## 4 Ground Evaluation Experiment
### Acceleration Noise and Resolution Evaluation  
The evaluation of the acceleration resolution level of the IS is based on a comprehensive test analysis of the noise affecting the system measurement. Due to the EH being rigidly connected to the measurement system, the external disturbing force effect on it can be ignored. Therefore, the system measurement resolution can be represented by the residual acceleration noise of the TM. The noise sources mainly come from the temperature disturbance, earth pulsation, processing defects of the sensitive structure, and the FEE noise. It is assumed that there is no statistical correlation among various noise sources, and the total residual acceleration noise \(\Delta_{\rm Total}\) is the root mean square of each noise contribution term \(\Delta_{\rm n}\). Table 4 shows the parameters obtained by measuring related equipment. When the temperature changes, the residual gas in the cavity will collide with the TM and lead to acceleration noise. The expression is:  
\[\Delta_{\rm Thr}=\frac{\rm PA}{2\rm m}.\frac{\delta T}{\rm T}\approx 1.5\times 10^{ -10}\ \rm m/s^{2}/Hz^{1/2} \tag{8}\]  
Generally, seismic noise is on the order of magnitude of \(10^{-6}\)\(\sim\)\(10^{-7}\ \rm m/s^{2}/Hz^{1/2}\)[41]. If the vibration isolation conditions are very good, it can reach the order of magnitude of \(10^{-8}\ \rm m/s^{2}/Hz^{1/2}\). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Value** & **Comment** \\ \hline \(\epsilon_{\rm r}\) & 1 & Relative permittivity \\ \(\epsilon_{0}\) & \(8.85\times 10^{-12}\ \rm F/m\) & Vacuum dielectric constant \\ T & 293 K & Environment temperature \\ \(\delta\)T & \(0.1\ \rm K/Hz^{1/2}\) & Temperature fluctuation \\ A & 947.4 mm\({}^{2}\) & Area of electrode X1, X2, X3 \\ \(\delta\)A & 0.2\% & Deviation of electrode area \\ d & 120 \(\rm\mu m\) & Distance between TM and EH \\ P & \(4\times 10^{-5}\ \rm Pa\) & Degree of vacuum \\ m & 42 g & Mass of TM \\ \(\zeta\) & \(5\times 10^{-5}\) & Coupling coefficient between TM and EH \\ \(\delta\rm E_{max}\) & \(10^{-6}\ \rm m/s^{2}/Hz^{1/2}\) & Environmental maximum possible noise \\ l & 0.55 m & Suspension wire length \\ \(\delta\rm V_{P}\) & \(1\times 10^{-5}\ \rm V/Hz^{1/2}\) & Bias voltage fluctuation \\ \(\delta\rm V_{d}\) & \(2\times 10^{-5}\ \rm V/Hz^{1/2}\) & Sensing voltage fluctuation \\ \(\delta\rm V_{f}\) & \(8\times 10^{-6}\ \rm V/Hz^{1/2}\) & Feedback voltage fluctuation \\ \(\rm V_{f}\) & 10 V & Peak of the feedback voltage \\ \(\delta\rm x\) & \(7.2\times 10^{-11}\ \rm m/Hz^{1/2}\) & Position measurement noise \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Related parameters list. Figure 11: The results of the control capability. We reference the measurement results of local earth pulsations [42; 43], analyze the actual vibration isolation conditions in our laboratory, and estimate that the seismic noise disturbance is about:  
\[\Delta_{\rm{Ear}}\approx 1\times 10^{-6}\rm{m}/s^{2}/Hz^{1/2} \tag{9}\]  
Due to processing discrepancy in the production of sensitive structure, it is difficult to make the electrode area totally symmetrical and the electrodes completely parallel to the TM. Therefore, the coupled acceleration noise around the TM in the environment does not exceed the following:  
\[\Delta_{\rm{Geo}}=\zeta\cdot\delta\rm{E}_{\rm{max}}\approx 5\times 10^{-11}\rm{ m}/s^{2}/Hz^{1/2} \tag{10}\]  
The acceleration noise caused by the area asymmetry can also get to:  
\[\Delta_{\rm{Dim}}=\frac{\varepsilon_{0}\varepsilon_{\rm{r}}\rm{A}\delta\rm{A }}{\rm{md}^{2}}(\rm{V}_{\rm{p}}\delta\rm{V}_{\rm{p}}+\rm{V}_{\rm{d}}\delta\rm{V }_{\rm{d}})\approx 3.6\times 10^{-12}\rm{m}/s^{2}/Hz^{1/2} \tag{11}\]  
The FEE noise primarily comes from detection noise and drive noise.