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CN109407159B - An Attitude Error Correction Method for Geomagnetic Total Element Sensors - Google Patents

An Attitude Error Correction Method for Geomagnetic Total Element Sensors Download PDF

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CN109407159B
CN109407159B CN201811348134.7A CN201811348134A CN109407159B CN 109407159 B CN109407159 B CN 109407159B CN 201811348134 A CN201811348134 A CN 201811348134A CN 109407159 B CN109407159 B CN 109407159B
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attitude
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CN109407159A (en
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葛健
霍治帆
董浩斌
邱香域
李晗
罗望
王文杰
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China University of Geosciences
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01VGEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
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Abstract

本发明提供一种地磁全要素传感器姿态误差校正方法,包括:S1测量地磁全要素传感器姿态偏转角α和测量点地磁场F;S2依次向第一线圈C1中分别通入大小相等、方向相反的电流,分别测量偏转磁场FI+和FI‑;S3依次向第二线圈C2中分别通入大小相等、方向相反的电流,分别测量偏转磁场FD+和FD‑;S4计算出磁倾角的变化量校正值ΔI′1和磁偏角的变化量校正值ΔD′1;S5计算磁倾角校正值I和磁偏角校正值D,校正公式为I=I0+ΔI′1,D=D0+ΔD′1。本发明的有益效果:解决了地磁全要素传感器在测量时姿态变化导致测量精度低的问题,使地磁全要素传感器可以应用于海洋领域,航空领域,以及姿态变化时的陆地测量领域。

Figure 201811348134

The present invention provides a method for correcting the attitude error of a geomagnetic all-element sensor, comprising: S1 measuring the attitude deflection angle α of the geomagnetic all-element sensor and the geomagnetic field F of the measurement point; S2 sequentially feeding equal-sized and opposite directions into the first coil C1. Current, measure deflection magnetic field F I+ and F I- respectively; S3 pass into the current of equal size and opposite direction respectively in second coil C2 in turn, measure deflection magnetic field F D+ and F D- respectively; S4 calculates the change of magnetic inclination angle S5 calculates the magnetic inclination angle correction value I and the magnetic declination angle correction value D, the correction formula is I =I 0 +ΔI′ 1 , D = D 0 +ΔD′ 1 . The beneficial effects of the invention are as follows: the problem of low measurement accuracy caused by the attitude change of the geomagnetic all-element sensor during measurement is solved, so that the geomagnetic all-element sensor can be applied to the marine field, the aviation field, and the land measurement field when the attitude changes.

Figure 201811348134

Description

Geomagnetic full-factor sensor attitude error correction method
Technical Field
The invention relates to the field of magnetic field measurement, in particular to a method for correcting attitude errors of a geomagnetic full-factor sensor.
Background
Referring to fig. 9, the geomagnetic field is a vector field and is composed of seven elements, i.e., a geomagnetic field T, a horizontal component H, a north component X, an east component Y, a vertical component Z, a declination angle I, and a declination angle D. Compared with the traditional geomagnetic field observation and three-component observation, the geomagnetic complete element contains more magnetic field information and can accurately reflect the characteristics of the research object. In practical application, appropriate magnetic field parameters need to be selected according to different scenes. In addition, the geomagnetic element data can be used for mapping a geomagnetic map, researching ancient geomagnetism, monitoring space weather, and the like. Therefore, high-precision geomagnetic factor data is important for exploring geological structures and earth origins, establishing a global magnetic field model and researching a space.
For the present, geomagnetic sensors may be classified into vector sensors and total field sensors according to measurement manners. Vector sensors are mainly classified into three categories: the first type is represented by a fluxgate sensor, which has a small volume and can directly acquire three-component geomagnetic information, but has the problems of orthogonality error, temperature drift, incapability of absolute observation and the like; the second type is a combined measurement mode combining a fluxgate sensor and a theodolite, and the magnetometer is also called a DI instrument, and can directly read a geomagnetic inclination angle and a declination angle through an optical system of the theodolite, but cannot automatically observe. The third type is a combined measurement mode combining a total field sensor and a helmholtz coil (magnetic field uniform generator), mainly including methods such as FHD, a three-axis coil method, ZHD, etc., and such sensors are mostly used for observation of a geomagnetic station, and measurement under sea, aviation, and land attitude change conditions causes a problem in the accuracy of the measurement value due to the attitude change, thereby limiting the application under sea, aviation, and land attitude change conditions. Therefore, how to realize high-precision integrated measurement of the geomagnetic total element information under the condition of posture change becomes an important point and a difficult point for realizing effective measurement.
Disclosure of Invention
In view of this, the embodiment of the present invention provides a method for correcting an attitude error of a geomagnetic full-scale element sensor.
Referring to fig. 1 and 2, an embodiment of the present invention provides a method for correcting an attitude error of a geomagnetic total element sensor, where the geomagnetic total element sensor includes a total field sensor and a uniform magnetic field generator surrounding the total field sensor, the uniform magnetic field generator includes a first coil C1 and a second coil C2 which are orthogonal to each other, and the first coil C1 and the total field sensor are disposed on a magnetic meridian plane, including the following steps:
s1, measuring a posture deflection angle α of the geomagnetic full-element sensor by using a posture sensor, wherein the pitching deflection angle α is an included angle between the total field sensor and a magnetic meridian plane, and measuring a geomagnetic field F of a measuring point by using the total field sensor;
s2 is sequentially sent to the second stepThe coils C1 are respectively connected with currents with equal and opposite directions, and the total field sensor is used for respectively measuring the deflection magnetic field FI+And FI-
S3 sequentially passing equal and opposite currents into the second coil C2, and measuring the deflection magnetic field F by the total field sensorD+And FD-
S4 deflection angle α, geomagnetic field F, and deflection magnetic field FI+And FI-Calculating a variation correction value Delta I' of the magnetic tilt angle based on the attitude deflection angle α, the geomagnetic field F, and the deflection magnetic field FD+And FD-Calculating a variable correction value delta D' of the declination;
s5, calculating a magnetic inclination angle correction value I and a magnetic declination angle correction value D, wherein the correction formula is that I is I0+ΔI′,D=D0+ΔD′,I0Reference declination angle for measuring point, D0Is the reference declination of the measurement point.
Further, the method includes step S6 of calculating a geomagnetic total element of the measurement point according to the magnetic inclination correction value I and the magnetic declination correction value D.
Further, the attitude change of the geomagnetic whole element sensor includes a pitch change, a horizontal change and a roll change.
Further, when the attitude of the geomagnetic total element sensor changes in pitch, the attitude yaw angle α is a pitch yaw angle, that is, an angle between the total field sensor and the magnetic meridian plane, and the step S4 is performed according to the attitude yaw angle α, the geomagnetic field F, and the yaw magnetic field FI+And FI-The specific calculation method for calculating the variation correction value delta I' of the magnetic inclination angle comprises the following steps:
respectively passing equal and opposite currents into the first coil C1 to generate bias magnetic fields with opposite directions and same magnitude, wherein the bias magnetic field magnitude is A'ISuperposed with the earth magnetic field F to form a deflecting magnetic field FI+And FI-From the cosine theorem
FI+ 2=A′I 2+F2-2A′IFcos(α2) (1)
FI- 2=A′I 2+F2+2A′IFcos(α2) (2)
Wherein, α2The angle between the bias magnetic field after the attitude change and the time magnetic field is obtained by adding the formula (1) and the formula (2)
Figure GDA0002327511410000031
And finding
Figure GDA0002327511410000032
Is provided with
Figure GDA0002327511410000033
Can be obtained by Taylor expansion
Figure GDA0002327511410000034
From geometrical relationships
Figure GDA0002327511410000035
From the expressions (5) and (6)
Figure GDA0002327511410000036
The variation of the magnetic inclination angle is a small value obtained from the geometric relationship α2≈α10(8)
Wherein
Figure GDA0002327511410000041
α1The included angle of the magnetic field generated by the current passing through the first coil C1 before the attitude change occurs,
then Δ I ═ cos (α) can be obtained from formulae (4) and (7)2)-α (9)
ΔI′=-cos(α10)-α (10)
Direct compensation of α yields Δ I ═ cos (α)10) (11)
α190 deg. and the relation of trigonometric function can be used to obtain delta I ═ sin (α)0)。 (12)
Further, when the attitude of the geomagnetic total element sensor changes in pitch, the step S4 is performed based on the attitude yaw angle α, the geomagnetic field F, and the yaw field FD+And FD-The calculation method of the variation correction value Δ D ' for calculating the declination is the same as the calculation method of the variation correction value Δ I ' for calculating the declination, and the calculation method is the same as the calculation method of the variation correction value Δ I ' for calculating the declination
Figure GDA0002327511410000042
Further, when the attitude of the geomagnetic total element sensor changes horizontally, the attitude deflection angle α is a horizontal deflection angle, that is, an angle between the total field sensor and the magnetic meridian plane, and the step S4 is performed based on the attitude deflection angle α, the geomagnetic field F, and the geomagnetic deflection field FD+And FD-The specific calculation method for calculating the variation correction value delta D' of the declination comprises the following steps:
respectively passing equal and opposite currents into the second coil C2 to generate bias magnetic fields with opposite directions and same magnitude, wherein the magnitude of the bias magnetic field is A'DSuperposed with the earth magnetic field F to form a deflecting magnetic field FD+And FD-From the cosine theorem, we can obtain:
FD+ 2=A′D 2+F2-2A′DFcos(α2) (13)
FD- 2=A′D 2+F2+2A′DFcos(α2) (14)
wherein, α2The angle between the bias magnetic field after the attitude change and the time magnetic field is obtained by adding the equations (13) and (14)
Figure GDA0002327511410000043
Calculate out
Figure GDA0002327511410000044
After the formula (16) is simplified and compensated, the product is obtained
Figure GDA0002327511410000051
Wherein
Figure GDA0002327511410000052
Further, when the attitude level of the geomagnetic sensor changes, the step S4 is performed based on the attitude yaw angle α, the geomagnetic field F, and the yaw field FI+And FI-The calculation method of the variation correction value deltai 'of the declination angle is the same as the calculation method of the variation correction value deltad' of the declination angle,
Figure GDA0002327511410000053
further, when the attitude of the geomagnetic total element sensor changes in a reversed manner, the calculation method of the variation correction value Δ I 'of the declination angle and the calculation method of the variation correction value Δ D' of the declination angle are the same as those in the attitude pitching and horizontal changes of the geomagnetic total element sensor, and the calculation methods are used for calculating
Figure GDA0002327511410000054
Figure GDA0002327511410000055
The technical scheme provided by the embodiment of the invention has the following beneficial effects: the invention discloses a method for correcting attitude errors of a geomagnetic full-factor sensor, which is used for performing classification calculation according to three change conditions of attitude pitching, leveling and overturning which are possibly encountered by the geomagnetic full-factor sensor during base station type measurement to obtain a magnetic dip angle variation correction value and a magnetic declination variation correction value, performing algorithm compensation on a measurement result to obtain a more accurate measurement value, solving the problem of low measurement precision caused by attitude change of the geomagnetic full-factor sensor during measurement, and enabling the geomagnetic full-factor sensor to be applied to the fields of oceans, aviation and land measurement during attitude change.
Drawings
Fig. 1 is a flowchart of a method for correcting an attitude error of a geomagnetic full-scale element sensor according to the present invention;
fig. 2 is a diagram of a geomagnetic whole element sensor measurement model;
fig. 3 is a schematic diagram of the geomagnetic total element sensor before and after the attitude change;
FIG. 4 is a diagram illustrating a variation of a magnetic tilt angle before and after a tilt change of an attitude of a geomagnetic total element sensor;
fig. 5 is a schematic diagram of the geomagnetic total element sensor before and after a change in attitude level;
fig. 6 is a schematic diagram illustrating a variation of declination before and after a change of an attitude level of the geomagnetic full factor sensor;
fig. 7 is a schematic diagram of the geomagnetic total element sensor before and after the attitude reversal change;
FIG. 8 is a schematic diagram illustrating variation of magnetic tilt angle before and after the attitude of the geomagnetic full factor sensor is flipped;
fig. 9 is a geometric relationship diagram of the geomagnetism holonomic element.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention will be further described with reference to the accompanying drawings.
Referring to fig. 1, an embodiment of the present invention provides a method for correcting an attitude error of a geomagnetic total element sensor, where the geomagnetic total element sensor includes a total field sensor and a uniform magnetic field generator surrounding the total field sensor, the uniform magnetic field generator includes a first coil C1 and a second coil C2 which are orthogonal to each other, and the first coil C1 and the total field sensor are placed in a magnetic meridian plane, including the following steps:
s1 measuring an attitude deflection angle α of the geomagnetic total element sensor using an attitude sensor, and measuring a geomagnetic field F at a measurement point using the total field sensor;
s2 sequentially supplying current with same magnitude and opposite direction to the first coil C1The total field sensor measures the deflection magnetic field F respectivelyI+And FI-
S3 sequentially passing equal and opposite currents into the second coil C2, and measuring the deflection magnetic field F by the total field sensorD+And FD-
S4 according to the pitch angle α, the geomagnetic field F and the yaw magnetic field FI+And FI-Calculating a variation correction value Delta I' of the inclination angle of the magnet based on the horizontal deflection angle α, the geomagnetic field F, and the deflection magnetic field FD+And FD-Calculating a variable correction value delta D' of the declination;
s5, calculating a magnetic inclination angle correction value I and a magnetic declination angle correction value D, wherein the correction formula is that I is I0+ΔI′, D=D0+ΔD′,I0Reference declination angle for measuring point, D0A reference declination for a measurement point;
s6 calculates the geomagnetic total element at the measurement point from the declination correction value I and the declination correction value D.
The attitude change of the geomagnetic whole element sensor comprises a pitch change, a horizontal change and a roll-over change, and the method is explained in detail by the following classification:
referring to fig. 3, the left side shows a schematic diagram of a measurement state before the attitude of the geomagnetic full-element sensor changes in pitch, the right side shows a schematic diagram of a measurement state after the attitude of the geomagnetic full-element sensor changes in pitch, when the attitude of the geomagnetic full-element sensor changes in pitch, the attitude deflection angle is α, i.e., the included angle between the total field sensor and the magnetic meridian plane, in step S4, the measurement state is determined according to the attitude deflection angle α, the geomagnetic field F and the magnetic deflection field FI+And FI-The specific calculation method for calculating the variation correction value delta I' of the magnetic inclination angle comprises the following steps:
referring to fig. 4, currents having the same magnitude and opposite directions are respectively supplied to the first coil C1 to generate bias magnetic fields a 'having the same magnitude and opposite directions'I+And A'I-A 'is the magnitude of the bias magnetic field'ISuperposed with the earth magnetic field F to form a deflecting magnetic field FI+And FI-From the cosine theorem
FI+ 2=A′I 2+F2-2A′IFcos(α2) (1)
FI- 2=A′I 2+F2+2A′IFcos(α2) (2)
Wherein, α2The angle between the bias magnetic field after the attitude change and the time magnetic field F is the angle between the bias magnetic field after the attitude change and the time magnetic field F, the geomagnetic field F is influenced by the bias magnetic field when being electrified before the first coil C1 is electrified, and the geomagnetic field is slightly deflected to generate
Is obtained by adding the formula (1) and the formula (2)
Figure GDA0002327511410000071
And finding
Figure GDA0002327511410000072
Is provided with
Figure GDA0002327511410000073
Can be obtained by Taylor expansion
Figure GDA0002327511410000074
From the geometrical relationships in FIG. 4
Figure GDA0002327511410000075
From the expressions (5) and (6)
Figure GDA0002327511410000081
Since the variation Δ I of the magnetic inclination angle is a minute value, α is obtained from the geometric relationship2≈α10(8)
α is the arc value of horizontal deflection angle of geomagnetic sensor, α0Is an angular representation of α and,
namely, it is
Figure GDA0002327511410000082
α1The included angle of the magnetic field generated by the current passing through the first coil C1 before the attitude change occurs,
then Δ I ═ cos (α) can be obtained from formulae (4) and (7)2)-α (9)
ΔI′=-cos(α10)-α (10)
Since pitch yaw angle α is a measured value, it can be directly compensated for, yielding Δ I ═ cos (α)10) (11)
Due to α190 deg. and the relation of trigonometric function can be used to obtain delta I ═ sin (α)0)。 (12)
The second coil C2 is relatively moved when the geomagnetic total element sensor changes its attitude only in the noon magnet plane in a pitching manner, but the geomagnetic total element sensor is offset only in the noon magnet plane, so that the bias magnetic field a 'generated by the second coil C2'DStill perpendicular to the magnetic meridian plane, the calculation result of the variation correction value Δ D' of the declination is not affected when the integrated measurement method is adopted for calculation, so that the variation of the second coil C2 when the magnetic meridian plane deviates does not cause the error of the declination variation Δ D.
According to the pitch deflection angle α, the geomagnetic field F and the deflection magnetic field FD+And FD-The calculation method of the variation correction value Δ D 'of the declination is the same as the calculation method of the variation correction value Δ I' of the declination, and the variation correction value of the declination can be calculated
Figure GDA0002327511410000083
And the magnetic declination variation correction value delta D' is consistent with the magnetic declination variation delta D formula before the attitude pitching variation.
Referring to fig. 5, the left side shows a schematic diagram of a measurement state before the attitude of the geomagnetic full element sensor changes horizontally, the right side shows a schematic diagram of a measurement state after the attitude of the geomagnetic full element sensor changes horizontally, and the attitude deflection angle α is a horizontal deflection angle when the attitude of the geomagnetic full element sensor changes horizontally, that is, the geomagnetic full element sensor changes horizontallyThe included angle between the total field sensor and the magnetic meridian plane is determined according to the attitude deflection angle α, the geomagnetic field F and the deflection magnetic field F in the step S4D+And FD-The specific calculation method for calculating the variation correction value delta D' of the declination comprises the following steps:
referring to fig. 6, currents with equal and opposite directions are respectively applied to the second coil C2 to generate bias magnetic fields a 'with opposite directions and equal magnitudes'D+And A'D-A 'is the magnitude of the bias magnetic field'DSuperposed with the earth magnetic field F to form a deflecting magnetic field FD+And FD-From the cosine theorem, we can obtain:
FD+ 2=A′D 2+F2-2A′DFcos(α2) (13)
FD- 2=A′D 2+F2+2A′DFcos(α2) (14)
is obtained by adding the formula (13) and the formula (14)
Figure GDA0002327511410000091
Calculate out
Figure GDA0002327511410000092
By simplifying the expression (16) by the same operation method as the expressions (5), (6) and (7) and compensating the same, the method can be obtained
Figure GDA0002327511410000093
The first coil C1 is relatively moved when the attitude level of the geomagnetic sensor changes in the PM plane, but the offset magnetic field a 'generated by the first coil C1 changes only in the PM plane'IStill parallel to the meridian plane of the magneton, the variation Δ I of the magnetic inclination angle is not affected, so that the variation of the first coil C2 when the magneton deviates from the meridian plane of the magneton does not cause an error in the variation Δ I of the magnetic inclination angleAnd (4) generating.
When the attitude of the geomagnetic total element sensor changes horizontally, the step S4 is performed based on the horizontal yaw angle α, the geomagnetic field F, and the yaw field FI+And FI-The calculation method of the variation correction value deltai 'of the declination angle is the same as the calculation method of the variation correction value deltad' of the declination angle,
Figure GDA0002327511410000094
the magnetic dip angle variation correction value delta I' is consistent with the magnetic dip angle variation delta I formula before the attitude horizontal variation.
Referring to fig. 7 and 8, the left side shows a measurement state diagram before the posture of the geomagnetic sensor is reversed and the right side shows a measurement state diagram after the posture of the geomagnetic sensor is reversed, when the posture of the geomagnetic sensor is reversed, the first coil C1 and the second coil C2 both move, but the first coil C1 is electrified to generate a bias magnetic field a'IA bias magnetic field A 'generated by the second coil C2 being energized while being parallel to the magnetic meridian plane and not affecting the change amount Delta I of the magnetic pitch angle'DStill perpendicular to the magnetic meridian plane, the variation Δ D of the declination angle is not affected, the pitch yaw angle and the horizontal yaw angle are both 0, and the variation correction value Δ I 'of the declination angle and the variation correction value Δ D' of the declination angle can be calculated by using the same calculation method for attitude pitch and horizontal variation:
Figure GDA0002327511410000101
Figure GDA0002327511410000102
after obtaining the magnetic inclination angle and the magnetic declination angle variable quantity after the attitude change is corrected by the algorithm, the reference magnetic inclination angle I of the measuring point is obtained0And a reference declination angle D0Reference magnetic declination angle I0And a reference declination angle D0Can be searched according to the coordinates of the measuring pointsAnd inquiring, and calculating to obtain a magnetic inclination angle correction value I and a magnetic declination angle correction value D of the current measurement point.
The specific calculation formula is as follows:
I=I0+ΔI′
D=D0+ΔD′
referring to fig. 9, the geomagnetic field is a vector field and is composed of seven elements, i.e., a geomagnetic field T, a horizontal component H, a north component X, an east component Y, a vertical component Z, a declination angle I, and a declination angle D. The coordinate system selects the direction of the x axis along the geographical meridian and points to the geographical true north, the direction of the y axis along the latitude circle and points to the geographical true east, and the z axis is vertical and downward. The total field T is BO in direction, the projection of the total field T on the X axis is a north component X, the projection of the total field T on the Y axis is an east component Y, the projection of the total field T on the Z axis is a vertical component Z, and the projection of the total field T on the xBz plane is a horizontal component H; the vertical plane zBO where the geomagnetic field T is located is a magneton meridian plane, the included angle (xBA) between the geographic meridian plane and the magneton meridian plane is a magnetic declination angle D, and the included Angle (ABO) between the horizontal plane and the geomagnetic field T is a magnetic declination angle.
All the required magnetic field elements, namely all the magnetic field elements can be obtained according to the geometric relationship of the geomagnetic elements by solving the magnetic inclination angle correction value I and the magnetic declination correction value D
Figure GDA0002327511410000111
In this document, the terms front, back, upper and lower are used to define the components in the drawings and the positions of the components relative to each other, and are used for clarity and convenience of the technical solution. It is to be understood that the use of the directional terms should not be taken to limit the scope of the claims.
The features of the embodiments and embodiments described herein above may be combined with each other without conflict.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims (2)

1. A method of correcting an attitude error of a geomagnetic whole-element sensor, the geomagnetic whole-element sensor including a total field sensor and a uniform magnetic field generator surrounding the total field sensor, the uniform magnetic field generator including a first coil C1 and a second coil C2 which are orthogonal, the first coil C1 and the total field sensor being placed in a magnetic meridian, the method comprising:
s1 measuring an attitude deflection angle α of the geomagnetic total element sensor using an attitude sensor, and measuring a geomagnetic field F at a measurement point using the total field sensor;
s2, sequentially passing equal and opposite currents into the first coil C1, respectively, and measuring the deflection magnetic field F by using the total field sensorI+And FI-
S3 sequentially passing equal and opposite currents into the second coil C2, and measuring the deflection magnetic field F by the total field sensorD+And FD-
S4 deflection angle α, geomagnetic field F, and deflection magnetic field FI+And FI-Calculating a variation correction value Delta I' of the magnetic tilt angle based on the attitude deflection angle α, the geomagnetic field F, and the deflection magnetic field FD+And FD-Calculating a variation correction value delta D' of the declination, wherein the calculation method comprises the following specific steps:
the attitude change of the geomagnetic total element sensor includes pitch change, horizontal change and roll-over change, and when the attitude of the geomagnetic total element sensor changes in pitch, the attitude deflection angle α is a pitch deflection angle, that is, an included angle between the total field sensor and the magnetic meridian plane, and a specific calculation method of a variation correction value Δ I' of a magnetic inclination angle is as follows:
respectively passing equal and opposite currents into the first coil C1 to generate bias magnetic fields with opposite directions and same magnitude, wherein the bias magnetic field magnitude is A'ISuperposed with the earth magnetic field F to form a deflecting magnetic field FI+And FI-From the cosine theorem
Figure FDA0002327511400000011
Figure FDA0002327511400000012
Wherein, α2The angle between the bias magnetic field after the attitude change and the time magnetic field is obtained by adding the formula (1) and the formula (2)
Figure FDA0002327511400000021
And finding
Figure FDA0002327511400000022
Is provided with
Figure FDA0002327511400000023
Can be obtained by Taylor expansion
Figure FDA0002327511400000024
From geometrical relationships
Figure FDA0002327511400000025
From the expressions (5) and (6)
Figure FDA0002327511400000026
The variation of the magnetic inclination angle is a small value obtained from the geometric relationship α2≈α10(8)
Wherein
Figure FDA0002327511400000027
α1The included angle of the magnetic field generated by the current passing through the first coil C1 before the attitude change occurs,
then Δ I ═ cos (α) can be obtained from formulae (4) and (7)2)-α (9)
ΔI′=-cos(α10)-α (10)
Direct compensation of α yields Δ I ═ cos (α)10) (11)
α190 deg. and the relation of trigonometric function can be used to obtain delta I ═ sin (α)0); (12)
According to attitude deflection angle α, geomagnetic field F and deflection magnetic field FD+And FD-The calculation method of the variation correction value Δ D ' for calculating the declination is the same as the calculation method of the variation correction value Δ I ' for calculating the declination, and the calculation method is the same as the calculation method of the variation correction value Δ I ' for calculating the declination
Figure FDA0002327511400000028
When the attitude of the geomagnetic total element sensor changes horizontally, the attitude deflection angle α is a horizontal deflection angle, that is, an included angle between the total field sensor and the magnetic meridian plane, and in step S4, the attitude deflection angle α, the geomagnetic field F, and the magnetic deflection field F are used as the basisD+And FD-The specific calculation method for calculating the variation correction value delta D' of the declination comprises the following steps:
respectively passing equal and opposite currents into the second coil C2 to generate bias magnetic fields with opposite directions and same magnitude, wherein the magnitude of the bias magnetic field is A'DSuperposed with the earth magnetic field F to form a deflecting magnetic field FD+And FD-From the cosine theorem, we can obtain:
Figure FDA0002327511400000031
Figure FDA0002327511400000032
wherein, α2The angle between the bias magnetic field after the attitude change and the time magnetic field is obtained by adding the equations (13) and (14)
Figure FDA0002327511400000033
Calculate out
Figure FDA0002327511400000034
After the formula (16) is simplified and compensated, the product is obtained
Figure FDA0002327511400000035
Wherein
Figure FDA0002327511400000036
According to attitude deflection angle α, geomagnetic field F and deflection magnetic field FI+And FI-The calculation method of the variation correction value deltai 'of the declination angle is the same as the calculation method of the variation correction value deltad' of the declination angle,
Figure FDA0002327511400000037
when the attitude of the geomagnetic total element sensor changes in a turnover manner, the calculation method of the variation correction value delta I 'of the magnetic inclination angle and the calculation method of the variation correction value delta D' of the magnetic declination angle are the same as those when the attitude of the geomagnetic total element sensor changes in a pitching and horizontal manner, and the calculation methods are used for calculating
Figure FDA0002327511400000038
Figure FDA0002327511400000039
S5, calculating a magnetic inclination angle correction value I and a magnetic declination angle correction value D, wherein the correction formula is that I is I0+ΔI′,D=D0+ΔD′,I0Reference declination angle for measuring point, D0Is the reference declination of the measurement point.
2. The method according to claim 1, wherein the method further comprises: further, S6 calculates a geomagnetic total element of the measurement point based on the declination correction value I and the declination correction value D.
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