## 3 Processing and Analysis of Measurements
### Segmentalized Principal Component Analysis (sPCA) for Acceleration Signal  
As mentioned before, the frequency characteristics of the human body's sway mainly focuses on the very low-frequency range, the capacitive accelerometer has satisfactory measurement performance within the bandwidth of very low frequencies, and thus, was utilized to detect the acceleration of the examinee's body sway in the experiment. However, the bind-in accelerometer inevitably tilted along with the examinee's body sway and hence, the X-Y-Z directions of the acceleration measurements were time-varying with respect to the fixed reference frame. Furthermore, the measurement of the capacitive accelerometer also includes the constant gravitation (g = 9.81 m/s\({}^{2}\)) in the vertical direction and thus, the acceleration measurements in the three directions may contain the gravitation projection components while the accelerometer was tilted along with the examinee's body sway. To the contrary, the COP signal components in ML and AP directions were obtained in the horizontal plane and were independent of the gravitation in the vertical direction. Therefore, it is definitely beneficial for deriving the correlation between the COP and acceleration measurements if the gravitation projection onto the three directions of acceleration signals can be removed. The concept of PCA that was proposed by [PERSON] [13] is to convert the measurements in which the variables may be correlated with each other into another sets of variables which are uncorrelated. The sets of variables in the other space are called principal components. The mathematical procedure of PCA is to transform the data sets of measurement into another coordinate system, where the principal components are located through an orthogonal matrix. In this coordinate system, the first principal component has the highest variance, and the subsequent components in turn have as high variance as possible. Therefore, the principal components in the new space are uncorrelated with each other or even orthogonal to each other. In order to resolve the stated problem of the axial directions variation as well as the gravitation projection issue, and to thereafter derive the relationship between the COP measurement and the acceleration signal, the PCA was employed to process the acceleration signals in this research. The acceleration measurements in X-, Y- and Z-directions were first transformed into another coordinate system where the principal components were located. The principal components in the new coordinate system are theoretically orthogonal to each other, and thus the operation of PCA can reflect the transformed signals in the way of most possible variability in the data [14; 15]. In this research, therefore, the variability of acceleration measurements along the three directions was first analyzed. Simply consider that the accelerometer is bound at the point A of the examinee's waist and sways in the AP direction, as shown in Figure 5. As the examinee's ways to maintain the body's balance status, the accelerometer moves from A to A', as shown in Figure 5. The acceleration measurements consist of the components perpendicular to the Z-direction as well as the component parallel to the Z-direction. Since the two acceleration components in Y- and Z-direction are proportional to the distance \(a\) and \(d\) respectively, it can be briefly proven that the acceleration has larger variance in Y-direction than in Z-direction if \(a\) is always greater than \(d\). First, assume \(d>a\) contradictory. The distance \(a\) in Y-direction can be determined from the geometric relationship, \(a=\sqrt{h^{2}-\left(h-d\right)^{2}}\), and hence, \(d>\sqrt{h^{2}-\left(h-d\right)^{2}}\). It is easy to derive the contradiction that the condition for \(d>a\) implies \(d>h\). Similarly, the same inference can be applied in the X-direction instead of the Y-direction. Therefore, it is reasonable to infer that the acceleration variance in Z-direction is smaller than those in X- and Y-directions.