## 3 Results and Discussion
However, the average accuracy on the \(y\)-axis resulted in 93.81%, with an average sensitivity of 98.7%. Notwithstanding, the \(x\)-axis and \(z\)-axis provided bad results, especially regarding some athletes' tests; these data can be exploited to further improve the results on the \(y\)-axis. Indeed, it has been noted that in some cases, when the algorithm failed to detect a kick on the \(y\)-axis, it was still correctly detected on one of the other two axes. Following this observation, the performances were evaluated by combining a logic OR with the result of the algorithm applied on each of the three axes. The results are reported in Table 3.  
Combining all three axes, an average accuracy of 97.5% was achieved with an average sensitivity of 99.33%. It is worth noting that using the three axes also makes the analysis independent of how the sensor was worn. An average error of two kicks every 100 m was computed among all training sessions. In Figure 6, the inertial sensors count vs. the gold standard is shown. In the optimal case, the regression line has a slope equal to one and an intercept equal to 0. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Test ID**} & \multicolumn{2}{c}{**\(x\)-Axis**} & \multicolumn{2}{c}{**\(y\)-Axis**} & \multicolumn{2}{c}{**\(z\)-Axis**} \\ \hline
**Athlete Number** & **Test Number** & **Acc [\%]** & **Sen [\%]** & **Acc [\%]** & **Sen** & **Acc [\%]** & **Sen [\%]** \\ \hline
1 & 1 & 69.5 & 100 & 98.2 & 99.80 & 71.10 & 99.8 \\
1 & 2 & 73.6 & 99.8 & 84.3 & 100 & 62.80 & 99.5 \\
2 & 1 & 36.6 & 100 & 99.4 & 100  
The linear regression was carried out using the MATLAB curve fitting tool, setting a robust fitting method and minimizing the least absolute residuals (LAR). Robust regression is less sensitive to outliers and the resulting model is less dependent on large changes in a small part of the data. As it can be seen, the curve fitting results had a very good linearity with an R\({}^{2}\) of 0.9986. The slope of the line was 1.01, resulting in a relative error in the slope line of 1%. The result obtained can be compared with results from the literature, showing some advantages. In [21] an algorithm was applied to a gyroscope to demonstrate the validity and the reliability of counting the kicks during a training session using inertial sensors. In this study, accuracy and sensitivity were not reported. However, the authors evaluated the goodness of the fit between the inertial sensor results and the kicks counted in the video footage, resulting in an R\({}^{2}\) of 0.957 with a slope of the line of 0.9101. The relative error \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Test ID** & \multicolumn{2}{c}{**\(x\)-Axis or \(y\)-Axis or \(z\)-Axis**} \\ \hline
**Athlete Number** & **Test Number** & **Acc [\%]** & **Sen [\%]** \\ \hline
1 & 1 & 98.5 & 99.8 \\
1 & 2 & 94.2 & 99.5 \\
2 & 1 & 99.6 & 99.8 \\
2 & 2 & 99.6 & 100 \\
3 & 1 & 90.7 & 99.8 \\
3 & 2 & 87.8 & 95 \\
4 & 1 & 98.9 & 99.3 \\
4 & 2 & 99.3 & 100 \\
5 & 1 & 99.1 & 98.9 \\
5 & 2 & 99.4 & 99.8 \\
6 & 1 & 97.8 & 98.2 \\
6 & 2 & 99.7 & 99.7 \\
7 & 1 & 98.1 & 100 \\
7 & 2 & 94.8 & 100 \\
8 & 1 & 98.6 & 100 \\
8 & 2 & 99.5 & 99.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Accuracy and sensitivity of the developed algorithm applied on each axis and combined with a logic OR. Figure 6: Relationship between the kick count acquired with the accelerometer and the kicks counted in the video footage for each test. on the slope line was 9%, much higher than that found in this study. Moreover, a future embedded implementation that relies on an algorithm based on only an accelerometer can lead to lower power consumption and a less expensive solution. Indeed, the stand-alone accelerometer solutions usually have a lower current consumption and costs concerning both stand-alone gyroscopes and integrated IMUs [24; 25]. In [22] a threshold algorithm for the kick count and kick rate based on only accelerometric data was reported. In this case, the accelerometer was worn on the swimmer's back.