## 4 Discussion  
The video-based marker tracking system (QMS) is here considered the reference value since it allows tracking of the trajectory of the jump with both high accuracy and precision. This is also considered the gold standard method by many authors [6,11]. Analysis of ABJ results reveals high accuracy and good precision (0.8 \(\pm\) 14.7 mm). This was somewhat surprising since it is difficult to guarantee solely vertical displacement of the jump to avoid an overestimate of the vertical jump height by adding anterior or posterior motion of the body. Researchers wishing to assume the accuracy and precision found in this study should emphasise to their participants the importance of a predominantly vertical displacement. The accuracy and precision results obtained from the flight-time methods using EJ, MP and FP devices data are consistent with those in the literature [7,10,14,26]. Considering the underestimation of the jump height, [PERSON] [26] found the smallest difference of 2 cm between video-based marker measurements and the flight-time method, but little difference for the take-off velocity method. Taking video analysis as a reference, [PERSON] et al. [14] found differences in jump height with the flight time method of 10.32 cm and 1.5 cm for the double integration method using a force platform. In contrast, [PERSON] [10] identified differences of 10.9 cm and 9.1 cm for men and women, respectively, between flight-time and the double integration methods applied to force platform data. A take-off velocity method provided the smallest difference. One of the main sources of error described in the literature for the flight-time method is the body posture in the aerial phase since the method assumes that the position of the centre of mass is the same at take-off and landing. Therefore, identifying the true instant of take-off, which is related to the device used for this purpose, is crucial, and so too is an understanding of the participant's landing technique. Typically, flight-time is increased by the participant landing with flexed lower-limb joints [10,11] to attenuate landing impact forces [27]. The vertical jump trajectory's position, velocity, and acceleration (a representative example of which is presented in Figure 5) revealed that participants complied with the countermovement protocol since the touchdown and the minimum velocity occur at approximately the same time the mass centre reaches the standing height reference. From the take-off instant, we can see that the calculated maximum velocity occurs before there is no contact with the floor and after the centre mass vertical movement starts. For this reason, the jump height in EJ has less accuracy than those obtained with the MP and FP. The double integration jump height measurement method used in this study was performed by time integration of the vertical acceleration extracted from the FP device or the vertical component of the tri-axial accelerometer data of the MP device. The numerical integration was performed from the jump movement's initiation until beyond the vertical trajectory's apex. Researchers have found that the double integration method is one of the most reliable and accurate when using ground reaction force data [10,11,14]. Although the double integration method can provide good accuracy when using ground reaction force data, the same was not observed when using acceleration data collected using the MP device. Analysis of the two vertical acceleration signals, as shown in Figure 6, demonstrate similar behaviour, but the acceleration obtained from the MP, which has a lower sampling frequency than the FP (200 Hz versus 2000 Hz), contains some fluctuations and less defined events at take-off and landing. Therefore, the acceleration signal from MP does not follow the signal recorded by the FP, such as take-off and landing events, and contains oscillations throughout the flight phase. Comparing the vertical position of MP, QMS, and FP, as shown in Figure 7, we found that the MP device exhibits a very different path.