CN109059960A - A kind of calibration method of three-dimensional electronic compass - Google Patents
A kind of calibration method of three-dimensional electronic compass Download PDFInfo
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Abstract
The present invention relates to a kind of calibration methods of three-dimensional electronic compass.Electronic compass is done to the movement of 8 words in space, acquires the data that three axis of Magnetic Sensor are read；Then collected data are subjected to ellipsoid fitting, obtain ellipsoid equation and sphere centre coordinate；The ellipsoid equation that fitting obtains is projected into the elliptical parameter found out respectively in three planes to three coordinate axial planes: α, b, long Shaft angle respectively again later；Finally the data newly obtained are calibrated according to resulting parameter.The method of the present invention makes the calibration process of electronic compass more flexible, and accuracy is higher, meets the requirement of field sport.
Description
Technical Field
The invention relates to a calibration method of a three-dimensional electronic compass.
Background
In recent years, electronic compasses are widely used in scenes such as navigation and body posture measurement. Because the GPS signals are weak in forests, dense buildings, etc., an electronic compass is usually needed to assist in positioning.
The working principle of the electronic compass is that the magnetic sensor is used for measuring the component intensity of the geomagnetism in a certain direction, and the included angle between the sensor and the geomagnetism is determined, so that the advancing azimuth is determined. However, the geomagnetic field is a weak magnetic field, and the measurement value of the magnetic sensor deviates from the true value due to the hard magnetic interference and the soft magnetic interference caused by the magnetic materials around the electronic compass. In addition, the measured value of the magnetic sensor may deviate from the true value due to the manufacturing process problems of the sensor itself, such as non-orthogonal axes.
If only the function of the geomagnetism exists, the data output by the three axes of the magnetic sensor corresponds to a positive sphere with the sphere center at the origin on the space rectangular coordinate system. However, the hard magnetic disturbance causes the positive sphere to become a positive sphere centered on the hard magnetic disturbance. If the effects of geomagnetism, hard magnetism and soft magnetism are considered at the same time, the positive sphere becomes an ellipsoid with the hard magnetic interference amount as the center of the sphere. Disturbances caused by non-orthogonal axes can be equivalent to soft and hard magnetic disturbances. Therefore, before the electronic compass is used, calibration is needed to compensate the data read by the three axes so that the data falls on the spherical surface of the true sphere with the sphere center at the origin.
The existing three-dimensional electronic compass calibration method needs the help of external equipment or has higher calibration process requirements, and most of the calibration methods do not carry out soft magnetic compensation. It is difficult to meet the requirements of field action.
Disclosure of Invention
The invention aims to provide a calibration method of a three-dimensional electronic compass, which carries out 8-shaped motion on the electronic compass in the space, namely, the electronic compass can compensate error interference caused by soft and hard magnetic interference and axis non-orthogonality, and then the electronic compass is calibrated; the method enables the calibration process of the electronic compass to be more flexible and higher in accuracy, and meets the requirements of field sports.
In order to achieve the purpose, the technical scheme is that the method for calibrating the three-dimensional electronic compass comprises the steps of enabling the electronic compass to move in a 8-shaped mode in space, collecting data read out by three axes of a magnetic sensor, then carrying out ellipsoid fitting on the collected data to obtain an ellipsoid equation and a sphere center coordinate, then projecting the ellipsoid equation obtained through fitting to three coordinate axis planes respectively to obtain parameters α, b and a major axis rotation angle of an ellipse on the three coordinate axis planes respectively, and finally calibrating the newly obtained data according to the obtained parameters.
In an embodiment of the present invention, the method specifically includes the following steps:
step S1: the electronic compass moves 8-shaped in space, so that the electronic compass collects eight azimuths, namely data corresponding to eight quadrants of a space rectangular coordinate system, namely, the upper, lower, east, south, west and north directions;
step S2: performing ellipsoid fitting, and solving 10 optimal parameters A, B, C, D, E, F, G, I, J and ellipsoid spherical center coordinates (X0, Y0 and Z0) of an ellipsoid by adopting a least square method fitting method; the general expression of the ellipsoid equation is:
Ax2+By2+Cz2+Dxy+Exz+Fyz+Gx+Hy+Iz+J＝0
let z be 0, x be 0, and y be 0 in the above formula, then the projection equations of the ellipsoids on the XOY, XOZ, and YOZ surfaces can be obtained:
Ax2+By2+Dxy+Gx+Hy+J＝0
Ax2+Cz2+Exz+Gx+Iz+J＝0
By2+Cz2+Fyz+Hy+Iz+J＝0
step S3: according to the projection equation of the ellipsoid on the XOY plane: ax2+By2And (3) determining parameters of the ellipse on the XOY plane, namely major axis rotation angles theta x, y, α x, y and bx, y, wherein the calculation formula is as follows:
wherein,
G'＝G·cos(θx,y)-H·sin(θx,y)
H'＝G·sin(θx,y)+H·cos(θx,y)
A'＝A·cos2(θx,y)-D·cos(θx,y)·sin(θx,y)+B·sin2(θx,y)
B'＝A·sin2(θx,y)+D·cos(θx,y)·sin(θx,y)+B·cos2(θx,y)
similarly, ellipse parameters theta x, z, α x, z, bx, z and theta y, z, α y, z, by and z of the ellipsoid equations on the XOZ surface and the YOZ surface can be obtained;
step S4: and performing soft and hard magnetic compensation calibration on the data acquired by the magnetic sensor according to the coordinates of the center of the ellipsoid (X0, Y0, Z0) and the parameters obtained in the step S3.
In an embodiment of the present invention, the specific implementation process of step S4 is as follows:
step S41, eliminating hard magnetic interference: the interference of the hard magnet causes the data output by the three axes of the magnetic sensor to be shifted by a fixed amount, namely the offset distance of the ellipsoidal spherical center (X0, Y0, Z0) from the origin; and performing hard magnetic compensation calibration on the hard magnetic interference on the three axes of the magnetic sensor, namely subtracting the offset fixed quantity from the data read by the three axes of the magnetic sensor respectively, namely:
xe＝xreading-X0
ye＝yreading-Y0
ze＝zreading-Z0
the method comprises the following steps that (1) xreading, reading and zreading are respectively data which are newly read by an X axis, a Y axis and a Z axis of a magnetic sensor, and xe, ye and ze are data of the magnetic sensor after hard magnetic interference is eliminated by the three axes of the magnetic sensor;
step S41, eliminating soft magnetic interference: respectively carrying out soft magnetic compensation calibration on an X axis-Y axis, an X axis-Z axis and a Y axis-Z axis; taking the soft magnetic compensation of the X-Y axis as an example, the rotation matrix R can be obtained from the obtained major axis rotation angle θ X, Y of the ellipse on the XOY plane:
and then rotating the data without the hard magnetic interference to a standard ellipse, specifically:
the above data is then stretched to the perfect circle: the method specifically comprises the following steps:
if α x, y > bx, y, there is:
xc＝xe0
if bx, y > α x, y, there is:
yc＝ye0
finally, the obtained data xc, yc are rotated back, and the following steps are carried out:
wherein xc0 and yc0 are data after soft and hard magnetic compensation calibration; the same principle is also applied to soft magnetic compensation of an X axis to a Z axis and a Y axis to the Z axis, so that six data can be obtained after repeated calculation, wherein the six data are respectively as follows:
for accuracy of the results, the six data were weighted averaged to obtain
Wherein, xvalue, yvalue, zvalue are the final data of the three axes of the magnetic sensor after soft and hard magnetic calibration.
Compared with the prior art, the invention has the following beneficial effects: in the invention, the calibration method of the electronic compass is innovated:
1. in the calibration process, the inclination angle sensor and other external equipment are not needed for assistance, and the calibration process only needs to move around the 8-shaped part in the space;
2. the invention adopts a least square method to fit an ellipsoid, and takes the rotation and the expansion of the ellipsoid caused by soft and hard magnetic interference into consideration to compensate the ellipsoid; the soft magnetic compensation scheme is realized based on the long axis corner of the ellipse, and has better effect than the existing 3-axis electronic compass calibration technology;
3. while eliminating soft and hard magnetic interference, the method also eliminates error interference caused by non-orthogonality of magnetic sensor axes;
compared with the prior calibration technology, the method has the advantages of more accurate result, more flexible calibration process and wide application prospect in the field of electronic compasses.
Drawings
Fig. 1 is a diagram of a calibration process of a three-dimensional electronic compass.
Fig. 2 is a diagram of the interference effect of soft magnetism on three axes of a magnetic sensor.
Fig. 3 is a diagram showing the effect of soft magnetism on the X-axis and Y-axis interference of a magnetic sensor.
Detailed Description
The technical scheme of the invention is specifically explained below with reference to the accompanying drawings.
The invention provides a calibration method of a three-dimensional electronic compass, which comprises the following steps of carrying out 8-shaped motion on the electronic compass in space, collecting data read out by three axes of a magnetic sensor, carrying out ellipsoid fitting on the collected data to obtain an ellipsoid equation and a spherical center coordinate, respectively projecting the ellipsoid equation obtained by fitting to three coordinate axis planes, respectively calculating parameters of ellipses on the three planes, namely α, b and major axis rotation angles, and finally calibrating the data according to the obtained parameters, wherein the method comprises the following specific implementation steps:
step S1: the electronic compass moves 8-shaped in space, so that the electronic compass collects eight azimuths, namely data corresponding to eight quadrants of a space rectangular coordinate system, namely, the upper, lower, east, south, west and north directions;
step S2: performing ellipsoid fitting, and solving 10 optimal parameters A, B, C, D, E, F, G, I, J and ellipsoid spherical center coordinates (X0, Y0 and Z0) of an ellipsoid by adopting a least square method fitting method; the general expression of the ellipsoid equation is:
Ax2+By2+Cz2+Dxy+Exz+Fyz+Gx+Hy+Iz+J＝0
let z be 0, x be 0, and y be 0 in the above formula, then the projection equations of the ellipsoids on the XOY, XOZ, and YOZ surfaces can be obtained:
Ax2+By2+Dxy+Gx+Hy+J＝0
Ax2+Cz2+Exz+Gx+Iz+J＝0
By2+Cz2+Fyz+Hy+Iz+J＝0
step S3: according to the projection equation of the ellipsoid on the XOY plane: ax2+By2And (3) determining parameters of the ellipse on the XOY plane, namely major axis rotation angles theta x, y, α x, y and bx, y, wherein the calculation formula is as follows:
wherein,
G'＝G·cos(θx,y)-H·sin(θx,y)
H'＝G·sin(θx,y)+H·cos(θx,y)
A'＝A·cos2(θx,y)-D·cos(θx,y)·sin(θx,y)+B·sin2(θx,y)
B'＝A·sin2(θx,y)+D·cos(θx,y)·sin(θx,y)+B·cos2(θx,y)
similarly, parameters theta x, z, α x, z, bx, z and theta y, z, α y, z, by, z of the projection ellipses of the ellipsoid equations on the XOZ surface and the YOZ surface can be respectively obtained;
step S4: and performing soft and hard magnetic compensation calibration on the data acquired by the magnetic sensor according to the coordinates of the center of the ellipsoid (X0, Y0, Z0) and the parameters obtained in the step S3. The specific implementation process of step S4 is as follows:
step S41, eliminating hard magnetic interference: the interference of the hard magnet causes the data output by the three axes of the magnetic sensor to be shifted by a fixed amount, namely the offset distance of the ellipsoidal spherical center (X0, Y0, Z0) from the origin; and performing hard magnetic compensation calibration on the hard magnetic interference on the three axes of the magnetic sensor, namely subtracting the offset fixed quantity from the data read by the three axes of the magnetic sensor respectively, namely:
xe＝xreading-X0
ye＝yreading-Y0
ze＝zreading-Z0
the method comprises the following steps that (1) xreading, reading and zreading are respectively data which are newly read by an X axis, a Y axis and a Z axis of a magnetic sensor, and xe, ye and ze are data of the magnetic sensor after hard magnetic interference is eliminated by the three axes of the magnetic sensor;
step S41, eliminating soft magnetic interference: respectively carrying out soft magnetic compensation calibration on an X axis-Y axis, an X axis-Z axis and a Y axis-Z axis; taking the soft magnetic compensation of the X-Y axis as an example, the rotation matrix R can be obtained from the obtained major axis rotation angle θ X, Y of the ellipse on the XOY plane:
and then rotating the data without the hard magnetic interference to a standard ellipse, specifically:
the above data is then stretched to the perfect circle: the method specifically comprises the following steps:
if α x, y > bx, y, there is:
xc＝xe0
if bx, y > α x, y, there is:
yc＝ye0
finally, the obtained data xc, yc are rotated back, and the following steps are carried out:
wherein xc0 and yc0 are data after soft and hard magnetic compensation calibration; the same principle is also applied to soft magnetic compensation of an X axis to a Z axis and a Y axis to the Z axis, so that six data can be obtained after repeated calculation, wherein the six data are respectively as follows:
for accuracy of the results, the six data were weighted averaged to obtain
Wherein, xvalue, yvalue, zvalue are the final data of the three axes of the magnetic sensor after soft and hard magnetic calibration.
The following is a specific implementation of the present invention.
The invention provides a convenient and accurate three-dimensional electronic compass calibration method, which can compensate error interference caused by soft and hard magnetic interference and axis non-orthogonality only by making an electronic compass perform 8-shaped motion in space, so as to calibrate the electronic compass. The method enables the calibration process of the electronic compass to be more flexible and higher in accuracy, and meets the requirements of field sports.
The calibration process of the three-dimensional electronic compass is shown in figure 1, the electronic compass does 8-shaped motion in space, data read out by three axes of the magnetic sensor are collected, then ellipsoid fitting is carried out on the collected data to obtain an ellipsoid equation and a sphere center coordinate, then the ellipsoid equation obtained by fitting is respectively projected to three coordinate axis planes to respectively obtain ellipse parameters α and b and a major axis corner on the three planes, and finally new data is calibrated according to the obtained parameters.
The electronic compass moves 8-shaped in space, and needs to acquire data of eight directions (corresponding to eight quadrants of a space rectangular coordinate system) of upper, lower, east, south, west and north as much as possible. The fitted ellipsoid is more accurate. The general expression of the ellipsoid equation is:
Ax2+By2+Cz2+Dxy+Exz+Fyz+Gx+Hy+Iz+J＝0
in the ellipsoid fitting process, 10 optimal parameters A, B, C, D, E, F, G, I and J of an ellipsoid and the coordinates (X0, Y0 and Z0) of the sphere center of the ellipsoid are obtained by adopting a least square method fitting method.
After obtaining a general expression of an ellipsoid equation, respectively projecting an ellipsoid to three coordinate planes of a space rectangular coordinate system: an XOY plane, an XOZ plane, and a YOZ plane. Taking the projection of an ellipsoid onto an XOY surface as an example, only a general expression of the ellipsoid is needed:
Ax2+By2+Cz2+Dxy+Exz+Fyz+Gx+Hy+Iz+J＝0
the variable x in (1) is 0, and then the projection equation of the ellipsoid on the XOY surface can be obtained:
Ax2+By2+Dxy+Gx+Hy+J＝0
by analogy, the projection equations of the ellipsoid on the XOZ and YOZ surfaces can be obtained respectively:
Ax2+Cz2+Exz+Gx+Iz+J＝0
and
By2+Cz2+Fyz+Hy+Iz+J＝0
when only the action of the geomagnetism exists, the electronic compass rotates in the space for a circle, the data output by three axes of the magnetic sensor corresponds to an orthosphere with the origin as the sphere center on a space rectangular coordinate system, the orthosphere is distorted into an ellipsoid by the interference of the soft magnetism, and the interference effect of the soft magnetism is shown in fig. 2. taking the interference analysis of the soft magnetism on the X axis and the Y axis as an example, as shown in fig. 3, if only the action of the geomagnetism exists, after the X axis and the Y axis of the magnetic sensor rotate for a circle on the water surface, the output data corresponds to an orthocircle with the center at the origin on the rectangular coordinate system, however, the interference of the soft magnetism stretches the data of the two axes into an ellipse, and rotates the ellipse for a certain angle, namely, the ellipse under the soft magnetism interference is not a standard ellipse, and has a certain rotation angle.
After obtaining general expressions of the ellipse equations on the three coordinate planes, the ellipse parameters α, b and the major axis rotation angle theta on each coordinate plane can be obtained according to the parameters of the general ellipse equations, taking the XOY plane as an example, the calculation formulas of the three parameters are as follows:
wherein,
G'＝G·cos(θx,y)-H·sin(θx,y)
H'＝G·sin(θx,y)+H·cos(θx,y)
A'＝A·cos2(θx,y)-D·cos(θx,y)·sin(θx,y)+B·sin2(θx,y)
B'＝A·sin2(θx,y)+D·cos(θx,y)·sin(θx,y)+B·cos2(θx,y)
similarly, the parameters θ x, z, α x, z, bx, z and θ y, z, α y, z, by, z on the XOZ plane and the YOZ plane can be obtained.
The three parameters (nine in total) of the center of the ellipsoid and the ellipse on each coordinate plane obtained in the above steps are compensation coefficients necessary for soft and hard magnetic compensation calibration of the electronic compass. Then, data acquired by the magnetic sensor must be calibrated through soft and hard magnetic compensation, and the specific calibration method is as follows:
the magnetically hard disturbance causes the three-axis output data of the magnetic sensor to be offset by a fixed amount, which is the offset distance from the origin of the center of the ellipsoid (X0, Y0, Z0). Taking the X-axis readout of the sensor as an example, the newly read data is offset by X0.
The data read out by the Y-axis and the Z-axis of the sensor are the same. And performing hard magnetic compensation calibration on the hard magnetic interference on the three axes of the magnetic sensor, namely subtracting the offset from the data read by the three axes of the magnetic sensor respectively, namely:
xe＝xreading-X0
ye＝yreading-Y0
ze＝zreading-Z0
the method comprises the steps of obtaining data of a magnetic sensor, and obtaining data of the magnetic sensor, wherein the data are obtained by reading the data of an X axis, a Y axis and a Z axis of the magnetic sensor respectively, the data are obtained by fitting X0, Y0 and Y0 of an ellipsoid sphere center coordinate, and the data are obtained by eliminating hard magnetic interference of the three axes of the magnetic sensor.
In order to eliminate soft magnetic interference, soft magnetic compensation calibration is respectively carried out on an X axis-Y axis, an X axis-Z axis and a Y axis-Z axis in the method. Taking the soft magnetic compensation of the X-Y axis as an example, the rotation matrix R can be obtained from the obtained major axis rotation angle θ X, Y of the ellipse on the XOY plane:
and then rotating the data without the hard magnetic interference to a standard ellipse, specifically:
the data above is then stretched to a perfect circle. The method specifically comprises the following steps:
if α x, y > bx, y, there is:
xc＝xe0
if bx, y > α x, y, there is:
yc＝ye0
finally, the obtained data xc, yc are rotated back, and the following steps are carried out:
wherein xc0 and yc0 are the data after the soft and hard magnetic compensation calibration. The same principle is also applied to soft magnetic compensation of an X axis to a Z axis and a Y axis to the Z axis, so that six data can be obtained after repeated calculation, wherein the six data are respectively as follows:
for the accuracy of the result, the six data are weighted and averaged in the method to obtain
Wherein, xvalue, yvalue, zvalue are the final data of the three axes of the magnetic sensor after soft and hard magnetic calibration.
The above process also eliminates the interference caused by magnetic sensor axis non-orthogonality, since the interference of axis non-orthogonality and soft-hard magnetic interference are mathematically equivalent.
The above are preferred embodiments of the present invention, and all changes made according to the technical scheme of the present invention that produce functional effects do not exceed the scope of the technical scheme of the present invention belong to the protection scope of the present invention.
Claims (3)
1. A three-dimensional electronic compass calibration method is characterized in that an electronic compass makes 8-shaped motion in space, data read out by three axes of a magnetic sensor are collected, then ellipsoid fitting is carried out on the collected data to obtain an ellipsoid equation and a spherical center coordinate, then the ellipsoid equation obtained by fitting is projected to three coordinate axis planes respectively to obtain parameters α, b and a major axis corner of an ellipse on the three planes respectively, and finally calibration is carried out on the newly obtained data according to the obtained parameters.
2. The method for calibrating a three-dimensional electronic compass according to claim 1, wherein the method comprises the following steps:
step S1: the electronic compass moves 8-shaped in space, so that the electronic compass collects eight azimuths, namely data corresponding to eight quadrants of a space rectangular coordinate system, namely, the upper, lower, east, south, west and north directions;
step S2: performing ellipsoid fitting, and solving 10 optimal parameters A, B, C, D, E, F, G, I, J and ellipsoid spherical center coordinates (X0, Y0 and Z0) of an ellipsoid by adopting a least square method fitting method; the general expression of the ellipsoid equation is:
Ax2+By2+Cz2+Dxy+Exz+Fyz+Gx+Hy+Iz+J＝0
let z be 0, x be 0, and y be 0 in the above formula, then the projection equations of the ellipsoids on the XOY, XOZ, and YOZ surfaces can be obtained:
Ax2+By2+Dxy+Gx+Hy+J＝0
Ax2+Cz2+Exz+Gx+Iz+J＝0
By2+Cz2+Fyz+Hy+Iz+J＝0
step S3: according to the projection equation of the ellipsoid on the XOY plane: ax2+By2And (3) determining parameters of the ellipse on the XOY plane, namely major axis rotation angles theta x, y, α x, y and bx, y, wherein the calculation formula is as follows:
wherein,
G'＝G·cos(θx,y)-H·sin(θx,y)
H'＝G·sin(θx,y)+H·cos(θx,y)
A'＝A·cos2(θx,y)-D·cos(θx,y)·sin(θx,y)+B·sin2(θx,y)
B'＝A·sin2(θx,y)+D·cos(θx,y)·sin(θx,y)+B·cos2(θx,y)
similarly, parameters theta x, z, α x, z, bx, z and theta y, z, α y, z, by, z of the projection ellipses of the ellipsoid equations on the XOZ surface and the YOZ surface can be respectively obtained;
step S4: and performing soft and hard magnetic compensation calibration on the data acquired by the magnetic sensor according to the coordinates of the center of the ellipsoid (X0, Y0, Z0) and the parameters obtained in the step S3.
3. The method for calibrating a three-dimensional electronic compass according to claim 2, wherein the step S4 is implemented as follows:
step S41, eliminating hard magnetic interference: the interference of the hard magnet causes the data output by the three axes of the magnetic sensor to be shifted by a fixed amount, namely the offset distance of the ellipsoidal spherical center (X0, Y0, Z0) from the origin; and performing hard magnetic compensation calibration on the hard magnetic interference on the three axes of the magnetic sensor, namely subtracting the offset fixed quantity from the data read by the three axes of the magnetic sensor respectively, namely:
xe＝xreading-X0
ye＝yreading-Y0
ze＝zreading-Z0
the method comprises the following steps that (1) xreading, reading and zreading are respectively data which are newly read by an X axis, a Y axis and a Z axis of a magnetic sensor, and xe, ye and ze are data of the magnetic sensor after hard magnetic interference is eliminated by the three axes of the magnetic sensor;
step S41, eliminating soft magnetic interference: respectively carrying out soft magnetic compensation calibration on an X axis-Y axis, an X axis-Z axis and a Y axis-Z axis; taking the soft magnetic compensation of the X-Y axis as an example, the rotation matrix R can be obtained from the obtained major axis rotation angle θ X, Y of the ellipse on the XOY plane:
and then rotating the data without the hard magnetic interference to a standard ellipse, specifically:
the above data is then stretched to the perfect circle: the method specifically comprises the following steps:
if α x, y > bx, y, there is:
xc＝xe0
if bx, y > α x, y, there is:
yc＝ye0
finally, the obtained data xc, yc are rotated back, and the following steps are carried out:
wherein xc0 and yc0 are data after soft and hard magnetic compensation calibration; the same principle is also applied to soft magnetic compensation of an X axis to a Z axis and a Y axis to the Z axis, so that six data can be obtained after repeated calculation, wherein the six data are respectively as follows:
for accuracy of the results, the six data were weighted averaged to obtain
Wherein, xvalue, yvalue, zvalue are the final data of the three axes of the magnetic sensor after soft and hard magnetic calibration.
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| CN110426057A (en) * | 2019-06-27 | 2019-11-08 | 华为技术有限公司 | A kind of method and magnetometer data calibrating installation of magnetometer data calibration |
| CN111998848A (en) * | 2020-08-28 | 2020-11-27 | 北京信息科技大学 | Ground rolling direction determining method and device |
| CN114723924A (en) * | 2022-03-23 | 2022-07-08 | 杭州易现先进科技有限公司 | Method, system, device and medium for positioning large-scene augmented reality |
| CN114812532A (en) * | 2022-05-30 | 2022-07-29 | 天津云圣智能科技有限责任公司 | Magnetic compass parameter calibration method, unmanned aerial vehicle course angle determination method and device |
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