## 3 Results and Discussion  
The result of the test by applying [PERSON]'s filter is satisfied. During a test, we moved our system device up and down three times. As shown in Figure 4, we got relatively accurate feedback of the 3D positioning data. Indeed, the Madgwick algorithm eliminates the drifting error from integrating the velocities. The three different curves stand for the changing distances over time on the X axis, Y axis, and Z axis in a 3D space. The dynamic distance on the Z axis (blue lines) shows exactly three times up and down of the device. The range of vertical movements is \(\sim\)0.33 m for the first moving-up  
Figure 3: (**a**) The acceleration data obtained from the IMU sensor; (**b**) the corresponding velocity data, which was calculated by the complementary Kalman-based filter. and down, \(\sim\)29 cm for the second circle, and \(\sim\)32 cm for the last one, respectively. The next step is to validate the accuracy of the device. It is well known that 3D motion capture technology provides accurate and objective analysis of a variety of human motor skills [14; 24; 25; 26; 27]. Therefore, we employed the synchronized data collection of the IMU and 3D motion capture (Figure 1b) for validating and improving the accuracy of the IMU device. There were eight synchronized tests performed to obtain thousands of data for our validation. Since we aimed to gain the dynamic vertical distance, the validation of the Z axis was selected. Figure 5 shows a typical test data. The synchronized data demonstrate a matching vertical excursion over time between the IMU data and the accurate 3D motion capture data. The results suggest that our device works principally. A magnitude comparison shows that the excursion of the VICON data was larger than that of the IMU data (Figure 5). A timely comparison between the synchronized data of all trials revealed that the two excursions ran in a quasi-parallel way, which suggested that we could apply a factor for re-calibrating the IMU device to improve the accuracy of the IMU data. After the quantitative comparison between the two excursions of all trials, a re-calibration factor of 1.31 was determined. Figure 4: The 3D positioning data obtained by the IMU with the Madgwick filter. Figure 5: A synchronized test data obtained from 3D motion capture (VICON data, top, sampling rate 200 Hz) and our IMU device without calibration (IMU data, bottom, sampling rate 50 Hz). After the simple re-calibration, a renewed synchronized measurement was done and the result is shown in Figure 6. This time, the average data error of our IMU data decreases to under 6%, which is accurate enough for sport skills analysis using the biomechanical modeling method [28; 29; 30; 31; 32]. Finally, it should be noted that our device needs an initial value for its application. As shown in Figure 6, the device will start at zero regardless of its actual vertical position. Therefore, for its application in the hammer throw, an accurate feedback needs the initial heights of the hip and wrist (H\({}_{\text{hip}}\) and H\({}_{\text{wrist}}\)) as shown in Figure 7.  
Figure 6: A renewed synchronized test data obtained from 3D motion capture (VICON data, top, sampling rate 200 Hz) and our IMU device after calibration (IMU data, bottom, sampling rate 50 Hz). Figure 7: The upper and lower limb coordination (i.e., motor control pattern) revealed by the vertical distances of hip and wrist as well as the wire tension during a hammer throw by a college-level athlete. The in-field test on the college-level athlete using our prototype device confirms the potential of using wire-tension and IMUs in real-time feedback training (Figure 7). In practice, the motor control of the hammer throw could be divided into four phases: Initiation, transition, turns, and throw. The goal of the initiation phase is to launch the circulation of the hammer around the body. It commonly consists of a forward and backward swing of the hammer (i.e., to set the hammer to motion) and two over-head arm rotations (i.e., to set the hammer into rotation).