Magnetic Interference Analysis and Compensation Method of Airborne Electronic Equipment in an Unmanned Aerial Vehicle

Abstract

At present, the research and application of aeromagnetic compensation are almost all based on the Tolles–Lawson (T–L) model. With the development of unmanned aerial vehicles (UAVs), the number of intelligent electronic devices in UAVs is increasing, and the magnetic environment of the platform is becoming more and more complicated. Research shows that the magnetic interference caused by airborne electronic equipment has been very significant, sometimes even reaching 100 nT. The traditional airborne magnetic compensation method based on the T–L model cannot effectively compensate the magnetic interference caused by airborne electronic equipment. Aiming at the problem of magnetic interference of airborne electronic equipment of UAVs, this paper analyzes the origin of magnetic interference of airborne electronic equipment using experiments, and it was found that it is related to the power supply current, and the characteristics of magnetic interference are similar to permanent magnet materials. Based on this feature, we eliminated the magnetic interference caused by the working current of airborne equipment by establishing a linear compensation model based on the current’s source. The experimental data show that the current interference source model proposed in this paper can effectively compensate the magnetic interference generated by airborne electronic equipment and the compensation improvement ratio (IR) is greater than 10.

1. Introduction

The UAV aerial magnetic survey is a method of detecting weak magnetic anomaly signals of underground or underwater targets by using a UAV equipped with a high-precision magnetometer to scan doubtful areas [1]. Compared with a manned vehicle, a UAV has the advantages of convenient takeoff and landing, small size, low flight cost and high safety, so it will become the main development trend in the future for UAVs to replace traditional manned vehicles for underwater antisubmarine detection and unexploded ordnance detection [2,3,4,5]. However, the electronic equipment in UAVs is highly integrated as the space limited and most of them are driven by electricity, so the electromagnetic environment of the UAV platform is complex [6,7]. Research shows the strong magnetic interference of about 100nT that small UAVs produce near the magnetometer during operation [8]. This seriously affects the quality of aeromagnetic observation data.

The traditional aeromagnetic compensation algorithm based on the T–L model can only compensate the magnetic interference generated by the ferromagnetic materials and conductive materials of the aircraft platform under the maneuvering action of the platform [9]. This does not effectively describe the magnetic interference generated by airborne electronic equipment, so it is difficult to achieve good results using the small UAV platform. For the magnetic interference caused by airborne electronic equipment, Zhiwen optimized the switching power supply circuit of the aeromagnetic system of a UAV and reduced the electromagnetic interference of the body power supply in [10]. In [11], Forrester proposed a technology to optimize the arrangement of each motor on the body. He did this by modeling the magnetic field of a single servo motor as a single permanent magnet dipole and then using genetic algorithms to find a combinatorial optimal configuration for the servo motor. Gerardo Noriega proposed a real-time dynamic compensation method in [12] to eliminate the weak magnetic interference caused by onboard electronic (OBE) equipment and verified the effectiveness of this method in the laboratory. In [13], a cancellation algorithm was proposed to remove any ON/OFF effects in the magnetic data while recovering the original data to its normal trend. It is a postprocessing method and is not suitable for real-time compensation. In [14], the author proposed to use OBE sensors to measure the equipment current and compensate the weak magnetic interference of about 0.2–1 Hz caused by beacon lights on a manned vehicle. Walter used the aeromagnetic system of the four-rotor UAV to design static and dynamic tests and found the correlation between the frequency of electromagnetic interference signals and the rotation frequency of the UAV motor [15]. This research has certain significance for weakening the electromagnetic interference of the aeromagnetic system of a UAV. In [16], Tuck built a simple magnetic field scanning device to draw a magnetic field distribution map of the body. Using this scanning device, the authors carried out magnetic interference tests on UAVs. The test results showed that the magnetic interference fields of fixed airfoil UAVs were mainly concentrated in the nose and tail of the engine, battery and servo motor. Zheng proposed a novel noise reduction method of UAV magnetic data based on complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN). However, several intrinsic mode functions (IMFs) of CEEMDAN do not have clear physical meanings [17].

In order to eliminate the magnetic interference of UAVs and improve the aeromagnetic data quality of UAVs, this paper analyzes the causes of magnetic interference generated by airborne electronic equipment and studies the characteristics of magnetic interference under different operating conditions using ground experiments. It was found that the magnetic interference of airborne electronic equipment is similar to that of permanent magnet materials and its amplitude is related to the supply current. Based on this discovery, with reference to the modeling method of the T–L model, this paper establishes a linear compensation model based on current interference sources and solves the model coefficients to model the interference using ground calibration experiments. The experiments show that the method proposed in this article can effectively reduce the magnetic interference caused by airborne electronic equipment and significantly improve the quality of aeromagnetic data.

In this paper, the sources and characteristics of UAV magnetic interference are experimentally studied, and a linear model of magnetic interference compensation based on the current measurement is proposed. Finally, the effectiveness of the model is verified using experiments.

2. Related Work

2.1. T–L Model

The airborne magnetic survey system consists of multiple modules that are mainly composed of an optical pump magnetometer (OPM), fluxgate magnetometer, radar altimeter, GPS navigation module and other units. Among them, OPM is a scalar total field magnetometer that provides high-precision measurement of space magnetic fields [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 numerically equivalent 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 UAV platform for aeromagnetic measurement. A fluxgate magnetometer can measure the vector of a space’s magnetic field. It can obtain the information of the included 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.

The space of the manned vehicle is large enough, so the magnetometer can be installed far away from the magnetic interference sources such as electronic equipment to eliminate magnetic interference. Therefore, the traditional compensation method considers the magnetic interference caused by the interaction between the airframe material and the background geomagnetic field during aircraft movement. In 1950, Tolles and Lawson proposed that the aircraft interference field can be divided into three parts: residual magnetic field, induction field and eddy current field [19,20,21]. The magnetic field is a vector, and it is necessary to establish a coordinate system for analysis. As shown in Figure 1, the position of the magnetometer on the aircraft is taken as the origin. The X-axis is parallel to the fuselage axis and points to the nose, the Y-axis is perpendicular to the profile of the fuselage and points to the right wing and the Z-axis is perpendicular to the plane. ${}_{\mathbf{e}}$ represents the geomagnetic field. $\alpha$, $\beta$, $\gamma$, respectively, represent the angle between the geomagnetic field vector and the triaxial coordinate system of the body.

(1) Residual magnetic field: It is generated by ferromagnetic materials in the aircraft and generally considered to be a constant vector in the coordinate system of the body. The measured value of a scalar magnetometer is the superposition of the projection of the geomagnetic field and magnetic anomaly field in the direction of the geomagnetic field, so the residual magnetic field interference can be expressed as

$$H_{rd}=\frac{H_e}{\left|H_e\right|}{·H}_r=H_{rx}\mathit{cos}\alpha +H_{ry}\mathit{cos}\beta +H_{rz}\mathit{cos}\gamma ={\left[\begin{array}{c}\mathit{cos}\alpha \\ \mathit{cos}\beta \\ \mathit{cos}\gamma \end{array}\right]}^T·\left[\begin{array}{c}{H}_{rx}\\ H_{ry}\\ H_{rz}\end{array}\right]$$

where $H_r$ represents the residual magnetic field vector. $H_{rx}$, $H_{ry}$ and $H_{rz}$ are the three components of XYZ of the constant magnetic field in the body coordinate system.

(2) Induced magnetic field: It is mainly generated by the magnetization of the soft magnetic material on the aircraft by the geomagnetic field. The magnetic material on the aircraft has various shapes and complex distribution. In the modeling, it is equivalent to three soft magnetic rods that are only magnetized in the X, Y and Z directions. Due to demagnetization, the induced magnetic field of the soft magnetic bar is in different directions from that of the magnetized magnetic field. Therefore, after the soft magnetic bar in the X direction is magnetized by the X component of the geomagnetic field, it induces magnetic fields along the X, Y and Z directions. Similarly, Y and Z direction soft magnetic bars also have the same effect. So, the induced magnetic field interference can be expressed as

$$H_{id}=\frac{H_e}{\left|H_e\right|}·\left(H_{ix}+H_{iy}+H_{iz}\right)={\left[\begin{array}{c}\mathit{cos}\alpha \\ \mathit{cos}\beta \\ \mathit{cos}\gamma \end{array}\right]}^T·\left[\begin{array}{ccc}{M}_{xx}& M_{xy}& M_{xz}\\ M_{yx}& M_{yy}& M_{yz}\\ M_{zx}& M_{zy}& M_{zz}\end{array}\right]·\left|H_e\right|\left[\begin{array}{c}\mathit{cos}\alpha \\ \mathit{cos}\beta \\ \mathit{cos}\gamma \end{array}\right]$$

(1)

$H_{ix}$, $H_{iy}$ and $H_{iz}$, respectively, represent the induced magnetic fields of the three equivalent magnetic bars. $M_{xx}$, $M_{xy}$, $M_{xz}$, respectively, represent the magnetic field action coefficients of the equivalent magnetic bar in the X direction magnetized by the X component of the geomagnetic field. $M_{yx}$, $M_{yy}$ and $M_{yz}$, respectively, represent the magnetic field action coefficients of the equivalent magnetic bar in the Y direction magnetized by the Y component of the geomagnetic field and $M_{zx}$, $M_{zy}$ and $M_{zz}$, respectively, represent the magnetic field action coefficients of the equivalent magnetic bar in the Z direction magnetized by the Z component of the geomagnetic field.

(3) Eddy current field: It comes from the eddy current effect generated by the cutting of the geomagnetic field by the conducting materials of the body in the process of movement. According to the properties of the eddy current field, its value is related to the external magnetic field and the changing rate of aircraft attitude. Eddy current field interference can be expressed as

$$H_{ed}={\frac{{\mathit{H}}_{\mathit{e}}}{\left|{\mathit{H}}_{\mathit{e}}\right|}·\mathit{H}}_{\mathit{e}\mathit{d}}={\left[\begin{array}{c}\mathit{cos}\alpha \\ \mathit{cos}\beta \\ \mathit{cos}\gamma \end{array}\right]}^T·\left[\begin{array}{ccc}{b}_{11}& b_{12}& b_{13}\\ b_{21}& b_{22}& b_{23}\\ b_{31}& b_{32}& b_{33}\end{array}\right]·\left|{\mathit{H}}_{\mathit{e}}\right|\left[\begin{array}{c}\frac{d\mathit{cos}\alpha }{dt}\\ \frac{d\mathit{cos}\beta }{dt}\\ \frac{d\mathit{cos}\gamma }{dt}\end{array}\right]$$

(2)

where $b_{ij},i=\mathrm{1,2},3;j=\mathrm{1,2},3$ represent the eddy field action coefficients.

So, a compensation model with 18 coefficients is established [22]:

$$H_I={\sum }_{i=1}^3{p}_i{c}_i+H_f{\sum }_{i=1}^3{\sum }_{j=1}^3{a}_{ij}{c}_i{c}_j+H_f{\sum }_{i=1}^3{\sum }_{j=1}^3{b}_{ij}{\dot{c}}_i{c}_j$$

(3)

where $p_i,a_{ij},b_{ij}$ are the coefficients of the T–L model; $H_f$ is the total magnetic field intensity measured using the 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 $H_i,\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}i=\mathrm{1,2},3$; the expression is (4); ${\dot{c}}_i$ is time derivative of $c_i$:

$$c_i=\frac{H_i}{\sqrt{H_1^2+H_2^2+H_3^2}},i=\mathrm{1,2},3$$

(4)

Then, the measured value of OPM can be expressed as the superposition of the geomagnetic field and aircraft magnetic interference as follows:

$$H_M=H_I+H_E$$

(5)

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 Earth’s low-frequency magnetic field and high-frequency interference can be eliminated using a suitable bandpass filter. After bandpass filtering, the magnetic data only contains magnetic anomaly target 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 bandpass filter is set to 0.04–0.3 Hz.

N data points are obtained using a calibration flight; then, the T–L linear model can be expressed as a matrix as follows:

$$B=AC+z$$

(6)

where $B={\left[B\left(1\right),B\left(2\right),\dots ,B\left(n\right)\right]}^T$ represents n scalar magnetometer field data after preprocessing. $\mathrm{A}=\left[\begin{array}{ccc}{\mathrm{A}}_1\left(1\right)& \cdots & {\mathrm{A}}_{18}\left(1\right)\\ ⋮& \ddots & ⋮\\ {\mathrm{A}}_1\left(\mathrm{n}\right)& \cdots & {\mathrm{A}}_{18}\left(\mathrm{n}\right)\end{array}\right]$ is the $n\times 18$ platform attitude matrix. $C={\left[c_1,c_2,\dots ,c_{18}\right]}^T$ is the $18\times 1$ coefficient matrix of the T–L compensation model. It is important to solve the compensation coefficients by using a calibration flight. Therefore, a calibration flight is needed before the aeromagnetic survey.

In order to obtain good calibration flight data, the calibration flight has certain requirements [23]. Firstly, the region with a stable geomagnetic field is usually selected for the calibration flight. A complete compensation flight needs to be performed in four directions, and three sets of actions need to be completed in each direction: pitch, yaw and roll. Each action needs to be repeated at least three times, where the standard amplitude of pitch flight is $\pm 5^{\mathrm{o}}$, the standard amplitude of yaw flight is $\pm {10}^{\mathrm{o}}$ and the standard amplitude of roll flight is $\pm 5^{\mathrm{o}}$. After the compensation is completed, 18 T–L compensation coefficients can be obtained by solving the T–L linear equation. The solution flow of magnetic interference compensation coefficients is shown in Figure 2, and the compensation flow of the T–L model is shown in Figure 3.

2.2. Comparison of T–L Model Compensation Effects

The comparison before and after the compensation of the T–L model in a manned vehicle is shown in Figure 4. It can be seen that the peak-to-peak value of the magnetic interference produced by maneuvering is about 1–2.5 nT and the peak-to-peak value of the magnetic interference can be reduced to less than 0.25 nT after compensation.

However, in the experiment, it was found that the amplitude of the UAV platform’s interference is much larger than that of the manned vehicle and the traditional T–L compensation algorithm had no compensation effect on the experimental data. The comparison before and after the compensation of the T–L model in a UAV is shown in Figure 5. The peak-to-peak value of the magnetic interference before compensation is about 60 nT, which is much larger than that of the manned vehicle and it increases to 600 nT after compensation. This reflects that the main magnetic interference of the UAV may not be generated by the ferromagnetic materials and conductive materials of the platform itself under maneuvering action but may be due to electromagnetic interference generated by airborne electronic equipment. This kind of electromagnetic interference is not described in the traditional T–L model, which leads to the deterioration of compensation results instead of improvement.

3. Theoretical Analysis and Experiment

In this section, the causes of magnetic interference of UAV electronic equipment are analyzed and the changes in the magnetic field and current of the UAV in different operating states are measured.

3.1. Theoretical Analysis

It is generally considered that the magnetic interference of airborne equipment is mainly caused by current. Previous papers show that the electronic equipment on a UAV can radiate complex electromagnetic fields to the surrounding area during operation and two kinds of airborne electronic equipment interference can affect detection: (1) The interference magnetic field generated by the UAV’s power source in the process of supplying power. This is related to the current and has a wide frequency spectrum and large amplitude. (2) The interference magnetic field generated by the control circuit’s changing current, such as the switching circuit and pulse digital circuit. This changes suddenly and has small amplitude [8].

According to electromagnetic field theory, the current can generate a magnetic field. In the low-frequency band, the magnetic interference generated by the current can be calculated by using the Biot–Savart law, which is shown in the following equation [24]:

$$d\overrightarrow{B}=\frac{{\mu }_0}{4\pi }\frac{Idl\times \overrightarrow{r}}{r^3}$$

(7)

$$\overrightarrow{B}={\oint }_L\frac{{\mu }_{0}I}{4\pi }\frac{dl\times r{\overrightarrow{e}}_r}{r^3}$$

(8)

where $I$ is the source current and $L$ is the integration path, $dl$ is a source current differentiation, ${\overrightarrow{e}}_r$ is the unit vector that source current differentiation points to the field point to be solved, $r$ is the distance of the current element from the field point to be solved, ${\mu }_0$ is permeability of vacuum. The magnetic interference caused by current is related to source current, wire shape and observation distance.

3.2. Experiment

In order to determine the relationship between the magnetic interference of UAV electronic equipment and the working state of a UAV and analyze the characteristics of magnetic interference, this paper tests the magnetic interference of airborne electronic equipment using experiments. As shown in Figure 6, (a) is a complete diagram of the UAV magnetic measurement system. It is composed of a UAV, fluxgate magnetometer, OPM and other equipment. Additionally, (b) is a cesium optical pump magnetometer developed independently at our laboratory. The parameters of the fluxgate magnetometer and the optical pump magnetometer are shown in

Table 1. Fluxgate magnetometer and optical pump magnetometer parameters.

Technical Index	Parameters
Magnetic Sensor	Fluxgate Magnetometer	OPM-CAS-18-VL
Measuring range	±100,000 nT	10,000–105,000 nT
Noise level	6 pT/sqrt Hz at 1 Hz	0.3 pT/sqrt Hz at 1 Hz
Size	32 × 32 × 152 mm	$\mathrm{\varnothing }$53 × 78 mm
Weight	160 g	500 g
Orthogonality error	${0.5}^{\mathrm{o}}$	— — — — — — — —
Resolution	0.1 nT	0.0001 nT
Maximum error	10 nT	2.5 nT

, and the current sensor parameters are shown in

Table 2. Current sensor parameters.

Current Sensor Parameters	Value
Measuring range	±150 A
Accuracy at 100 A	±0.45%
di/dt accurately followed	>200A/µs
Offset current	±0.1 mA
Linearity	<0.15%
Size	36.5 × 27.2 × 14.3 mm
Weight	18 g

. The material of the body is mainly carbon fiber, and the connection positions are reinforced using metal. The whole system is purely electric and powered using batteries.

3.2.1. Experimental Equipment and Environment

The layout of each module of the UAV magnetic exploration system used in this experiment is shown in Figure 7. The fluxgate magnetometer and the OPM were installed at the nose position. The fluxgate magnetometer was used to measure the geomagnetic field vector in the UAV coordinate system. The OPM was used to measure the magnetic total field. The batteries are located at the rear side of the wing, which supplies power to the OPM, fluxgate magnetometer, flight control inertial navigation module, engine and other modules through the power supply line. The current sensor was installed at the main power supply line to measure the total current output by the batteries. The schematic diagram of the circuit principle of the UAV magnetic exploration system is shown in Figure 8.

A three-axis parallel fluxgate magnetometer, which is what we used in this work, consists of an excitation module, a pickup module and a signal processing module for each axis. There are a pair of excitation coils with ferromagnetic wires as cores in them in each excitation module. The larger coil surrounding the excitation coils is the pickup module. The ferromagnetic core is a cobalt-rich amorphous wire (Co_68.2Fe_4.3Si_12.5B₁₅) 100 μm in diameter and 20 mm in length. The function of the signal processing module includes generating the excitation signals and demodulating the induction signals. The diagram of the fluxgate sensor is shown in Figure 9. The photograph of the fluxgate magnetometer is shown in Figure 10. The parameters of the fluxgate sensor are listed in

Table 3. Structural parameters of the fluxgate sensor [26].

Parameters	Symbol	Value
Diameter of core	${\mathsf{\Phi }}_{\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{e}}$	100 μm
Length of core	L	20 mm
Wire diameter of excitation coil	${\mathsf{\Phi }}_{\mathrm{e}\mathrm{x}\mathrm{c}}$	0.05 mm
Turn number of excitation coil	${\mathrm{N}}_{\mathrm{e}\mathrm{x}\mathrm{c}}$	900
Wire diameter of pick-up coil	${\mathsf{\Phi }}_{\mathrm{p}\mathrm{i}\mathrm{c}\mathrm{k}-\mathrm{u}\mathrm{p}}$	0.08 mm
Turn number of pick-up coil	${\mathrm{N}}_{\mathrm{p}\mathrm{i}\mathrm{c}\mathrm{k}-\mathrm{u}\mathrm{p}}$	1045
Feedback resistance	$Rfb$	6 kΩ

[25].

For accurately measuring the magnetic interference generated by UAV electronic equipment, the experimental region was in an open field far away from town and with a stable magnetic field. As shown in the Figure 11 There were no interference magnetic sources such as buildings and high-voltage lines around.

3.2.2. Experimental Process

The measured value of OPM is the sum of the modulus of the geomagnetic field vector and other magnetic field vectors. It is numerically equivalent to the sum of the modulus of geomagnetic field vector and the projections of other magnetic fields in the direction of the geomagnetic field [26]. So, the direction of the geomagnetic field may affect the OPM’s measured value. To verify this conjecture, as shown in the Figure 12, the UAV was placed in different directions and repeat experiments to observe the experimental phenomenon.

The ground experiment process was as follows:

(1)

Install the UAV on the test bracket and place it in the north–south direction. Turn on the power supply but keep the engine off and the propeller still. All sensors start measuring synchronously;

(2)

Static test for 5 min to ensure that the experimental instruments are normal and there is no other magnetic interference in the environment;

(3)

Start the engine and keep the propeller turning for 30 s. Repeat 3 times, with an interval of 3 min each time;

(4)

Place the UAV in the east–west direction and repeat steps (2) and (3).

3.2.3. Experimental Results and Analysis

Figure 13 shows the corresponding relations between the power supply current and the engine state during the experiment. The power supply current increases sharply when the engine is started. While the engine is running smoothly, the current is about 30A and there are fluctuations of peak value of 10A. The current decreases rapidly after engine stops, which proves that the engine is the main electrical equipment on the UAV and the engine operation can bring large current.

The changes in magnetic field and current during the experiment are shown in Figure 14. The large current can cause great magnetic interference when the engine is running. As the engine is power equipment; it needs to work continuously as long as the aircraft is flying in the air, so if no measures are taken, the magnetic interference of UAV electronic equipment can always exist.

Figure 15 shows the changes in power supply current and total magnetic field when the engine is not working. According to the figure, the power supply current is less than 0.85A when the engine is not running, and the time-domain magnetic field has no obvious fluctuation. The magnetic field’s peak-to-peak value is less than 0.2 nT after filtering. This proves that the experimental environment is stable and the influence of small current on magnetic measurement is not obvious.

Figure 16 and Figure 17, respectively, depict the changes in power supply current and total magnetic field when the UAV is placed in the north–south direction and the east–west direction. The graph, from top to bottom, is the current curve, the original magnetic field curve and the magnetic field curve after bandpass filtering. Comparing the current curve in Figure 16 and Figure 17, the amplitude of the power supply current is basically the same when the engine is running, which is about 30 A. Combining the three curve graphs, it was found that the engine can generate large magnetic interference when it is running, and the magnetic interference has a strong correlation with the current change in time.

It can be found that the total magnetic field is reduced by about 200 nT when the engine is running and the UAV is placed in the north–south direction but the total magnetic field is increased by about 100 nT when the UAV is placed in the east–west direction. Comparing the current curve and the original magnetic field curve in Figure 16 and Figure 17, it was found that the characteristics of magnetic interference caused by the same current in different placement directions are different.

According to the vector synthesis relationship, the included angle between the magnetic interference of UAV electronic equipment and the geomagnetic field vector should be obtuse when the UAV is placed in the north–south direction. When placed in the east–west direction, the angle between the magnetic interference of UAV electronic equipment and the geomagnetic field vector should be acute. That is to say, the magnetic interference vector of UAV electronic equipment should be similar to the characteristics of permanent magnet materials, regardless of the magnetic field’s magnetization.

It can be found from the magnetic field curve, after bandpass filtering, that the waveform of the magnetic interference that is caused by the suddenly changed current is similar to the magnetic target signals. This causes serious interference in target recognition.

To sum up, three conclusions can be drawn:

(1)

When the UAV engine is running, it brings large current to supply power and also produces great magnetic interference.

(2)

The magnetic interference of UAV airborne electronic equipment is mainly generated by power supply current. The magnetic interference vector of UAV electronic equipment should be similar to the characteristics of permanent magnet materials, regardless of the magnetic field’s magnetization.

(3)

The filtered waveform of the magnetic interference caused by the sudden change in current when the engine starts and stops is similar to the magnetic target signal. It causes serious interference to target recognition.

4. Proposed Method

Based on the previous analysis, the magnetic interference of UAV airborne electronic equipment is mainly caused by power supply current, and the magnetic interference vector of UAV electronic equipment should be similar to the characteristics of permanent magnet materials. So, we established a linear compensation model based on current interference sources under inspiration of the T–L modeling method of the constant magnetic field. The model uses UAV current data, fluxgate magnetometer data and OPM data obtained during the ground calibration experiment to calculate the model coefficients. The coefficients and the current interference source matrix can be used to estimate the magnetic interference and then subtract the modeling interference from the OPM data to achieve compensation.

4.1. Compensation Principle

According to the foregoing, the magnetic interference vector caused by current can be divided into two parts: the magnetic interference caused by constant current and the magnetic interference caused by changed current and the magnetic interference vector should be projected in the direction of the geomagnetic field. So, we established a compensation model with six coefficients.

Assume that the magnetic interference vector caused by the current is shown in Equation (9).

$${\mathit{H}}_d\left(t\right)={\mathit{H}}_I\left(t\right)+{\mathit{H}}_{I^{\mathrm{\prime }}}\left(t\right)$$

(9)

where ${\mathit{H}}_I\left(t\right)$ is the magnetic interference vector linearly dependent on the current, and ${\mathit{H}}_{I^{\mathrm{\prime }}}\left(t\right)$ is the magnetic interference vector linearly dependent on the time derivative of the current.

The magnitude of the magnetic anomaly signal measured using the optical pump magnetometer is numerically approximate to the projection of the magnetic anomaly vector in the direction of the geomagnetic field vector. Therefore, the magnetic interference caused by the current can be expressed as follows:

$$H_{pd}\left(t\right)=\left[\begin{array}{ccc}{H}_{I_x}\left(t\right)& H_{I_y}\left(t\right)& H_{I_z}\left(t\right)\end{array}\right]\cdot \left[\begin{array}{c}\cos \alpha \\ \cos \beta \\ \cos \gamma \end{array}\right]+\left[\begin{array}{ccc}{H}_{I_x^{\mathrm{\prime }}}\left(t\right)& H_{I_y^{\mathrm{\prime }}}\left(t\right)& H_{I_z^{\mathrm{\prime }}}\left(t\right)\end{array}\right]\cdot \left[\begin{array}{c}\cos \alpha \\ \cos \beta \\ \cos \gamma \end{array}\right]$$

(10)

$$\cos \alpha =X\left(t\right)/\sqrt{{X\left(t\right)}^2+{Y\left(t\right)}^2+{Z\left(t\right)}^2}$$

(11)

$$\cos \beta =Y\left(t\right)/\sqrt{{X\left(t\right)}^2+{Y\left(t\right)}^2+{Z\left(t\right)}^2}$$

(12)

$$\cos \gamma =Z\left(t\right)/\sqrt{{X\left(t\right)}^2+{Y\left(t\right)}^2+{Z\left(t\right)}^2}$$

(13)

where $H_{I_x}\left(t\right)$, $H_{I_y}\left(t\right)$ and $H_{I_z}\left(t\right)$ are, respectively, XYZ three components of ${\mathit{H}}_I\left(t\right)$ in the body coordinate system, while $H_{I_x^{\mathrm{\prime }}}\left(t\right)$, $H_{I_y^{\mathrm{\prime }}}\left(t\right)$ and $H_{I_z^{\mathrm{\prime }}}\left(t\right)$ are, respectively, XYZ three components of ${\mathit{H}}_{I^{\mathrm{\prime }}}\left(t\right)$ in the body coordinate system. $X\left(t\right)$, $Y\left(t\right)$ and $Z\left(t\right)$ are fluxgate XYZ triaxial measurements. The XYZ three components of ${\mathit{H}}_I\left(t\right)$ are all linearly dependent on the current $I\left(t\right)$, and the XYZ three components of ${\mathit{H}}_{I^{\prime }}\left(t\right)$ are all linearly dependent on the time reciprocal of the current $I\prime \left(t\right)$. Therefore, Equation (8) can be written as follows:

$$\begin{gathered} H_{pd}\left(t\right)=C_{1}I\left(t\right)\cos \alpha +C_{2}I\left(t\right)\cos \beta +C_{3}I\left(t\right)\cos \gamma + \\ {C}_4{I}^{\mathrm{\prime }}\left(t\right)\cos \alpha +{C_{5}I}^{\mathrm{\prime }}\left(t\right)\cos \beta +C_6{I}^{\mathrm{\prime }}\left(t\right)\cos \gamma \end{gathered}$$

(14)

where $I\left(t\right)$ is current and $I^{\mathrm{\prime }}\left(t\right)$ is current derivative to time. Coefficient $C_k\left(k=1,2,\cdots ,6\right)$ are the magnetic compensation coefficients of UAV electronic equipment. $\mathrm{Cos}\alpha$,$\cos \beta$,$\cos \gamma$, respectively, represent the direction cosine of the geomagnetic field in the UAV coordinate system. It is expressed in matrix form as follows:

$$H_{n\times 1}=A_{n\times 6}{C}_{6\times 1}+Z_{n\times 1}$$

(15)

$$A=\left[I\left(t\right)\cos \alpha I\left(t\right)\cos \beta I\left(t\right)\cos \gamma I^{\mathrm{\prime }}\left(t\right)\cos \alpha I^{\mathrm{\prime }}\left(t\right)\cos \beta I^{\mathrm{\prime }}\left(t\right)\cos \gamma \right]$$

(16)

where $H$ is the interference magnetic field of the UAV platform and $C$ is the coefficient in the aeromagnetic compensation model. A is the current interference matrix composed of current and current derivative to time and $Z$ is the model error.

The above formula is a linear equation, and the compensation coefficients can be solved by ground calibration data using the least square algorithm (LS).

The least square solution of the compensation coefficients C are as follows [27]:

$$C={\left(A^{T}A\right)}^{-1}{A}^T{H}_d$$

(17)

4.2. Calibration Process

The calibration experiment of magnetic compensation of UAV electronic equipment can be carried out on the ground. The UAV magnetic measurement system is placed in the north–south direction and the east–west direction in turn and the electronic equipment is periodically connected and separated in each direction. There should be a certain time interval between the connection and separation of electronic equipment to obtain the analog state signal (usually voltage/current) and changing magnetic field data of the equipment in the calibration experiment.

4.3. Data Processing Flow

The specific process is as follows:

(1)

Obtain the original magnetic data from the OPM and preprocess the magnetic data, mainly filtering.

(2)

Obtain original current data from a current sensor and combine the direction cosine information of the geomagnetic field from fluxgate magnetometer to construct the current matrix of the compensation model.

(3)

Calculate the compensation coefficients using the least square algorithm (LS).

(4)

The modeling interference is calculated using the current matrix and compensation coefficients, and the modeling interference is subtracted from the filtered OPM data to generate the magnetic field data after compensation.

The data processing flow of the compensation coefficients solution is shown in Figure 18, and the compensation flow of the magnetic interference caused by UAV electronic equipment is shown in Figure 19.

4.4. Performance Metrics

The viability and reliability of using the standard deviation of the signal as an assessment criterion were proven by Gerardo Noriega using a large number of aeromagnetic trials [28,29]. At present, the general evaluation standard for the compensation effect of the aeromagnetic survey is to use standard deviation (STD) as the measure of data interference, and to use improved ratio (IR) to measure the compensation effect of the algorithm on data [30]. The higher the IR, the better the compensation effect. STD is defined as (18) and IR as (19).

$$\mathrm{STD}=\sqrt{\frac{1}{n}{\sum }_{i=1}^n\left(x_i-\mu \right)}$$

(18)

$$IR=\frac{\mathrm{STD}\left(H_b\right)}{\mathrm{STD}\left(H_a\right)}$$

(19)

where $\mu$ is the arithmetic mean of $x_i$ and $H_b$, $H_a$ represent the OPM data before and after compensation, respectively.

5. Result

5.1. Experimental Result

The ground calibration experiment was carried out on the Yellow River Beach in China in April 2022. The experimental environment is far away from towns and the magnetic field is stable. The aircraft platform was a UAV designed and assembled independently in China. The data sampling rate was 10 Hz. Then, the flight experiment was conducted to obtain the real flight data. The flight experiment consists of three parts: climb, cruise and landing. The cruise maintained a flight altitude of 2000 m. The ground calibration experiment data were used as the calibration dataset to calculate the current model compensation coefficients using the least squares algorithm, as shown in

Table 4. The current model compensation coefficients.

Current Compensation Model Coefficients	Value	Current Compensation Model Coefficients	Value
c1	−4.9112	c4	−3.8696
c2	−10.7720	c5	5.3090
c3	−1.4785	c6	−5.0002

. The real flight data were used as the verification flight dataset to verify the effect of the current compensation model. The magnetic interference curves before and after compensation of the ground calibration experiment are shown in Figure 20. Figure 21 and Figure 22 more specifically show the magnetic interference curves before and after compensation when the UAV was placed in the north–south direction and the east–west direction.

The flight altitude variation curve is shown in Figure 23. The magnetic interference curves before and after compensation in the flight experiment are shown in Figure 24, Figure 25 and Figure 26, showing the magnetic interference curves before and after compensation during climb, cruise and landing, respectively. (a) Represents unfiltered data and (b) represents bandpass-filtered data.

5.2. Result Analysis

The magnetic interference waveforms before and after compensation of calibration data are shown in Figure 20, Figure 21 and Figure 22. According to the general compensation evaluation standard of airborne magnetic surveys, the quantitative compensation results are shown in

Table 5. The magnetic interference standard deviation and improvement ratio before and after compensation.

	Current Model Compensated
Std before compensation (nT)	15.5613
Std after compensation (nT)	1.5225
IR	10.2210

. The standard deviation of interference before compensation is 15.5613 nT and the standard deviation of interference after compensation using the current interference source model is 1.5225 nT. IR is greater than 10. It shows that the current interference source model can compensate most of the magnetic interference generated by UAV electronic equipment, but there is still a certain amount of residual magnetic interference that may be caused by model errors or coupling interference between the power supply current and the aircraft’s maneuverability. From the time-domain situation of interference, as shown in

Table 6. The peak-to-peak value of magnetic interference before and after compensation.

	Current Model Compensated
P–p before compensation (nT)	185.4457
P–p after compensation (nT)	12.5225

, the peak-to-peak value of magnetic interference before compensation is greater than 180 nT and the peak-to-peak value of magnetic interference after compensation using the current interference source model is reduced to 12.5225 nT. This proves that the current interference source model has an obvious compensation effect on the sudden interference that UAV electronic equipment causes.

The magnetic interference waveforms before and after compensation of the actual flight data are shown in Figure 24, Figure 25 and Figure 26. The coefficients of Table 4 were used for the compensation of the flight data, and the quantitative compensation results are shown in

Table 7. The standard deviation and improvement ratio of magnetic interference before and after compensation in flight experiment.

Flight Experiment	Std before Compensation (nT)	Std after Compensation (nT)	IR
Climb	64.2361	26.9110	2.3870
Cruise	53.3411	20.6491	2.5832
Landing	12.1922	6.0670	2.0096

. In the climbing data, the standard deviation of the magnetic interference before compensation is 64.2361 nT, and the standard deviation of the residual magnetic interference after compensation is 26.9110 nT. In the cruising data, the standard deviation of the magnetic interference before compensation is 53.3411 nT, and the standard deviation of the residual magnetic interference after compensation is 20.6491 nT. In the landing data, the standard deviation of the magnetic interference before compensation is 12.1922 nT, and the standard deviation of the residual magnetic interference after compensation is 6.0670 nT. The compensation improvement ratio is greater than two for all three sets of data.

Because the small UAV is limited by endurance and control mode, it was not used to carry out a maneuvering magnetic interference calibration flight. So, the magnetic interference caused by aircraft maneuvers was not eliminated and was reflected in the residual noise.

As shown in Figure 24 and Figure 26, the magnetic interference of airborne electronic equipment persisted throughout the entire flight process. It can be seen that the magnetic interference waveform is similar to magnetic anomalies signal. After compensation, the magnetic interference caused by most airborne equipment can be significantly eliminated.

To sum up, the compensation method proposed in this paper is feasible and effective. As shown in Figure 20, the proposed compensation model only compensates the magnetic interference caused by the current and does not affect the maneuvering magnetic interference. So, it can be combined with the traditional T–L model to improve the signal-to-noise ratio of magnetic anomaly signals.

6. Conclusions

At present, the research and application of aviation magnetic compensation methods are almost all based on the T–L model, which can only compensate the magnetic interference caused by the ferromagnetic and conductive materials of the aircraft platform under maneuvering action. It is ineffective regarding the magnetic interference caused to the UAV platform, even leading to the deterioration of compensation results.

Aiming at the problem of UAV magnetic interference, this paper analyzed the causes of magnetic interference in a UAV and actually measured the changes in magnetic field and current in different operating states. Using experiments, it was found that the magnetic interference of UAV airborne electronic equipment is mainly generated by the power supply’s current. The magnetic interference vector of UAV electronic equipment should be similar to the characteristics of permanent magnet materials, regardless of the magnetic field’s magnetization. The filtered waveform of the magnetic interference caused by the sudden change in current when the engine starts and stops is similar to the magnetic target signals. This causes serious interference to target recognition. In this paper, through monitoring the changes in power supply current related to magnetic interference, a linear compensation model based on current interference sources was established using inspiration from the T–L modeling method of the constant magnetic field. The modeling magnetic interference was subtracted from the OPM data to complete compensation. In fact, the compensation method proposed in this paper can also compensate for magnetic interference, similar to the characteristics of permanent magnetic materials on the other carrier platform, by monitoring the related electrophysical quantities.

The experimental data show that the compensation method proposed in this paper greatly reduces the magnetic interference caused by UAV airborne electronic equipment and significantly improves the quality of aeromagnetic data. It also can be combined with the traditional T–L model to improve the signal-to-noise ratio of magnetic anomaly signals and is beneficial to the development of subsequent magnetic anomaly detection algorithms.