## 1 Introduction  
Ahlete 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].