## 2 Materials and Methods
### Spatial Multi-Dimensional Pulse Wave Signal Processing Method
The minimum gain value for Algorithm III is \(-\)1.28 dB, while the maximum gain value for Algorithm I and II is less than \(-\)20 dB, as shown in \[y=\frac{P_{i}}{P_{j}}*x_{j}\;(j=L_{2}(k);\;i=P_{2}(k);\;k=\{1,2,\ldots\}) \tag{13}\]0 Therefore, Algorithm III outperforms both Algorithm I and II for the property of gain between the algorithm's processing results and the standard input signal. Comparing the processing results under different test regions reflects the relevance of the algorithm to the test region. The DTW distances between Algorithm I's results and the standard input signals are 10.95, 12.48, and 10.81 at the three test positions, respectively, which change considerably. Simultaneously, Algorithm I has a more remarkable change in gain at the corresponding test location, \(-\)20.68 dB, \(-\)25.24 dB, and \(-\)20.76 dB, respectively, as shown in column 2 of \[y=\frac{P_{i}}{P_{j}}*x_{j}\;(j=L_{2}(k);\;i=P_{2}(k);\;k=\{1,2,\ldots\}) \tag{13}\]1 Therefore, there is a strong correlation between the processing results of Algorithm I and the test location. Based on the same evaluation method, there is also a correlation between the processing results of Algorithm II and the test location. However, the performance of Algorithm III is more stable under different test regions. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Algorithm I** & **Algorithm II** & **Algorithm III** \\ \hline Position 1 & 10.95 & 10.74 & 2.38 \\ Position 2 & 12.48 & 11.99 & 2.37 \\ Position 3 & 10.81 & 10.81 & 2.34 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Dynamic Time Warping (DTW) distance of Algorithm I, II, and III processed results with standard input signals. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Algorithm I** & **Algorithm II** & **Algorithm III** \\ \hline Position 1 & \(-\)20.68 & \(-\)20.17 & \(-\)1.28 \\ Position 2 & \(-\)25.24 & \(-\)23.70 & \(-\)0.87 \\ Position 3 & \(-\)20.76 & \(-\)20.76 & \(-\)0.80 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The gain of Algorithm I, II, and III processed results relative to the standard input signals. The DTW distances of Algorithm III are 2.38, 2.37, and 2.34 at the three test regions, which is almost indiscriminate. The gain of Algorithm III is also a little changed at all test regions. Here, we illustrate the variation in sensor test states under different test regions, partly explaining the above algorithms' performance differences. Figure 6 depicts a schematic representation of the sensor contact between SPVG and PAWS at different test positions. At location A, the ZM-300 is in contact with sensor 1, sensor 2, and sensor 3. As in Equation (15), the sum of the dynamic forces tested by the PAWS' sensors is the same as the ZM-300. The dynamic force ratios to total dynamic force tested by sensor 1, sensor 2, and sensor 3 were 10%, 80%, and 10%, respectively. The signal measured by sensor 2 has the highest amplitude value. Therefore, sensor 2 is selected as the representative sensor in Algorithm I, and the pulse wave data collected by sensor 2 is the processing result of Algorithm I. At location B, the ZM-300 is only in contact with sensors 2 and 3, and the latter two share 60% and 40% of the dynamic force. Sensor 2 will continue to be considered as a representative sensor for the entire sensor array in the processing of Algorithm I. However, the dynamic force tested by Sensor 2 has changed, from 60% of the total dynamic force to 80%. Either at position A or position B, Algorithm's representative sensor I acquires only a portion of the entire pulse signal, 80% in the former, and 60% in the latter. Therefore, the energy of Algorithm I's result is less than the standard input signal, which is why the gain value of Algorithm I is less than zero. Furthermore, since the standard input signal's amplitude is the same at both position A and position B, there is a massive difference between the calculation results of Algorithm I at position A and position B.