GPS technology was restricted to military uses, but in the 1980s it was Correspondence: H. MacLeod, School of Science and Technology, Nottingham Trent University, Clifton Campus, Nottingham NG11 8NS, UK. ISSN print/issn X online Ó 2009 Taylor & Francis DOI: /

2 122 H. MacLeod et al. made available for civilian use, although a deliberate error was put into the system. The effect of the deliberate error could be reduced by use of differential GPS, which incorporates stationary receivers placed at known locations on the ground comparing their fixed position with the position given by the orbiting satellites (Larsson, 2003). However, in 2000, the US Department of Defense reduced the deliberate error put into the system, allowing for an increase in the accuracy of the nondifferential variant of the GPS technology (Larsson, 2003). Townshend and colleagues (2008) have argued that this change was important because non-differential systems are lighter, smaller, cheaper, and require less complex data collection procedures, which means non-differential GPS technology could have useful applications in many sporting contexts. To utilize GPS technology during match-play and training, Larsson (2003) argued that a valid reliable system would need to possess specific features: for measurements to be sufficiently accurate and precise, a nine-channel GPS receiver (at least) would be required; a suitable device would need a large memory capacity and interface with a computer for downloading; and a suitable device would need to be located with clear visibility to the sky. Such systems have been developed and have been used for the measurement of distances and speeds during physical activity and training (Larsson, 2003; Schutz & Herren, 2000; Terrier, Ladetto, Merminod, & Schutz, 2001; Townshend et al., 2008; Witte & Wilson, 2004). However, the validity of these systems for accurately measuring certain movement characteristics during match-play or training in field hockey, or in other intermittent sports such as association football and rugby union, has not been established. Also, to date, no published studies have assessed the validity of a non-differential GPS system, incorporating a triaxial accelerometer, which allows acceleration, impacts, and specific movements to be identified. Validity is generally referred to as the ability of a measurement tool to reflect what it is designed to measure (Atkinson & Nevill, 1998). There are four types of validity (logical, content, criterion, and construct) that reflect the wide variety of circumstances under which measurements are made (Thomas, Nelson, & Silverman, 2005). Criterion validity assess the extent to which scores on a test are related to some recognized standard (Thomas et al., 2005). In the present study, criterion validity was determined, with respect to distance and speed, for a non-differential GPS system, incorporating a triaxial accelerometer. Although GPS technology has great potential to enable sports scientists to describe and analyse more accurately the activity pattern of games players, and to assess the characteristics of competitive sport, it has not been thoroughly evaluated. The aim of the present study was to assess the criterion validity of a non-differential GPS system for assessing player movement patterns (i.e. the distances covered at particular speeds) during field hockey matches. Methods Participants Five male and four female participants volunteered for the study, all of whom had at least two years experience of games play. Their mean age, height, and body mass were 23.3 years (s ¼ 2.8), 1.79 m (s ¼ 7.9), and 70.0 kg (s ¼ 12.7) respectively. All participants completed the validity trials. In addition, seven of the nine participants also completed the time-of-day trials. The study had institutional ethics committee approval and informed consent was obtained from all participants. Procedure To ensure that the exercise undertaken by the participants in the study had ecological foundation, a time motion analysis of international field hockey players during National League games in the season was used as the basis for the movement patterns required in the circuit described below (MacLeod, Bussell, & Sunderland, 2007). Using these time motion data, a circuit was developed that required participants to perform a variety of field hockey-related movements, including a T-shaped shuttle drill (13.0 m), a straight-line shuttle (52.3 m), a straight-line sprint shuttle (26.0 m), and a zigzag shuttle (8.5 m) (Figure 1), in addition to walking and variable-speed running. All movements were in a forward direction apart from during the T-shaped shuttle drill, which incorporated side-stepping, backwards and forward movement. All participants were required to complete 14 laps of the measured circuit, which was painted onto an Astroturf sports surface. The time taken to complete the 14 laps averaged 52 min (s ¼ 4) and the participants completed 6818 m in total. This time and total distance were again based on the typical duration of involvement in a hockey match and the typical distance completed (MacLeod et al., 2007). Timing gates were used to record the time taken to complete each of the four shuttle movements (Brower Timing, USA). A stopwatch (Quantum Quartz, China) was used to time each lap and the total time taken to complete the trial to the nearest second. A trundle wheel pedometer was used to

3 Validity of GPS for assessing player movements 123 Figure 1. Plan of circuit and movement patterns. measure the exact length of the circuit. The trundle wheel was calibrated using a known distance (Fisco tape measure, UK, British Standard) so that it measured 1.0 m per full revolution. Each participant was verbally instructed as to which motion was required for each section of the circuit. Players were tracked over the entire circuit using a GPS athlete-tracking device (SPI Elite TM, GPSports, Canberra, Australia). The GPS unit was placed in a backpack harness and positioned between the participant s shoulder blades. The total weight of the device was 76 g. For the GPS unit to receive a signal, it was essential that the participant be outdoors with a clear view of the sky. The GPS unit measures at 1 Hz and the integrated accelerometer at 100 Hz. After completion of the circuit, the data were downloaded to a personal computer. The data were analysed using software (V , GPSports, Canberra, Australia) to establish the time, speed, and distance at each timing gate, for each lap, and for the whole circuit. Validity Validity was determined by comparing the GPS distance and speed with the actual distance, time, and speed of the participant at various stages of the predetermined circuit. The distances for the four shuttle movements (13.0 m, 52.3 m, 26.0 m, 8.5 m; n ¼ 126; nine participants completing 14 laps), each lap (487 m; n ¼ 126), and total distance (6818 m; n ¼ 9) were assessed. The time and thus mean speed recorded by the timing gates for the four shuttle movements were compared with the mean speeds reported by the GPS for these same four movement patterns for the group data. The start of the four shuttle movements for the GPS was determined by the position and trace on the map (all required at least a 908 change in direction) and verified by the change in speed and acceleration. The mean speed for each lap, determined by the circuit distance divided by stopwatch time, was also compared with the mean speed reported by the GPS system. A further validation of the speed of movement of participants was also made, using data from each timing gate and data from each participant separately over a range of speeds. Time of day Seven participants completed triplicate trials at different times of day. Each trial was conducted on a different day at , 13.00, and h to determine whether satellite or GPS positioning had any effect on the validity of the system. The position of the GPS will depend on the participant s cadence and gait. Total distance and distance per lap during the triplicate repeat trials were compared. The effect

4 124 H. MacLeod et al. of time of day upon speed measurements was assessed by comparing the accuracy of the speed recordings at 09.00, 13.00, and h. Statistical analysis To assess criterion validity, the Bland and Altman 95% limits of agreement were employed (Bland & Altman, 1986). The data were tested for heteroscedasticity by plotting a figure of absolute difference against the mean and computing the correlation (Atkinson & Nevill, 1998). A Pearson product moment correlation was used to assess the validity of the speed measurements recorded at each of the four gates for each of the nine participants. A one-sample t-test was used to compare differences in the measured distance with that recorded by the GPS, for each timing gate. Paired t-tests were used to compare speed recorded by the timing gates with that derived from the GPS. To determine whether the time of day affected the results, a one-way analysis of variance (ANOVA) with correction for sphericity was used to establish if there was any difference in the accuracy of the speed measurements, and any difference in the accuracy of the total distance measurements at 09.00, 13.00, and h. The results are presented as means and standard deviations. Statistical significance was set at P Results Validity The Pearson correlation (r) for the mean speed recorded by the timing gates and the GPS for the shuttle movements was Figure 2 shows a mean difference and 95% limits of agreement of km h 71 for the mean speeds recorded by the GPS and the timing gates during the four shuttle movements. The data did not show any heteroscedasticity. Table I provides a summary of validity for the different speed measurements made at each timing gate, for each lap, and for the complete circuit. The t-test for the mean speed measured by the GPS and timing gates during the shuttle movements showed no difference for the T-shaped shuttle, straight line shuttle or zigzag shuttle. However, a significant difference was recorded for the straight line sprint shuttle (P ). Table II presents the speed measurements for each participant during the timed shuttle movements. The mean maximum speed recorded by the GPS for the nine participants was 20.2 km h 71 (s ¼ 2.2). The mean distance measured by the GPS was m (s ¼ 6.8), compared with an actual distance of m. Table III shows the validity for the distance measurements made by the GPS at each timing gate, for each lap, and for the total circuit. The one-sample t-test for the distances recorded at the four gates showed significant differences for all four shuttle movements (P ). For the T-shaped shuttle, straight line shuttle, and straight line sprint shuttle, the GPS overestimated the distance by 0.1 m (s ¼ 0.5), 0.2 m (s ¼ 0.6), and 0.1 m (s ¼ 0.5) respectively. For the zigzag shuttle, the GPS underestimated the distance by 70.1 m (s ¼ 0.4). Time of day The mean difference in speed between the recorded speeds (timing gates) and the GPS speed for each time of day are presented in Table IV. An ANOVA revealed no difference in the validity of the speed measurement at different times of the day. The mean for the total distance covered was m (s ¼ 6.5), m (s ¼ 7.6), and m (s ¼ 6.4) for the 09.00, 13.00, and h trial respectively. The ANOVA revealed no significant difference in the validity of the total distance measurements. Figure 2. Bland-Altman plot for speed at each timing gate (n ¼ 504; 9 participants completing 14 circuits with 4 timing gates per circuit). Mean difference + LOA ¼ km h 71.

5 Validity of GPS for assessing player movements 125 Discussion The aim of the present study was to investigate the criterion validity of a non-differential GPS system and its associated algorithms, to establish if the system could provide an adequate tool for assessing player movement patterns during field hockey matches. The correlations between the speed of participants measured via the timing gates and the values from the GPS system were all very strong (all r 0.99), suggesting that the GPS system generated valid measurements of how quickly performers were moving over a variety of speeds. That the system was able to assess participant speed adequately was also T-shaped shuttle Straight line shuttle Straight line sprint shuttle Zigzag shuttle Per lap Complete circuit (n ¼ 9) Table I. Validity for the speed measurements. Mean timing gate speed (+s) Speed (km h 71 ) Mean GPS speed (+s) Range Mean difference (+LOA) * Note: n ¼ 126 for 9 participants completing 14 laps; n ¼ 9 for each participant completing the circuit. *Significantly different from timing gate speed (p ). demonstrated by the mean difference + limits of agreement of km h 71 for the speeds measured during the four shuttle movements by the timing gates and the GPS. The non-differential GPS system studied also generated valid measurements of distance as the mean difference + limits of agreement for the total distance covered during the 14 laps of the circuit was m, and the range for the distance covered in total (6818 m) varied from 6810 to 6828 m. Satellite positioning at different times of the day did not affect the validity of the system. Therefore, it would appear that the nondifferential GPS system used in the present study does provide a valid measurement tool for assessing player movement patterns typical of those seen in field hockey, an intermittent sport. Various studies have investigated the validity of GPS systems for measuring distance and speed. It is difficult to compare the results of the present study with those of other research reported in the literature because of the different equipment, methods, and analyses used. Also, it has been argued that the specific algorithms employed by manufacturers has the greatest influence on the accuracy of a GPS system (Witte & Wilson, 2004), and thus the findings from a particular study are very specific. Nonetheless, among the studies that assessed the validity of differential GPS, the variant of the technology that utilizes land-based receivers to enhance a system s accuracy, mean errors of 0.8 and 0.1 m have been reported when walking and running over 110 and 247 m respectively (Larsson & Henriksson-Larsen, 2001), with correlation coefficients of 0.99 reported for speed assessed by chronometry and differential GPS (Schutz & Herren, 2000; Larsson & Henriksson-Larsen, 2001). In the present study, the mean difference + limits of agreement for the total distance covered was m, and the correlation coefficients for speed were all Therefore, the validity of the non-differential GPS system (with a 1-Hz sampling frequency and an Table II. Validity for the speed measurements recorded during the four shuttle movements for each participant. Speed (km h 71 ) Participant Mean timing gate speed (+s) Mean GPS speed (+s) Range Correlation (r) Mean difference (+LOA) Note: n ¼ 56 measurements for each participant; 14 laps with 4 timing gates per lap.

6 126 H. MacLeod et al. Table III. Statistical summary of the validity for distance covered for each shuttle movement. Distance (m) Actual distance (+s) Mean GPS distance (+s) Range Mean difference (+LOA) T-shaped shuttle * Straight line shuttle * Straight line sprint shuttle * Zigzag shuttle * Per lap Complete circuit (n ¼ 9) Note: n ¼ 126 for 9 participants completing 14 laps; n ¼ 9 for each participant completing the circuit. *Significantly different from actual distance (p ). Table IV. Difference in speed between the timing gate speed and GPS speed at 09.00, 13.00, and h (mean + s). Speed (km/h) Gate 1 (n ¼ 98) Gate 2 (n ¼ 98) Gate 3 (n ¼ 98) Gate 4 (n ¼ 98) Per lap (n ¼ 98) Complete circuit (n ¼ 7) h h h associated accelerometer) used in the present study does appear to be comparable with that of differential systems, which, certainly in the past, might have been expected to generate more accurate results than a non-differential system. Other research has been undertaken into the validity of non-differential GPS systems. Witte and Wilson (2004) evaluated a non-differential GPS system (1 Hz, no accelerometer) for measuring speed during cycling around a running track, around two circular areas of 16 and 30 m diameter, and along a straight road, at speeds from 15 to 35 km h 71. They found that 64% of the speed values generated by the non-differential GPS system were within 1.4 km h 71 of that of a calibrated custom-made bicycle speedometer, while 15.5% were at least 3.6 km h 71 different from the speedometer value. This seems to contrast with the mean difference + limits of agreement of km h 71 for the speeds measured during the four shuttle movements by the timing gates and the GPS (non-differential, 1 Hz, with accelerometer) in the present study. The system evaluated by Witte and Wilson (2004) was also less accurate when the cyclists were negotiating the circular areas. They concluded that the system was sufficiently accurate for determination of speed when moving relatively constantly in a straight line and when accelerations were steady, but the system was inadequate when changes in speed were rapid. Such conclusions are in contrast to those reached in the present study and certainly such a system would not be suitable for use in field hockey where rapid changes in movement and direction are common. However, Witte and Wilson (2004) did note that the inadequacy of the system to resolve rapid changes in speed was probably a function of the smoothing inherent in the system s mathematical algorithm, and the 1-s sampling frequency. Clearly, the algorithms used in the present system are able to account for rapid changes in speed, although it should also be recognized that in the present study the participants were running and not cycling and so the peak speed achieved was less than that of the cyclist evaluated by Witte and Wilson (2004). Townshend and colleagues (2008) also concluded that a non-differential GPS system (1 Hz, no accelerometer) offered a valid method of assessing human locomotion. In agreement with the present study, they found that the correlation between speed over a straight 60-m course and speed on a circular path of 10 m radius, measured by GPS and by electronic timing gates, was Also in line with the present study, they concluded that a nondifferential GPS system can provide a valid estimate of distance: they reported that the mean estimate of distance over a 100-m course was m (s ¼ 0.49). While non-differential GPS systems are a relatively recent addition to the forms of technology that can be used to assess player movement patterns, camerabased systems have been employed for this purpose and to assess the demands of various sports for over 30 years. Early systems relied on a single camera, and

7 Validity of GPS for assessing player movements 127 the reliability of time motion analysis using such technology to assess movement patterns in rugby union has been shown to be moderate to poor for time spent in a movement category ( % TEM), and good to poor for the frequency in a motion category ( % TEM; Duthie, Pyne, & Hooper, 2003). More recently, multiple-camera systems have been developed and these would be expected to show enhanced reliability and validity. A two-camera system was used to assess speeds during handball in a sports hall and root mean square errors of % were recorded for the speed measurements (Pers et al., 2002). Roberts and colleagues (2006) used a five-camera system to assess an individual s speed of movement and the distances they covered on a rugby union pitch, and found that the total distance estimated using digitized video was within 2.1% of the measured distance, while calculated speed was within 8.0% of that measured using photocells. The non-differential GPS system used in the present study certainly compares favourably with this, measuring distance to within 0.5% and speed to within 1.5% of the actual values, although obviously such a system cannot be used indoors and would have been unable to undertake the analysis conducted by Pers and colleagues (2002). However, it should be recognized that while video analysis provides detailed and valuable information, it can be very time-consuming, with Roberts et al. (2006) reporting it took 8 h to analyse the speeds and distances covered by one rugby union player in a match. More recently, a multiple-camera-based system that is able to track all players on the field of play at real-time has increased in popularity. Prozone 1 is a new computerized video system currently used by a number of soccer clubs. Di Salvo et al. (2006) assessed displacement velocities over a maximum distance of 60 m using such a system. Despite showing excellent correlations (r ¼ ) between Prozone 1 and actual velocity, no data were made available for distance covered and no attempt was made to assess the typical movement patterns and distances performed over the course of a game (Di Salvo et al., 2006). Although the non-differential GPS system used in the present study demonstrated criterion validity, and hence the potential for use in investigating player movement patterns, there are some potential problems with such systems that need to be recognized. Limited access to satellites in built-up areas or stadiums can make the utility of a non-differential GPS system questionable, and the use of such technology is illegal in sports and competitions (such as at World Cups and Olympic Games) where players are not permitted to wear equipment other than that needed to play. In addition, assessment of activities such as tackling or assessment of the direction of movement (running forwards or backwards) cannot be made without using GPS alongside video-based tracking. However, where conditions and regulations allow, and particularly during training, small global positioning satellite units can provide a relatively simple tool for the objective monitoring of individual sports performers and their training programmes. The practical implications of using non-differential GPS technology for assessing movement patterns are wide-ranging. Devices based on differential systems are too cumbersome for use in many sporting contexts, while non-differential GPS units are lighter, smaller, cheaper, and much simpler to use for data collection (Townshend et al., 2008). During competitive international field hockey matches, athletes reported no restriction to play while wearing the units. They are portable, non-invasive, and currently permitted during international field hockey matches and many similar team sports. Unlike current video-based methods, data analysis is relatively quick and feedback to a coach or sports scientist is possible within a few hours. Furthermore, the GPS system analysed in this study also included an accelerometer and incorporated heart rate telemetry, both of which can provide additional measures of physiological strain and training load, and are potentially methods for assessing energy expenditure. Two of the key advantages of a nondifferential GPS system over camera-based systems are that it is relatively inexpensive and does not require a stadium for camera positions (Witte & Wilson, 2004). Consequently, in sports where resources are limited and competitions take place in a variety of arenas, a non-differential GPS system could offer a relatively cheap, accurate, and userfriendly tool for assessing distance covered and movement patterns. The results of this study suggest that a nondifferential GPS system and its associated algorithms (Spi Elite TM ) could provide a valid tool for measuring speed and distance during hockey match-play and training. Although it does have some practical limitations, such a system does have the potential to provide the scientist, coach, and player with objective information about certain movement patterns during competitive games and during training. References Atkinson, G., & Nevill, A. M. (1998). Statistical methods for assessing measurement error (reliability) in variables relevant to sports medicine. Sports Medicine, 26, Bangsbo, J., Norregaard, L., & Thorso, F. (1991). Activity profile of competition soccer. Canadian Journal of Sport Sciences Revue Canadienne des Sciences du Sport, 16,

8 128 H. MacLeod et al. Bland, J. M., & Altman, D. G. (1986). Statistical methods for assessing agreement between two methods of clinical measurement. Lancet, 1, Di Salvo, V., Collins, A., McNeill, B., & Cardinale, M. (2006). Validation of Prozone: A new video-based performance analysis system. International Journal of Performance Analysis in Sport, 6, Duthie, G., Pyne, D., & Hooper, S. (2003). The reliability of video based time motion analysis. Jounal of Human Movement Studies, 44, Duthie, G., Pyne, D., & Hooper, S. (2005). Time motion analysis of 2001 and 2002 super 12 rugby. Journal of Sports Sciences, 23, Larsson, P. (2003). Global positioning system and sport-specific testing. Sports Medicine, 33, Larsson, P., & Henriksson-Larsen, K. (2001). The use of dgps and simultaneous metabolic measurements during orienteering. Medicine and Science in Sports and Exercise, 33, Lothian, F., & Farrally, M. (1992). Estimating the energy cost of women s hockey using heart rate and video analysis. Journal of Human Movement Studies, 23, MacLeod, H., Bussell, C., & Sunderland, C. (2007). Time motion analysis of elite women s field hockey, with particular reference to maximum intensity movement patterns. International Journal of Performance Analysis in Sport, 7, Pers, J., Bon, M., Kovacic, S., Sibila, M., & Dezman, B. (2002). Observation and analysis of large-scale human motion. Human Movement Science, 21, Reilly, T., & Thomas, V. (1976). A motion analysis of work-rate in different positional roles in football match-play. Journal of Human Movement Studies, 2, Roberts, S., Trewartha, G., & Stokes, K. (2006). A comparison of time motion analysis methods for field-based sports. International Journal of Sports Physiology and Performance, 1, Schutz, Y., & Herren, R. (2000). Assessment of speed of human locomotion using a differential satellite global positioning system. Medicine and Science in Sports and Exercise, 32, Terrier, P., Ladetto, Q., Merminod, B., & Schutz, Y. (2001). Measurement of the mechanical power of walking by satellite positioning system (GPS). Medicine and Science in Sports and Exercise, 33, Thomas, J. R., Nelson, J. K., & Silverman, S. J. (2005). Research methods in physical activity. Champaign, IL: Human Kinetics. Townshend, A. D., Worringham, C. J., & Stewart, I. B. (2008). Assessment of speed and position during human locomotion using nondifferential GPS. Medicine and Science in Sports and Exercise, 40, Witte, T. H., & Wilson, A. M. (2004). Accuracy of nondifferential GPS for the determination of speed over ground. Journal of Biomechanics, 37,

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