## 2 Traditional Aeromagnetic Compensation Model  
According to the classical Tolles-Lawson (T-L) aeromagnetic compensation model, the aircraft interference field \(H_{T}(t)\) is a sum of the permanent magnetic field \(H_{P}(t)\), the induced magnetic field \(H_{I}(t)\), and the eddy current magnetic field \(H_{E}(t)\), and is expressed as the following equation:  
\[H_{T}(t)=H_{P}(t)+H_{I}(t)+H_{E}(t). \tag{1}\]  
Usually, a three-axis magnetometer is used to measure the attitude of the platform during the aeromagnetic compensation flight. The quantities \(T\), \(L\), and \(V\) can be used as the three component outputs of the geomagnetic field \(H_{e}(t)\). The cosine values of the angles  
The design of the flight path of the calibration compensation experiment is shown in Figure 2a. The sampling rate of the recording system was 40 Hz. The helicopter flev at a height of about 3000 m to avoid interference from the ground. The compensating flight executed standard maneuvers, including a series of \(\pm 10^{\circ}\) rolls, \(\pm 5^{\circ}\) pitches, and \(\pm 5^{\circ}\) yaws maneuvers along each line in the box. Figure 2 details the flight path and information. After calculating by the LS solution, the compensation parameters of the OPM-I and OPM-II were calculated and separately listed in Tables 1 and 2. Consistent with the actual installation, we found that the compensation parameters of OPM-II were much larger. Figures 3 and 4 show the compensation results of the calibration flight data using the compensation parameters of Tables 1 and 2. The blue dashed and solid lines represent the data before and after the compensation, respectively. Figures 3a and 4a present the results of the processing of the compensation data through a high-pass filter with a cut-off frequency of 0.5 Hz. The signals and the noise power spectral density of the uncompensated flight data and the compensated data are shown in Figures 3b and 4b, respectively. The aeromagnetic compensation had an obvious effect on the low-frequency electromagnetic interference, with a frequency below 2 Hz. Taking OPM-I as an example, the compensated interference field dropped from 45 pT/ VHz at 1 Hz to 18 pT/ VHz at 1 Hz. At higher frequencies, the traditional compensation model had essentially no effect. However, there were still many selective frequency interferences with the measurement magnetic field at 0.72 Hz, 1.445 Hz, 6.48 Hz, and so on. These multi-frequency interferences were mainly caused by the motion of the probe and the vibration interference field caused by the rotation of the propeller, which could not be eliminated by the basic aeromagnetic compensation operation. The correlation coefficient of the residual interference magnetic field was calculated after the OPM-I and OPM-II magnetic compensation process, as shown in Figure 5. According to this figure, the correlation coefficient was high and reached or exceeded 0.8 in the fixed frequency points of the probe vibration and the rotation of the propeller, at 1.445 Hz, 2.15 Hz, 2.89 Hz, 6.48 Hz, and so on. The high correlation values indicate that the vibration interference field compensation based on the data of dual magnetometer had high feasibility to eliminate the interferences at the fixed frequencies. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Parameter** & **Value** & **Parameter** & **Value** & **Parameter** & **Value** & **Parameter** & **Value** \\ \hline c1 & 302.7 nT & c2 & 130.9 nT & c3 & \(-181.1\)nT & c4 & \(1.59\times 10^{4}\) \\ c5 & \(2.70\times 10^{4}\) & c6 & \(-5.00\times 10^{6}\) & c7 & \(3.20\times 10^{3}\) & c8 & \(1.77\times 10^{3}\) \\ c9 & \(-8.51\times 10^{4}\) & c10 & \(-3.49\times 10^{4}\) & c11 & \(-3.10\times 10^{4}\) & c12 & \(4.51\times 10^{4}\) \\ c13 & \(-1.53\times 10^{3}\) & c14 & \(-1.37\times 10^{3}\) & c15 & \(-3.31\times 10^{4}\) & c16 & \(-2.91\times 10^{4}\) \\ \hline \end{tabular}
\end{table} 
Table 2: Compensation parameters of OPM-II.