## 4 Discussion and Implication
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 \(\pm\)0.79 m\(\cdot\)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\(\cdot\)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\(\cdot\)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\(\cdot\)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\(\cdot\)s\({}^{-2}\) for linear movement and stop of motion and 1.21 m\(\cdot\)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.