## 1 Introduction
[17] proposed a decoupling calibration method based on a genetic algorithm, which optimizes the fitness function and genetic operators to obtain an optimal decoupled calibration matrix. This approach eliminates errors associated with traditional matrix inversion, achieving a maximum relative error of only 1.90% for synthesized electric field measurements. Nevertheless, the overall calibration framework is not yet fully refined. [PERSON] et al. [18] further improved the calibration model by incorporating dimensional coupling and angular deviation. Using a differential evolution algorithm, they solved the sensitivity coefficient matrix, effectively reducing system errors. However, this method does not fully account for coupling noise effects on calibration accuracy and remains susceptible to local optima. [PERSON] et al. [19] proposed a support vector regression-based decoupling calibration method, leveraging multi-objective optimization to derive the optimal decoupling matrix and minimize computational errors. While this approach offers notable advantages, its effectiveness is highly dependent on kernel function selection and hyperparameter tuning, resulting in increased computational complexity. Overall, existing 3D airborne electric field measurement techniques still face challenges in measurement accuracy, anti-interference capability, and decoupling calibration methodologies. In recent years, with the rapid development of artificial neural networks and other technologies, some emerging decoupling methods such as Extreme Learning Machine (ELM) and Radial Basis Function (RBF) neural networks, have been widely applied in fields such as multi-dimensional force sensors and acceleration sensors [20; 21; 22]. These methods usually employ complex algorithms, such as the Whale Optimization Algorithm (WOA) with the ELM, or utilize RBF neural networks to achieve sensor decoupling. By learning the complex relationships in the sensor calibration data, these methods can effectively decouple sensors and improve measurement accuracy to some extent. However, these methods also have some limitations. First, the complexity of the algorithms limits the real-time performance of the decoupling process. In addition, some of these methods may have lower linearity, resulting in larger errors. In addition, neural network methods are prone to overfitting problems during training, which affects their generalization ability in practical applications, resulting in potential instability and reliability issues in real-world environments. To address the challenge of inter-axis coupling interference in 3D electric field measurements using electric field sensors, this paper proposes a novel MEMS electric field sensor with a dual-orthogonal induction structure, along with a spatial electric field decoupling method. The sensor features two pairs of orthogonally arranged sensing electrodes on the surface of a cylindrical structure, effectively suppressing common-mode interference and enabling accurate 3D electric field measurements. Additionally, a spatially symmetric structure is employed to achieve differential decoupling. Building on this sensor architecture, a 3D electric field decoupling calibration model is established, and an optimized spatial decoupling method is introduced. By computing the Cramer-Rao lower bound (CRLB) under a linear model, the optimal decoupled calibration matrix is derived to enhance measurement accuracy. Furthermore, a coordinate transformation model for 3D electric field calibration is established, and a sensor prototype along with a dedicated calibration fixture is developed. A calibration and testing system is constructed to experimentally validate the decoupling performance of the proposed method. Experimental results demonstrate that the proposed method significantly reduces coupling interference between electric field components. The computed synthetic field closely aligns theoretical values, exhibiting smaller errors compared to the conventional sensitivity matrix inversion method.