CN112698258B - An integrated error correction method for a three-axis magnetometer - Google Patents

Abstract

The invention discloses an integrated error correction method of a three-axis magnetometer, which comprises the following steps: s1, establishing an error correction model of the three-axis magnetometer; s2, fixing the three-axis magnetometer on a nonmagnetic rotating platform in a uniform magnetic field environment, enabling the x axis and the y axis of the three-axis magnetometer to be parallel to the rotating plane of the nonmagnetic rotating platform, enabling the x axis and the z axis of the three-axis magnetometer to be parallel to the rotating plane of the nonmagnetic rotating platform, enabling the y axis and the z axis of the three-axis magnetometer to be parallel to the rotating plane of the nonmagnetic rotating platform, enabling the nonmagnetic rotating platform to rotate at equal intervals under three conditions, and acquiring the measurement data of the three-axis magnetometer; s3, solving each parameter of the error correction model established in the step S1 by using the measured data under the three conditions in the step S2; and S4, carrying out error correction on the measurement value of the three-axis magnetometer by using the solved error correction model.

Description

An integrated error correction method for a three-axis magnetometer

technical field

The invention relates to the field of magnetic detection, in particular to an integrated error correction method for a three-axis magnetometer.

Background technique

The three-axis magnetometer is an indispensable device for measuring weak magnetic fields in space. Ideally, the three-axis magnetometer is completely aligned with the calibration three-axis. However, due to the influence of the manufacturing process, the three-axis of the magnetometer is not strictly aligned. In addition, due to factors such as zero-point drift and long-term magnetic offset, the measured magnetic field data is not ideal, and it needs to be corrected for errors. The current non-alignment correction for the magnetometer is mainly to perform non-orthogonal correction on its three axes, and the corrected orthogonal three axes are not necessarily aligned with the calibrated three axes.

In the current three-axis non-orthogonal error correction model, the corrected orthogonal three-axis are inconsistent with the calibrated three-axis of the three-axis magnetometer, and it is not enough to perform three-axis non-orthogonal correction on the magnetometer. , there is also a non-alignment error, the corrected orthogonal three-axis is based on an actual axis of the magnetometer to establish an orthogonal three-axis coordinate system, and the total magnetic field strength is used as the correction standard for correction. At present, the magnetic calibration model is only suitable for the total magnetic field measurement and the vector magnetic field applications with low positioning requirements. There is almost no calibration research on the alignment of the three axes calibrated on the magnetometer with the actual three axes. In application, it is necessary to correct the calibration three-axis and the actual three-axis.

SUMMARY OF THE INVENTION

In order to solve the problems raised in the above background technology, the purpose of the present invention is to provide an integrated error correction method for a three-axis magnetometer.

To achieve the above object, the technical scheme adopted in the present invention is:

An integrated error correction method for a three-axis magnetometer, comprising the following steps:

S1, establish an error correction model of the three-axis magnetometer, and the error correction model includes the effects of zero bias error, three-axis sensitivity error, three-axis non-orthogonal error and non-alignment error;

S2, in a uniform magnetic field environment, fix the three-axis magnetometer on the non-magnetic rotating platform, and make the x-axis and y-axis of the three-axis magnetometer parallel to the rotation plane of the non-magnetic rotating platform, and the three-axis magnetic The x-axis and z-axis of the meter are parallel to the rotation plane of the non-magnetic rotating platform, and the y-axis and z-axis of the three-axis magnetometer are parallel to the rotation plane of the non-magnetic rotating platform. Rotate at equal intervals and obtain the measurement data of the three-axis magnetometer;

S3, using the measurement data measured under the three conditions in step S2, solve each parameter of the error correction model established in step S1;

S4, using the solved error correction model to perform error correction on the measured value of the three-axis magnetometer.

In some embodiments, in step S1, the specific steps of establishing the error correction model of the three-axis magnetometer are as follows:

x_m轴在yz平面的投影与y 轴的夹角为β₁；y_m轴与y轴的夹角为α₂，y_m轴与z轴的夹角为

y_m轴在xz平面的投影与z轴的夹角为β₂；z_m轴与z轴的夹角为α₃，z_m轴与x轴的夹角为

z_m轴在xy平面的投影与x轴的夹角为β₃；Let x, y, and z represent the ideal calibration axes of the three-axis magnetometer, respectively, the three axes of x, y, and z are orthogonal to each other, and x _m , y _m , and z _m represent the actual three axes of the three-axis magnetometer, respectively. The angle between the x _m axis and the x axis is α ₁ , and the angle between the x _m axis and the y axis is

The angle between the projection of the x _m axis on the yz plane and the y axis is β ₁ ; the angle between the y _m axis and the y axis is α ₂ , and the angle between the y _m axis and the z axis is

The angle between the projection of the y _m axis on the xz plane and the z axis is β ₂ ; the angle between the z _m axis and the z axis is α ₃ , and the angle between the z _m axis and the x axis is

The angle between the projection of the z _m axis on the xy plane and the x axis is β ₃ ;

Then the actual output value of the three-axis magnetometer is represented by the theoretical value of the three-axis output as:

Among them, k _x , _ky , and k _z are the three-axis sensitivity coefficients, respectively, B _x0 , _By0 , and B _z0 are the three-axis zero offset errors, respectively, and B _x , By , and B _z are the three-axis magnetometer _values . To calibrate the theoretical value of the three-axis output, B _xm , _Bym , and B _zm are the actual output values of the three-axis magnetometer;

Transforming formula (1), the theoretical value of the three-axis output of the three-axis magnetometer is expressed as:

Equations (1) and (2) are the error correction models of the three-axis magnetometer.

In some embodiments, step S2 specifically includes the following steps:

In a uniform magnetic field environment, the uniform magnetic field strength is B and the geomagnetic inclination is I, then the magnetic field strength of the uniform magnetic field strength in the rotating plane and the vertical direction can be expressed as:

In the formula, B _rot is the magnetic field component whose uniform magnetic field strength is B in the rotating plane, and B _w is the magnetic field component whose uniform magnetic field strength is B in the vertical direction of the rotating plane;

When the non-magnetic rotating platform rotates, let θ be the rotation angle, and θ _x be the initial angle between B _rot and the y-axis;

When the calibration x-axis and y-axis of the three-axis magnetometer are parallel to the rotation plane of the non-magnetic rotating platform, the platform is rotated at equal intervals, and the measured theoretical value is:

Substituting Equation (4) into Equation (1), the actual output values B _xm1 , _Bym1 , and B _zm1 of the three-axis magnetometer can be expressed as:

B _xm1 =k _x cosα ₁ B _rot sin(θ+θ _x )+k _x sinα ₁ cosβ ₁ B _rot cos(θ+θ _x )+k _x sinα ₁ sinβ ₁ B _w +B _x0 (5)

B _ym1 =k _y sinα ₂ sinβ ₂ B _rot sin(θ+θ _x )+k _y cosα ₂ B _rot cos(θ+θ _x )+k _y sinα ₂ cosβ ₂ B _w +B _y0

B _zm1 =k _z sinα ₃ cosβ ₃ B _rot sin(θ+θ _x )+k _z sinα ₃ sinβ ₃ B _rot cos(θ+θ _x )+k _z cosα ₃ B _w +B _z0

Equation (5) can be simplified as:

B _xm1 =A ₁ sin((θ+θ _x )+η ₁ )+k _x sinα ₁ sinβ ₁ B _w +B _x0 =A ₁ sin(θ+b ₁ )+C ₁ (6)

B _ym1 =A ₂ sin((θ+θ _x )+η ₂ )+k _y sinα ₂ cosβ ₂ B _w +B _y0 =A ₂ sin(θ+b ₂ )+C ₂

B _zm1 =k _z sinα ₃ B _rot sin(θ+θ _x +β ₃ )+k _z cosα ₃ B _w +B _z0 =A ₃ sin(θ+b ₃ )+C ₃

In formula (6), η ₁ and η ₂ are constants, and the variables A ₁ , A ₂ , A ₃ , b ₁ , b ₂ , b ₃ , C ₁ , C ₂ , and C ₃ are the characteristic parameters of the fitting function. The actual output value is fitted;

Flip the magnetometer, make the calibrated x-axis and z-axis of the three-axis magnetometer parallel to the rotation plane of the non-magnetic rotating platform, and rotate the platform at equal intervals. The measured theoretical value is:

Substituting Equation (7) into Equation (1), the actual output values B _xm2 , _Bym2 , and B _zm2 of the three-axis magnetometer can be expressed as:

B _xm2 =k _x cosα ₁ B _rot cos(θ+θ _x )+k _x sinα ₁ cosβ ₁ B _w +k _x sinα ₁ sinβ ₁ B _rot sin(θ+θ _x )+B _x0 (8)

B _ym2 = k _y sinα ₂ sinβ ₂ B _rot cos(θ+θ _x )+k _y cosα ₂ B _w +k _y sinα ₂ cosβ ₂ B _rot sin(θ+θ _x )+B _y0

B zm2 =k _{z sinα 3} cosβ ₃ B _rot cos(θ+θ _x )+k _z sinα ₃ sinβ ₃ B _w +k _z cosα ₃ B _rot sin(θ+θ _x )+B _z0

Equation (8) can be simplified as:

B _xm2 =A ₄ sin((θ+θ _x )+η ₄ )+k _x sinα ₁ cosβ ₁ B _w +B _x0 =A ₄ sin(θ+b ₄ )+C ₄ (9)

B _ym2 = k _y sinα ₂ B _rot sin((θ+θ _x )+β ₂ )+k _y cosα ₂ B _w +B _y0 =A ₅ sin(θ+b ₅ )+C ₅

B _zm2 =A ₆ sin((θ+θ _x )+η ₆ )+k _z sinα ₃ sinβ ₃ B _w +B _z0 =A ₆ sin(θ+b ₆ )+C ₆

In formula (9), η ₄ and η ₆ are constants, and the variables A ₄ , A ₅ , A ₆ , b ₄ , b ₅ , b ₆ , C ₄ , C ₅ , and C ₆ are the characteristic parameters of the fitting function, which are represented by The actual output value is fitted;

Flip the sensor, when the calibration y-axis and z-axis of the three-axis magnetometer are parallel to the rotation plane of the non-magnetic rotating platform, and rotate the platform at equal intervals, the measured theoretical value is:

Substituting Equation (10) into Equation (1), the actual output values B _xm3 , _Bym3 , and B _zm3 of the three-axis magnetometer can be expressed as:

B _xm3 =k _x cosα ₁ B _w +k _x sinα ₁ cosβ ₁ B _rot sin(θ+θ _x )+k _x sinα ₁ sinβ ₁ B _rot cos(θ+θ _x )+B _x0 (11)

B _ym3 = k _y sinα ₂ sinβ ₂ B _w +k _y cosα ₂ B _rot sin(θ+θ _x )+k _y sinα ₂ cosβ ₂ B _rot cos(θ+θ _x )+B _y0

B _zm3 =k _z sinα ₃ cosβ ₃ B _w +k _z sinα ₃ sinβ ₃ B _rot sin(θ+θ _x )+k _z cosα ₃ B _rot cos(θ+θ _x )+B _z0

Equation (11) can be simplified as:

B _xm3 =k _x sinα ₁ B _rot sin((θ+θ _x )+β ₁ )+k _x cosα ₁ B _w +B _x0 =A ₇ sin(θ+b ₇ )+C ₇ (12)

B _ym3 =A ₈ sin((θ+θ _x )+η ₈ )+k _y sinα ₂ sinβ ₂ B _w +B _y0 =A ₈ sin(θ+b ₈ )+C ₈

B _zm3 =A ₉ sin((θ+θ _x )+η ₉ )+k _z sinα ₃ cosβ ₃ B _w +B _z0 =A ₉ sin(θ+b ₉ )+C ₉

In formula (12), η ₈ and η ₉ are constants, and the variables A ₇ , A8 , A9 , b ₇ , b ₈ , b ₉ , C ₇ , C ₈ , and C ₉ are the characteristic parameters of the fitting function, which are output by the actual value fitted.

In some embodiments, in step S3, the specific steps for solving each parameter of the error correction model established in step S1 are as follows:

From equations (6) (9) (12), the parameters k _x , α ₁ , β ₁ , and B _x0 of the error correction model satisfy:

Solving equation (13), we know that β ₁ satisfies:

make

0<β ₁ <π, when solving for β ₁ , if

Then β ₁ has only one solution, namely:

like

Then β ₁ has two solutions:

After solving for β ₁ , substitute into equation (13), we can get:

From equations (6) (9) (12), the parameters _ky , α ₂ , β ₂ , and _By0 of the error correction model satisfy:

k _y sinα ₂ cosβ ₂ B _w +B _y0 =C ₂ (15)

k _y cosα ₂ B _w +B _y0 =C ₅

k _y sinα ₂ sinβ ₂ B _w +B _y0 =C ₈

k _y sinα ₂ B _rot =A ₅

Solving equation (15), we know that β ₂ satisfies:

make

0<β ₂ <π, when solving for β ₂ , if

Then β ₂ has only one solution, namely:

like

Then β ₂ has two solutions:

After solving for β ₂ , substitute into equation (15), we can get:

From equations (6) (9) (12), the parameters k _z , α ₃ , β ₃ , and B _z0 of the error correction model satisfy:

k _y sinα ₂ cosβ ₂ B _w +B _y0 =C ₂ (17)

k _y cosα ₂ B _w +B _y0 =C ₅

k _y sinα ₂ sinβ ₂ B _w +B _y0 =C ₈

k _y sinα ₂ B _rot =A ₅

Solving equation (17), we know that β ₃ satisfies:

make

0<β ₃ <π, when solving for β ₃ , if

Then β ₃ has only one solution, namely:

like

Then β ₃ has two solutions:

After solving for β ₃ , substitute into equation (17), we can get:

Thus, all parameters of the error correction model are obtained. For the case where there are two solutions for β ₁ , β ₂ , and β ₃ , the parameters obtained in the two cases are substituted into the error correction model, and β 1 , β ₁ , β 3 are determined according to the actual correction effect. The value of β ₂ , β ₃ .

Compared with the prior art, the beneficial effects of the present invention are:

The integrated error correction method of the three-axis magnetometer provided by the present invention proposes a three-axis non-orthogonal and non-aligned model in which the three axes are not coincident, and solves the non-orthogonal error of the sensor and the calibration after orthogonality at one time. Three-axis misalignment error, and the zero bias error and sensitivity coefficient error are modeled together, and the error coefficient is solved by trigonometric function fitting to achieve extremely high-precision error correction.

Description of drawings

Figure 1 is a schematic diagram of the actual axis and theoretical axis of the three-axis magnetometer;

2a-2c are schematic diagrams of actual output values and fitted values of a three-axis magnetometer in a specific embodiment.

Detailed ways

In order to make the technical means, creative features, achievement goals and effects realized by the present invention easy to understand, how the present invention is implemented is further described below with reference to the accompanying drawings and specific embodiments.

The invention provides an integrated error correction method for a three-axis magnetometer, comprising the following steps:

S1, establish an error correction model of the three-axis magnetometer, and the error correction model includes the effects of zero bias error, three-axis sensitivity error, three-axis non-orthogonal error and non-alignment error;

S2, in a uniform magnetic field environment, fix the three-axis magnetometer on the non-magnetic rotating platform, and make the x-axis and y-axis of the three-axis magnetometer parallel to the rotation plane of the non-magnetic rotating platform, and the three-axis magnetic The x-axis and z-axis of the meter are parallel to the rotation plane of the non-magnetic rotating platform, and the y-axis and z-axis of the three-axis magnetometer are parallel to the rotation plane of the non-magnetic rotating platform. Rotate at equal intervals and obtain the measurement data of the three-axis magnetometer;

S3, using the measurement data measured under the three conditions in step S2, solve each parameter of the error correction model established in step S1;

S4, using the solved error correction model to perform error correction on the measured value of the three-axis magnetometer.

Further, in step S1, the specific steps for establishing the error correction model of the three-axis magnetometer are as follows:

x_m轴在yz平面的投影与y轴的夹角为β₁；y_m轴与y轴的夹角为α₂，y_m轴与z轴的夹角为

y_m轴在xz平面的投影与z轴的夹角为β₂；z_m轴与z轴的夹角为α₃，z_m轴与x轴的夹角为

z_m轴在xy平面的投影与x轴的夹角为β₃；As shown in Figure 1, let x, y, and z represent the ideal calibration axes of the three-axis magnetometer, respectively, the three axes of x, y, and z are orthogonal to each other, and x _m , y _m , and z _m respectively represent the three-axis magnetometer. The actual _{three axes of} the

The angle between the projection of the x _m axis on the yz plane and the y axis is β ₁ ; the angle between the y _m axis and the y axis is α ₂ , and the angle between the y _m axis and the z axis is

The angle between the projection of the y _m axis on the xz plane and the z axis is β ₂ ; the angle between the z _m axis and the z axis is α ₃ , and the angle between the z _m axis and the x axis is

The angle between the projection of the z _m axis on the xy plane and the x axis is β ₃ ;

Then the actual output value of the three-axis magnetometer is represented by the theoretical value of the three-axis output as:

Among them, k _x , _ky , and k _z are the three-axis sensitivity coefficients, respectively, B _x0 , _By0 , and B _z0 are the three-axis zero offset errors, respectively, and B _x , By , and B _z are the three-axis magnetometer _values . The theoretical value output value, B _xm , _Bym , B _zm are the actual output values of the three-axis magnetometer;

Transforming formula (1), the theoretical value of the three-axis output of the three-axis magnetometer is expressed as:

Equations (1) and (2) are the error correction models of the three-axis magnetometer.

Further, in step S2, it specifically includes the following steps:

In a uniform magnetic field environment, the uniform magnetic field strength is B and the geomagnetic inclination is I, then the magnetic field strength of the uniform magnetic field strength in the rotating plane and the vertical direction can be expressed as:

In the formula, B _rot is the magnetic field component of the uniform magnetic field strength B in the rotating plane, B _w is the magnetic field component of the uniform magnetic field strength B in the vertical direction of the rotating plane;

When the non-magnetic rotating platform rotates, let θ be the rotation angle, and θ _x be the initial angle between B _rot and the y-axis;

When the x _m axis and y _m axis of the three-axis magnetometer are parallel to the rotation plane of the non-magnetic rotating platform, the measured theoretical value is:

Substituting Equation (4) into Equation (1), the actual output values B _xm1 , _Bym1 , and B _zm1 of the three-axis magnetometer can be expressed as:

B _xm1 =k _x cosα ₁ B _rot sin(θ+θ _x )+k _x sinα ₁ cosβ ₁ B _rot cos(θ+θ _x )+k _x sinα ₁ sinβ ₁ B _w +B _x0 (5)

B _ym1 =k _y sinα ₂ sinβ ₂ B _rot sin(θ+θ _x )+k _y cosα ₂ B _rot cos(θ+θ _x )+k _y sinα ₂ cosβ ₂ B _w +B _y0

B _zm1 =k _z sinα ₃ cosβ ₃ B _rot sin(θ+θ _x )+k _z sinα ₃ sinβ ₃ B _rot cos(θ+θ _x )+k _z cosα ₃ B _w +B _z0

Equation (5) can be simplified as:

B _xm1 =A ₁ sin((θ+θ _x )+η ₁ )+k _x sinα ₁ sinβ ₁ B _w +B _x0 =A ₁ sin(θ+b ₁ )+C ₁ (6)

B _ym1 =A ₂ sin((θ+θ _x )+η ₂ )+k _y sinα ₂ cosβ ₂ B _w +B _y0 =A ₂ sin(θ+b ₂ )+C ₂

B _zm1 =k _z sinα ₃ B _rot sin(θ+θ _x +β ₃ )+k _z cosα ₃ B _w +B _z0 =A ₃ sin(θ+b ₃ )+C ₃

In formula (6), η ₁ and η ₂ are constants, and the variables A ₁ , A ₂ , A ₃ , b ₁ , b ₂ , b ₃ , C ₁ , C ₂ , and C ₃ are the characteristic parameters of the fitting function. The actual output value is fitted;

When the calibration x-axis and z-axis of the three-axis magnetometer are parallel to the rotation plane of the non-magnetic rotating platform, the measured theoretical value is:

Substituting Equation (7) into Equation (1), the actual output values B _xm2 , _Bym2 , and B _zm2 of the three-axis magnetometer can be expressed as:

B _xm2 =k _x cosα ₁ B _rot cos(θ+θ _x )+k _x sinα ₁ cosβ ₁ B _w +k _x sinα ₁ sinβ ₁ B _rot sin(θ+θ _x )+B _x0 (8)

B _ym2 = k _y sinα ₂ sinβ ₂ B _rot cos(θ+θ _x )+k _y cosα ₂ B _w +k _y sinα ₂ cosβ ₂ B _rot sin(θ+θ _x )+B _y0

B zm2 =k _{z sinα 3} cosβ ₃ B _rot cos(θ+θ _x )+k _z sinα ₃ sinβ ₃ B _w +k _z cosα ₃ B _rot sin(θ+θ _x )+B _z0

Equation (8) can be simplified as:

B _xm2 =A ₄ sin((θ+θ _x )+η ₄ )+k _x sinα ₁ cosβ ₁ B _w +B _x0 =A ₄ sin(θ+b ₄ )+C ₄ (9)

B _ym2 = k _y sinα ₂ B _rot sin((θ+θ _x )+β ₂ )+k _y cosα ₂ B _w +B _y0 =A ₅ sin(θ+b ₅ )+C ₅

B _zm2 =A ₆ sin((θ+θ _x )+η ₆ )+k _z sinα ₃ sinβ ₃ B _w +B _z0 =A ₆ sin(θ+b ₆ )+C ₆

In formula (9), η ₄ and η ₆ are constants, and the variables A ₄ , A ₅ , A ₆ , b ₄ , b ₅ , b ₆ , C ₄ , C ₅ , and C ₆ are the characteristic parameters of the fitting function, which are represented by The actual output value is fitted;

When the magnetometer is flipped and the calibrated y-axis and z-axis of the three-axis magnetometer are parallel to the rotation plane of the non-magnetic rotating platform, the measured theoretical value is:

Substituting Equation (10) into Equation (1), the actual output values B _xm3 , _Bym3 , and B _zm3 of the three-axis magnetometer can be expressed as:

B _xm3 =k _x cosα ₁ B _w +k _x sinα ₁ cosβ ₁ B _rot sin(θ+θ _x )+k _x sinα ₁ sinβ ₁ B _rot cos(θ+θ _x )+B _x0 (11)

B _ym3 = k _y sinα ₂ sinβ ₂ B _w +k _y cosα ₂ B _rot sin(θ+θ _x )+k _y sinα ₂ cosβ ₂ B _rot cos(θ+θ _x )+B _y0

B _zm3 =k _z sinα ₃ cosβ ₃ B _w +k _z sinα ₃ sinβ ₃ B _rot sin(θ+θ _x )+k _z cosα ₃ B _rot cos(θ+θ _x )+B _z0

Equation (11) can be simplified as:

B _xm3 =k _x sinα ₁ B _rot sin((θ+θ _x )+β ₁ )+k _x cosα ₁ B _w +B _x0 =A ₇ sin(θ+b ₇ )+C ₇ (12)

B _ym3 =A ₈ sin((θ+θ _x )+η ₈ )+k _y sinα ₂ sinβ ₂ B _w +B _y0 =A ₈ sin(θ+b ₈ )+C ₈

B _zm3 =A ₉ sin((θ+θ _x )+η ₉ )+k _z sinα ₃ cosβ ₃ B _w +B _z0 =A ₉ sin(θ+b ₉ )+C ₉

In formula (12), η ₈ and η ₉ are constants, and the variables A ₇ , A8 , A9 , b ₇ , b ₈ , b ₉ , C ₇ , C ₈ , and C ₉ are the characteristic parameters of the fitting function, which are output by the actual value fitted.

Further, in step S3, the specific steps for solving each parameter of the error correction model established in step S1 are as follows:

From equations (6) (9) (12), the parameters k _x , α ₁ , β ₁ , and B _x0 of the error correction model satisfy:

Solving equation (13), we know that β ₁ satisfies:

make

0<β ₁ <π, when solving for β ₁ , if

Then β ₁ has only one solution, namely:

like

Then β ₁ has two solutions:

After solving for β ₁ , substitute into equation (13), we can get:

From equations (6) (9) (12), it can be obtained that the parameters _ky , α ₂ , β ₂ , and _By0 of the error correction model satisfy:

k _y sinα ₂ cosβ ₂ B _w +B _y0 =C ₂ (15)

k _y cosα ₂ B _w +B _y0 =C ₅

k _y sinα ₂ sinβ ₂ B _w +B _y0 =C ₈

k _y sinα ₂ B _rot =A ₅

Solving equation (15), we know that β ₂ satisfies:

make

0<β ₂ <π, when solving for β ₂ , if

Then β ₂ has only one solution, namely:

like

Then β ₂ has two solutions:

After solving for β ₂ , substitute into equation (15), we can get:

From equations (6) (9) (12), the parameters k _z , α ₃ , β ₃ , and B _z0 of the error correction model satisfy:

k _y sinα ₂ cosβ ₂ B _w +B _y0 =C ₂ (17)

k _y cosα ₂ B _w +B _y0 =C ₅

k _y sinα ₂ sinβ ₂ B _w +B _y0 =C ₈

k _y sinα ₂ B _rot =A ₅

Solving equation (17), we know that β ₃ satisfies:

make

0<β ₃ <π, when solving for β ₃ , if

Then β ₃ has only one solution, namely:

like

Then β ₃ has two solutions:

After solving for β ₃ , substitute into equation (17), we can get:

Thus, all parameters of the error correction model are obtained. For the case where there are two solutions for β ₁ , β ₂ , and β ₃ , the parameters obtained from the two solutions are substituted into the error correction model, and β 1 , β ₁ , β 3 are determined according to the actual correction effect. The value of β ₂ , β ₃ .

Next, in a specific embodiment, simulation analysis is performed on the integrated error correction method of the three-axis magnetometer provided by the present invention.

The zero drift errors of the three axes of the three-axis magnetometer are set as:

B _x0 =152nT, _By0 =95.4nT, B _z0 =125.3nT

The three-axis sensitivity errors are:

k _x =0.921, k _y =1.151, k _z =1.131

The non-orthogonal and non-aligned angles of the three axes are:

α ₁ =1.20°, β ₁ =30.0°, α ₂ =1.34°, β ₂ =40.7°,α ₃ =1.02°,β ₃ =24.5°

Uniform Magnetic Field Strength:

B=50000nT

Magnetic dip:

I=43°

First, make the x-axis and y-axis of the three-axis magnetometer parallel to the rotation plane of the non-magnetic rotating platform, and the non-magnetic rotating platform rotates at equal intervals of π/18 to obtain the actual output value of the three-axis magnetometer and Using formula (6) to establish the fitting value obtained by the custom fitting function, the actual output value and the image of the fitting value are shown in Figure 2a-Figure 2c. It can be seen from the figure that the fitting value and the actual output value are basically consistent. The fitting curve expression obtained by the computer is:

B _xm1 = 33677sin(θ+0.6465)-176.8591

B _ym1 =-42083sin(θ-0.9577)-600.4528

B _zm1 =736.2320sin(θ+1.0559)-38436

in,

Combined with formula (6), the values of characteristic parameters A ₁ , A ₂ , A ₃ , b ₁ , b ₂ , b ₃ , C ₁ , C ₂ , and C ₃ of the fitting function are obtained.

Next, flip the three-axis magnetometer so that its x-axis and z-axis are parallel to the rotation plane of the non-magnetic rotating platform. Based on similar steps, the fitting curve expression is obtained as:

B _xm2 = 33673sin(θ+2.1886)-417.6006

B _ym2 =984.2725sin(θ+1.3387)-39143

B _zm2 =41357sin(θ+0.6445)-159.4066

Combined with formula (9), the values of characteristic parameters A ₄ , A ₅ , A ₆ , b ₄ , b ₅ , b ₆ , C ₄ , C ₅ , and C ₆ of the fitting function are obtained.

Flip the three-axis magnetometer again so that its y-axis and z-axis are parallel to the rotation plane of the non-magnetic rotating platform. Based on similar steps, the fitting curve expression is obtained as:

B _xm3 = 705.3164sin(θ+1.1519)-31247

B _ym3 =42083sin(θ+0.6461)-503.1279

B _zm3 =41353sin(θ+2.1917)-499.4316

Combined with formula (12), the values of characteristic parameters A ₇ , A8 , A9 , b ₇ , b ₈ , b ₉ , C ₇ , C ₈ , and C ₉ of the fitting function are obtained.

By bringing each characteristic parameter into the formula of each calibration parameter, each calibration parameter can be obtained as:

B _x0 = 152.0nT

B _y0 =95.4nT

B _z0 =125.3nT

α ₁ =1.200°, α ₂ =1.3400°, α ₃ =1.020°

β ₁ =30.000°, β ₂ =40.700°, β ₁ =24.500°

k _x =0.9210, k _y =1.1510, k _z =1.1310

It can be seen that the obtained calibration parameters of the triaxial magnetometer are equal to the original set values, and the calibration parameters can be substituted into the error correction model of the sensor to realize sensor calibration, thereby verifying the correctness of the present invention.

It has been verified by experiments that for a certain triaxial magnetometer, the absolute error between the actual output value and the theoretical value is 6147.6nT at most before calibration; after the error correction is performed by the method provided by the present invention, the difference between the calibration value and the theoretical value is very different. is small, the order of magnitude is 10 ⁻¹¹ , which can be ignored, thus verifying the effectiveness of the present invention.

To sum up, the integrated error correction method of the three-axis magnetometer provided by the present invention proposes a three-axis non-orthogonal and non-aligned model in which the three axes are not coincident, and solves the non-orthogonal error and orthogonality of the sensor at one time. After calibration, the error of the misalignment of the three axes is calculated, and the zero bias error and sensitivity coefficient error are modeled together, and the error coefficient is solved by trigonometric function fitting; after correction, the magnitude of the absolute error of the sensor output is reduced from 10 ³ nT to 10 ^-11 nT, the correction accuracy is very high.

Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be Modifications or equivalent substitutions, without departing from the spirit and scope of the technical solutions of the present invention, should all be included in the scope of the claims of the present invention.

Claims (3)

1. An integrated error correction method of a three-axis magnetometer is characterized by comprising the following steps:

s1, establishing an error correction model of the triaxial magnetometer, wherein the error correction model comprises the influences caused by zero offset errors, triaxial sensitivity errors, triaxial non-orthogonal errors and non-alignment errors;

s2, fixing the three-axis magnetometer on a nonmagnetic rotating platform in a uniform magnetic field environment, enabling the x axis and the y axis of the three-axis magnetometer to be parallel to the rotating plane of the nonmagnetic rotating platform, enabling the x axis and the z axis of the three-axis magnetometer to be parallel to the rotating plane of the nonmagnetic rotating platform, enabling the y axis and the z axis of the three-axis magnetometer to be parallel to the rotating plane of the nonmagnetic rotating platform, enabling the nonmagnetic rotating platform to rotate at equal intervals under three conditions, and acquiring the measurement data of the three-axis magnetometer;

s3, solving each parameter of the error correction model established in the step S1 by using the measured data under the three conditions in the step S2;

s4, carrying out error correction on the measurement value of the three-axis magnetometer by using the solved error correction model;

in step S1, the specific steps of establishing the error correction model of the three-axis magnetometer are as follows:

let x, y, and z respectively representIdeal calibration axis of three-axis magnetometer, x, y, z three axes are orthogonal, x_m、y_m、z_mRespectively representing the actual three axes of a three-axis magnetometer, let x_mThe axis forms an angle alpha with the x-axis₁，x_mThe axis forms an included angle with the y-axis

x_mThe projection of the axis on the yz plane forms an included angle beta with the y axis₁；y_mThe included angle between the axis and the y axis is alpha₂，y_mThe axis forms an angle with the z-axis

y_mThe projection of the axis on the xz plane forms an included angle beta with the z axis₂；z_mThe included angle between the axis and the z axis is alpha₃，z_mThe axis forms an angle with the x-axis

z_mThe projection of the axis on the xy plane forms an included angle beta with the x axis₃；

The actual output value of the triaxial magnetometer is expressed by the triaxial output theoretical value as:

wherein k is_x、k_y、k_zRespectively, the three-axis sensitivity coefficient, B_x0、B_y0、B_z0Respectively, three-axis zero offset error, B_x、B_y、B_zRespectively, the nominal triaxial output theoretical value, B, of the triaxial magnetometer_xm、B_ym、B_zmRespectively the actual output values of the three-axis magnetometer;

by transforming equation (1), the theoretical value of the triaxial output of the triaxial magnetometer is expressed as:

the formula (1) and the formula (2) are error correction models of the three-axis magnetometer.

2. The integrated error correction method of the three-axis magnetometer of claim 1, wherein step S2 specifically includes the following steps:

if the magnetic field intensity is B and the geomagnetic inclination angle is I, the magnetic field intensity of the uniform magnetic field in the rotation plane and the vertical direction can be represented as follows:

in the formula, B_rotThe magnetic field strength is B component of the uniform magnetic field in the rotating plane_wThe uniform magnetic field intensity is a magnetic field component of B in the vertical direction of the rotating plane;

when the non-magnetic rotary platform rotates, the theta is set as the rotation angle_xIs B_rotAn initial angle to the y-axis;

when the calibration x-axis and y-axis of the three-axis magnetometer are parallel to the rotating plane of the nonmagnetic rotating platform, the platform is rotated at equal intervals, and the measured theoretical values are as follows:

the formula (4) is substituted into the formula (1), and the actual output value B of the triaxial magnetometer is obtained at the moment_xm1、B_ym1、B_zm1Can be expressed as:

B_xm1＝k_xcosα₁B_rotsin(θ+θ_x)+k_xsinα₁cosβ₁B_rotcos(θ+θ_x)+k_xsinα₁sinβ₁B_w+B_x0 (5)

B_ym1＝k_ysinα₂sinβ₂B_rotsin(θ+θ_x)+k_ycosα₂B_rotcos(θ+θ_x)+k_ysinα₂cosβ₂B_w+B_y0

B_zm1＝k_zsinα₃cosβ₃B_rotsin(θ+θ_x)+k_zsinα₃sinβ₃B_rotcos(θ+θ_x)+k_zcosα₃B_w+B_z0

equation (5) can be simplified to:

B_xm1＝A₁sin((θ+θ_x)+η₁)+k_xsinα₁sinβ₁B_w+B_x0＝A₁sin(θ+b₁)+C₁ (6)

B_ym1＝A₂sin((θ+θ_x)+η₂)+k_ysinα₂cosβ₂B_w+B_y0＝A₂sin(θ+b₂)+C₂

B_zm1＝k_zsinα₃B_rotsin(θ+θ_x+β₃)+k_zcosα₃B_w+B_z0＝A₃sin(θ+b₃)+C₃

in the formula (6), eta₁、η₂Is a constant, variable A₁、A₂、A₃、b₁、b₂、b₃、C₁、C₂、C₃Fitting the characteristic parameters of the fitting function by using the actual output values;

turning over the magnetometer to enable the calibration x axis and the calibration z axis of the triaxial magnetometer to be parallel to the rotating plane of the nonmagnetic rotating platform, rotating the platform at equal intervals, and measuring theoretical values as follows:

the formula (7) is substituted into the formula (1), and the actual output value B of the triaxial magnetometer is obtained at the moment_xm2、B_ym2、B_zm2Can be expressed as:

B_xm2＝k_xcosα₁B_rotcos(θ+θ_x)+k_xsinα₁cosβ₁B_w+k_xsinα₁sinβ₁B_rotsin(θ+θ_x)+B_x0 (8)

B_ym2＝k_ysinα₂sinβ₂B_rotcos(θ+θ_x)+k_ycosα₂B_w+k_ysinα₂cosβ₂B_rotsin(θ+θ_x)+B_y0

B_zm2＝k_zsinα₃cosβ₃B_rotcos(θ+θ_x)+k_zsinα₃sinβ₃B_w+k_zcosα₃B_rotsin(θ+θ_x)+B_z0

equation (8) can be simplified to:

B_xm2＝A₄sin((θ+θ_x)+η₄)+k_xsinα₁cosβ₁B_w+B_x0＝A₄sin(θ+b₄)+C₄ (9)

B_ym2＝k_ysinα₂B_rotsin((θ+θ_x)+β₂)+k_ycosα₂B_w+B_y0＝A₅sin(θ+b₅)+C₅

B_zm2＝A₆sin((θ+θ_x)+η₆)+k_zsinα₃sinβ₃B_w+B_z0＝A₆sin(θ+b₆)+C₆

in the formula (9), eta₄、η₆Is a constant, variable A₄、A₅、A₆、b₄、b₅、b₆、C₄、C₅、C₆Fitting the characteristic parameters of the fitting function by using the actual output values;

turning over the fluxgate, rotating the platform at equal intervals when the calibration y axis and the calibration z axis of the three-axis magnetometer are parallel to the rotating plane of the nonmagnetic rotating platform, and measuring the theoretical values as follows:

the formula (10) is substituted into the formula (1), and the actual output value B of the three-axis magnetometer is obtained at the moment_xm3、B_ym3、B_zm3Can be expressed as:

B_xm3＝k_xcosα₁B_w+k_xsinα₁cosβ₁B_rotsin(θ+θ_x)+k_xsinα₁sinβ₁B_rotcos(θ+θ_x)+B_x0 (11)

B_ym3＝k_ysinα₂sinβ₂B_w+k_ycosα₂B_rotsin(θ+θ_x)+k_ysinα₂cosβ₂B_rotcos(θ+θ_x)+B_y0

B_zm3＝k_zsinα₃cosβ₃B_w+k_zsinα₃sinβ₃B_rotsin(θ+θ_x)+k_zcosα₃B_rotcos(θ+θ_x)+B_z0

equation (11) can be simplified to:

B_xm3＝k_xsinα₁B_rotsin((θ+θ_x)+β₁)+k_xcosα₁B_w+B_x0＝A₇sin(θ+b₇)+C₇ (12)

B_ym3＝A₈sin((θ+θ_x)+η₈)+k_ysinα₂sinβ₂B_w+B_y0＝A₈sin(θ+b₈)+C₈

B_zm3＝A₉sin((θ+θ_x)+η₉)+k_zsinα₃cosβ₃B_w+B_z0＝A₉sin(θ+b₉)+C₉

in the formula (12), eta₈、η₉Is a constant, variable A₇、A₈、A₉、b₇、b₈、b₉、C₇、C₈、C₉The characteristic parameters of the fitting function are obtained by fitting actual output values.

3. The method for integrally correcting errors of a three-axis magnetometer according to claim 2, wherein in step S3, the specific steps for solving the parameters of the error correction model established in step S1 are as follows:

the parameters k of the error correction model can be obtained from the equations (6), (9) and (12)_x、α₁、β₁、B_x0Satisfies the following conditions:

by solving the equation (13), beta is found₁Satisfies the following conditions:

order to

Has a value of 0 < beta₁< pi, in solving for beta₁When, if

Then beta is₁Only one solution, namely:

if it is

Then beta is₁There are two solutions:

or

Get beta by solution₁Then, by substituting the formula (13), it is possible to obtain:

the parameters k of the error correction model can be obtained from the equations (6), (9) and (12)_y、α₂、β₂、B_y0Satisfies the following conditions:

k_ysinα₂cosβ₂B_w+B_y0＝C₂ (15)

k_ycosα₂B_w+B_y0＝C₅

k_ysinα₂sinβ₂B_w+B_y0＝C₈

k_ysinα₂B_rot＝A₅

by solving equation (15), beta is found₂Satisfies the following conditions:

order to

Has a value of 0 < beta₂< pi, in solving for beta₂When, if

Then beta is₂Only one solution, namely:

if it is

Then beta is₂There are two solutions:

or

Get beta by solution₂Then, by substituting the formula (15), it is possible to obtain:

the parameters k of the error correction model can be obtained from the equations (6), (9) and (12)_z、α₃、β₃、B_z0Satisfies the following conditions:

k_ysinα₂cosβ₂B_w+B_y0＝C₂ (17)

k_ycosα₂B_w+B_y0＝C₅

k_ysinα₂sinβ₂B_w+B_y0＝C₈

k_ysinα₂B_rot＝A₅

by solving equation (17), beta is found₃Satisfies the following conditions:

order to

Has a value of 0 < beta₃< pi, in solving for beta₃When, if

Then beta is₃Only one solution, namely:

if it is

Then beta is₃There are two solutions:

or

Get beta by solution₃Then, by substituting equation (17), it is possible to obtain:

thus solving all parameters of the error correction model for beta₁、β₂、β₃If there are two solutions, substituting the parameters obtained by the two solutions into the error correction model, and determining beta according to the actual correction effect₁、β₂、β₃The value of (c).

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