## 5 Experimental Validation and Results
### Three-Dimensional Electric Field Testing  
The performance of the sensor was evaluated. The sensor was rotated to a random orientation, and a standard electric field ranging from 0 to 50 kV/m was applied in 10 kV/m increments. The three components of the electric field and the resultant electric field were calculated using the decoupling method based on the CRLB, and their variations with respect to the applied electric field were plotted, as shown in Figure 9. The linearity of the decoupled electric field components in the X-, Y-, and Z-directions was calculated to be 2.60%, 1.20%, and 1.78%, respectively, while the linearity of the resultant electric field was 0.74%. The maximum relative error over the full measurement range was 0.80%.  
Furthermore, the sensor was rotated to different orientations, and standard electric fields of 20 kV/m, 30 kV/m, 40 kV/m, and 50 kV/m were applied. The accuracy of the resultant electric field measurements obtained using the two decoupling methods was evaluated, as summarized in Table 1. The results indicate that for different sensor orientations and input electric field conditions, the calculated resultant electric field values obtained using both decoupling methods were in good agreement with the actual values, effectively eliminating coupling interference and enabling accurate 3D electric field measurements. In all 18 tests, 15 of the tests showed that the decoupled electric field's relative errors obtained using the proposed method were significantly smaller than those obtained with the traditional methods, while the remaining 3 tests showed comparable errors between both methods. This demonstrates that the proposed method achieves higher accuracy under a variety of electric field conditions. Moreover, at Angle 4 and an electric field strength of 20 kV/m, the relative error of the traditional method was significantly higher than that of the proposed method. This suggests that at lower electric field strengths, the decoupling performance of the traditional method is limited and more prone to coupling interference, while the proposed method exhibits greater stability under these conditions.  
Table 2 summarizes the relative errors between the calculated and theoretical resultant electric field values obtained using the two decoupling methods and provides a comparison with the best-performing decoupling method reported in [17]. As shown in Table 2, compared to the sensitivity matrix inversion-based decoupling method, the CRLB-based method reduced the maximum error from 3.14% to 1.20%, representing a 61.78% decrease. This demonstrates the ability of the proposed method to effectively suppress coupling interference among electric field components, thereby improving the accuracy of the electric field calculations. When compared to the genetic algorithm-based decoupling method presented in [17], the proposed method achieves a 36.84% reduction in the maximum error, showing its robustness in practical applications. Similarly, the average error decreased from 0.98% to 0.43%, a reduction of 56.12%. In comparison with the genetic algorithm-based  
Figure 9: Decoupled synthetic electric field output curves under applied standard electric field.  
method from [17], the proposed method achieved a 27.12% reduction in average error, further highlighting its superiority in practical measurements. In conclusion, the CRLB-based decoupling method proposed in this paper demonstrates a significant improvement in accuracy under various electric field conditions. Compared to the traditional sensitivity matrix inversion method and the genetic algorithm-based method in [17], the proposed method is more effective in suppressing coupling interference, leading to enhanced 3D electric field measurement accuracy. Therefore, the proposed method provides a more reliable solution for precise decoupling in electric field measurements, with broad potential for applications that require high accuracy.