CN104459828B - Based on the non-aligned bearing calibration of earth magnetism vector system around method of principal axes - Google Patents

Abstract

The invention belongs to the field of magnetic measurement technology, and specifically provides a non-alignment correction method for a geomagnetic vector system based on an axis-circling method, including the following steps: (S1) setting a non-magnetic turntable; (S2) installing a magnetic sensor in the geomagnetic vector measurement system and the accelerometer are packaged in a non-magnetic regular hexahedron; (S3) place the non-magnetic regular hexahedron on the table of the non-magnetic turntable, keep the X-axis direction of the non-magnetic regular hexahedron consistent with the direction of the rotation axis, and rotate N ₁ times around the X-axis , to obtain the measured values of N ₁ sets of magnetic sensors and accelerometers; (S4) keep the Z-axis direction of the non-magnetic regular hexahedron consistent with the direction of the rotation axis, rotate N ₂ times around the Z-axis, and obtain N ₂ sets of magnetic sensors and accelerometers Measured value; (S5) Calculate the misalignment angle of the magnetic sensor to the non-magnetic regular hexahedron and the misalignment angle of the accelerometer to the non-magnetic regular hexahedron respectively; (S6) determine the coordinate system conversion between the magnetic sensor and the accelerometer relationship, the calibration is complete.

Description

Non-alignment correction method of geomagnetic vector system based on axis-circling method

technical field

The invention belongs to the technical field of magnetic measurement, and in particular relates to a non-alignment error correction method for a geomagnetic vector measurement system.

Background technique

The three-axis magnetic sensor is widely used because it can provide component information, and its measurement value is the projection size of the geomagnetic field on the three sensitive axes of the magnetic sensor. If the Euler angle relationship between the rectangular coordinate system formed by the three sensitive axes of the magnetic sensor and the geographic coordinate system is known, the geomagnetic components in the geographic coordinate system can be calculated: the geomagnetic field northward component, eastward component, and vertical component. How to effectively obtain the geomagnetic component in the geographic coordinate system is the problem of geomagnetic vector measurement, and the geomagnetic vector measurement is completed through the geomagnetic vector measurement system. The geomagnetic vector measurement requires the use of a three-axis magnetic sensor, and at the same time, the orientation of the magnetic sensor needs to be determined to solve the problem of the orientation of the three-axis magnetic sensor. Attitude determination accuracy is a key factor in vector measurement. To achieve a certain accuracy in vector measurement, the requirements for attitude determination are very strict.

The geomagnetic vector measurement system is mainly composed of a direct strap-down of a magnetic sensor and an inertial navigation system. The magnetic sensor is used to measure the magnetic field component of the magnetic sensor coordinate system, and the inertial navigation system provides various attitude information for the magnetic sensor: heading, pitch, and roll angles. Through conversion, the three components of the magnetic field vector in the geographic coordinate system can be obtained. The inertial navigation includes a three-axis gyroscope and a three-axis accelerometer. In the geomagnetic vector system, the accelerometer coordinate system and the gyro coordinate system can be considered to be consistent. There will inevitably be some errors during the installation process of the geomagnetic vector measurement system. Among them, the coordinate system error between the magnetic sensor measurement axis and the inertial navigation measurement axis is called "non-alignment error". "Misalignment error" has become an important factor affecting the measurement accuracy of geomagnetic elements, and it is difficult to solve the misalignment problem by mechanical alignment methods. In a geomagnetic environment, a misalignment error of 1° can cause a vector measurement error of several hundred nT (nT is the unit of magnetic field strength). Therefore, it is of great significance to study the misalignment error correction technology to improve the accuracy of the geomagnetic vector measurement system. Since the inertial navigation coordinate system and the magnetic sensor coordinate system are invisible, and different from the calibration of the sensor coordinate system in the array, the inertial navigation and magnetic sensors measure different physical quantities, which increases the difficulty of calibration.

Aiming at the misalignment errors of different systems, some scholars have proposed related correction methods. Rong Zhu et al. (Rong Zhu, Zhaoying Zhou, Calibration of three-dimensional integrated sensors for improved system accuracy, Sensors and Actuators A 127 (2006) 340–344) used regular hexahedral optical prisms and an orthogonal optical coordinate system to perform micro The misalignment error of the integrated sensor system of the electromechanical system (MEMS, Micro-Electro-Mechanical System) is corrected, and the misalignment of the magnetic sensor and the accelerometer to the optical system coordinate system is calculated by using the magnetic field and gravity projection values of the optical system coordinate system. quasi error. However, this method requires precise adjustment of the three-dimensional coordinate system of the optical system, the use of local magnetic inclination information, and ensuring that the initial coordinate system of the regular hexahedral optical prism is consistent with the local north, east, and ground coordinate systems. Therefore, this method has high requirements for the precise adjustment of the optical system and the initial coordinate system of the optical prism. Erin L. Renk et al. (Erin L. Renk, W. C., Matthew Rizzo, Fuju Lee, and Dennis S. Bernstein. Calibrating a Triaxial Accelerometer-Magnetometer. IEEE Control Systems Magazine (2005) 86–95) used a six-dimensional robot to calibrate non- Alignment error; Similarly, this method requires precise control of attitude, and needs to provide heading angle, pitch angle, and roll angle, and the operation is complicated. J.Vcelak et al. (J.Vcelak, P.Ripka, J.Kubik, A.Platil and P.Kaspar, AMR navigation systems and methods of their calibration, Sensors and Actuators A 123–124 (2005) 122–128) utilize no The magnetic turntable corrects the misalignment error of the electronic magnetic compass, and estimates the misalignment angle by going around two axes of the turntable. Its core idea is to use the magnetic field and gravity in the direction of the rotation axis to be constant, so as to calculate the misalignment error of the magnetic sensor and the accelerometer, respectively. This method needs the attitude information provided by the accelerometer when calculating the misalignment error of the magnetic sensor roll angle. In addition, the above method ignores the roll angle misalignment error of the accelerometer when building the model. David Jurman (David Jurman, Marko Jankovec, Roman Kamnik, Marko Topic, Calibration and datafusion solution for the miniature attitude and heading reference system, Sensors and Actuators A 138 (2007) 411–420) and others aimed at the MEMS magnetic compass, the magnetic sensor The accelerometer is packaged into an open plastic resin material regular hexahedron. The principle of the calibration method is the same as that of J.Vcelak et al. The difference is that a non-magnetic flat plate is used, and attitude information also needs to be provided.

Regarding the misalignment correction of the geomagnetic vector measurement system, Pang Hongfeng and others applied for a national invention patent (application number: 201210355541.7, for the misalignment error correction method of the geomagnetic element measurement system, announcement date: January 16, 2013) using a right angle The non-magnetic regular hexahedron is turned over several times, so that the non-magnetic regular hexahedron is still close to the right-angled countertop. The misalignment angle between the magnetic field sensor and the inertial navigation system is calculated by using the principle of invariance of the projected component of the gravity vector on the right-angled table. This method requires the flatness and verticality of the right-angle table top to be very high, and every time it is turned over, the table top and the cabinet are required to fit closely. This method requires high processing precision and operation precision of the equipment. In addition, since the geomagnetic projection component value and misalignment angle of the right-angle table are both parameters to be estimated, there are many parameters to be estimated, and the degree of mutual coupling between the geomagnetic projection component value and the misalignment angle parameter is high.

All in all, the correction methods for the misalignment angle error of the above-mentioned geomagnetic vector system all have shortcomings such as complicated equipment and operation, require high experimental equipment and researchers' operating experience, or need to provide accurate attitude information, which affects the correction accuracy.

Contents of the invention

Aiming at the technical problems existing in the prior art, the invention provides a misalignment error correction method for a geomagnetic vector measurement system with simple components, easy implementation, easy operation and high correction accuracy.

The specific technical scheme is as follows:

A method for correcting misalignment of a geomagnetic vector system based on an axis-circling method, comprising the following steps:

(S1) setting a non-magnetic turntable, including a base, a table top and a rotating shaft, the rotating shaft vertically connects the base and the table top;

(S2) Encapsulate the magnetic sensor and the accelerometer in the geomagnetic vector measurement system in a non-magnetic regular hexahedron, and set the coordinate system of the non-magnetic regular hexahedron as XYZ;

(S3) Place the non-magnetic regular hexahedron on the table of the non-magnetic regular hexahedron, keep the X-axis direction of the non-magnetic regular hexahedron consistent with the direction of the rotation axis, and rotate the non-magnetic regular hexahedron on the table of the non-magnetic regular hexahedron to rotate any angle around the X-axis, Record the measured values of the magnetic sensor and the accelerometer, and rotate N ₁ times around the X axis to obtain N ₁ sets of measured values of the magnetic sensor and the accelerometer;

(S4) Flip the non-magnetic regular hexahedron, keep the Z-axis direction of the non-magnetic regular hexahedron in the same direction as the rotation axis, rotate the non-magnetic turntable table to make the non-magnetic regular hexahedron rotate at any angle around the Z-axis, and record the measurements of the magnetic sensor and the accelerometer value, and rotate N ₂ times around the Z axis to obtain the measured values of N ₂ sets of magnetic sensors and accelerometers;

(S5) Calculate the misalignment angles from the magnetic sensor to the non-magnetic regular hexahedron according to the N1 and _N2 groups _of measured values obtained from the magnetic sensor and the accelerometer, and according to the principle that the magnetic field and gravity components in the direction of the rotation axis remain unchanged and the misalignment angle of the accelerometer to the non-magnetic regular hexahedron;

(S6) According to the misalignment angle from the magnetic sensor to the nonmagnetic regular hexahedron and the misalignment angle from the accelerometer to the nonmagnetic regular hexahedron, determine the coordinate system conversion relationship between the magnetic sensor and the accelerometer, that is, complete the calibration.

Further, in the step (S5), according to the N1 group and _N2 group measured values _of the magnetic sensor and the accelerometer, the specific process of calculating the misalignment angle of the magnetic sensor to the nonmagnetic regular hexahedron is as follows:

(S501) Establish the relationship between the magnetic sensor measurement value, the magnetic field projection value and the misalignment angle according to the following formula:

in, is the measured value of the magnetic sensor when the non-magnetic regular hexahedron rotates around the X axis, is the measured value of the magnetic sensor when the non-magnetic regular hexahedron rotates around the Z axis; H ^x is the projected value of the geomagnetic field on the X-axis of the non-magnetic regular hexahedron when the non-magnetic regular hexahedron rotates around the X-axis; H ^z is the non-magnetic regular hexahedron around the Z-axis When rotating, the geomagnetic field is projected on the Z-axis of the non-magnetic regular hexahedron; α _mag , β _mag , γ _mag represent the misalignment angle between the magnetic sensor and the non-magnetic regular hexahedron;

(S502) Calculate the misalignment angles α _mag , β _mag , and γ _mag between the magnetic sensor and the non-magnetic regular hexahedron by using the measured values of N ₁ and N ₂ groups according to the following formula:

with

in, Indicates N1 sets _of measured values output by the magnetic sensor when the non-magnetic regular hexahedron rotates around the X axis; Indicates N ₂ sets of measured values output by the magnetic sensor when the non-magnetic regular hexahedron rotates around the Z axis;

The specific process of calculating the misalignment angle of the accelerometer to the non-magnetic regular hexahedron in the step (S5) is:

(S511) Establish the relationship between the accelerometer measurement value, the gravity projection value and the misalignment angle according to the following formula,

in, is the measured value of the accelerometer when the non-magnetic regular hexahedron rotates around the X axis, is the measured value of the magnetic sensor when the non-magnetic regular hexahedron rotates around the Z axis, g ^x is the projection value of gravity on the X-axis of the non-magnetic regular hexahedron when the non-magnetic regular hexahedron rotates around the X-axis; g ^z is the non-magnetic regular hexahedron rotating around the Z-axis , the projection value of gravity on the Z-axis of the non-magnetic regular hexahedron; α _acc , β _acc , γ _acc are the misalignment angles between the accelerometer and the non-magnetic regular hexahedron;

(S512) Calculate the misalignment angles α _acc , β _acc , and γ _acc between the accelerometer and the nonmagnetic regular hexahedron by using the measured values of N ₁ and N ₂ groups according to the following formula:

with

in, Indicates N1 sets _of measured values output by the accelerometer when the non-magnetic regular hexahedron rotates around the X axis; Indicates N ₂ sets of measured values output by the accelerometer when the non-magnetic regular hexahedron rotates around the Z axis.

Further, the specific process of the step (S6) is:

(S61) Realize the magnetic sensor measurement value according to α _mag , β _mag , γ _mag Converted to the projection value of the magnetic field on the non-magnetic regular hexahedron Calculated as follows:

(S62) According to α _acc , β _acc , γ _acc , realize Magnetic field projection values converted to the accelerometer coordinate system Calculated as follows:

Therefore, the coordinate system conversion relationship between the magnetic sensor and the accelerometer is obtained, that is, the calibration is completed.

Further, the magnetic sensor adopts a three-axis magnetic sensor, and the accelerometer adopts a three-axis accelerometer.

Further, the non-magnetic regular hexahedron is a regular hexahedron made of plastic resin material.

In order to meet the representativeness of the calculated misalignment angle and fully motivate the error parameters, the measured data of magnetic sensors rotating around different axes are used. is the magnetic sensor measurement output value, After correcting for misalignment errors, the projected value of the magnetic field in the accelerometer coordinate system. After non-alignment error correction, the coordinate system of the magnetic sensor is consistent with the accelerometer, and the geomagnetic vector measurement can be performed directly.

Compared with the prior art, the technical effects obtained by adopting the present invention are as follows: 1. After the correction method of the present invention is applied, the entire correction equipment is simple, and there is no need to process a high-precision right-angle table, and only a simple non-magnetic rotating structure is required and the regular hexahedron to calculate the misalignment angle. 2. After the correction method of the present invention is applied, the requirements for the processing of the non-magnetic regular hexahedron are greatly reduced, and there is no need to require high perpendicularity between the faces of the non-magnetic regular hexahedron, only a high perpendicularity between the two faces is required That's it. 3. The correction method of the present invention is simple to operate in the whole correction process. It is not necessary to flip the non-magnetic regular hexahedron in full posture, and it is not necessary to strictly require the non-magnetic regular hexahedron to fit closely with the right-angled table. It only needs to turn the non-magnetic regular hexahedron under a stable magnetic field environment. The magnetic regular hexahedron rotates around its axis, and there are no strict requirements on the initial posture of the system placement, no precise control on the rotation angle, and no strict requirements on the rotation direction, which reduces the difficulty of the experiment. 4. With the correction method of the present invention, the parameter estimation model is simplified, and the parameters to be estimated only include misalignment angles, the degree of parameter coupling is reduced, and the requirements for parameter estimation algorithms are reduced. 5. With the correction method of the present invention, the misalignment correction of the magnetic sensor does not need to introduce auxiliary information such as the attitude information of the accelerometer, the geomagnetic inclination angle, the geographical orientation, and the optical system.

Description of drawings

Fig. 1 is a schematic flow sheet of the present invention;

Fig. 2 is a schematic diagram when the present invention is in an initial state in a specific application example;

Fig. 3 is a schematic diagram of the rotation of a non-magnetic regular hexahedron around the X axis;

Fig. 4 is a schematic diagram of the rotation of a non-magnetic regular hexahedron around the Z axis;

Figure 5 is a schematic diagram of the misalignment angle of the magnetic sensor and the accelerometer to the non-magnetic regular hexahedron.

illustration:

1. Base; 2. Rotation axis; 3. Table top; 4. Non-magnetic regular hexahedron; 5. Magnetic sensor; 6. Accelerometer; 7. Magnetic field vector projection along the rotation axis; 8. Gravity vector projection along the rotation axis; 9 , Non-magnetic regular hexahedron coordinate system XYZ.

detailed description

In order to better understand the technical scheme of the present invention, its principle and calculation formula are now described in detail as follows:

The misalignment error correction method used in the geomagnetic vector measurement system of the present invention is as follows: the magnetic sensor 5 and the accelerometer 6 are packaged in a non-magnetic regular hexahedron 4, and the coordinate system relationship of the two sensors is indirectly transformed into the non-magnetic regular hexahedron The relationship of the coordinate system 9 ; the non-magnetic regular hexahedron 4 is placed on the non-magnetic turntable table 3 . When the non-magnetic regular hexahedron 4 is rotated, the magnetic field vector rotation axis projection 7 can be analytically expressed by the measured value of the magnetic sensor 5 and the misalignment angle during the rotation process. The misalignment error angle is an unknown parameter, and the non-linear equations are established by using the measured values of the magnetic sensor 5 during the rotation, so as to calculate the misalignment error from the coordinate system of the magnetic sensor 5 to the non-magnetic regular hexahedron 4 . Similarly, the misalignment error between the accelerometer 6 and the non-magnetic regular hexahedron 4 can be calculated, so as to realize the misalignment error correction between the magnetic sensor 5 and the accelerometer 6 .

As shown in Figure 1, the specific implementation steps of the inventive method are:

① The base 1 of the non-magnetic turntable is placed on a stable ground and does not need to be placed strictly horizontally.

② Referring to Fig. 2, the magnetic sensor 5 and the accelerometer 6 of the geomagnetic vector measurement system are integrally packaged in a non-magnetic regular hexahedron 4, and the magnetic sensor 5 and the accelerometer 6 are strapped down; the non-magnetic regular hexahedron 4 is placed in a non-magnetic Turntable table 1. Establish the non-magnetic regular hexahedron coordinate system 9 of the non-magnetic regular hexahedron 4, and the coordinate axes of the non-magnetic regular hexahedron coordinate system 9 are X, Y, and Z; Schematic diagram of quasi-angle.

In this example, as shown in Figure 2, at the initial position, the X-axis of the coordinate system 9 of the non-magnetic regular hexahedron 4 is parallel to the rotation axis, the magnetic field vector is projected 7 along the rotation axis and the gravity vector is projected 8 along the rotation axis, which is The magnetic field vector is projected along the X-axis of the non-magnetic regular hexahedron and the gravity vector is projected along the X-axis of the non-magnetic regular hexahedron. The magnetic sensor 5 adopts a three-axis magnetic sensor, and the accelerometer 6 adopts a three-axis accelerometer. The geomagnetic field is denoted as H ^x in the 9 projection of the non-magnetic regular hexahedron coordinate system, The magnetic sensor measures The relationship between the two is as follows:

Formula (1) transforms into:

in

Wherein, α _mag , β _mag , and γ _mag are misalignment angles between the magnetic sensor 5 and the non-magnetic regular hexahedron coordinate system 9 .

3. As shown in Figure 3, turn the non-magnetic turntable table 3, then the non-magnetic regular hexahedron 4 rotates around its X-axis, and the geomagnetic field is unchanged on the ^X -axis projection Hx of the non-magnetic regular hexahedron coordinate system 9. Simultaneously record the measured value of magnetic sensor 5 as During the rotation process, the relationship between the magnetic sensor 5 measured value and the X-axis geomagnetic field projection H ^x of the non-magnetic regular hexahedron coordinate system 9 is as follows:

If the misalignment angle error is zero, then a ₁₁ =1, a ₂₁ =0, a ₃₁ =0, then During the rotation process, N1 sets _of magnetic sensor output values are measured. The non-linear least squares method is used to solve the non-linear equations, and the parameters are estimated to calculate α _mag , β _mag . Such as formula (5):

in:

④ It can be seen that when rotating around the X-axis of the non-magnetic regular hexahedron coordinate system 9, only α _mag and β _mag can be calculated, but γ _mag cannot be calculated. As shown in FIG. 4 , the Z axis of the non-magnetic regular hexahedron coordinate system 9 rotates. During the rotation process, the relationship between the magnetic sensor 5 measured value and the ^Z axis of the non-magnetic regular hexahedron coordinate system 9 is as follows:

During the rotation process, N ₂ sets of measured values output by the magnetic sensor are obtained. Using the nonlinear least squares method to solve the nonlinear equations, estimate the parameters, and calculate γ _mag , as follows:

in:

In order to better estimate the parameters, it is preferable to use data of different attitudes, that is, the output data of the rotation of the non-magnetic regular hexahedron around X and around Z are simultaneously used for calculation.

After calculating α _mag , β _mag , and γ _mag , bring the misalignment parameters back to formula (1), and correct the measured value of the magnetic sensor rotating around the X-axis to the magnetic field projection value of the hexahedral coordinate system. According to the X-axis before and after correction The error comparison between the measured value and the true value is used to evaluate the estimated α _mag , β _mag , and γ _mag .

⑤Similarly, when the non-magnetic regular hexahedron rotates around the X axis, the measured value of the accelerometer 6 and the projection g ^x of gravity in the non-magnetic regular hexahedron coordinate system 9, The relationship is:

To obtain the misalignment angle between the accelerometer 6 and the non-magnetic regular hexahedron coordinate system 9, the operation calculation process is exactly the same as that of the magnetic sensor. During rotation around the X-axis of the non-magnetic regular hexahedron coordinate system 9, because there is an angle error between the accelerometer 6 coordinate system and the non-magnetic regular hexahedron coordinate system 9, the gravity vector rotation axis projection 8 and the X-axis of the accelerometer 6 The angle between them is constantly changing, causing the X-axis output of the accelerometer 6 to fluctuate constantly. When the X-axis and Z-axis of the non-magnetic regular hexahedron coordinate system 9 are rotated respectively, the output value of the accelerometer 6 is recorded at the same time.

The nonlinear least squares method is used for parameter estimation, and the misalignment angles α _acc , β _acc , and γ _acc between the accelerometer and the nonmagnetic regular hexahedron are calculated by solving equations.

After calculating α _acc , β _acc , and γ _acc , bring the misalignment angle parameters back to Equation (10), the measured value of the accelerometer rotating around the X axis can be corrected to the gravity projection value of the hexahedral coordinate system, according to the X before and after correction Estimated α _acc , β _acc , and γ _acc are evaluated by comparing the errors between axis measurements and true values.

⑥ After calculating α _mag , β _mag , γ _mag and α _acc , β _acc , γ _acc , the misalignment angle between the accelerometer 6 and the magnetic sensor 5 can be corrected indirectly. The misalignment error is corrected for the measured value of the magnetic sensor 5 , that is, the conversion between the magnetic sensor coordinate system and the accelerometer coordinate system is performed. First, according to α _mag , β _mag , γ _mag , realize the magnetic sensor measurement value Converted to the projection value of the magnetic field on the non-magnetic regular hexahedron The calculation process is as follows:

Secondly, according to α _acc , β _acc , γ _acc , realize Magnetic field projection values converted to the accelerometer coordinate system as follows:

in, is the measured value of the magnetic sensor (that is, the component of the magnetic sensor relative to its own coordinate system. In the calibration process, the coordinate system conversion is divided into two steps. First, the measured value of the magnetic sensor is converted to the projection value of the non-magnetic regular hexahedron coordinate system, followed by The projection value of the non-magnetic regular hexahedron coordinate system is converted to the projection value of the accelerometer coordinate system), After correcting for misalignment errors, the projected value of the magnetic field in the accelerometer coordinate system. After non-alignment error correction, the coordinate system of the magnetic sensor is consistent with the accelerometer, and the geomagnetic vector measurement can be performed directly.

Below, the present invention will be described in further detail in combination with specific embodiments.

The three-axis magnetic field sensor and the inertial navigation system (including the accelerometer) are fixedly installed in a non-magnetic regular hexahedron. In the outskirts of Changsha City, Hunan Province, a flat terrain area was selected for non-alignment correction. Pre-set the non-alignment angle between the magnetic sensor and the non-magnetic regular hexahedron: [α _mag β _mag γ _mag ]=[0.5° 0.8° 0.9°]; pre-set the non-alignment angle between the accelerometer and the non-magnetic regular hexahedron Alignment angle: [α _acc β _acc γ _acc ]=[0.6° 0.8° 1°]. The measurement noise of the magnetic sensor is 5nT, and the measurement noise of the accelerometer is 0.005m/s ² . At the initial attitude, the geomagnetic field is projected into [35000; The projection is [9.5; 0.8; 0.5] m/s ² .

Define the three coordinate axes of the magnetic sensor coordinate system as X _C , Y _C , Z _C ; the three coordinate axes of the accelerometer coordinate system as X _g , Y _g , Z _g ;

1. First, the non-magnetic regular hexahedron rotates around its X-axis, and the rotation angle interval is 10°. The measured values of the X- _C axis of the magnetic sensor are shown in Table 1; the measured values of the X- _g axis of the accelerometer are shown in Table 3;

2. Secondly, the non-magnetic regular hexahedron rotates around its Z axis, and the rotation angle interval is 10°. The measured values of the magnetic sensor Z _C axis are shown in Table 1; the measured values of the accelerometer Z _g axis are shown in Table 3;

3. During the measurement process, the average value of the rotation around the axis is used as the reference value of the projection of the rotation axis. When the non-magnetic regular hexahedron rotates around its X axis, the measured average value of the magnetic sensor X _C axis is 35005nT, and the measured average value of the accelerometer X _g axis is 9.502m/s ² . When the non-magnetic regular hexahedron rotates around its Z axis, the measured average value of the Z _C axis of the magnetic sensor is 34979nT, and the measured average value of the Z _g axis of the accelerometer is 9.498m/s ² . Since it is difficult to obtain the X-axis projection of the geomagnetic field in the non-magnetic regular hexahedron coordinate system in the actual operation process: 35000nT, in order to be closer to the actual situation in the simulation experiment, the measured average value of the rotation around the axis is used as the projected real value H ^x and H ^z Make parameter estimates.

4. Use formula (5) and formula (8) to solve nonlinear equations, and calculate the misalignment angle of the magnetic sensor: [α _mag β _mag γ _mag ]=[0.4998° 0.8° 0.86°], it can be known that the magnetic sensor is not The alignment angle estimation error is less than 5%. Similarly, the misalignment angle of the accelerometer is calculated: [α _acc β _acc γ _acc ]=[0.596° 0.802° 1.12°], it can be seen that the estimation error is less than 13%. It shows that the misalignment angle estimation accuracy is better. Next, using the estimated misalignment angle, the measured values are projectively transformed to evaluate the effect of the misalignment angle correction on the measured values.

5. According to the calculated misalignment angle between the magnetic sensor and the non-magnetic regular hexahedron, the measured value of the magnetic sensor can be transformed into the projection of the magnetic field in the non-magnetic regular hexahedron coordinate system. Theoretically, after misalignment angle correction, when the non-magnetic regular hexahedron rotates around its X-axis, the X-axis measurement value of the magnetic sensor is more consistent during the rotation process, and should always be 35000nT; before and after misalignment correction The error of the measured value of the magnetic sensor can be compared to evaluate the correction effect of the non-alignment parameter. The comparison of the X- _C axis measurement error of the magnetic sensor is shown in Table 2. Similarly, when the non-magnetic regular hexahedron rotates around its Z axis, the measured value of the magnetic sensor Z _C axis is relatively consistent during the rotation process, and should always be 35000nT. The comparison of the magnetic sensor Z _C axis measurement error is shown in Table 2. It can be seen that after the misalignment correction between the magnetic sensor and the non-magnetic regular hexahedron, the measurement consistency of the magnetic sensor in the direction of the rotation axis is significantly improved, and it is closer to the real projection value of the magnetic field on the non-magnetic regular hexahedron, indicating that this method can effectively estimate the magnetic sensor misaligned corners.

Table 1 Measurement data of the three-axis magnetic field sensor (rotating around the X and Z axes respectively)

Table 2 Comparison of measurement errors of three-axis magnetic field sensors (rotating around X and Z axes respectively)

6. According to the calculated misalignment angle between the accelerometer and the non-magnetic regular hexahedron, the measured value of the accelerometer can be transformed into the projection of gravity in the non-magnetic regular hexahedron coordinate system. Theoretically, after the misalignment angle is corrected, when the non-magnetic regular hexahedron rotates around its X-axis, the measured value of the accelerometer's X _g -axis is relatively consistent during the rotation process, and should always be 9.5m/s ² ; yes By comparing the error of the measured value before and after the misalignment correction, the correction effect of the misalignment parameter can be evaluated. The comparison of the measurement error of the accelerometer X _g axis is shown in Table 4. Similarly, when the non-magnetic regular hexahedron rotates around its Z-axis, the accelerometer Z _g -axis measurement value is relatively consistent during the rotation process, and should always be 9.5m/s ² , the accelerometer Z _g -axis measurement error comparison is shown in the table 4. It can be seen that after the misalignment correction between the accelerometer and the non-magnetic regular hexahedron, the measurement consistency of the accelerometer in the direction of the rotation axis is significantly improved, and it is closer to the real projection value of gravity on the non-magnetic regular hexahedron, indicating that this method can effectively estimate the accelerometer misaligned corners.

Table 3 Measurement data of the three-axis accelerometer (rotating around the X and Z axes respectively)

Table 4 Comparison of measurement errors of three-axis accelerometers (rotating around X and Z axes respectively)

The above are only preferred implementations of the present invention, and the protection scope of the present invention is not limited to the above-mentioned embodiments, and all technical solutions under the idea of the present invention belong to the protection scope of the present invention. It should be pointed out that for those skilled in the art, some improvements and modifications without departing from the principle of the present invention should be regarded as the protection scope of the present invention.

Claims (1)

1. A geomagnetic vector system misalignment correction method based on an axis-winding method is characterized by comprising the following steps:

(S1) arranging a non-magnetic turntable, which comprises a base, a table top and a rotating shaft, wherein the rotating shaft is vertically connected with the base and the table top;

(S2) packaging a magnetic sensor and an accelerometer in the geomagnetic vector measurement system in a nonmagnetic regular hexahedron, and setting a coordinate system of the nonmagnetic regular hexahedron as XYZ;

(S3) placing the nonmagnetic regular hexahedron on the table top of the nonmagnetic turntable to keep nonmagneticThe X-axis direction of the regular hexahedron is consistent with the direction of the rotating shaft, the table top of the non-magnetic rotary table is rotated to enable the non-magnetic regular hexahedron to rotate for any angle around the X-axis, the measured values of the magnetic sensor and the accelerometer are recorded, and the non-magnetic regular hexahedron rotates for N degrees around the X-axis₁Then, obtain N₁Grouping measurements of magnetic sensors and accelerometers;

(S4) turning the nonmagnetic regular hexahedron, keeping the direction of the Z axis of the nonmagnetic regular hexahedron consistent with the direction of the rotating shaft, rotating the tabletop of the nonmagnetic turntable to enable the nonmagnetic regular hexahedron to rotate for any angle around the Z axis, recording the measured values of the magnetic sensor and the accelerometer, and rotating N around the Z axis₂Then, obtain N₂Grouping measurements of magnetic sensors and accelerometers;

(S5) obtaining N of the magnetic sensor and the accelerometer₁Group and N₂The group measurement value is obtained by respectively calculating the non-alignment angle from the magnetic sensor to the non-magnetic regular hexahedron and the non-alignment angle from the accelerometer to the non-magnetic regular hexahedron according to the principle that the magnetic field and the gravity component in the direction of the rotating shaft are unchanged;

(S6) determining the coordinate system conversion relation between the magnetic sensor and the accelerometer according to the non-alignment angle from the magnetic sensor to the non-magnetic regular hexahedron and the non-alignment angle from the accelerometer to the non-magnetic regular hexahedron, namely completing the correction;

in the step (S5), N is the number of magnetic sensors and accelerometers₁Group and N₂The specific process of calculating the non-alignment angle from the magnetic sensor to the regular hexahedron by grouping the measured values is as follows:

(S501) establishing a relationship among the magnetic sensor measurement value, the magnetic field projection value, and the misalignment angle according to the following formula:

wherein,is nonmagneticThe magnetic sensor measures the value when the hexahedron rotates about the X-axis,the measured value of the magnetic sensor is measured when the non-magnetic regular hexahedron rotates around the Z axis; h^xWhen the non-magnetic regular hexahedron rotates around the X axis, the projection value of the geomagnetic field on the X axis of the non-magnetic regular hexahedron is obtained; h^zWhen the non-magnetic regular hexahedron rotates around the Z axis, the projection value of the geomagnetic field on the Z axis of the non-magnetic regular hexahedron is obtained; α_mag,β_mag,γ_magrepresenting the misalignment angle between the magnetic sensor and the nonmagnetic regular hexahedron;

(S502) utilizing N according to the following formula₁Group and N₂Group measurements calculate misalignment angle α between magnetic sensor and nonmagnetic cube_mag,β_mag,γ_mag：

And

wherein,n representing the output of a magnetic sensor when a non-magnetic regular hexahedron is rotated about the X-axis₁Group measurement values;n representing the output of a magnetic sensor when a non-magnetic regular hexahedron is rotated about the Z-axis₂Group measurement values;

the specific process of calculating the non-aligned angle from the accelerometer to the non-magnetic regular hexahedron in the step (S5) is as follows:

(S511) establishing the relation among the accelerometer measurement value, the gravity projection value and the misalignment angle according to the following formula,

wherein,is the accelerometer measurement value when the non-magnetic regular hexahedron rotates around the X axis,the measured value of the magnetic sensor is measured when the non-magnetic regular hexahedron rotates around the Z axis; g^xWhen the non-magnetic regular hexahedron rotates around the X axis, the projection value of gravity on the X axis of the non-magnetic regular hexahedron is obtained; g^zWhen the non-magnetic regular hexahedron rotates around the Z axis, the gravity is the projection value of the Z axis of the non-magnetic regular hexahedron; α_acc,β_acc,γ_accis a non-alignment angle between the accelerometer and the non-magnetic regular hexahedron;

(S512) using N according to the following formula₁Group and N₂The set of measurements calculates the misalignment angle α between the accelerometer and the nonmagnetic cube_acc,β_acc,γ_acc：

And

wherein,representing N output by the accelerometer when the non-magnetic regular hexahedron rotates about the X-axis₁Group measurement values;…，representing N output by the accelerometer when the non-magnetic regular hexahedron rotates about the Z-axis₂Group measurement values;

the specific process of the step (S6) is as follows:

(S61) according to α_mag,β_mag,γ_magImplementing magnetic sensor measurementsConverted into the projection value of the magnetic field in the nonmagnetic regular hexahedronThe calculation formula is as follows:

(S62) according to α_acc,β_acc,γ_accTo realizeMagnetic field projection values converted to accelerometer coordinate systemThe calculation formula is as follows:

therefore, the coordinate system conversion relation between the magnetic sensor and the accelerometer is obtained, and the correction is completed;

the magnetic sensor adopts a three-axis magnetic sensor, and the accelerometer adopts a three-axis accelerometer;

the non-magnetic regular hexahedron is made of plastic resin materials.