# Can IMU Provide an Accurate Vertical Jump Height Estimate?
## 2 Materials and Methods
### Flight Time Measurement  
The methodological approach to the JH calculation is summarized in Figure 1. In the signal acquisition phase, the raw signal of acceleration is acquired for the X, Y and Z axis. The signal processing phase combines the filtering of the raw signals, followed by the calculation of the absolute acceleration and event detection. After that, in the final step, the flight time is calculated from the timestamps of the obtained events (take-off and landing) and the jump height is calculated from the determined flight time by Equation (1).  
The IMU accelerometer measures the 3D acceleration vector including gravity acceleration projected on the sensor axes in accordance with the sensor orientation.  
The measurement of the flight time is based on the detection of take-off and landing events from the acquired absolute acceleration signal. During take-off and landing, pronounced acceleration pulses occur at the selected location of the sensor; the amplitude of both pulses exceeds gravity for the size class. When detecting take-off and landing events, we can, therefore, choose a threshold value that is much higher than the gravitational acceleration. Consequently, gravity has no significant effect on measuring the time between these two events. An example of the measured acceleration signals with the acceleration threshold marker and the time markers of the detected events is given in Figure 2.  
Figure 1: The methodology of JH calculation from IMU data.  
Taking into account the sampling frequency of 200 Hz, it should be noted that the analog acceleration signal is filtered in the LMS6 DS33 chip with a 100 Hz low pass anti-aliasing filter, as defined in the manufacturer's datasheet [30]. In addition, the acquired signal was filtered using a Butterworth low-pass filter (order = 5, \(f_{\text{cof}}\) = 40 Hz). A much lower filter cut-off frequency (\(f_{\text{cof}}\) = 10 Hz) is commonly used in the processing of signals obtained on different human movements, which is aimed towards the elimination of the signal components originating from external factors. However, for the purposes of VJ height estimation, such an approach is inappropriate in relation to the landing phase of the jump in which the athlete's body collides with the surface thus providing an intensive jerk and high acceleration values which can exceed the sensor threshold. Figure 2 shows the detection of take-off and landing events using 5 \(g_{0}\) threshold on raw and signals filtered using 40 and 20 Hz f\({}_{\text{cof}}\) (red, blue and black, respectively). Due to the signal being filtered in A/D conversion it can be noted that even raw signal can be used for event detection. However, as the external conditions of in-field measurement may vary additional filtering is implemented. Reducing acceleration signal spectra under 40 Hz introduces errors in detecting the landing event, which can be clearly seen in Figure 2.  
The acceleration threshold value (5 \(g_{0}\)) used as a trigger for event detection is optimally set in terms of minimization of the flight time bias and is synchronized to the FP in terms of accurate take-off detection.  
The error in calculating a vertical jump height is directly affected by flight time measurement error, according to Equation (1). Therefore, for a relatively small flight time error, we can use a linearized model to calculate the jump height error, as given by Equation (2).  
\[e_{h}=\frac{e_{t}\cdot t_{F}\cdot g_{0}}{4} \tag{2}\]  
Where \(e_{h}\) is the JH measurement error, \(e_{t}\) is the FT measurement error, \(t_{F}\) is the flight time and \(g_{0}\) is gravity acceleration (9.81 ms\({}^{-2}\)).