CN104459828B - Based on the non-aligned bearing calibration of earth magnetism vector system around method of principal axes - Google Patents
Based on the non-aligned bearing calibration of earth magnetism vector system around method of principal axes Download PDFInfo
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Abstract
Invention belongs to Magnetic Measurement Technology field, specifically provides a kind of non-aligned bearing calibration of earth magnetism vector system based on around method of principal axes, comprises the following steps：(S1) set without magnetic turntable；(S2) by the Magnetic Sensor and accelerometer package in earth magnetism vector measurement system in without magnetic regular hexahedron；(S3) will be positioned on the table top without magnetic turntable without magnetic regular hexahedron, keep the X-direction without magnetic regular hexahedron consistent with rotation direction of principal axis, N is rotated around X-axis1It is secondary, obtain N1The measured value of group Magnetic Sensor and accelerometer；(S4) keep the Z-direction without magnetic regular hexahedron consistent with rotation direction of principal axis, N is rotated about the z axis2It is secondary, obtain N2The measured value of group Magnetic Sensor and accelerometer；(S5) Magnetic Sensor is calculated respectively to the non-aligned angle without magnetic regular hexahedron and accelerometer to the non-aligned angle without magnetic regular hexahedron；(S6) determine the coordinate system transformational relation between Magnetic Sensor and accelerometer, that is, complete correction.
Description
Technical Field
The invention belongs to the technical field of magnetic measurement, and particularly relates to a non-alignment error correction method for a geomagnetic vector measurement system.
Background
Three-axis magnetic sensors are widely used because they provide component information, and their measured values are the size of the projection of the earth's magnetic field on the three sensitive axes of the magnetic sensor. If the Euler angle relation between a rectangular coordinate system formed by three sensitive axes of the magnetic sensor and a geographic coordinate system is known, the geomagnetic component under the geographic coordinate system can be calculated: the north component, the east component, and the vertical component of the earth magnetic field. How to effectively acquire the geomagnetic components in the geographic coordinate system is the problem of geomagnetic vector measurement, and the geomagnetic vector measurement is completed through a geomagnetic vector measurement system. The geomagnetic vector measurement needs to use a three-axis magnetic sensor, and the azimuth of the magnetic sensor needs to be determined, so that the problem of attitude determination of the three-axis magnetic sensor is solved. The attitude determination precision is a key factor of vector measurement, and the requirements for attitude determination are strict to ensure that the vector measurement reaches certain precision.
The geomagnetic vector measurement system is mainly composed of a magnetic sensor and an inertial navigation direct strapdown, wherein the magnetic sensor is used for measuring a magnetic field component of a magnetic sensor coordinate system, and the inertial navigation provides various attitude information for the magnetic sensor: course, pitch, roll angle. Three components of a magnetic field vector in a geographic coordinate system can be obtained through conversion, wherein inertial navigation comprises a three-axis gyroscope and a three-axis accelerometer, and an accelerometer coordinate system in a geomagnetic vector system can be considered to be consistent with a gyroscope coordinate system. Some errors are inevitable in the geomagnetic vector measurement system during installation, wherein the coordinate system error between the measurement axis of the magnetic sensor and the measurement axis of the inertial navigation system is called as a "misalignment error". The "misalignment error" becomes an important factor affecting the measurement accuracy of the geomagnetic element, and the misalignment problem is difficult to solve by the mechanical alignment method. In a geomagnetic environment, a misalignment error of 1 ° may cause a vector measurement error of several hundred nT (nT is a unit of magnetic field strength). Therefore, the research on the non-alignment error correction technology has important significance for improving the precision of the geomagnetic vector measurement system. Because 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 coordinate system and the magnetic sensor measure different physical quantities, and the calibration difficulty is increased.
Some scholars propose related correction methods for misalignment errors of different systems. Rong Zhu et al (Rong Zhu, Zhuoying Zhuou, Calibration of three-dimensional integrated sensor for improved systems of Sensors and Actuators A127 (2006)340 and 344) adopt a regular hexahedral optical prism and an orthogonal optical coordinate System to correct the misalignment error of the Micro-Electro-Mechanical System (MEMS), and calculate the misalignment error of the magnetic sensor and the accelerometer to the optical System coordinate System respectively by using the magnetic field and the gravity projection value of the optical System coordinate System. However, this method requires precise adjustment of the three-dimensional coordinate system of the optical system, and requires the local magnetic tilt information to be used, and to ensure that the initial coordinate system of the regular hexahedron optical prism is consistent with the local north, east and ground coordinate systems. Therefore, the method has high requirement on the accuracy of the adjustment of the initial coordinate system of the optical system and the optical prism. Erin L.Renk et al (Erin L.Renk, W.C., Matthew Rizzo, Fuju Lee, and Dennis S.Bernstein.Calibration a Triaxial Accelerometer-Magnetometer. IEEEControl Systems Magazine (2005) 86-95) use a six-dimensional degree of freedom robot to correct misalignment errors; also, the method needs to accurately control the attitude, needs to provide a course angle, a pitch angle and a roll angle, and is complex to operate. Vcelak et al (J.Vcelak, P.Ripka, J.Kubik, A.Platil and P.Kaspar, AMR navigation systems and methods of the same calibration, Sensors and Actuators A123-. The core idea of the method is that the magnetic field and the gravity in the direction of a rotating shaft are unchanged, so that the misalignment errors of the magnetic sensor and the accelerometer are calculated respectively. The method needs to use attitude information provided by an accelerometer when calculating the roll angle misalignment error of the magnetic sensor. In addition, the method ignores the roll angle misalignment error of the accelerometer when establishing the model. David Jurman (David Jurman, Marko Jankov, Roman Kamnik, Marko topo, Calibration and data fusion solution for the miniature attachment and attachment reference system, Sensors and Actuators A138 (2007) 411-420) et al have packaged the magnetic sensor and accelerometer into an open right hexahedron of plastic material for MEMS magnetic compasses, the Calibration method being the same as the J.Vcelak et al method, except that a non-magnetic plate is used, again requiring the provision of attitude information.
Regarding the non-alignment correction of the geomagnetic vector measurement system, numerous hongfeng et al applied for a national invention patent (application number: 201210355541.7, a non-alignment error correction method for a geomagnetic element measurement system, bulletin date: 2013, 1 month, 16 days) by using a right-angle table top and a regular hexahedral box body, and the turned non-magnetic regular hexahedron is still close to the right-angle table top by turning the non-magnetic regular hexahedron for many times. And calculating the non-alignment angle between the magnetic field sensor and the inertial navigation system by utilizing the principle that the projection component of the gravity vector on the right-angle table-board is unchanged. The method requires that the planeness and the verticality of the right-angle table-board are very high, and the table-board and the box body are required to be tightly fit each time the table-board is turned over. The method has higher requirements on the processing precision and the operation precision of equipment. In addition, because the geomagnetic projection component values and the non-alignment angles of the right-angle table top are both parameters to be estimated, the parameters to be estimated are more, and the mutual coupling degree of the geomagnetic projection component values and the non-alignment angle parameters is high.
In summary, the above-mentioned correction methods for the misalignment angle errors of the geomagnetic vector system all have the disadvantages of complicated equipment and operation, etc., and have high requirements on experimental equipment and the operation experience of researchers, or require accurate attitude information, which affects the correction accuracy.
Disclosure of Invention
Aiming at the technical problems in the prior art, the invention provides the non-alignment error correction method for the geomagnetic vector measurement system, which has the advantages of simple original, easy realization, easy operation and higher correction precision.
The specific technical scheme is as follows:
a geomagnetic vector system non-alignment correction method based on an axis-winding method comprises 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 non-magnetic regular hexahedron on the table top of the non-magnetic rotary table, keeping the X-axis direction of the non-magnetic regular hexahedron consistent with the direction of the rotating shaft, rotating the table top of the non-magnetic rotary table to enable the non-magnetic regular hexahedron to rotate around the X-axis by any angle, recording the measured values of the magnetic sensor and the accelerometer, and rotating N 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) according to the non-aligned angle from the magnetic sensor to the non-magnetic regular hexahedron and the non-aligned angle from the accelerometer to the non-magnetic regular hexahedron, determining the coordinate system conversion relation between the magnetic sensor and the accelerometer, namely completing the correction.
Further, 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 non-magnetic regular hexahedron comprises the following steps:
(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 the measured value of the magnetic sensor 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; hxWhen 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; hzWhen the non-magnetic regular hexahedron rotates around the Z axis, the earth magnetismThe projection value of the field on the Z axis of the nonmagnetic regular hexahedron; αmag,βmag,γmagrepresenting 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 cubemag,βmag,γmag：
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,measured value g of the magnetic sensor when the non-magnetic regular hexahedron rotates around the Z axisxWhen 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; gzWhen 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;αacc,βacc,γaccis 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 cubeacc,βacc,γacc：
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-axis2The measurements are grouped.
Further, the specific process of the step (S6) is as follows:
(S61) according to αmag,βmag,γmagImplementing magnetic sensor measurementsConverted into the projection value of the magnetic field in the nonmagnetic regular hexahedronThe calculation formula is as follows:
(S62) according to αacc,βacc,γaccTo 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.
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 materials.
In order to satisfy the computed non-alignment angle as representative, the error parameters are sufficiently excited, and the measurement data of the magnetic sensors rotating around different axes are all used.For the magnetic sensor to measure the output value,and correcting the misalignment error, and then obtaining the projection value of the magnetic field in the accelerometer coordinate system. After the non-alignment error correction, the coordinate system of the magnetic sensor is consistent with the accelerometer, and the geomagnetic vector measurement can be directly carried out.
Compared with the prior art, the technical effects obtained by adopting the invention are as follows: 1. after the correction method is applied, the whole correction equipment is simple, a high-precision right-angle table top does not need to be processed, and the non-alignment angle can be calculated only by a simple non-magnetic rotating structure and a regular hexahedron. 2. After the correction method is applied, the processing requirement on the non-magnetic regular hexahedron is greatly reduced, high verticality does not need to be required between all surfaces of the non-magnetic regular hexahedron, and only high verticality is required between the two surfaces. 3. The correction method disclosed by the invention has the advantages that the whole correction process is simple to operate, the non-magnetic regular hexahedron does not need to be turned over in a full posture, the strict requirement on the close fit between the non-magnetic regular hexahedron and a right-angle table top is not required, the non-magnetic regular hexahedron only needs to be rotated around a shaft in a stable magnetic field environment, the strict requirement on the initial posture of the system placement is avoided, the accurate control on the rotation angle is not required, the strict requirement on the rotation direction is also avoided, and the experiment difficulty is reduced. 4. According to the correction method, the parameter estimation model is simplified, the parameter to be estimated only contains the non-alignment angle, the parameter coupling degree is reduced, and the requirement of the parameter estimation algorithm is reduced. 5. The correction method of the invention does not need to introduce auxiliary information of attitude information, geomagnetic inclination angle, geographic orientation, optical system and the like of the accelerometer to the non-alignment correction of the magnetic sensor.
Drawings
FIG. 1 is a schematic flow diagram of the present invention;
FIG. 2 is a schematic diagram of the present invention in an initial state in a specific application example;
FIG. 3 is a schematic view of a nonmagnetic regular hexahedron rotated about the X-axis;
FIG. 4 is a schematic view of a non-magnetic regular hexahedron rotated about the Z-axis;
figure 5 is a schematic view of the non-aligned angles of a magnetic sensor and accelerometer to a nonmagnetic cube.
Illustration of the drawings:
1. a base; 2. a rotating shaft; 3. a table top; 4. a non-magnetic regular hexahedron; 5. a magnetic sensor; 6. an accelerometer; 7. the magnetic field vector is projected along the rotation axis; 8. the gravity vector is projected along the rotating shaft; 9. and XYZ coordinate system of the nonmagnetic regular hexahedron.
Detailed Description
In order to better understand the technical solution of the present invention, the following details are provided for the derivation of the principle and the calculation formula:
the invention relates to a non-alignment error correction method for a geomagnetic vector measurement system, which comprises the following steps: packaging a magnetic sensor 5 and an accelerometer 6 into a non-magnetic regular hexahedron 4, and indirectly converting the relationship between the coordinate systems of the two sensors into the relationship between the coordinate system of the non-magnetic regular hexahedron 9; the non-magnetic regular hexahedron 4 is placed on the table top 3 of the non-magnetic rotary table. The non-magnetic regular hexahedron 4 is rotated, and the projection 7 of the magnetic field vector rotating shaft in the rotating process can be analytically represented by the measured value and the non-alignment angle of the magnetic sensor 5. The misalignment error angle is an unknown parameter, and a nonlinear equation set is established by using the measured value of the magnetic sensor 5 in the rotation process, so that the misalignment error from the coordinate system of the magnetic sensor 5 to the non-magnetic regular hexahedron 4 is calculated. Similarly, the misalignment error from the accelerometer 6 to the nonmagnetic regular hexahedron 4 can be calculated, so that the misalignment error between the magnetic sensor 5 and the accelerometer 6 can be corrected.
As shown in FIG. 1, the method of the present invention comprises the following steps:
firstly, the non-magnetic turntable base 1 is placed on a stable ground without being strictly horizontally placed.
Referring to fig. 2, a magnetic sensor 5 and an 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 connected in a strapdown manner; the non-magnetic regular hexahedron 4 is placed on the non-magnetic turntable table top 1. Establishing a non-magnetic regular hexahedron coordinate system 9 of the non-magnetic regular hexahedron 4, wherein the coordinate axis of the non-magnetic regular hexahedron coordinate system 9 is X, Y and Z; as shown in fig. 5, the misalignment angle of the magnetic sensor and accelerometer to a nonmagnetic cube is shown schematically.
In this example, as shown in fig. 2, in the initial position, the X-axis of the coordinate system 9 of the nonmagnetic regular hexahedron 4 is parallel to the rotation axis, and the projection 7 of the magnetic field vector along the rotation axis and the projection 8 of the gravity vector along the rotation axis are the projection of the magnetic field vector along the X-axis of the nonmagnetic regular hexahedron and the projection of the gravity vector along the X-axis of the nonmagnetic regular hexahedron. The magnetic sensor 5 adopts a three-axis magnetic sensor, and the accelerometer 6 adopts a three-axis accelerometer. The projection of the geomagnetic field in the nonmagnetic regular hexahedron coordinate system 9 is marked as Hx,The magnetic sensor measures a value ofThe relationship between the two is as follows:
the formula (1) is converted into:
wherein
Wherein, αmag,βmag,γmagIs the misalignment angle between the magnetic sensor 5 and the nonmagnetic regular hexahedral coordinate system 9.
③ As shown in FIG. 3, when the non-magnetic turntable table top 3 is rotated, the non-magnetic regular hexahedron 4 rotates around its X-axis, and the projection H of the geomagnetic field on the X-axis of the non-magnetic regular hexahedron coordinate system 9xAnd is not changed. The simultaneous recording of the measured values of the magnetic sensor 5 is notedDuring the rotation, the measured value of the magnetic sensor 5 and the X-axis magnetic field projection H of the nonmagnetic regular hexahedron coordinate system 9xThe relationship is as follows:
if the misalignment angle error is zero, then a11＝1,a21＝0,a31When the value is equal to 0, thenDuring the rotation, N is measured1Solving the nonlinear equation set by adopting a nonlinear least square method, carrying out parameter estimation, and calculating αmag,βmag. As shown in formula (5):
wherein:
④ it can be seen that only α can be calculated by rotating around the X-axis of the nonmagnetic regular hexahedral coordinate system 9mag,βmagCannot calculate gammamag. As shown in fig. 4, there is no Z-axis rotation of the magnetic regular hexahedral coordinate system 9. During the rotation, the measured value of the magnetic sensor 5 and the geomagnetic field H of the Z axis of the nonmagnetic regular hexahedron coordinate system 9zThe relationship is as follows:
during the rotation, N of the output of the magnetic sensor is obtained2The measurements are grouped. Solving a nonlinear equation set by adopting a nonlinear least square method, performing parameter estimation, and calculating gammamagThe following formula:
wherein:
in order to better estimate the parameters, it is preferable to use the data of different postures, that is, the data output by the rotation of the nonmagnetic regular hexahedron around the X and the rotation around the Z, and simultaneously adopt the calculation.
Calculate αmag,βmag,γmagThen, the measured value of the magnetic sensor rotating around the X axis can be corrected to the projected value of the magnetic field of the hexahedral coordinate system by taking the non-alignment parameter back to the formula (1), and the estimated α is corrected according to the error comparison between the measured value of the X axis and the actual value before and after correctionmag,βmag,γmagEvaluation was performed.
⑤ same principle, non-magnetic regular hexahedronAccelerometer 6 measures the value of a body rotating about the X axisProjection g of gravity on nonmagnetic regular hexahedron coordinate system 9x,The relationship is as follows:
and acquiring a non-alignment angle between the accelerometer 6 and the non-magnetic regular hexahedron coordinate system 9, wherein the operation and calculation process is completely the same as that of the magnetic sensor. In the process of rotating around the X axis of the non-magnetic regular hexahedron coordinate system 9, because an included angle error exists between the coordinate system of the accelerometer 6 and the non-magnetic regular hexahedron coordinate system 9, the angle between the gravity vector rotating axis projection 8 and the X axis of the accelerometer 6 is changed continuously, and the X axis output of the accelerometer 6 is caused to fluctuate continuously. And when the X axis and the Z axis of the nonmagnetic regular hexahedron coordinate system 9 are respectively rotated, the output value of the accelerometer 6 is recorded at the same time.
Performing parameter estimation by using nonlinear least square method, and calculating misalignment angle α between accelerometer and nonmagnetic regular hexahedron by solving equation setacc,βacc,γacc。
Calculate αacc,βacc,γaccThen, the non-alignment angle parameter is brought back to the formula (10), the accelerometer measured value rotating around the X axis can be corrected to the gravity projection value of the hexahedral coordinate system, and the estimated α is compared according to the error comparison between the measured value and the actual value of the X axis before and after correctionacc,βacc,γaccEvaluation was performed.
⑥ calculation αmag,βmag,γmagAnd αacc,βacc,γaccThereafter, the misalignment angle between the accelerometer 6 and the magnetic sensor 5 can be corrected indirectly. Correction of misalignment errors in the measured values of the magnetic sensor 5I.e. the conversion between the magnetic sensor coordinate system and the accelerometer coordinate system, first, according to αmag,βmag,γmagImplementing magnetic sensor measurementsConverted into the projection value of the magnetic field in the nonmagnetic regular hexahedronThe calculation process is as follows:
secondly, according to αacc,βacc,γaccTo realizeMagnetic field projection values converted to accelerometer coordinate systemThe following formula:
wherein,for the magnetic sensor measurements (i.e. the components of the magnetic sensor with respect to its own coordinate system, during the calibration process, the coordinate system transformation is divided into two steps, first the magnetic sensor measurements are transformed into the non-magnetic regular hexahedral coordinate system projections, and second the non-magnetic regular hexahedral coordinate system projections are transformed into the accelerometer coordinate system projections),and correcting the misalignment error, and then obtaining the projection value of the magnetic field in the accelerometer coordinate system. ThroughAfter the non-alignment error is corrected, the coordinate system of the magnetic sensor is consistent with that of the accelerometer, and then geomagnetic vector measurement can be directly carried out.
The present invention will be described in further detail with reference to specific examples.
A three-axis magnetic field sensor and an inertial navigation system (including an accelerometer) are fixedly arranged in a non-magnetic regular hexahedron, a flat terrain area is selected for non-alignment correction in the suburbs of Changsha, Hunan, and the non-alignment angle between the magnetic sensor and the non-magnetic regular hexahedron is preset [ α ]magβmagγmag]＝[0.5° 0.8° 0.9°]Presetting the non-alignment angle between the accelerometer and the non-magnetic regular hexahedron [ α ]accβaccγacc]＝[0.6° 0.8° 1°]. The measuring noise of the magnetic sensor is 5nT, and the measuring noise of the accelerometer is 0.005m/s2When in initial attitude, the projection of the geomagnetic field in the nonmagnetic regular hexahedral coordinate system is [ 35000; 33000; -2000]nT, the projection of the gravity on the nonmagnetic regular hexahedron is [ 9.5; 0.8; 0.5]m/s2。
Defining the coordinate system of the magnetic sensor as three coordinate axes denoted XC,YC,ZC(ii) a The accelerometer coordinate system has three coordinate axes denoted as Xg,Yg,Zg；
1. Firstly, the non-magnetic regular hexahedron rotates around the X axis, the rotation angle interval is 10 degrees, and the magnetic sensor XCThe shaft measurements are shown in table 1; accelerometer XgAxis measurements are as in table 3;
2. secondly, the non-magnetic regular hexahedron rotates around the Z axis, and the rotation angle interval is 10 degrees. Magnetic sensor ZCThe shaft measurements are shown in table 1; accelerometer ZgAxis measurements are as in table 3;
3. and in the measuring process, the rotating shaft rotating measurement average value is used as a rotating shaft projection reference value. When the non-magnetic regular hexahedron rotates around the X axis thereof, the magnetic sensor XCThe average value of the measurement of the axis is 35005nT, and the accelerometer XgThe measured average value of the shaft was 9.502m/s2. Non-magnetic regular hexahedral windingWhen the Z axis rotates, the magnetic sensor ZCThe measured average value of the axis is 34979nT, accelerometer ZgThe measured average value of the shaft was 9.498m/s2. Because in the actual operation process, it is difficult to obtain the X-axis projection of the geomagnetic field in the nonmagnetic regular hexahedron coordinate system: 35000nT, simulation experiment to get closer to the actual situation, so measured average value of axial rotation is used as projection true value HxAnd HzAnd performing parameter estimation.
4. Solving a nonlinear equation system by adopting an equation (5) and an equation (8) to calculate the misalignment angle of the magnetic sensor [ α ]magβmagγmag]＝[0.4998° 0.8° 0.86°]The estimated error of the misalignment angle of the magnetic sensor is less than 5%, and the misalignment angle of the accelerometer is calculated [ α ]accβaccγacc]＝[0.596° 0.802° 1.12°]It can be seen that the estimation error is less than 13%. It is shown that the misalignment angle estimation accuracy is better. Next, the measured value is projection-converted using the estimated misalignment angle, thereby evaluating the effect of the misalignment angle on the correction of the measured value.
5. According to the calculated non-alignment angle between the magnetic sensor and the non-magnetic regular hexahedron, the measured value of the magnetic sensor can be converted into the projection of a magnetic field in a non-magnetic regular hexahedron coordinate system. Theoretically, after the correction of the misalignment angle, when the non-magnetic regular hexahedron rotates around the X axis, the consistency of the measured value of the X axis of the magnetic sensor is better in the rotating process, and the measured value of the X axis of the magnetic sensor is 35000nT all the time; the measured value errors before and after the misalignment correction are compared, the correction effect of the misalignment parameters can be evaluated, and the magnetic sensor XCAxis measurement error pairs are shown in table 2. Also, when the nonmagnetic regular hexahedron rotates about its Z axis, the magnetic sensor ZCThe shaft measurement values are relatively good in consistency during rotation and should always be 35000nT, the magnetic sensor ZCAxis measurement error pairs are shown in table 2. Therefore, after the misalignment between the magnetic sensor and the non-magnetic regular hexahedron is corrected, the measurement consistency of the magnetic sensor in the rotating shaft direction is obviously improved and is closer to the real projection value of the magnetic field in the non-magnetic regular hexahedron, and the method can effectively estimate the misalignment angle of the magnetic sensor.
TABLE 1 measurement data of a three-axis magnetic field sensor (rotation about X and Z axes, respectively)
TABLE 2 comparison of measurement errors for three-axis magnetic field sensors (rotation about X and Z axes, respectively)
6. According to the calculated non-alignment angle between the accelerometer and the non-magnetic regular hexahedron, the measured value of the accelerometer can be converted into the projection of gravity on the non-magnetic regular hexahedron coordinate system. Theoretically, after correction by the misalignment angle, the accelerometer X rotates about its X-axis when the non-magnetic regular hexahedron rotates about its X-axisgThe shaft measurements are relatively consistent during rotation and should always be 9.5m/s2(ii) a The measured value error before and after the misalignment correction is compared, the correction effect of the misalignment parameters can be evaluated, and an accelerometer XgAxis measurement error pairs are shown in table 4. Similarly, when the non-magnetic regular hexahedron rotates around its Z axis, the accelerometer ZgThe shaft measurements are relatively consistent during rotation and should always be 9.5m/s2Accelerometer ZgAxis measurement error pairs are shown in table 4. Therefore, after the misalignment between the accelerometer and the nonmagnetic regular hexahedron is corrected, the measurement consistency of the accelerometer in the direction of the rotating shaft is obviously improved and is closer to the real projection value of gravity on the nonmagnetic regular hexahedron, and the method can effectively estimate the misalignment angle of the accelerometer.
TABLE 3 measurement data of three-axis accelerometer (rotation about X and Z axes, respectively)
TABLE 4 comparison of measurement errors for three-axis accelerometers (rotation about X and Z axes, respectively)
The above is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above-mentioned embodiments, and all technical solutions belonging to the idea of the present invention belong to the protection scope of the present invention. It should be noted that modifications and embellishments within the scope of the invention may be made by those skilled in the art without departing from the principle of the 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; hxWhen 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; hzWhen 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; αmag,βmag,γmagrepresenting 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 cubemag,βmag,γmag：
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; gxWhen 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; gzWhen 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; αacc,βacc,γaccis 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 cubeacc,βacc,γacc：
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 αmag,βmag,γmagImplementing magnetic sensor measurementsConverted into the projection value of the magnetic field in the nonmagnetic regular hexahedronThe calculation formula is as follows:
(S62) according to αacc,βacc,γaccTo 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.
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