## 6 Conclusions
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Error (\%)**} & \multicolumn{2}{c}{\begin{tabular}{c} **Sensitivity Matrix** \\ **Inversion-Based** \\ **Decoupling Method** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Genetic Algorithm-Based** \\ **Decoupling Method** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Method Proposed** \\ **in This Paper** \\ \end{tabular} } \\  & & & & & \\ \hline Maximum Relative Error & 3.14 & 1.90 & 1.20 \\ Average Relative Error & 0.98 & 0.59 & 0.43 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Relative error between the calculated and theoretical electric field values obtained by different methods. A dedicated calibration and test system was built to experimentally validate the proposed decoupling method. Results demonstrated that within an applied electric field range of 0-50 kV/m, the proposed decoupling method resulted in linearities of 2.60%, 1.20%, and 1.78% for the X, Y, and Z components, respectively, while the resultant electric field exhibited a linearity of 0.74% with a maximum full-scale relative error of 0.80%. Compared to the sensitivity matrix inversion-based decoupling method, the CRLB-based approach reduced the maximum relative error of the resultant electric field from 3.14% to 1.20%, and the average relative error from 0.98% to 0.43%. These results indicate that the proposed MEMS-based electric field sensor and spatial decoupling method effectively suppressed coupling interference, significantly improving the accuracy of 3D electric field measurements. Although the MEMS electric field sensor and decoupling method proposed in this paper have shown excellent performance in experiments, there are still some challenges in real-world applications. The long-term stability of the sensor may be affected by material fatigue and performance degradation of the MEMS components, thus requiring regular calibration or design improvements to ensure sustained accuracy. Additionally, variations in temperature and humidity can impact the sensor's precision. Future research could focus on enhancing the sensor's environmental adaptability, such as by designing temperature compensation algorithms or using more stable materials. Finally, future work could explore more effective decoupling methods and noise suppression techniques to enable 3D electric field detection in complex environments, thereby improving the system's practicality and reliability. Conceptualization, [PERSON] ([PERSON]); methodology, [PERSON] ([PERSON]); software, [PERSON] ([PERSON]), [PERSON] ([PERSON]), and Y.L. ; validation, [PERSON] ([PERSON]) and J.W. ; formal analysis, [PERSON] ([PERSON]), J.W., and W.L. ; investigation, [PERSON] ([PERSON]) and R.R. ; resources, C.P. ; data curation, [PERSON] ([PERSON]) and [PERSON]; writing--original draft preparation, [PERSON] ([PERSON]); writing--review and editing, [PERSON] ([PERSON]); visualization, [PERSON] ([PERSON]) and [PERSON]; supervision, C.P. ; project administration, C.P. ; funding acquisition, C.P. All authors have read and agreed to the published version of the manuscript. This research was funded by National Key R&D Program of China (Grant No. 2022 YFB3207300), and the National Natural Science Foundation of China (Grant No. 62031025), and the Scientific Instrument Developing Project of Chinese Academy of Sciences (Grant No. PTYQ2024 BJ0009). The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author. This work was partly carried out at the State Key Laboratory of Transducer Technology. The authors would like to thank the comrades, who gave us valuable suggestions. During the preparation of this manuscript, the authors used ChatGPT-4o for the purposes of language refinement and grammar checking. The authors have reviewed and edited the output and take full responsibility for the content of this publication. The authors declare no conflicts of interest.