Accuracy of GNSS-Derived Acceleration Data for Dynamic Team Sport Movements: A Comparative Study of Smoothing Techniques

Abstract

This study examined the impact of various smoothing techniques on acceleration data obtained from a Global Navigation Satellite System (GNSS) device during accelerating and decelerating movements, resembling those commonly observed in team sports. Eight participants performed six different accelerating and decelerating movements at different intensities and starting speeds for a total of 46 trials each. The movements were collected concurrently at 10 Hz using a GNSS device (Vector S7, Catapult Sports) at 100 Hz using a motion analysis system (Vicon). Acceleration data were smoothed using (I) a fourth-order Butterworth filter (cut-off frequencies ranging from raw to 4.9 Hz), (II) exponential smoothing (smoothing constant ranging from 0.1 to 0.9), and (III) moving average (sliding window ranging from 0.2 s to 2.0 s). To determine the ability of a GNSS to quantify acceleration, a variety of measurement indices of validity were obtained for each movement and each smoothing technique. The fourth-order Butterworth filter with a cut-off frequency of 2 Hz (mean bias 0.00 m·s⁻², 95% LoA ± 1.55 m·s⁻², RMSE 0.79 m·s⁻²) showed the strongest relationship with the Vicon data. These results indicate that this smoothing technique is more accurate than those currently used and accepted on GNSS devices in the sports science community.

1. Introduction

Athlete tracking technologies, such as Global Navigation Satellite System (GNSS), have allowed for the quantification of athlete movement in team sports [1]. A GNSS device is used to determine the location of an athlete on Earth via trilateration, which is expressed as longitude and latitude and is used to determine athlete displacement [2]. Athlete speed is measured via Doppler-shift, which is a change in the satellite signal frequency caused by the movement of the GNSS device [3]. Speed derived from Doppler-shift is preferred over speed derived from positional differentiation (speed calculated by the derivative of distance caused by the change in the GNSS device location) due to its increased accuracy and lower error [4], and it is subsequently used to derive acceleration data. Some GNSS devices also include a triaxial accelerometer, gyroscope, and magnetometer, allowing for the measurement of variables such as player impact and human activity recognition [5,6]. It is important to note that accelerometer acceleration is not the same as that derived from the GNSS Doppler-shift speed.

Acceleration derived from GNSS speed is the most widely used type of acceleration data by practitioners and researchers in team sports [7]. Acceleration data are of great importance to inform team-sport performance, as changes in speed (acceleration or negative acceleration, i.e., deceleration) often occur in games [8]. Quickly changing speed in the shortest time possible (accelerate/decelerate) will, for example, allow players to be the quickest to the ball or avoid tackles. The ability of an athlete to reach their maximum speed in team sports is also often restricted by spatial limitations or opponents [9], highlighting the importance of accelerating and decelerating. Furthermore, accelerating and decelerating actions have been associated with increased muscle soreness and decreased neuromuscular performance in team-sport athletes [10]. Therefore, practitioners and researchers in team sports are interested in monitoring and quantifying acceleration and deceleration. Typically, the GNSS time series acceleration data recorded during team sport activity are quantified by converting the data into a summary metric. Commonly used acceleration metrics are time/efforts in acceleration zones [7,11]. The acceleration metrics can be used to design training programs to enhance performance, quantify training load, and reduce injury risk [12,13]. However, fundamental to the practicality of a GNSS to measure acceleration in team sports is the underlying validity of the time-series acceleration data.

All kinematic data, which are measures of human movement, are contaminated with noise [14]. The noise is any unwanted portion of a signal that typically has different characteristics from the true signal (e.g., lower in amplitude, different frequency range). Noise from the measurement of a human movement signal may be associated with electrical interferences, skin movement, or other factors [15]. Noise is exacerbated when differentiated, increasing its amplitude linearly with frequency [16]. Noise is exacerbated in the acceleration data of GNSS devices, as practically all GNSS systems obtain speed information, which must be differentiated to create acceleration data. To decrease the noise in GNSS speed data, some form of data treatment must be adopted. The general technique to remove noise with a different frequency to those in the true signal is known as smoothing [15]. Many smoothing techniques exist, where exponential smoothing, moving average, and digital filtering are widely used techniques for smoothing time-series data, each with distinct characteristics [7]. Users should be aware of how the different smoothing techniques affect their data to avoid errors [14]. For example, exponential smoothing applies a smoothing constant that weighs recent observations more heavily than older ones, allowing the signal to adapt to recent changes while reducing random noise [17]. This makes it computationally efficient and suitable for capturing trends. Moving averages, on the other hand, smooth data by averaging values within a sliding window, applying equal weight to all points within this window. While effective at removing short-term fluctuations, moving averages are less responsive to rapid changes in the data [15]. Digital filtering, such as a low-pass Butterworth filter, applies a frequency-based approach to smoothing, filtering out high-frequency noise components while preserving lower-frequency signals that often represent meaningful trends [15]. This frequency-selective method allows for the precise control over the bandwidth of smoothed data, making digital filters particularly adaptable for applications requiring the exact noise reduction parameters. Insufficient smoothing will maintain high levels of noise, and over smoothing could eliminate important portions of the signal by smoothing the peaks. As such, bad choices of smoothing techniques can be detrimental by distorting the true component of the signal of interest (e.g., lowering the amplitude of a high acceleration so much that it is removed from the summary metrics). For example, many GNSS acceleration metrics are threshold-based, where time/counts/distance spent in a threshold (e.g., ≥3 m·s⁻²) are analysed [2,7,18]. If a practitioner wants to know when their players have performed a high acceleration (≥3 m·s⁻²), applying bad smoothing could lower the acceleration values, resulting in the data not reaching the high threshold zone (although it was a high acceleration). Thus, determining the correct smoothing technique for a dataset is important, especially if summary metrics are of interest.

The acceleration data of GNSS devices have typically been validated across the literature with the criterion measure of an infrared camera-based motion capture system [19,20,21]. The sampling frequencies of the validated GNSS systems vary from 1 to 18 Hz [1,22]. The validity and reliability of GNSS data generally have smaller error margins for devices with increased sampling frequencies of ≥10 Hz [22,23], however, 10 Hz GNSS devices are superior to 5 Hz GNSS devices that are interpolated to 15 Hz [24]. The validity of 1 and 5 Hz GNSS devices is impacted by high rates of change in speed, running from stationary or slow-moving starts and changes of direction [25,26], where 1 Hz devices are less valid in complex courses [27]. Devices with sampling frequencies of ≥10 Hz are not greatly affected by short straight-line movements, frequent changes of direction, or high-speed movements [19,26,28,29]. It is recommended for practitioners to utilise a GNSS device with a sampling frequence of ≥10 Hz. Smoothing has shown to improve the validity of data [30,31]. However, GNSS manufacturer smoothing techniques have shown to be detrimental to effort-based acceleration summary metrics [18,20]. Currently, it is unknown as to how changes to the smoothing technique affect the acceleration of GNSS devices, which in turn affects the effort-based summary metrics.

In research using athlete tracking technologies, the smoothing techniques used are often not reported, limiting the reproducibility of the research and the ability to compare results [7,32]. Smoothing techniques are often not reported, as researchers and practitioners are unaware of the smoothing performed inside the manufacture’s software, and there is no consensus on the selection of the most suitable smoothing technique for obtaining valid acceleration data. Therefore, this study aimed to examine how various smoothing techniques changed the acceleration data obtained from a GNSS device during accelerating and decelerating movements, resembling those commonly observed in team sports. By investigating the effect of different smoothing techniques, valuable insights can be gained regarding the selection of the most suitable technique that minimises noise, maintains the true signal components, and ensures the validity of the acceleration data.

2. Materials and Methods

2.1. Participants

Nine participants, partaking in recreational team sports activities were recruited. All participants received verbal and written explanations of the study prior to participation. The study took place within a period of three days, with three participants each day. One participant was excluded from analysis due to equipment failure, resulting in a total study sample of eight participants (4 males, 4 females, age: 27 ± 3 years, height: 174.2 ± 7.7 cm, body mass: 71.6 ± 11.1 kg). Precision of the 95% limits of agreement (LoA) was used to assess the adequacy of the sample size to compare smoothing techniques. An expected standard deviation of the difference of 0.04 m·s⁻² between each smoothing parameter (e.g., cutoff frequencies) within each smoothing technique (e.g., Butterworth filter) was expected based on the pilot data. To confidently determine the most accurate smoothing technique, a precision (standard error) of the 95% LoA smaller than this expected difference was required. Therefore, the standard error of the 95% LoA needed to be <0.04 m·s⁻². To be confident in the data, a standard error of half the expected difference, which equalled 0.02 m·s⁻², was chosen. A minimum sample size of 8 was needed to achieve a 0.02 m·s⁻² error of the 95% LoA, which was based on precision calculations of the 95% LoA [33]. Note that the number (N) of participants does not reflect the sample size, but the N of the samples collected in total (trials) is used for pairwise comparisons and is of importance. Data collection was performed outside during daylight (9 a.m.–4 p.m.) on an empty synthetic soccer pitch that was not surrounded by stands. The procedures used in this study were conducted in accordance with the Declaration of Helsinki and received approval from the Human Research Ethics Committee of La Trobe University (reference number: HEC22066).

2.2. Equipment

The participants’ movements were measured concurrently with an athlete tracking technology device consisting of 10-Hz GNSS (Vector S7, Catapult Innovations, Melbourne, Australia) and a 3D motion analysis system (Vicon, Oxford, UK) sampling at 100 Hz. The GNSS device was placed between the athlete’s scapulae using the manufacturer’s vest with a tight fit to avoid unnecessary device movement. Data collection procedures were in accordance with the guidelines of Malone, Lovell, Varley, and Coutts [2], with each participant having their own specific device. The study sample had an average (±SD) horizontal dilution of precision (HDOP) of 0.72 ± 0.12 and 15 ± 3 number of satellites. A 10-camera motion capture system (Vantage 16, 18 mm, Vicon) was used to provide the criterion real-time measurements of distance, velocity, and acceleration (Figure 1). This system has previously been used to determine the criterion measurements for athlete tracking systems [19,34]. To ensure stable marker recognition within the 15 × 9 m measurement area, retro-reflective markers with a diameter of 26 mm were used. One retro-reflective marker was firmly attached to the participant on each of the following locations: (1) the outside of the manufacturer supplied vest, in correspondence with the middle of the GNSS device; (2) the acromion of each shoulder of the participant; (3) each anterior superior iliac spine; (4) fifth lumbar vertebra (Figure 2). The marker corresponding to the middle of the GNSS device was used for analysis; all other markers were used for gap filling where needed. Gaps in the data ≤ 50 ms (5 samples) were filled using spline interpolation or rigid body fill, gaps ≥ 50 ms were excluded from analysis. Out of all trials, 50 data samples (4 gaps) were excluded, which equalled 0.045% of data being excluded.

2.3. Data Collection

The GNSS devices were switched on 20 min prior to the start of data collection to ensure that they had a stable connection to the satellites. Participants performed a range of physical tasks in the capture area consisting of six different accelerating and decelerating movements, resembling those commonly observed in team sports [35]. Each participant performed the following movements (in order): two accelerating movements (linear movement, jump), two decelerating movements (stop, jump), and two combined accelerating and decelerating movements (change of direction < 90°, change of direction 90–180). To obtain a representative dataset, each movement was performed from a medium and maximum acceleration and deceleration intensity, and from a variety of starting speeds (standing still 0 m·s⁻¹, walking 1–2 m·s⁻¹, jogging 2–3.5 m·s⁻¹, sprinting > 3.5 m·s⁻¹). All movements originated from the start spot in Figure 1, unless the starting speed was standing still, then the participant started in the movement area. Each change in pace (e.g., medium or maximum acceleration/deceleration) as well as changes of direction, jumps, and stop of motion occurred within the movement area. For example, linear movement with a walking starting speed and maximum acceleration intensity: the participant started at the start spot, walked until they reached the movement area, and then maximally accelerated until they were outside the movement area. In the change of direction trials, participants decelerated prior to executing the directional change and accelerated upon exiting the change. All movements, descriptions, starting speeds, and accelerating/decelerating intensities can be found in

Table 1. Description of the different accelerating and decelerating movements performed in the trials with the corresponding starting speeds (standing still, walking, jogging, and sprinting) and acceleration and deceleration intensities (M = medium, X = max).

Movements	Definition	Still		Walk		Jog		Sprint
		M	X	M	X	M	X	M	X
Linear movement	Moving in one dimension, in a straight line, over a total distance of approximately 14 m.	✓	✓	✓	✓	✓	✓	✕	✕
Jump accelerating	Push off the ground and into the air using legs, with a shallow take off angle, over a total distance of approximately 8 m.	✓	✓	✓	✓	✓	✓	✕	✕
Stop	Cease of motion, over a total distance of approximately 8 m.	✕	✕	✓	✓	✓	✓	✓	✓
Jump decelerating	Push off the ground and into the air using legs, with a very steep take off angle, over a total distance of approximately 8 m.	✕	✕	✓	✓	✓	✓	✓	✓
COD < 90°	Change of direction less than 90 degrees from the previous direction either left or right over a total distance of approximately 14 m.	✕	✕	✓	✓	✓	✓	✓	✓
COD 90–180°	Change of direction between 90 and 180 degrees from the previous direction either left or right over a total distance of approximately 14 m.	✕	✕	✓	✓	✓	✓	✓	✕

✓ Trial was performed at the indicated starting speed and accelerating/decelerating intensity. ✕ Trial was not performed at the indicated staring speed and accelerating/decelerating intensity. M = medium, X = maximum intensity acceleration/deceleration. ■ The cells shaded in grey represent instances where a combination of decelerating and accelerating intensities was applied: M combinations (decelerating/accelerating): M/M (i.e., medium deceleration followed by medium acceleration) and M/X; X combinations were (X/X, X/M).

.

Catapult live-data streaming was used to obtain an indication of the starting speeds of the participant. It was impractical to assign specific thresholds to the accelerating and decelerating intensities, as these would vary depending on the starting speed (e.g., maximum accelerating from a jogging start will have a much lower acceleration than accelerating from standing still). Instead, the participants were instructed to accelerate or decelerate to their perceived maximum or medium intensity (half their perceived maximum). The intensities of similar trials were compared with Catapult live-data streaming to confirm that the participants’ perceived medium intensity was at most half their maximum intensity. For example, a trial with a stop from a jogging start with a 1.3 m·s⁻² medium intensity deceleration and a 2.8 m·s⁻² maximum intensity deceleration was included (1.3 m·s⁻² is ≤half of 2.8 m·s⁻²), while the same trial with values of 2.1 m·s⁻² medium intensity and 2.9 m·s⁻² maximum intensity deceleration was excluded (2.1 m·s⁻² is >half of 2.9 m·s⁻²). Trials that did not meet the criteria were repeated. A total of 46 trials per participant were included.

Prior to data collection, each participant completed a standardised warm-up followed by clear demonstrations and guidelines on the upcoming physical tasks. The participant performed two practice runs of each movement and was instructed to perform one counter movement jump, followed by standing still for 3 s at the start and end of each task. During data collection, one researcher coded the trials live, noting down the timestamp the participant performed each trial.

2.4. Data Analysis

Vicon data were labelled and processed with Vicon Nexus 2.14. Raw Vicon data were filtered with a fourth-order (zero lag) low pass Butterworth filter with a cut-off frequency of 6 Hz, which was determined based on residual analysis [30,34,36]. XY-coordinates of the filtered 100 Hz Vicon data were used for analysis; the z-coordinates (vertical-axis) were neglected in the calculations as the used GNSS tracking system does not collect data in the third dimension. The Vicon data were subjected to six different processing steps to calculate the acceleration data; for clarity and reproducibility, all processing steps are detailed and presented in

Table 2. Data processing steps performed in order on the Vicon data (raw coordinate data until acceleration data) and on the GNSS data (raw speed data until acceleration data).

VICON	GNSS
Raw coordinates: $[x_{raw}, y_{raw}]$ where $x_{raw}, y_{raw}$ are the raw Vicon coordinates.
Filtered coordinates: $\left[x_{filt}, y_{filt}\right]=\left[F\right(x_{raw}),F(y_{raw}\left)\right]$ where $x_{filt}, y_{filt}$ are the filtered coordinates. The filtering process ($F$) is a fourth-order (zero lag) low pass Butterworth filter with a cut-off frequency of 6 Hz, performed on the raw coordinates ($x_{raw}, y_{raw}$)
Distance between samples: ${Dp}_{\left(i\right)}=\sqrt{{(x_{filt (i+1)}-x_{filt \left(i\right)})}^2+{(y_{filt (i+1)}-y_{filt \left(i\right)})}^2}$ where $Dp$ is the distance between the samples calculated of the filtered coordinates ($x_{filt}, y_{filt}$); i is the index of a sample in the 100 Hz data.
Total distance: $D_{\left(i\right)}=\sum \left(j=1 to i\right) {Dp}_{\left(i\right)}$ where $D$ is the cumulative sum of the distance between samples ($Dp$).
Speed (first-order central difference method): $S_{\left(i\right)}={\displaystyle \frac{(D_{ (i+1)}-D_{ (i-1)})}{2t}}$ where $S$ is the speed calculated of the distance ($D$) and the sample rate of the Vicon data ($t=0.01 \mathrm{s}$)	Raw speed data: $W_{raw}$ where $W_{raw}$ is the raw Doppler-shift speed data of the GNSS, completely unfiltered by any software.
Filtered speed: $S_{filt}=G\left(S\right)$ where $S_{filt}$ is the filtered speed data. The filtering process ($G$) is a fourth-order (zero lag) low pass Butterworth filter with a cut-off frequency of 2 Hz, performed on the speed ($S$)	Filtered speed: $Q_{filt}=Z\left(W_{raw}\right)$ where $Q_{filt}$ is the filtered raw speed data. The following filters were tested for $Z$: Fourth-order (zero lag) low pass Butterworth filter with a cut-off frequency ranging from 0.5 to 4.9 Hz in steps of 0.1 Hz. Single exponential smoothing, with a smoothing constant ranging from 0.1 to 0.9 in steps of 0.1. Moving average, with a sliding window ranging from 0.2 s to 2 s in steps of 0.1 s.
Acceleration (first-order central difference method): $A_{\left(i\right)}={\displaystyle \frac{(S_{filt (i+1)}-S_{filt (i-1)})}{2t}}$ where $A$ is the acceleration data calculated of the filtered speed ($S_{filt}$) and the sample rate of the Vicon data ($t=0.01 \mathrm{s}$)	Acceleration (central difference method): $B_{\left(i\right)}={\displaystyle \frac{(Q_{filt (i+1)}-Q_{filt (i-1)})}{2t}}$ where $B$ is the acceleration data calculated of the filtered speed ($Q_{filt}$) and the sample rate of the GNSS data ($t=0.1 \mathrm{s}$).

. To select a suitable smoothing technique for the Vicon speed data, frequency analysis using fast Fourier transform and time–frequency analysis using a spectrogram were performed on the unfiltered Vicon speed data. The characteristics of team sport-specific human movement patterns and potential sources of error or variability in the data were studied and taken into consideration. The frequency bandwidth containing 99% of the total power of the speed signal was identified to be at 2 Hz. Therefore, a fourth-order (zero lag) low pass Butterworth filter with a cut-off frequency of 2 Hz was performed on the Vicon speed data. This ensured that the selected smoothing for the Vicon data were relevant and suitable for the specific type of data, making the Vicon data an accurate representation of the real world. The raw (not smoothed in any way by the manufacturer software) GNSS Doppler-shift speed data were exported and retrieved from the Catapult software file folder. It was chosen to use the speed derived from Doppler-shift as it is more frequently used and preferred to the speed of positional differentiation due to its increased accuracy, lower error, and default measure of speed of most manufacturers [4,7]. The smoothed GNSS acceleration data (smoothed by the manufacturer software) were exported from the manufacturer’s software (Openfield version 3.9.0, Catapult Innovations, Melbourne, Australia).

Each GNSS file was partitioned to align with the 3D motion capture Vicon trials based on the coded timestamps of the trials and standing still for 3 s at the start and end of each trial. Due to the difference in sampling frequencies between the Vicon and GNSS, the files could not be directly combined. As this study was to investigate how closely the GNSS acceleration data matched the VICON data, the 10 Hz GNSS data were used for further analysis to avoid any potential additional noise in the data due to upsampling, while downsampling the Vicon data. The additional noise due to upsampling would have been created by introducing new data points that did not exist in the original dataset through interpolation. This could have led to inaccuracies because the data that were filled in were never measured, making it less reliable. Downsampling the 100 Hz VICON data retained the real measured data by selecting a subset of the original data. Furthermore, this approach ensured that the GNSS data are a true representation of that used in the field by practitioners and researchers. The downsampling process is detailed in

Table 3. Downsampling of the 100 Hz 3D motion capture Vicon data to align with the 10 Hz GNSS data.

(Step 1) For each of the two datasets (GNSS & 3D motion capture), extract a synchronisation point which is a clearly identifiable peak or valley. Symbols used in figures: ○ = synchronisation point ● = 10 Hz GNSS data x = 100 Hz 3D motion capture data
(Step 2) Align datasets based on synchronisation point.
(Step 3) Down sample 100 Hz 3D motion analysis data (ensuring the synchronisation point is included) to 10 Hz data to match the GNSS data.
(Step 4) Calculate RMSE and correlation between the two datasets.
(Step 5) Repeat step 1 shifting the synchronisation point for the 100 Hz 3D motion capture data one sample. Repeat steps 3 and 4. Repeat this process for five samples forward and backward from the initial synchronisation point, this will cover all down sample combinations.
(Step 6) The synchronisation point and down sampling combination that provided the lowest RMSE and highest correlation was used to combine the GNSS & 3D motion capture data.

. The raw GNSS Doppler-shift speed data were processed using three different smoothing techniques (I) a fourth-order (zero lag) low pass Butterworth filter (cut-off frequencies ranging from raw to 4.9 Hz, steps of 0.1 Hz), (II) exponential smoothing (smoothing constant ranging from 0.1 to 0.9, steps of 0.1), and (III) moving average (sliding window ranging from 0.2 s to 2.0 s, steps of 0.1 s). The boundaries of all smoothing parameters (e.g., cut-off frequencies ranging from raw to 4.9 Hz) were set to their maximum possible values to experiment with all potential options for the smoothing techniques (maximal smoothing to minimal smoothing). A small step size of 0.1 for each smoothing boundary was set to allow for more options in testing, helping identify the best possible combination of smoothing technique and smoothing parameter. These three techniques were chosen as they are widely used techniques for smoothing time-series acceleration data, each with distinct characteristics that balance noise reduction and signal preservation in dynamic acceleration data [7,15]. Smoothing the raw Doppler-shift speed data before deriving the acceleration data will ensure that any noise present in the speed data will not be increased due to deriving. Details on the used smoothing techniques and processing steps of the GNSS data can be found in Table 2. Next to the custom smoothed GNSS data, GNSS manufacturer smoothed acceleration data and raw GNSS acceleration data (calculated with the central difference method on the raw GNSS Doppler-shift speed data) were also used. It was discovered that the GNSS manufacturer smoothed acceleration data had not been accurately aligned upon export from the manufacturer’s software; please note that this was for the software version used in this study (Openfield version 3.9.0). In fact, there was a time difference of 0.5 s, meaning that the acceleration data were ahead of the speed data. To rectify this misalignment and achieve proper synchronisation with the GNSS speed data, the manufacturer smoothed acceleration data needed to be shifted back in time by 0.5 s.

2.5. Statistical Analysis

Data used for the statistical analysis consisted of 333 trials, measured across the 6 different accelerating and decelerating movements.

To determine the ability of a GNSS to quantify acceleration, a variety of measurement indices of validity were obtained: the level of agreement (95% limits of agreement, LoA [37]), accuracy (mean bias), and precision (root mean square error, RMSE, [38]). The details of these measures are provided in Equations (1)–(3):

$$LoA=mean(GNSS-Vicon)\pm (standard deviation\ast 1.96)$$

(1)

$$Mean bias=mean(GNSS-Vicon)$$

(2)

$$RMSE=\sqrt{{\displaystyle \frac{{{\sum }_{i=1}^{number of observations}({GNSS}_i-{Vicon}_i)}^2}{number of observations}}}$$

(3)

The smoothing technique showing the overall best level of accuracy (mean bias closest to zero), agreement (smallest 95% LoA), and precision (RMSE closest to zero) was used for further analysis. A one-way analysis of variance (ANOVA) with an alpha level of 0.05 was conducted to determine whether differences existed between the six different acceleration and deceleration movements of the GNSS acceleration data using the best smoothing technique and Vicon data. Tukey’s post hoc analysis was conducted to examine the source of the difference. All analyses were performed in MATLAB (version 9.14.0 (R2023a), The MathWorks Inc., Natick, MA, USA).

3. Results

The results of all smoothing techniques are presented in Figure 3, Figure 4 and Figure 5. The most accurate smoothing technique showing the strongest relationship with the Vicon acceleration data (closest approximation to the real-world) was GNSS data processed with a fourth-order (zero lag) low pass Butterworth filter with a cut-off frequency of 2 Hz (mean bias 0.00 m·s⁻², 95% LoA ± 1.55 m·s⁻², RMSE 0.79 m·s⁻²).

The validity of the 2 Hz Butterworth smoothed GNSS data across all movements is presented in

Table 4. Comparison (GNSS-Vicon) of GNSS and Vicon acceleration data of six different accelerating and decelerating movements. GNSS acceleration data smoothed with a fourth-order (zero lag) low pass Butterworth filter with a cut-off frequency of 2 Hz compared to the Vicon data.

Movement	Mean Bias ± SD Acceleration (m·s−2)	95% LoA (m·s−2)	RMSE (m·s−2)
COD180	0.00 ± 0.72	−1.41 to 1.41	0.72
COD90	−0.02 ± 0.58	−1.12 to 1.16	0.58
JumpA	0.00 ± 1.05	−2.06 to 2.06	1.05
JumpD	0.00 ± 1.22	−2.39 to 2.39	1.21
Linear	0.03 ± 0.52	−0.99 to 1.05	0.52
Stop	0.01 ± 0.52	−1.01 to 1.03	0.52

. No significant differences were found between the GNSS and Vicon acceleration within each movement category, nor were the movements different from each other. The average deviation (RMSE) between the GNSS acceleration data and Vicon was the largest for the decelerating jumping movement (average deviation of 1.21 m·s⁻²) and smallest for linear movement and stop of motion (average deviation of 0.52 m·s⁻²).

The GNSS manufacturer smoothed data deviated from the Vicon data by 1.21 m·s⁻² on average. The raw GNSS data had the largest deviation across all conditions and deviated from the Vicon data by 2.24 m·s⁻².

Overall, the GNSS data processed with exponential smoothing provided the strongest smoothing, and therefore the biggest discrepancy with the Vicon acceleration data, followed by the moving average and Butterworth filter.

4. Discussion and Implication

This study examined the validity of a GNSS device to measure acceleration during different accelerating and decelerating movements, resembling those commonly observed in team sports. The main findings indicate that the GNSS device had an acceptable validity for acceleration data when the raw speed data were smoothed with a fourth-order (zero lag) low pass Butterworth filter with a cut-off frequency of 2 Hz. A secondary finding was that the type of movement performed influenced the validity.

The raw GNSS data showed the largest deviation from the Vicon data with a RMSE of 2.24 m·s⁻². Acceleration metrics derived from raw data should therefore be interpreted with caution. When using threshold-based metrics with raw data, an athlete’s movement profile will be overestimated compared with their “true” profile. Practitioners using raw acceleration data should be aware that the reported acceleration values and threshold-based metrics could be overestimated. On the other hand, the manufacturer smoothed data were more accurate than the raw data, but still had a larger deviation from the Vicon data compared to the most accurate smoothing technique. Practitioners using manufacturer smoothed acceleration data should be mindful that the acceleration data could deviate from the true value by 1.21 m·s². When solely using manufacturer smoothed data, the accuracy of the acceleration data will stay consistent and should not impact the decisions made by practitioners. However, problems will arise when using raw data in combination with the manufacturer smoothed data. As the deviations from the Vicon data were different between the manufacturer smoothed data and raw data, using both data types together could cause inaccurate data. For example, if using raw data to set a high acceleration threshold (e.g., 80% of max acceleration), this threshold could be overestimated by 2.24 m·s⁻². When this threshold is then applied to the manufacturer smoothed acceleration data, which has a stronger smoothing (smaller deviation from the truth compared to the raw data), the data will almost never reach the threshold. Practitioners should also be aware that the manufacturer smoothed acceleration data, exported by different GNSS manufacturers, may not be comparable because they may be have been processed using different smoothing techniques.

Using a smoothing technique improved the GNSS validity, with a 2 Hz Butterworth filter cut-off frequency showing the best level of agreement, accuracy, and precision across all smoothing techniques and levels assessed. The Butterworth filter potentially performed best due to its ability to effectively reduce high-frequency noise while preserving the underlying low-frequency components (which typically correspond to the actual movement) [30]. This is particularly useful in athlete tracking where high-frequency noise often arises from sensor imperfections or external interference [15]. The Butterworth filter, unlike other smoothing techniques, does not distort the timing of the data [15], which is important when analysing and comparing acceleration data where the timing needs to be precise. A datapoint was on average ±0.79 m·s⁻² away from the actual acceleration value. When using threshold-based summary acceleration metrics close to the maximum and minimum values, one should be aware of the precision ranges. For example, if an athlete has a maximum acceleration of 4.5 m·s⁻², it is possible that the acceleration is reported by a GNSS device anywhere within the precision range of 3.71–5.29 m·s⁻². If a practitioner decides to set their high acceleration threshold based on a percentage of this maximum acceleration value, it could be under or overestimated by 0.79 m·s⁻². If the higher side of the precision range is used to set the high threshold, the metrics calculated based on the threshold could be underestimated, and vice versa. Thus, when using threshold-based metrics, practitioners and researchers should keep the precision measures in mind when setting their thresholds.

The most valid Butterworth cut-off frequency of this study seems to be higher than the 1 Hz reported in the literature for GNSS acceleration data [36]. The cut-off frequency reported in the literature was determined based on the data of GNSS devices different from those used for this study, which could have caused the difference in results. Using the lower cut-off frequency (1 Hz) will result in stronger smoothing and overall underestimated acceleration values. Therefore, caution should be taken if interpreting GNSS acceleration values when using low (<2 Hz) cut-off frequencies.

Different team-sport movements had different acceleration profiles, however, no movement was shown to be statistically different from one another. The movements were performed in a controlled environment, which could have reduced the variability of the acceleration data within each movement. The study did, however, try to account for the reduced variability by including varying the starting speeds and acceleration and deceleration intensities for each movement. Linear movement and stop of motion had the best and decelerating jump had the worst validity. An error of 0.52 m·s⁻² for linear movement and stop of motion and 1.21 m·s⁻² for decelerating jump over or under the actual value was expected to be recorded by the GNSS. Jumping was the movement with the largest deceleration value and was underestimated compared to Vicon. The jumping movement could have been subjected to more high frequency, and the selected cut-off frequency possibly decreased the higher frequency content of the GNSS data, resulting in a stronger smoothing effect. A higher cut-off frequency might be more appropriate to assess the decelerating jumping movement.

It is important to highlight that different athlete tracking systems, such as a local positioning system (LPS), optical tracking system, and accelerometer, are more commonly used in team sports [11]. All of these devices track data over a variety of samples (~10–100 Hz) and likely need different types of smoothing to have valid acceleration data. Similar research, but investigating the maximum acceleration of an accelerometer [31], found that the accelerometer data needed to be smoothed to provide valid data compared to a 3D motion analysis system. Their suggested smoothing technique was a Butterworth filter, however, their most valid cut-off frequency was much higher (8 Hz and 10 Hz) than those observed in this study. This can be explained by the sampling frequency of their accelerometer, 100 Hz vs 10 Hz for this study, highlighting that different athlete tracking systems might need different smoothing techniques. Researchers and practitioners using the acceleration data of athlete tracking systems different from the one used in this study should be aware that the smoothing techniques presented could affect their data differently.

Three different smoothing techniques were used for this study, specifically a Butterworth filter, single exponential smoothing, and moving average, as these are commonly applied to athlete tracking system acceleration data [7] and have distinct characteristics that balance noise reduction and signal preservation in dynamic acceleration data (see Introduction for more in-depth information) [15,17]. However, other smoothing techniques, median filters, polynomial smoothing, and weighted Gaussian filters, have been reported in the literature to be used on athlete tracking system acceleration data [7]. These specific smoothing techniques were not chosen for this study as they could have introduced distortions, computational complexity, or overfitting that could have been detrimental to the quality and responsiveness of the smoothed data [15,17]. Furthermore, other smoothing techniques (e.g., wavelet smoothing) exist that might result in more valid acceleration data. Further research is needed to investigate the commonly applied smoothing techniques to GNSS acceleration data. The authors suggest that researchers and practitioners using raw GNSS data (instead of the manufacturer smoothed/processed data) apply a variety of smoothing techniques on their data and investigate the influence of the smoothing on the data of interest. For example, if interested in acceleration efforts, it is recommended that the smoothing techniques are applied to the raw speed data before deriving the acceleration and investigating the influence it has on the acceleration efforts.

While this research has provided valuable insights into the acceleration data of GNSS devices, the limitations need to be acknowledged. The use of 10 Hz GNSS devices to measure time-series acceleration data has been widely adopted in the sports science community [1,39]. It is also widely accepted, based on validation studies, that 10 Hz GNSS devices are sufficient to measure high-intensity acceleration-based movements accurately [19,40,41]. However, there are some limitations to take into consideration when evaluating validation studies. There are currently no universal standards for acceptable errors in athlete tracking technology validity research. To improve consistency and comparability, future research should establish these standards, aiding in cross-study comparisons and providing universally interpretable results. Since this research aimed at improving the accuracy of acceleration data from a widely used and accepted 10 Hz GNSS device through various smoothing techniques, rather than assessing its suitability for measuring acceleration, no acceptable error thresholds were set. The results of this research showed that the manufacturer smoothed acceleration data of the GNSS device (which are the data widely used and accepted in the sports science community) had a larger deviation from the 3D motion analysis data compared to the most accurate smoothing technique. Thus, the most accurate smoothing technique used in this study is more accurate than those currently used and accepted in the sports science community.

Research including this study have used location data from gold standard 3D motion analysis systems, such as VICON, as a criterion measure to validate the acceleration data of 10 Hz GNSS devices. Data from these systems are often reduced to 10 Hz to be able to compare and validate datasets [20]. Furthermore, the displacement data of 3D motion analysis systems need to be double differentiated to calculate acceleration and is subject to smoothing processes, which was shown by this study and previous research to affect the data output [42,43]. This data processing and downsampling may impose a bias when measuring acceleration, and it is currently unknown as to whether 3D motion analysis systems accurately represent acceleration data.

Only one type of GNSS device was used (Catapult S7), so the findings might not apply to other GNSS devices. However, similar research on GNSS acceleration data [36] has shown that following the application of a 1-Hz low-pass Butterworth filter on the raw speed data of different GNSS devices, the derived acceleration variables had decreased differences, suggesting that one smoothing technique used across different GNSS devices might be appropriate, although further research is required to confirm this. To compare the GNSS and 3D motion analysis time-series acceleration, both datasets were synchronised and aligned to achieve the lowest RMSE and highest correlation. Minor alignment inaccuracies may arise when the data are synchronised without an electronic synchronisation point. Including an electronic trigger to create a synchronisation point in both datasets during data collection would enable precise synchronisation. However, to the authors’ knowledge, such a solution is currently unavailable. Future research should explore methods to establish a synchronisation point between GNSS and 3D motion analysis data. Data collection was performed outside in optimal conditions on an empty synthetic soccer pitch that was not surrounded by stands. While these conditions are applicable to most field-based team sports, competition usually takes place in stadia surrounded by stands that obstruct the GNSS signal, decreasing the accuracy of the GNSS devices, so the results of this study may therefore not apply to these conditions.