## 4 Results  
### Experimental Result  
The flight experiment was conducted in the seas south of Hainan, China, in 12 and 21 July 2022. The experimental region is an open field far away from town and with a stable magnetic field. There are no interference magnetic sources, such as buildings. The aircraft platform is a Y-9 transport aircraft and a connecting rod was installed on the tail cone of the aircraft to reduce the influence of the aircraft's magnetic field interference on the magnetic sensor. The data sampling rate is 10 Hz and filtering bandwidth is 0.04-0.3 Hz. In this experiment, the calibration flight data on July 12 are used as the calibration flight dataset to calculate the compensation coefficients. The calibration flight data on 21 July are used as the verification flight dataset, as shown in the Figure 5. For flight paths (a) on 12 July 2022 and (b) on 21 July 2022, the red part in (a) shows the trajectory of the calibration flight segment on 12 July. The red part in (b) is the trajectory of the calibration flight segment on 21 July. The flight altitude is 3000 m. The planes will perform the rolls (\(\pm 10^{\circ}\)), pitches (\(\pm 5^{\circ}\)), and yaws (\(\pm 5^{\circ}\)) in sequence on each side. Using the calibration flight data set, the 18 compensation coefficients only based on the fluxgate magnetometer and only based on INS/GPS information are obtained by the least squares algorithm as shown in Table 3. The 36 compensation coefficients of the conjunctive compensation model are shown in Table 4.  
The compensation coefficients in Tables 3 and 4 are substituted into the calibration flight dataset and the verification flight dataset. The calibration flight data before and after compensation and the verification flight data before and after compensation are shown in Figures 6 and 7, respectively. The uncompensated data are shown in (a) and the comparison between compensated data using these three sets of compensation coefficients is shown in (b). Figures 8 and 9 show the magnetic interference power spectral density of the calibration flight data before and after compensation and the verification flight data before and after compensation, respectively. To evaluate the performance of the three compensation coefficients, the STD and IR are calculated as shown in Tables 5 and 6. Figure 5: Flight paths (a) on 12 July 2022 and (b) on 21 July 2022. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Conjunctive** & \multicolumn{3}{c}{**Conjunctive**} \\
**Compensation** & **Value** & **Compensation** & **Value** \\
**Model Coefficients** & \multicolumn{3}{c}{**Model Coefficients**} \\ \hline c1 & 19.3471 & c19 & \(-1.8367\) \\ c2 & \(-1.2289\) & c20 & 2.2227 \\ c3 & 13.3915 & c21 & 2.2764 \\ c4 & \(-5.5459\times 10^{-4}\) & c22 & \(1.5645\times 10^{-4}\) \\ c5 & \(1.9485\times 10^{-5}\) & c23 & \(-1.1847\times 10^{-4}\) \\ c6 & \(-6.2487\times 10^{-5}\) & c24 & \(6.5468\times 10^{-5}\) \\ c7 & \(-2.0969\times 10^{-4}\) & c25 & \(1.5699\times 10^{-4}\) \\ c8 & \(6.2506\times 10^{-7}\) & c26 & \(-4.5371\times 10^{-6}\) \\ c9 & \(-2.1416\times 10^{-4}\) & c27 & \(1.4092\times 10^{-4}\) \\ c10 & \(0.0240\) & c28 & \(-0.0092\) \\ c11 & \(-2.9659\times 10^{-5}\) & c29 & \(1.7255\times 10^{-4}\) \\ c12 & \(2.4828\times 10^{-4}\) & c30 & \(2.4131\times 10^{-5}\) \\ c13 & \(-5.1210\times 10^{-5}\) & c31 & \(-3.1431\times 10^{-5}\) \\ c14 & \(0.0240\) & c32 & \(-0.0096\) \\ c15 & \(-1.5170\times 10^{-4}\) & c33 & \(-3.2166\times 10^{-6}\) \\ c16 & \(1.2771\times 10^{-4}\) & c34 & \(2.8985\times 10^{-5}\) \\ c17 & \(9.4952\times 10^{-5}\) & c35 & \(-2.4998\times 10^{-5}\) \\ c18 & \(0.0225\) & c36 & \(-0.0095\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The 36 compensation coefficients of the conjunctive compensation model.