## 6 Conclusions  
In this paper, a dual-orthogonal induction MEMS electric field sensor and a spatial electric field decoupling method were proposed to mitigate coupling interference in 3D electric field measurements. The sensor employs two pairs of orthogonally arranged sensing electrodes on the surface of its cylindrical structure to suppress common-mode interference, while MEMS-based electric field-sensing chips enable precise 3D electric field measurements. A 3D electric field decoupling calibration model was established based on the structural characteristics of the sensor, and a linear optimal spatial decoupling method was developed. By deriving the CRLB for the linear model, an optimal linear estimation of unknown electric fields was achieved. Additionally, a coordinate transformation model for sensor calibration was constructed, and a sensor prototype along with a calibration fixture was designed. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{3}{*}{**Angle**} & \multirow{3}{*}{\begin{tabular}{c} **Applied** \\ **Electric Field** \\ **(kV/m)** \\ \end{tabular} } & \multirow{3}{*}{\begin{tabular}{c} **Chip 1** \\ **Output** \\ \end{tabular} } & \multirow{3}{*}{\begin{tabular}{c} **Chip 2** \\ **Output** \\ \end{tabular} } & \multirow{3}{*}{\begin{tabular}{c} **Chip 3** \\ **Output** \\ \end{tabular} } & \multirow{3}{*}{\begin{tabular}{c} **Chip 4** \\ **Output** \\ \end{tabular} } & \multirow{3}{*}{\
\begin{tabular}{c} **Sensitive Matrix** \\ **Inversion-Based** \\ **Decoupling Method** \\ \end{tabular} } & \multirow{3}{*}{
\begin{tabular}{c} **Method Proposed** \\ **in This Paper** \\ \end{tabular} } \\  & & & & & & & & \\ \hline \multirow{3}{*}{Angle 1} & 30 & \(-1.5605\) & 0.8540 & 0.5017 & \(-0.3904\) & 29.9529 & \(-0.1569\) & 30.0340 & 0.1133 \\  & 40 & \(-2.0517\) & 1.2246 & 0.7795 & \(-0.4241\) & 40.1963 & 0.4906 & 39.8480 & \(-0.3800\) \\  & 50 & \(-2.5862\) & 1.5655 & 0.9748 & \(-0.5436\) & 50.8974 & 1.7947 & 50.4352 & 0.8704 \\ \hline \multirow{3}{*}{Angle 2} & 30 & \(-0.8947\) & 0.5504 & \(-0.8389\) & 0.8597 & 30.0686 & 0.2287 & 30.0240 & 0.0799 \\  & 40 & \(-1.2016\) & 0.7139 & \(-1.1234\) & 1.1353 & 39.9884 & \(-0.0290\) & 39.9490 & \(-0.1274\) \\  & 50 & \(-1.5097\) & 0.8879 & \(-1.4108\) & 1.4097 & 50.0004 & 0.0007 & 49.9617 & \(-0.0766\) \\ \hline \multirow{3}{*}{Angle 3} & 20 & \(-0.7919\) & \(-0.0565\) & 0.7871 & \(-0.1510\) & 20.1022 & 0.5108 & 20.0342 & 0.1709 \\  & 30 & \(-1.1828\) & \(-0.0734\) & 1.1926 & \(-0.2354\) & 30.3099 & 1.0331 & 30.2222 & 0.7405 \\ \hline \multirow{3}{*}{Angle 4} & 20 & \(0.7758\) & \(-0.5570\) & \(-0.1766\) & 0.5028 & 19.3720 & \(-3.1398\) & 19.8506 & \(-0.7469\) \\  & 30 & \(-1.1879\) & 0.6568 & 0.7300 & \(-0.7096\) & 29.8631 & \(-0.4563\) & 30.0415 & 0.1382 \\  & 40 & \(-1.5951\) & 0.8264 & 0.8914 & \(-0.9782\) & 39.1579 & \(-2.1052\) & 39.6570 & \(-0.8575\) \\  & 50 & \(-1.9939\) & 1.0417 & 1.1603 & \(-1.1997\) & 49.1539 & \(-1.6921\) & 49.6567 & \(-0.6866\) \\ \hline \multirow{3}{*}{Angle 6} & 30 & \(-1.3949\) & 0.0148 & 1.1200 & \(-0.0827\) & 30.1511 & 0.5035 & 30.0829 & 0.2763 \\  & 40 & \(-1.8419\) & \(-0.0434\) & 1.4948 & \(-0.0956\) & 40.2161 & 0.5403 & 40.0813 & 0.2034 \\  & 50 & \(-2.3049\) & \(-0.0276\) & 1.8528 & \(-0.1330\) & 49.9997 & \(-0.0006\) & 49.8436 & \(-0.3128\) \\ \hline \multirow{3}{*}{Angle 7} & 30 & \(1.2808\) & \(-0.6690\) & \(-0.6763\) & 0.6413 & 29.4107 & \(-1.9642\) & 29.6403 & \(-1.1991\) \\  & 40 & \(1.7120\) & \(-0.9192\) & \(-0.8863\) & 0.8711 & 39.5225 & \(-1.1937\) & 39.8358 & \(-0.4106\) \\ \cline{1-1}  & 50 & \(2.1928\) & \(-1.0571\) & \(-1.0370\) & 1.1394 & 49.0831 & \(-1.8337\) & 49.8662 & \(-0.2676\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of the synthetic electric field and relative error for two decoupling methods under different angles and applied electric fields.