CN111190229B - A magnetic target detection method - Google Patents

Abstract

The present invention provides a magnetic target detection method, the detection method comprises the following steps: step 1, firstly use the STAR method to calculate the initial value of the position vector and the magnetic moment vector; step 2, then calculate the new position vector and the magnetic moment vector; Step 3: Repeat step 2 until the difference between the two position vectors before and after satisfies the convergence condition or the number of iterations reaches the limit. The invention discloses the mechanism of both the direction error and the distance error, and proposes an NSM that uses the iterative method to compensate the direction error and the distance error at the same time; NSM reduces the average positioning errors of the STAR method, LSM and WSM respectively. It is 95.1%, 46.0%, and 43.3% smaller, which further improves the magnetic detection accuracy of the three magnetic detection methods.

Description

A magnetic target detection method

technical field

The invention relates to a magnetic target detection method, which belongs to the technical field of magnetic detection.

Background technique

Magnetic detection can detect non-cooperating magnetic targets in real time, which is a research hotspot in many fields. In the field of military engineering, it can be used to detect underwater submarines, unexploded ordnance (UXO), magnetic obstacles, etc. In the field of medical research, it can be used for wireless capsule tracking, detection of targeted cancer cells, tongue tracking, etc. In the field of geophysics, it can be used for mineral exploration, cave mapping, geomagnetic field evolution, etc.

Magnetic detection method is the core research content of magnetic detection, and the improvement of magnetic detection method is an important means to improve the accuracy of magnetic detection. The earth's magnetic field is an inherent property of the earth, and only magnetic detection methods that are not affected by the earth's magnetic field can be widely used. Based on the invariant of the magnetic gradient tensor, Wiegert proposed the scalar triangulation and ranging (STAR) method. The STAR method can not only detect magnetic targets in real time, but also the detection accuracy is not affected by the geomagnetic field, which has received extensive attention. Due to the existence of the aspheric coefficient, the STAR method will generate errors when calculating the distance and direction of the magnetic target, which is called "aspheric error". In order to further improve the detection accuracy of the STAR method, the existing research compensates the aspheric error.

In the existing improved STAR method, there are the following problems:

1. Only the direction error of the STAR method is compensated, and it cannot be used in actual magnetic detection.

In 2015, some scholars used the iterative method to compensate the direction error, and this magnetic detection method is called SSM in this paper. In the range of detection distance of 8 to 11.31m, the detection error of SSM does not exceed 1%. But SSM only compensates for the direction error, and does not compensate for the distance error. And the SSM can only be used under the condition that the signal-to-noise ratio is greater than 200, which is almost impossible to appear in the actual magnetic detection. Therefore, SSM cannot be used in practical magnetic detection.

2. Both the direction error and the distance error are compensated, but the improved detection accuracy is very limited.

In 2015, some scholars proposed the invariant of the magnetic gradient tensor without aspheric coefficients, which compensated for the direction error and distance error of the STAR method. This magnetic detection method is called LSM in this paper. When the magnetic target moves on a circular trajectory parallel to the x-y plane, the detection error of the LSM is only reduced by 10.9% compared to the STAR method. Therefore, LSM only compensates a small part of the aspherical error, and the improved detection accuracy is very limited.

3. Only the direction error of the STAR method is compensated, which limits the further improvement of the detection accuracy.

In 2016, some scholars compensated the orientation error of the STAR method by using the invariant and iterative method of the modified magnetic gradient tensor. This magnetic detection method is called WSM in this paper. When the magnetic target moves on a circular trajectory parallel to the x-y plane, the detection error of WSM is reduced by 68.5% compared to the STAR method. The orientation error is the main component of the aspherical error, but the magnetic detection accuracy cannot be further improved without compensating for the distance error of the STAR method.

SUMMARY OF THE INVENTION

The purpose of the present invention is to propose a magnetic target detection method to solve the problem that SSM only compensates the direction error of the STAR method, and cannot be used in actual magnetic detection; LSM compensates both the direction error and the distance error, but improves the detection accuracy. Very limited; WSM only compensates for the orientation error of the STAR method, which limits the further improvement of detection accuracy.

A magnetic target detection method, the detection method comprises the following steps:

Step 1. First use the STAR method to calculate the initial value of the position vector and the magnetic moment vector;

Step 2, then use formula (12) and formula (13) to calculate new position vector and magnetic moment vector, wherein, the formula (12) is:

表示z轴正方向的非球面系数，

表示z轴负方向的非球面系数，

表示z轴正方向的C_T，C_T为磁梯度张量的不变量，

表示z轴负方向的C_T，D_z为基线距离，

为传感器指向磁目标的位置向量，

为(0,0,1)，▽C为补偿后的磁梯度张量的不变量，in

represents the aspheric coefficient in the positive direction of the z-axis,

represents the aspheric coefficient in the negative direction of the z-axis,

C _T represents the positive direction of the z-axis, C _T is the invariant of the magnetic gradient tensor,

C _T represents the negative direction of the z-axis, D _z is the baseline distance,

is the position vector of the sensor pointing to the magnetic target,

is (0,0,1), ▽C is the invariant of the compensated magnetic gradient tensor,

The formula (13) is:

In the formula,

Step 3: Repeat step 2 until the difference between the two position vectors before and after satisfies the convergence condition or the number of iterations reaches the limit.

Further, in step 1, specifically, a space rectangular coordinate system is established with the center of the tensor gradiometer as the origin, and the full tensor of the magnetic target is calculated according to the magnetic dipole model.

为磁矩向量，

为传感器指向磁目标的位置向量，r为

的大小，δ_ij是克罗内克函数，i,j＝x,y,z，利用式(1)可计算出磁梯度张量的不变量C_T：In formula (1), the vacuum permeability μ0=4π×10-7T·m/A,

is the magnetic moment vector,

is the position vector of the sensor pointing to the magnetic target, r is

, δ _ij is the Kronecker function, i, j=x, y, z, the invariant C _T of the magnetic gradient tensor can be calculated by using formula (1):

为：In formula (2), M is the magnitude of the magnetic moment vector, the direction vector of the magnetic target

for:

代表磁目标相对于张量梯度仪的方向，简称为磁目标的方向，k的值是随着磁目标的方向的变化而变化的：in,

Represents the direction of the magnetic target relative to the tensor gradiometer, referred to as the direction of the magnetic target for short, and the value of k changes with the direction of the magnetic target:

与

的夹角，根据式(2)、(4)，得到：where γ is

and

The included angle of , according to formulas (2) and (4), we get:

是

的单位向量，方向误差是非球面误差的主要组成部分，带有偏差的方向向量

为：in,

Yes

The unit vector of , the direction error is the main component of the aspheric error, the direction vector with the bias

for:

where:

Assuming that there is no error in the calculation of the distance r, define the direction error ω:

Substitute equation (6) into equation (7) to get:

From equation (8), it can be seen that the direction error ω has a linear relationship with the distance r, and has a nonlinear relationship with the included angle γ. In order to compensate the aspherical error, the invariant ▽C of the magnetic gradient tensor after compensation is defined,

Combining formula (5) and formula (9), we can get:

It can be seen from equation (10) that ▽C points to the magnetic target, and combined with the tensor gradiometer of the regular hexahedron structure, the equation of the distance r can be obtained.

Combining equations (10) and (11), the position vector of the magnetic target can be obtained

After calculating the position vector of the magnetic target, calculate the magnetic moment vector according to formula (1) and the least square method:

where:

The main advantages of the present invention are:

(1) The aspherical error of the STAR method includes two parts: the direction error and the distance error. This paper reveals the mechanism of the direction error and the distance error, and proposes an iterative method to measure the direction error and the distance error at the same time. Compensated NSM.

(2) NSM reduces the average positioning errors of STAR method, LSM and WSM by 95.1%, 46.0% and 43.3% respectively, which further improves the magnetic detection accuracy of these three magnetic detection methods.

Description of drawings

Figure 1 shows the direction error at different angles γ when the distance r=0.5m;

2 is a schematic diagram of a magnetic target motion trajectory;

Figure 3 shows the positioning error of the magnetic detection method on a circular trajectory.

Detailed ways

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

A magnetic target detection method, the detection method comprises the following steps:

Step 1. First use the STAR method to calculate the initial value of the position vector and the magnetic moment vector;

Step 2, then use formula (12) and formula (13) to calculate new position vector and magnetic moment vector, wherein, the formula (12) is:

表示z轴正方向的非球面系数，

表示z轴负方向的非球面系数，

表示z轴正方向的C_T，C_T为磁梯度张量的不变量，

表示z轴负方向的C_T，D_z为基线距离，

为传感器指向磁目标的位置向量，

为(0,0,1)，▽C为补偿后的磁梯度张量的不变量，in

represents the aspheric coefficient in the positive direction of the z-axis,

represents the aspheric coefficient in the negative direction of the z-axis,

C _T represents the positive direction of the z-axis, C _T is the invariant of the magnetic gradient tensor,

C _T represents the negative direction of the z-axis, D _z is the baseline distance,

is the position vector of the sensor pointing to the magnetic target,

is (0,0,1), ▽C is the invariant of the compensated magnetic gradient tensor,

The formula (13) is:

In the formula,

Step 3: Repeat step 2 until the difference between the two position vectors before and after satisfies the convergence condition or the number of iterations reaches the limit.

In the preferred embodiment of this section, in step 1, specifically, the magnetic target in the magnetic detection can generally be regarded as a magnetic dipole. The space rectangular coordinate system is established with the center of the tensor gradiometer as the origin, and the full tensor of the magnetic target can be calculated according to the magnetic dipole model

为磁矩向量，

为传感器指向磁目标的位置向量，r是

的大小。δ_ij是克罗内克函数，i,j＝x,y,z。利用式(1)可计算出磁梯度张量的不变量C_T：In formula (1), the vacuum permeability μ0=4π×10-7T·m/A,

is the magnetic moment vector,

is the position vector of the sensor pointing to the magnetic target, r is

the size of. δ _ij is the Kronecker function, i,j=x,y,z. Using formula (1), the invariant C _T of the magnetic gradient tensor can be calculated:

为：In formula (2), M is the magnitude of the magnetic moment vector. In the STAR method, the aspheric coefficient k is assumed to be a constant value, then C _T is only related to the distance r, and the gradient of C _T ▽ C _T points to the magnetic target. Direction vector of the magnetic target

for:

代表磁目标相对于张量梯度仪的方向，将其简称为磁目标的方向。实际上，k的值是随着磁目标的方向的变化而变化的。

Represents the orientation of the magnetic target relative to the tensor gradiometer, which is simply referred to as the orientation of the magnetic target. In practice, the value of k varies with the orientation of the magnetic target.

与

的夹角。根据式(2)、(4)可得到：where γ is

and

angle. According to formulas (2) and (4), it can be obtained:

是

的单位向量，由式(5)可知，▽C_T不再指向磁目标，这是STAR法存在方向误差的根本原因。方向误差是非球面误差的主要组成部分。带有偏差的方向向量

为：

Yes

It can be seen from equation (5) that ▽ _CT no longer points to the magnetic target, which is the fundamental reason for the directional error of the STAR method. Orientation error is the main component of aspheric error. direction vector with bias

for:

in the formula

Assuming that there is no error in the calculation of the distance r, define the direction error ω:

Substitute equation (6) into equation (7) to get:

It can be seen from equation (8) that the direction error ω has a linear relationship with the distance r, and has a nonlinear relationship with the included angle γ. When the distance is constant, the direction error is only related to the included angle γ. When the distance r=0.5m, the direction error ω under different included angles γ is shown in Figure 1. It can be seen from the figure that when γ=60° or γ=120°, the direction error is the largest; when γ=0° or γ=90° or γ=180°, there is no direction error.

In order to compensate the aspherical error, the invariant ▽C of the magnetic gradient tensor after compensation is defined.

Combining formula (5) and formula (9), we can get:

It can be known from equation (10) that ▽C points to the magnetic target. Combined with the tensor gradiometer of the regular hexahedron structure, the equation of the distance r can be obtained.

表示z轴正方向的非球面系数，

表示z轴负方向的非球面系数。

表示z轴正方向的C_T，

表示z轴负方向的C_T，D_z为基线距离。结合式(10)和式(11)可得到磁目标的位置向量

in

represents the aspheric coefficient in the positive direction of the z-axis,

Indicates the aspheric coefficient in the negative z-axis direction.

C _T representing the positive direction of the z-axis,

C _T represents the negative direction of the z-axis, and D _z is the baseline distance. Combining equations (10) and (11), the position vector of the magnetic target can be obtained

After the position vector of the magnetic target is calculated, the magnetic moment vector is calculated according to formula (1) and the least square method.

m=(A ^T ·A) ^-1 A ^T ·G (13)

where:

A specific embodiment is provided below:

基线距离D、传感器的分辨率S、高斯白噪声的标准差σ的值如表1所示。在此工况中，先不考虑张量梯度仪的标定误差。Let the magnetic target move on _a circular trajectory T1 parallel to the xy plane, as shown in Figure 2. In the trajectory T1, the height h ₌ 0.25m and the radius R=0.433m. The geomagnetic field amplitude is 55000nT, the geomagnetic declination is -10°, and the geomagnetic dip is 60°. Detection distance r, magnetic moment vector

The values of the baseline distance D, the resolution S of the sensor, and the standard deviation σ of Gaussian white noise are shown in Table 1. In this case, the calibration error of the tensor gradiometer is not considered first.

Table 1 Simulation conditions

Because the magnetic moment vector is calculated from the position vector, the positioning error δ is used to measure the detection error.

来衡量磁探测方法的探测精度，

越小，探测精度越高。图3展示了磁探测方法在圆形轨迹上的定位误差。从图中可以看出NSM的定位误差是最小的。磁探测方法在轨迹T₁上定位误差的平均值如表2所示。从表中可以看出，NSM分别将STAR法、LSM、WSM的平均定位误差减小了95.1％、46.0％、43.3％，进一步提高了三种磁探测方法的磁探测精度。Where x _t , y _t , and z _t are the real values of the coordinates of the magnetic target in the x, y, and z directions, respectively, and x _c , y _c , and z _c are the calculated values of the coordinates in the x, y, and z directions, respectively. mean positioning error

To measure the detection accuracy of the magnetic detection method,

The smaller the value, the higher the detection accuracy. Figure 3 shows the localization error of the magnetic detection method on a circular trajectory. It can be seen from the figure that the positioning error of NSM is the smallest. The average value of the positioning error of the magnetic detection method on the track T1 is shown in Table ₂ . It can be seen from the table that NSM reduces the average positioning errors of the STAR method, LSM, and WSM by 95.1%, 46.0%, and 43.3%, respectively, and further improves the magnetic detection accuracy of the three magnetic detection methods.

Table 2. Average positioning error of magnetic detection methods.

Claims (2)

1. a magnetic target detection method, is characterized in that, described detection method comprises the following steps: Step 1. First use the STAR method to calculate the initial value of the position vector and the magnetic moment vector; Step 2, then use formula (12) and formula (13) to calculate new position vector and magnetic moment vector, wherein, the formula (12) is:

in

represents the aspheric coefficient in the positive direction of the z-axis,

represents the aspheric coefficient in the negative direction of the z-axis,

C _T represents the positive direction of the z-axis, C _T is the invariant of the magnetic gradient tensor,

C _T represents the negative direction of the z-axis, D _z is the baseline distance,

is the position vector of the sensor pointing to the magnetic target,

is (0,0,1),

is the invariant of the compensated magnetic gradient tensor, The formula (13) is:

In the formula,

Step 3: Repeat step 2 until the difference between the two position vectors before and after meets the convergence condition or the number of iterations reaches the limit. In step 1, specifically, a space rectangular coordinate system is established with the center of the tensor gradiometer as the origin, and the full tensor of the magnetic target is calculated according to the magnetic dipole model

In formula (1), the vacuum permeability μ ₀ =4π×10 ^-7 T·m/A,

is the magnetic moment vector,

is the position vector of the sensor pointing to the magnetic target, r is

, δ _ij is the Kronecker function, i=x, y, z, j=x, y, z, the invariant C _T of the magnetic gradient tensor can be calculated by using formula (1):

In formula (2), M is the magnitude of the magnetic moment vector, the direction vector of the magnetic target

for:

where the value of k varies with the orientation of the magnetic target:

where γ is

and

The included angle of , according to formulas (2) and (4), we get:

in,

Yes

The unit vector of , the direction error is the main component of the aspheric error, the direction vector with the bias

for:

where:

Assuming that there is no error in the calculation of the distance r, define the direction error ω:

Substitute equation (6) into equation (7) to get:

It can be seen from equation (8) that the direction error ω has a linear relationship with the distance r, and has a nonlinear relationship with the included angle γ. 2. a kind of magnetic target detection method according to claim 1, is characterized in that, in step 2, concretely, in order to compensate the aspheric surface error, define the invariant ▽C of the magnetic gradient tensor after compensation,

Combining formula (5) and formula (9), we can get:

From formula (10), it can be known that,

Pointing to the magnetic target, combined with the tensor gradiometer of the regular hexahedron structure, the equation of the distance r can be obtained,

Combining equations (10) and (11), the position vector of the magnetic target can be obtained

After calculating the position vector of the magnetic target, calculate the magnetic moment vector according to formula (1) and the least square method:

where:

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