CN102927981A - Method of locating magnetic target based on tri-axial vector magnetic sensor array - Google Patents

Abstract

The invention discloses a method of locating a magnetic target based on a tri-axial vector magnetic sensor array. According to the method, the magnetic target is located by a magnetic gradient tensor measuring array formed by five tri-axial vector magnetic sensors at high locating precision. The specific scheme of the method comprises the following steps of: at first, measuring the magnetic gradient tensor of any point on the periphery of the magnetic target by utilizing the magnetic gradient tensor measuring array; secondly, resolving a relative distance between the magnetic target and the magnetic measuring array and relative coordinates by utilizing the magnetic tensor; and at last, locating the magnetic target according to the resolved relative distance and the relative position coordinates. The locating method has the advantages of simplicity, practicability and high locating precision.

Description

A kind of magnetic target localization method based on three axis vector magnetic sensor battle arrays

Technical field

The present invention relates to a kind of high-precision magnetic target localization method, be specifically related to a kind of magnetic target localization method based on three axis vector magnetic sensor battle arrays, belong to the magnetic measurement field.

Background technology

The magnetic detection technology is widely used in the fields such as navigator fix, geologic prospecting, biologic medical, raising of a wreck.The magnetic orientation technology is one of core technology of magnetic detection technology.

At present the most frequently used magnetic positioning method is derived corresponding ranging formula according to the magnetic target magnetic field model of setting up exactly, and then positions according to measured magnetic field value and to find the solution.This is actually a refutation process, relates to and finds the solution Nonlinear System of Equations, and common method for solving has neural network, the stepwise regression method, and Genetic algorithm searching is found the solution, and POWELL method, genetic algorithm and simplicial method are united and are found the solution etc.

Above-mentioned this traditional magnetic positioning method exists data volume large, calculation of complex, the shortcoming such as solving result is unstable, and real-time is poor, and positioning error is large.

Summary of the invention

In view of this, the present invention proposes a kind of magnetic target localization method based on three axis vector magnetic sensor battle arrays, the method utilization forms magnetic gradient Tensor measuring array by five three axis vector magnetic sensors and comes magnetic target is positioned, bearing accuracy is high, can overcome the deficiency of above-mentioned traditional magnetic positioning method.

The step that adopts the method to carry out the magnetic target location is:

Step 1: arrange magnetic gradient Tensor measuring array

Magnetic gradient Tensor measuring array is comprised of five three axis vector magnetic sensors, and when arranging magnetic gradient Tensor measuring array, three axis vector magnetic sensors that are positioned at the sensing point place are reference sensor.Other three axis vector magnetic sensor is distributed in around the reference sensor, is reference sensor.If three sensitive axes directions of reference sensor be respectively x to, y to z to, should guarantee that three sensitive axes corresponding to all three axis vector magnetic sensors are parallel mutually when arranging magnetic gradient Tensor measuring array.X to forward and negative sense respectively arrange a reference sensor, y to forward and negative sense respectively arrange a reference sensor, four reference sensors all equate with distance between the reference sensor.

Step 2: utilize magnetic gradient Tensor measuring array measurement magnetic target that step 1 sets up in magnetic gradient tensor G and the magnetic induction density B at sensing point place

If reference sensor is No. 1 sensor.Being positioned at x is No. 2 sensors to forward reference sensor, and being positioned at x is No. 4 sensors to the reference sensor on the negative sense, and being positioned at y is No. 3 sensors to forward reference sensor, and being positioned at y is No. 5 sensors to the reference sensor on the negative sense.Distance between four reference sensors and the reference sensor is d.

The data of five three axis vector magnetic sensors outputs are respectively: (B _1x, B _1y, B _1z), (B _2x, B _2y, B _2z), (B _3x, B _3y, B _3z), (B _4x, B _4y, B _4z), (B _5x, B _5y, B _5z).

B wherein _AbRepresent the magnetic induction density on the b direction that a three axis vector magnetic sensors record, a=1,2,3,4,5, b=x, y, z.

Then magnetic target at the magnetic gradient tensor G at sensing point place is:

$G=\left[\begin{array}{ccc}{B}_{\mathrm{xx}}\≈\frac{B_{2x}-B_{4x}}{2d}& B_{\mathrm{xy}}\≈\frac{B_{2y}-B_{4y}}{2d}& B_{\mathrm{xz}}\≈\frac{B_{2z}-B_{4z}}{2d}\\ B_{\mathrm{yx}}\≈\frac{B_{3x}-B_{5x}}{2d}& B_{\mathrm{yy}}\≈\frac{B_{3y}-B_{5y}}{2d}& B_{\mathrm{yz}}\≈\frac{B_{3z}-B_{5z}}{2d}\\ B_{\mathrm{zx}}\≈\frac{B_{2z}-B_{4z}}{2d}& B_{\mathrm{zy}}\≈\frac{B_{3z}-B_{5z}}{2d}& B_{\mathrm{zz}}\≈\frac{B_{4x}+B_{5y}-B_{2x}-B_{3y}}{2d}\end{array}\right]---\left(\text{1}\right)$

Described magnetic target in the magnetic induction density B at sensing point place is: (B _1x, B _1y, B _1z) (2)

B in the formula (1) _IjThe derivative of magnetic induction density on the j direction on the expression i direction, i=x, y, z, j=x, y, z.

Step 3: utilize magnetic gradient tensor G and magnetic induction density B to calculate the relative position coordinates of magnetic gradient Tensor measuring array and magnetic target

Be magnetic dipole with magnetic target equivalence to be measured, take magnetic dipole as true origin, the distance of establishing between sensing point and magnetic dipole is

Then have:

$\stackrel{\→}{r}=\left[\begin{array}{c}x\\ y\\ z\end{array}\right]=-3G^{-1}B---\left(3\right)$

The magnetic target that step 2 is obtained is at sensing point place magnetic induction density B and magnetic gradient tensor G substitution formula (3), and then the position coordinates (x, y, z) of sensing point in the coordinate system take magnetic dipole as initial point is:

$\stackrel{\→}{r}=\left[\begin{array}{c}x\\ y\\ z\end{array}\right]=-3{\left[\begin{array}{ccc}{B}_{\mathrm{xx}}\≈\frac{B_{2x}-B_{4x}}{2d}& B_{\mathrm{xy}}\≈\frac{B_{2y}-B_{4y}}{2d}& B_{\mathrm{xz}}\≈\frac{B_{2z}-B_{4z}}{2d}\\ B_{\mathrm{yx}}\≈\frac{B_{3x}-B_{5x}}{2d}& B_{\mathrm{yy}}\≈\frac{B_{3y}-B_{5y}}{2d}& B_{\mathrm{yz}}\≈\frac{B_{3z}-B_{5z}}{2d}\\ B_{\mathrm{zx}}\≈\frac{B_{2z}-B_{4z}}{2d}& B_{\mathrm{zy}}\≈\frac{B_{3z}-B_{5z}}{2d}& B_{\mathrm{zz}}\≈\frac{B_{4x}+B_{5y}-B_{2x}-B_{3y}}{2d}\end{array}\right]}^{-1}\left[\begin{array}{c}{B}_{1x}\\ B_{1y}\\ B_{1z}\end{array}\right]---\left(4\right)$

The sensing point that calculates by formula (4) just can be realized the location to magnetic target with respect to the position coordinates of magnetic target, and above-mentioned formula (4) is magnetic gradient tensor ranging formula.

Beneficial effect

The present invention utilizes five three-component vector Magnetic Sensors to form detection array and surveys, and utilizes the magnetic gradient tensor to carry out the magnetic target location, and localization method is simple, practical, bearing accuracy is high.

Description of drawings

The structural representation of the magnetic survey array that five three axis vector magnetic sensors of Fig. 1 form;

Fig. 2 is for adopting the method to carry out the process flow diagram of magnetic target location;

Fig. 3 adopts the method to carry out the design sketch of magnetic target location.

Embodiment

Below in conjunction with the accompanying drawing embodiment that develops simultaneously, describe the present invention.

The present embodiment provides a kind of magnetic target localization method based on three axis vector magnetic sensor battle arrays, and the magnetic gradient Tensor measuring array that the method utilizes five three axis vector magnetic sensors to form comes magnetic target is positioned.

The arrangement of magnetic gradient Tensor measuring array as shown in Figure 1, the numbering of establishing five three axis vector magnetic sensors is respectively No. 1～No. 5.As reference sensor, other three axis vector magnetic sensor is as the reference sensor with No. 1 three axis vector magnetic sensors being arranged in the sensing point place.If three sensitive axes directions of reference sensor be respectively x to, y to z to, set up coordinate system xyz, three sensitive axes that all three axis vector magnetic sensors are corresponding are parallel mutually.In four reference sensors No. 2 and No. 4 three axis vector magnetic sensors be arranged in x to forward and negative sense, No. 3 and No. 5 three axis vector magnetic sensors be arranged in y to forward and negative sense; Distance between four reference sensors and the reference sensor is d.

Adopt concrete steps that this magnetic gradient Tensor measuring array carries out magnetic target location as shown in Figure 2:

Step 1: arrange magnetic gradient Tensor measuring array according to above-mentioned requirements;

Step 2: utilize magnetic gradient Tensor measuring array measurement magnetic target in magnetic gradient tensor G and the magnetic induction density B at sensing point place

Magnetic field is vector field, has magnetic field around magnetic target, and the second-order tensor in magnetic field is called the magnetic gradient tensor, is designated as G.The expression formula of magnetic gradient tensor G is:

$G=\left[\begin{array}{ccc}\frac{\∂B_x}{\∂x}& \frac{\∂B_x}{\∂y}& \frac{\∂B_x}{\∂z}\\ \frac{\∂B_y}{\∂x}& \frac{\∂B_y}{\∂y}& \frac{\∂B_y}{\∂z}\\ \frac{\∂B_z}{\∂x}& \frac{\∂B_z}{\∂y}& \frac{\∂B_z}{\∂z}\end{array}\right]=\left[\begin{array}{ccc}{B}_{\mathrm{xx}}& B_{\mathrm{xy}}& B_{\mathrm{xz}}\\ B_{\mathrm{yx}}& B_{\mathrm{yy}}& B_{\mathrm{yz}}\\ B_{\mathrm{zx}}& B_{\mathrm{zy}}& B_{\mathrm{zz}}\end{array}\right]---\left(1\right)$

B wherein _IjThe derivative (i=x, y, z, j=x, y, z) of magnetic induction density on the j direction on the expression i direction.

By Theory of Electromagnetic Field, the magnetic field that magnetic bodies produces is passive irrotational field, and therefore, the matrix of magnetic gradient tensor G has symmetry, namely when i ≠ j, and B _Ij=B _Ji, and B is arranged _Zz-B _Xx-B _Yy=0

Then have:

$\left\{\begin{array}{c}{B}_{\mathrm{xy}}=B_{\mathrm{yx}}\\ B_{\mathrm{xz}}=B_{\mathrm{zx}}\\ B_{\mathrm{yz}}=B_{\mathrm{zx}}\\ B_{\mathrm{zz}}=-B_{\mathrm{xx}}-B_{\mathrm{yy}}\end{array}\right.$

Reference sensor is used for measuring the magnetic induction density B of magnetic target among Fig. 1, and reference sensor is used for measuring the magnetic gradient tensor G of magnetic target.If the data of No. 1～No. 5 three axis vector magnetic sensors outputs are respectively: (B _1x, B _1y, B _1z), (B _2x, B _2y, B _2z), (B _3x, B _3y, B _3z), (B _4x, B _4y, B _4z), (B _5x, B _5y, B _5z), utilize calculus of differences to replace differentiating in the formula (1), then magnetic target at the magnetic gradient tensor G at sensing point place is:

$G=\left[\begin{array}{ccc}{B}_{\mathrm{xx}}\≈\frac{B_{2x}-B_{4x}}{2d}& B_{\mathrm{xy}}\≈\frac{B_{2y}-B_{4y}}{2d}& B_{\mathrm{xz}}\≈\frac{B_{2z}-B_{4z}}{2d}\\ B_{\mathrm{yx}}\≈\frac{B_{3x}-B_{5x}}{2d}& B_{\mathrm{yy}}\≈\frac{B_{3y}-B_{5y}}{2d}& B_{\mathrm{yz}}\≈\frac{B_{3z}-B_{5z}}{2d}\\ B_{\mathrm{zx}}\≈\frac{B_{2z}-B_{4z}}{2d}& B_{\mathrm{zy}}\≈\frac{B_{3z}-B_{5z}}{2d}& B_{\mathrm{zz}}\≈\frac{B_{4x}+B_{5y}-B_{2x}-B_{3y}}{2d}\end{array}\right]---\left(\text{2}\right)$

Magnetic target in the magnetic induction density B at sensing point place is: B=(B _1x, B _1y, B _1z) (3)

B wherein _AbRepresent the magnetic induction density on the b direction (a=1,2,3,4,5, b=x, y, z) that a three axis vector magnetic sensors record

Step 3: utilize the relative coordinate between magnetic gradient tensor G calculating magnetic target and magnetic gradient Tensor measuring array

Because any magnetic target is outer in certain distance can equivalence to be dipole model of magnetic all, therefore, is magnetic dipole with magnetic target equivalence to be measured, take magnetic dipole as true origin, the distance of establishing between sensing point and magnetic dipole is

Then the magnetic induction density B at sensing point place is:

$B=\frac{{\mathrm{\μ}}_0}{4\mathrm{\π}{\left|\stackrel{\→}{r}\right|}^5}[3(\stackrel{\→}{r}\·\stackrel{\→}{m})\stackrel{\→}{r}-{\left|\stackrel{\→}{r}\right|}^2\stackrel{\→}{m}]---\left(4\right)$

In the formula:

Be position vector, $\stackrel{\→}{r}=\left[\begin{array}{c}x\\ y\\ z\end{array}\right],$

Be the distance between sensing point and magnetic dipole;

Be the magnetic moment vector of magnetic dipole, μ ₀Be permeability of vacuum;

Convolution (1) and formula (4) have:

$\stackrel{\→}{r}=-3G^{-1}B---\left(5\right)$

G in the formula ^-1Inverse matrix for magnetic gradient tensor G.

With the formula in the step 1 (2) and formula (3) substitution formula (5), then the position coordinates (x, y, z) of sensing point in take magnetic dipole (magnetic target) as the coordinate system of initial point is:

$\stackrel{\→}{r}=\left[\begin{array}{c}x\\ y\\ z\end{array}\right]=-3{\left[\begin{array}{ccc}{B}_{\mathrm{xx}}\≈\frac{B_{2x}-B_{4x}}{2d}& B_{\mathrm{xy}}\≈\frac{B_{2y}-B_{4y}}{2d}& B_{\mathrm{xz}}\≈\frac{B_{2z}-B_{4z}}{2d}\\ B_{\mathrm{yx}}\≈\frac{B_{3x}-B_{5x}}{2d}& B_{\mathrm{yy}}\≈\frac{B_{3y}-B_{5y}}{2d}& B_{\mathrm{yz}}\≈\frac{B_{3z}-B_{5z}}{2d}\\ B_{\mathrm{zx}}\≈\frac{B_{2z}-B_{4z}}{2d}& B_{\mathrm{zy}}\≈\frac{B_{3z}-B_{5z}}{2d}& B_{\mathrm{zz}}\≈\frac{B_{4x}+B_{5y}-B_{2x}-B_{3y}}{2d}\end{array}\right]}^{-1}\left[\begin{array}{c}{B}_{1x}\\ B_{1y}\\ B_{1z}\end{array}\right]---\left(6\right)$

Just can realize location to magnetic target by above-mentioned formula (6).Adopt effect that the method carries out the magnetic target location as shown in Figure 3, the error between detecting location and the actual position is very little, shows that the method measuring accuracy is high.

Magnetic positioning method provided by the present invention is not limited to magnetic target is carried out Detection location, also can be used for magnetic target is followed the tracks of, and speed, the flight path of magnetic target measured and estimate etc.

In sum, above is preferred embodiment of the present invention only, is not for limiting protection scope of the present invention.Within the spirit and principles in the present invention all, any modification of doing, be equal to replacement, improvement etc., all should be included within protection scope of the present invention.

Claims (1)

1. the magnetic target localization method based on three axis vector magnetic sensor battle arrays is characterized in that,

Step 1: arrange magnetic gradient Tensor measuring array

Described magnetic gradient Tensor measuring array is comprised of five three axis vector magnetic sensors, and when arranging magnetic gradient Tensor measuring array, three axis vector magnetic sensors that are positioned at the sensing point place are reference sensor; Other three axis vector magnetic sensor is distributed in around the reference sensor, is reference sensor; If three sensitive axes directions of reference sensor be respectively x to, y to z to, should guarantee that three sensitive axes corresponding to all three axis vector magnetic sensors are parallel mutually when arranging magnetic gradient Tensor measuring array; X to forward and negative sense respectively arrange a reference sensor, y to forward and negative sense respectively arrange a reference sensor, four reference sensors all equate with distance between the reference sensor;

Step 2: utilize magnetic gradient Tensor measuring array measurement magnetic target that step 1 sets up in magnetic gradient tensor G and the magnetic induction density B at sensing point place

If reference sensor is No. 1 sensor; Being positioned at x is No. 2 sensors to forward reference sensor, and being positioned at x is No. 4 sensors to the reference sensor on the negative sense, and being positioned at y is No. 3 sensors to forward reference sensor, and being positioned at y is No. 5 sensors to the reference sensor on the negative sense; Distance between four reference sensors and the reference sensor is d;

The data of five three axis vector magnetic sensors outputs are respectively: (B _1x, B _1y, B _1z), (B _2x, B _2y, B _2z), (B _3x, B _3y, B _3z), (B _4x, B _4y, B _4z), (B _5x, B _5y, B _5z);

B wherein _AbRepresent the magnetic induction density on the b direction that a three axis vector magnetic sensors record, a=1,2,3,4,5, b=x, y, z;

Then magnetic target at the magnetic gradient tensor G at sensing point place is:

Described magnetic target in the magnetic induction density B at sensing point place is: (B _1x, B _1y, B _1z) (2)

B in the formula (1) _IjThe derivative of magnetic induction density on the j direction on the expression i direction, i=x, y, z, j=x, y, z;

Step 3: utilize magnetic gradient tensor G and magnetic induction density B to calculate the relative position relation of magnetic gradient Tensor measuring array and magnetic target

Be magnetic dipole with magnetic target equivalence to be measured, take magnetic dipole as true origin, the distance of establishing between sensing point and magnetic dipole is

Then have:

The magnetic target that step 2 is obtained is at sensing point place magnetic induction density B and magnetic gradient tensor G substitution formula (3), and then the position coordinates (x, y, z) of sensing point in the coordinate system take magnetic dipole as initial point is:

By the coordinate position of the relative magnetic target of sensing point in the formula (4), just can realize the location to magnetic target.

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