## 2 Related Work  
### T-L Model  
The airborne magnetic survey systems consist of multiple modules that are mainly composed of OPM, fluxgate magnetometer, radar altimeter, INS, GPS and other units. Among them, OPM is a scalar total field magnetometer, which realizes high-precision measurement of the magnetic field [18]. Its measurement is the sum of the modulus of the geomagnetic field vector and other magnetic field vectors (magnetic interference, target signal, etc.). It is equivalent numerically to the sum of the modulus of the geomagnetic field vector and the projections of other magnetic fields in the direction of the geomagnetic field. The obtained signal is the superposition of other interference fields and magnetic target signals after filtering the slowly changing geomagnetic field. So, it is important to eliminate the magnetic interference of the aircraft platform for aeromagnetic measurement. Fluxgate magnetometer can measure the vector of the magnetic field. It can obtain the information of the angle between the coordinate system of the flight platform and the geomagnetic field vector through the fluxgate magnetometer fixedly connecting to the flight platform, so as to measure the attitude of the flight platform. A radar altimeter uses radar echo to measure the altitude of the flight platform to the ground. The INS records the angle of roll, pitch, and yaw speed and other motion parameter information of the aircraft. The GPS records the longitude, latitude, and altitude information of the flight platform and provides auxiliary information for data post-processing. The space of the aircraft is sufficient, so the magnetometer can be installed far away from the magnetic interference sources, such as electronic equipment, to eliminate the magnetic interference of electronic equipment. Therefore, the magnetic interferences caused by the interaction between the airframe material and the background geomagnetic field during the aircraft movement are predominant. In 1950, [PERSON] and [PERSON] proposed that the aircraft interference field can be divided into three parts: permanent magnetic field, induction field, and eddy current field, and established a compensation model with 18 coefficients [19]:  
\[H_{I}=H_{IP}+H_{II}+H_{IE}=\sum_{i=1}^{3}p_{i}c_{i}+H_{f}\sum_{i=1}^{3}\sum_{j =1}^{3}a_{ij}c_{i}c_{j}+H_{f}\sum_{i=1}^{3}\sum_{j=1}^{3}b_{ij}\dot{c}_{i}c_{j} \tag{1}\]  
where \(p_{i},a_{ij},\) and \(b_{ij}\) are the coefficient of the T-L model, \(H_{f}\) is the total magnetic field intensity measured by fluxgate magnetometer, \(c_{i}\) is the cosine of the angle between the three axes of the aircraft coordinate system, which can be measured from the three axes of the fluxgate magnetometer \(H_{i},\ i=1,2,3\), the expression is (2), and \(\dot{c}_{i}\) is time derivative of \(c_{i}\)  
\[c_{i}=\frac{H_{i}}{\sqrt{H_{1}^{2}+H_{2}^{2}+H_{3}^{2}}},i=1,\ 2,\ 3. \tag{2}\]  
Then, the measured value of OPM can be expressed as the superposition of the geomagnetic field and aircraft magnetic interference as follows:  
\[H_{M}=H_{I}+H_{E} \tag{3}\]  
where \(H_{E}\) is the geomagnetic field and \(H_{M}\) is the measured value of OPM. Generally, the earth's magnetic field is slowly changing and its frequency is extremely low. Therefore, the low-frequency geomagnetic field and high-frequency interference can be eliminated by the suitable band-pass filter. After band-pass filtering, the magnetic data only contain magnetic anomaly signals and aircraft magnetic interference. In the detection of aeromagnetic targets, the magnetic anomaly signals generated by the detected targets are usually in the extremely low frequency band (<1 Hz). In order to match the target recognition, we usually pay attention to the low-frequency magnetic field with the frequency range of 0.04-0.3 Hz. In this paper, the band of the band-pass filter is set to 0.04-0.3 Hz.