## 1 Introduction
[8] proposed to examine the effectiveness of visual biofeedback (VBF) signals and accelerometer sensors for improving human balance. They showed that the location of VBF signals had a significant effect on each postural parameter of COP and trunk segments. The approximate entropy values were computed to reflect the amount of irregularity hiding in the COP [9]. The data analysis demonstrated that this method enables us to quantify the postural stability. A point of application (POA) approach was used to determine the accuracy, precision and reliability of COP measurement in a low-cost force plate, called the balance tracking system, and showed an excellent agreement between the POAs and measured COP [10]. In 2018, [PERSON] et al. [11] used the three-axis accelerometer to quantify the postural stability of patients with cerebellar disorder. Their study demonstrated that the pathological balance control can be identified through the three-dimensional (3D) postural analysis. Although the COP-based quantification of balancing ability has been employed by medical doctors for decades and is still the major means for evaluating the balance condition of patients, the studies of replacing the COP measurements for balance evaluation have been explored and the feasibility has also been verified. Based on the state-of-art of balance measurement of the human body, a solid and consistent transformation between the COP and acceleration measurements is the crucial step for accurately estimating the balancing ability of the human body. On the other hand, the swaying frequencies of the human body mainly concentrate around the very low-frequency band, as compared to the frequency range of mechanical structural vibration. As for considering the volume, weight, cost and measured bandwidth of the accelerometer, the capacitive accelerometer would be an appropriate one to be bound with the human body and then utilized to measure the swaying acceleration at extremely low frequencies. However, the capacitive accelerometer inherently contains the gravity component on the vertical axis and the gravitation may be projected onto the measurements on the three axes with a time-varying manner, while the bind-in accelerometer tilts along with the human body's swaying. It is definitely an obstacle and there is difficulty deriving the correlation between the COP signal and acceleration measurement. Based on the problem statements, the objective of this research is to investigate the feasibility of deriving the transformation from the acceleration measurement to the COP signal, so that the COP-based evaluation of the human body's balancing ability can be estimated in terms of the swaying acceleration measurements. The empirical mode decomposition (EMD) method [12] was employed to separate the non-stationary acceleration signals and then extract the swaying-related components at the very low-frequency range. With the EMD process, the traditional filtering process in which the central frequency and bandwidth must be first decided would not be needed. The segmentalized PCA (sPCA) was proposed to alleviate the influence of the time-varying gravitation projection onto the acceleration measurements on the three axes. The equilibrium score (EQs) was also estimated through the measured acceleration signals in this research. The results show that high correlation coefficients of more than 0.7 can be obtained between the processed acceleration signals and the COP measurements. The estimated EQs values have mean average percentage error (MAPE) of 4.89 with respect to the EQs values that were calculated by the commercial computer-aid balance testing apparatus. Experiment Design for Relationship Derivation between Acceleration and the Center-of-Pressure (COP)  
The sensory organization test (SOT) has been broadly employed to evaluate the balancing ability of the human body in the fields of clinical medicine and biomedical engineering. Among all the external factors that influence the balancing ability of the human body, the majority contains the visual conditions.