CN109059960A - A kind of calibration method of three-dimensional electronic compass - Google Patents

Abstract

The invention relates to a method for calibrating a three-dimensional electronic compass. Move the electronic compass in a figure-of-eight motion in space, and collect the data read by the three axes of the magnetic sensor; then perform ellipsoid fitting on the collected data to obtain the ellipsoid equation and the coordinates of the center of the sphere; The ellipsoid equation is projected to the three coordinate axis planes respectively, and the parameters of the ellipse on the three planes are calculated respectively: α, b, major axis rotation angle; finally, the newly obtained data is calibrated according to the obtained parameters. The method of the invention makes the calibration process of the electronic compass more flexible and more accurate, and meets the requirements of field sports.

Description

A calibration method for a three-dimensional electronic compass

technical field

The invention relates to a method for calibrating a three-dimensional electronic compass.

Background technique

In recent years, electronic compasses have been widely used in navigation, human body posture measurement and other scenarios. Since the GPS signal is very weak in places such as forests and dense buildings, an electronic compass is usually needed to assist in positioning.

The working principle of the electronic compass is to measure the component strength of the geomagnetism in a certain direction through a magnetic sensor, determine the angle between the sensor and the geomagnetism, and then determine the heading. However, the earth's magnetic field is a weak magnetic field, and the hard magnetic interference and soft magnetic interference brought by the magnetic materials around the electronic compass will cause the measured value of the magnetic sensor to deviate from the true value. In addition, due to the process problems of the sensor itself, such as the non-orthogonal axis, the measured value of the magnetic sensor will also deviate from the true value.

If there is only the effect of geomagnetism, the data output by the three axes of the magnetic sensor should be a positive sphere whose center is at the origin corresponding to the space Cartesian coordinate system. However, the hard magnetic interference will make this true sphere become a true sphere with the hard magnetic interference as the center. If the effects of geomagnetism, hard magnetism and soft magnetism are considered at the same time, the above-mentioned positive sphere will become an ellipsoid with the hard magnetism as the center. The interference caused by non-orthogonal axes can be equivalent to soft and hard magnetic interference. Therefore, before using the electronic compass, it needs to be calibrated, and the data read out by its three axes should be compensated so that it falls on the perfect spherical surface whose center is at the origin.

The existing three-dimensional electronic compass calibration methods either require the help of external equipment, or have high requirements for the calibration process, and most of them do not perform soft magnetic compensation. Difficult to meet the needs of field operations.

Contents of the invention

The purpose of the present invention is to provide a calibration method for a three-dimensional electronic compass. The method moves the electronic compass in a figure-of-eight motion in space, which can compensate the error interference caused by soft and hard magnetic interference and non-orthogonal axes, and perform electronic compass calibration. Calibration; this method makes the calibration process of the electronic compass more flexible and more accurate, and meets the requirements of field sports.

In order to achieve the above object, the technical solution of the present invention is: a calibration method of a three-dimensional electronic compass, which moves the electronic compass in a figure-of-eight movement in space, and collects the data read by the three axes of the magnetic sensor; then the collected data Perform ellipsoid fitting to obtain the ellipsoid equation and the coordinates of the center of the sphere; then project the fitted ellipsoid equation onto the three coordinate axis planes respectively, and obtain the parameters of the ellipse on the three planes: α, b, Major axis rotation angle; finally, the newly obtained data is calibrated according to the obtained parameters.

In an embodiment of the present invention, the specific implementation steps of the method are as follows:

Step S1: Make the electronic compass move in figures of eight in space, so that the electronic compass collects data corresponding to eight directions of up, down, east, south, west and north, that is, the eight quadrants of the spatial rectangular coordinate system;

Step S2: Carry out ellipsoid fitting, and use the least square method to find the 10 best parameters A, B, C, D, E, F, G, I, J of the ellipsoid and the coordinates of the center of the ellipsoid (X0 ,Y0,Z0); the general expression of the ellipsoid equation is:

Ax ² +By ² +Cz ² +Dxy+Exz+Fyz+Gx+Hy+Iz+J＝0

Respectively make z=0, x=0, y=0 in the above formula, then the projection equations of the ellipsoid on the XOY, XOZ, YOZ planes can be obtained respectively:

Ax ² +By ² +Dxy+Gx+Hy+J＝0

Ax ² +Cz ² +Exz+Gx+Iz+J＝0

By ² +Cz ² +Fyz+Hy+Iz+J＝0

Step S3: According to the projection equation of the ellipsoid on the XOY surface: Ax ² +By ² +Dxy+Gx+Hy+J=0, calculate the parameters of the ellipse on the XOY surface: major axis rotation angle θx,y, αx,y and bx,y, the calculation formula is as follows:

in,

G'＝G·cos(θx,y)-H·sin(θx,y)

H'＝G sin(θx,y)+H cos(θx,y)

A'＝A·cos ² (θx,y)-D·cos(θx,y)·sin(θx,y)+B·sin ² (θx,y)

B'＝A·sin ² (θx,y)+D·cos(θx,y)·sin(θx,y)+B·cos ² (θx,y)

In the same way, the respective elliptic parameters θx, z, αx, z, bx, z and θy, z, αy, z, by, z of the ellipsoid equation on the XOZ surface and YOZ surface can be obtained;

Step S4: According to the coordinates of the center of the ellipsoid (X0, Y0, Z0) and the parameters obtained in step S3, the soft and hard magnetic compensation calibration can be performed on the data obtained by the magnetic sensor.

In an embodiment of the present invention, the specific implementation process of the step S4 is as follows:

Step S41, eliminate hard magnetic interference: hard magnetic interference causes the data output by the three axes of the magnetic sensor to shift by a fixed amount, which is the deviation distance from the center of the ellipsoid (X0, Y0, Z0) to the origin; The hard magnetic compensation calibration for the hard magnetic interference received by the three axes of the sensor is to subtract the above-mentioned offset fixed amount from the data read by the three axes of the magnetic sensor respectively, which is:

xe=xreading-X0

ye=yreading-Y0

ze=zreading-Z0

Among them, xreading, yreading, and zreading are the data newly read by the magnetic sensor on the X-axis, Y-axis, and Z-axis respectively, and xe, ye, and ze are the data after the hard magnetic interference has been eliminated on the three axes of the magnetic sensor;

Step S41. Eliminate soft magnetic interference: Carry out soft magnetic compensation calibration for X-axis-Y-axis, X-axis-Z-axis, and Y-axis-Z-axis respectively; The major axis rotation angle θx, y of the ellipse on the XOY plane of , the rotation matrix R can be obtained:

Then rotate the data after removing the hard magnetic interference to the standard ellipse, specifically:

Then stretch the above data to a perfect circle: specifically:

If αx,y>bx,y, there are:

xc=xe0

If bx,y>αx,y, there are:

yc=ye0

Finally, rotate the obtained data xc, yc back, there are:

Among them, xc0 and yc0 are the calibrated data of soft and hard magnetic compensation; the same is true for soft magnetic compensation of X axis-Z axis and Y axis-Z axis. After repeated calculations, six data can be obtained, which are:

For the accuracy of the results, the weighted average of the six data is obtained

Among them, xvalue, yvalue, and zvalue are the final data of the three-axis magnetic sensor after soft and hard magnetic calibration.

Compared with the prior art, the present invention has the following beneficial effects: In the present invention, the calibration method of the electronic compass is innovated:

1. The calibration process does not require the assistance of external equipment such as inclination sensors, and only needs to move around the figure 8 in space;

2. The present invention adopts the least square method to fit the ellipsoid, and considers the ellipsoid rotation and expansion and contraction caused by soft and hard magnetic interference, and compensates it; wherein the soft magnetic compensation scheme is realized based on the major axis rotation angle of the ellipse, compared to The existing 3-axis electronic compass calibration technology works better;

3. While eliminating the soft and hard magnetic interference, this method also eliminates the error interference caused by the non-orthogonal axis of the magnetic sensor;

Compared with the existing calibration technology, the result obtained by the invention is more accurate, and the calibration process is more flexible, and has wide application prospects in the field of electronic compass.

Description of drawings

Figure 1 is a diagram of the calibration process of a three-dimensional electronic compass.

Figure 2 is a diagram of the interference effect of the soft magnetism on the three axes of the magnetic sensor.

Figure 3 is a diagram of the interference effect of the soft magnetism on the X-axis and Y-axis of the magnetic sensor.

Detailed ways

The technical solution of the present invention will be specifically described below in conjunction with the accompanying drawings.

The invention provides a method for calibrating a three-dimensional electronic compass. The electronic compass is moved in a figure-of-eight motion in space, and the data read by the three axes of the magnetic sensor are collected; then the collected data are fitted with an ellipsoid to obtain The spherical equation and the coordinates of the center of the sphere; then project the fitted ellipsoid equation onto the three coordinate axis planes respectively, and obtain the parameters of the ellipse on the three planes: α, b, and major axis rotation angle; finally, according to the obtained Parameter pairs for data calibration. The specific implementation steps of this method are as follows:

Step S1: Make the electronic compass move in figures of eight in space, so that the electronic compass collects data corresponding to eight directions of up, down, east, south, west and north, that is, the eight quadrants of the spatial rectangular coordinate system;

Step S2: Carry out ellipsoid fitting, and use the least square method to find the 10 best parameters A, B, C, D, E, F, G, I, J of the ellipsoid and the coordinates of the center of the ellipsoid (X0 ,Y0,Z0); the general expression of the ellipsoid equation is:

Ax ² +By ² +Cz ² +Dxy+Exz+Fyz+Gx+Hy+Iz+J＝0

Respectively make z=0, x=0, y=0 in the above formula, then the projection equations of the ellipsoid on the XOY, XOZ, YOZ planes can be obtained respectively:

Ax ² +By ² +Dxy+Gx+Hy+J＝0

Ax ² +Cz ² +Exz+Gx+Iz+J＝0

By ² +Cz ² +Fyz+Hy+Iz+J＝0

Step S3: According to the projection equation of the ellipsoid on the XOY surface: Ax ² +By ² +Dxy+Gx+Hy+J=0, calculate the parameters of the ellipse on the XOY surface: major axis rotation angle θx,y, αx,y and bx,y, the calculation formula is as follows:

in,

G'＝G·cos(θx,y)-H·sin(θx,y)

H'＝G sin(θx,y)+H cos(θx,y)

A'＝A·cos ² (θx,y)-D·cos(θx,y)·sin(θx,y)+B·sin ² (θx,y)

B'＝A·sin ² (θx,y)+D·cos(θx,y)·sin(θx,y)+B·cos ² (θx,y)

In the same way, the parameters θx, z, αx, z, bx, z and θy, z, αy, z, by, z of the projected ellipse of the ellipsoid equation on the XOZ surface and on the YOZ surface can be obtained respectively;

Step S4: According to the coordinates of the center of the ellipsoid (X0, Y0, Z0) and the parameters obtained in step S3, the soft and hard magnetic compensation calibration can be performed on the data obtained by the magnetic sensor. The concrete realization process of described step S4 is as follows:

Step S41, eliminate hard magnetic interference: hard magnetic interference causes the data output by the three axes of the magnetic sensor to shift by a fixed amount, which is the deviation distance from the center of the ellipsoid (X0, Y0, Z0) to the origin; The hard magnetic compensation calibration for the hard magnetic interference received by the three axes of the sensor is to subtract the above-mentioned offset fixed amount from the data read by the three axes of the magnetic sensor respectively, which is:

xe=xreading-X0

ye=yreading-Y0

ze=zreading-Z0

Among them, xreading, yreading, and zreading are the data newly read by the magnetic sensor on the X-axis, Y-axis, and Z-axis respectively, and xe, ye, and ze are the data after the hard magnetic interference has been eliminated on the three axes of the magnetic sensor;

Step S41. Eliminate soft magnetic interference: Carry out soft magnetic compensation calibration for X-axis-Y-axis, X-axis-Z-axis, and Y-axis-Z-axis respectively; The major axis rotation angle θx, y of the ellipse on the XOY plane of , the rotation matrix R can be obtained:

Then rotate the data after removing the hard magnetic interference to the standard ellipse, specifically:

Then stretch the above data to a perfect circle: specifically:

If αx,y>bx,y, there are:

xc=xe0

If bx,y>αx,y, there are:

yc=ye0

Finally, rotate the obtained data xc, yc back, there are:

Among them, xc0 and yc0 are the calibrated data of soft and hard magnetic compensation; the same is true for soft magnetic compensation of X axis-Z axis and Y axis-Z axis. After repeated calculations, six data can be obtained, which are:

For the accuracy of the results, the weighted average of the six data is obtained

Among them, xvalue, yvalue, and zvalue are the final data of the three-axis magnetic sensor after soft and hard magnetic calibration.

The following is the specific implementation process of the present invention.

The invention provides a convenient and accurate three-dimensional electronic compass calibration method, which can compensate the error interference caused by soft and hard magnetic interference and non-orthogonal axes by simply moving the electronic compass in a figure-of-eight movement in space. Calibration of electronic compass. This method makes the calibration process of the electronic compass more flexible and more accurate, and meets the requirements of field sports.

The calibration process of the three-dimensional electronic compass is shown in Figure 1: first, the electronic compass is moved in a figure-of-eight movement in space, and the data read by the three axes of the magnetic sensor are collected; The spherical equation and the coordinates of the center of the sphere; then project the fitted ellipsoid equation onto the three coordinate axis planes respectively, and calculate the ellipse parameters on the three planes: α, b, and major axis rotation angle; finally, according to the obtained parameters Calibrate to new data. The entire calibration process does not require additional inclination sensors or other equipment assistance.

To move the electronic compass in a figure-of-eight movement in space, it is necessary to make the electronic compass collect the data of the eight azimuths (corresponding to the eight quadrants of the space Cartesian coordinate system) of up, down, east, south, west, and north. The ellipsoid fitted in this way has higher accuracy. The general expression of the ellipsoid equation is:

Ax ² +By ² +Cz ² +Dxy+Exz+Fyz+Gx+Hy+Iz+J＝0

Described ellipsoid fitting process adopts the least square method fitting method to find out 10 optimal parameters A of ellipsoid, B, C, D, E, F, G, I, J and ellipsoid spherical center coordinates (X0 ,Y0,Z0).

After obtaining the general expression of the ellipsoid equation, project the ellipsoid to three coordinate planes of the space Cartesian coordinate system: XOY plane, XOZ plane and YOZ plane. Taking the projection of the ellipsoid to the XOY plane as an example, only the general expression of the ellipsoid is:

Ax ² +By ² +Cz ² +Dxy+Exz+Fyz+Gx+Hy+Iz+J＝0

The x variable in is set to 0, and the projection equation of the ellipsoid on the XOY surface can be obtained:

Ax ² +By ² +Dxy+Gx+Hy+J＝0

By analogy, the projection equations of the ellipsoid on the XOZ and YOZ surfaces can be obtained respectively:

Ax ² +Cz ² +Exz+Gx+Iz+J＝0

and

By ² +Cz ² +Fyz+Hy+Iz+J＝0

When there is only the effect of geomagnetism, rotate the electronic compass once in space, and the data output by the three axes of the magnetic sensor corresponds to a perfect sphere with the origin as the center on the space Cartesian coordinate system. However, the interference of soft magnetism will make the orthosphere distort into an ellipsoid, and the interference effect of soft magnetism is shown in Fig. 2 . Take the analysis of the interference of soft magnetism on the X-axis and Y-axis as an example, as shown in Figure 3, if there is only geomagnetic action, after the X-axis and Y-axis of the magnetic sensor rotate a circle on the water surface, the output data corresponds to the Cartesian coordinate system It is a perfect circle with the center at the origin, but the soft magnetic interference stretches the two-axis data into an ellipse and rotates the ellipse by a certain angle, that is, the ellipse under the soft magnetic interference is not a standard ellipse, it has a certain Major axis angle. In order to eliminate soft magnetic interference, it is necessary to rotate the ellipse back to the standard ellipse, and then stretch the ellipse into a perfect circle according to the ratio of the major axis to the minor axis. The same is true for the soft magnetic interference and compensation calibration of the Z axis. Therefore, in order to perform accurate soft magnetic calibration on the three-axis output data of the magnetic sensor, it is necessary to separately calculate the ellipse parameters on the three coordinate planes: α, b, and the major axis rotation angle θ.

After obtaining the general expressions of the equations of the ellipse on the three coordinate planes, the parameters of the ellipse on each coordinate plane can be obtained according to the parameters of the general equation of the ellipse: α, b and the major axis rotation angle θ. Taking the XOY surface as an example, the calculation formulas of the three parameters are as follows:

in,

G'＝G·cos(θx,y)-H·sin(θx,y)

H'＝G sin(θx,y)+H cos(θx,y)

A'＝A·cos ² (θx,y)-D·cos(θx,y)·sin(θx,y)+B·sin ² (θx,y)

B'＝A·sin ² (θx,y)+D·cos(θx,y)·sin(θx,y)+B·cos ² (θx,y)

In the same way, the respective parameters θx, z, αx, z, bx, z and θy, z, αy, z, by, z of the XOZ surface and YOZ surface can be obtained.

The center of the ellipsoid and the three parameters (nine in total) of the ellipse on each coordinate plane obtained in the above steps are the compensation coefficients necessary for the soft and hard magnetic compensation calibration of the electronic compass. Afterwards, the data acquired by the magnetic sensor must be calibrated by soft and hard magnetic compensation. The specific calibration method is as follows:

The interference of the hard magnet causes the data output by the three axes of the magnetic sensor to deviate by a fixed amount, which is the distance from the center of the ellipsoid (X0, Y0, Z0) to the origin. Taking the data read by the X axis of the sensor as an example, the newly read data is offset by X0.

The data read by the Y-axis and Z-axis of the sensor are the same. Hard magnetic compensation calibration for the hard magnetic interference received by the three axes of the magnetic sensor is to subtract the above-mentioned offset from the data read by the three axes of the magnetic sensor respectively, which is:

xe=xreading-X0

ye=yreading-Y0

ze=zreading-Z0

Among them, xreading, yreading, and zreading are the data newly read by the magnetic sensor on the X-axis, Y-axis, and Z-axis respectively; X0, Y0, and Y0 are the coordinates of the center of the ellipsoid after fitting; xe, ye, and ze are the three coordinates of the magnetic sensor Axis data after eliminating hard magnetic interference.

In order to eliminate soft magnetic interference, in this method, soft magnetic compensation calibration is performed on X-axis-Y-axis, X-axis-Z-axis, and Y-axis-Z-axis respectively. Taking the soft magnetic compensation of the X-axis and Y-axis as an example, according to the major axis rotation angle θx,y of the ellipse on the XOY surface obtained, the rotation matrix R can be obtained:

Then rotate the data after removing the hard magnetic interference to the standard ellipse, specifically:

Then stretch the above data to a perfect circle. Specifically:

If αx,y>bx,y, there are:

xc=xe0

If bx,y>αx,y, there are:

yc=ye0

Finally, rotate the obtained data xc, yc back, there are:

Among them, xc0 and yc0 are the data after soft and hard magnetic compensation calibration. The same is true for the soft magnetic compensation of the X-axis-Z-axis and Y-axis-Z axis. After such repeated calculations, six data can be obtained, which are:

For the accuracy of the results, in this method, the weighted average of the six data is obtained.

Among them, xvalue, yvalue, and zvalue are the final data of the three-axis magnetic sensor after soft and hard magnetic calibration.

Since the non-orthogonal axis interference and the soft and hard magnetic interference are mathematically equivalent, the above process also eliminates the interference caused by the non-orthogonal axis of the magnetic sensor.

The above are the preferred embodiments of the present invention, and all changes made according to the technical solution of the present invention, when the functional effect produced does not exceed the scope of the technical solution of the present invention, all belong to the protection scope of the present invention.

Claims (3)

1. a kind of calibration method of three-dimensional electronic compass, it is characterized in that, electronic compass is done figure-of-eight motion in space, gathers the data that the three axes of magnetic sensor are read; Then the data that gathers is carried out ellipsoid fitting, Obtain the ellipsoid equation and the coordinates of the center of the sphere; then project the fitted ellipsoid equation to the three coordinate axis planes respectively, and obtain the parameters of the ellipse on the three planes: α, b, major axis rotation angle; finally according to The resulting parameters were calibrated against newly acquired data. 2. the calibration method of a kind of three-dimensional electronic compass according to claim 1, is characterized in that, the concrete realization steps of this method are as follows: Step S1: Make the electronic compass move in figures of eight in space, so that the electronic compass collects data corresponding to eight directions of up, down, east, south, west and north, that is, the eight quadrants of the spatial rectangular coordinate system; Step S2: Carry out ellipsoid fitting, and use the least square method to find the 10 best parameters A, B, C, D, E, F, G, I, J of the ellipsoid and the coordinates of the center of the ellipsoid (X0 ,Y0,Z0); the general expression of the ellipsoid equation is: Ax ² +By ² +Cz ² +Dxy+Exz+Fyz+Gx+Hy+Iz+J＝0 Respectively make z=0, x=0, y=0 in the above formula, then the projection equations of the ellipsoid on the XOY, XOZ, YOZ planes can be obtained respectively: Ax ² +By ² +Dxy+Gx+Hy+J＝0 Ax ² +Cz ² +Exz+Gx+Iz+J＝0 By ² +Cz ² +Fyz+Hy+Iz+J＝0 Step S3: According to the projection equation of the ellipsoid on the XOY surface: Ax ² +By ² +Dxy+Gx+Hy+J=0, calculate the parameters of the ellipse on the XOY surface: major axis rotation angle θx,y, αx,y and bx,y, the calculation formula is as follows: in, G'＝G·cos(θx,y)-H·sin(θx,y) H'＝G sin(θx,y)+H cos(θx,y) A'＝A·cos ² (θx,y)-D·cos(θx,y)·sin(θx,y)+B·sin ² (θx,y) B'＝A·sin ² (θx,y)+D·cos(θx,y)·sin(θx,y)+B·cos ² (θx,y) In the same way, the parameters θx, z, αx, z, bx, z and θy, z, αy, z, by, z of the projected ellipse of the ellipsoid equation on the XOZ surface and on the YOZ surface can be obtained respectively; Step S4: According to the coordinates of the center of the ellipsoid (X0, Y0, Z0) and the parameters obtained in step S3, the soft and hard magnetic compensation calibration can be performed on the data obtained by the magnetic sensor. 3. the calibration method of a kind of three-dimensional electronic compass according to claim 2, is characterized in that, the concrete realization process of described step S4 is as follows: Step S41, eliminate hard magnetic interference: hard magnetic interference causes the data output by the three axes of the magnetic sensor to shift by a fixed amount, which is the deviation distance from the center of the ellipsoid (X0, Y0, Z0) to the origin; The hard magnetic compensation calibration for the hard magnetic interference received by the three axes of the sensor is to subtract the above-mentioned offset fixed amount from the data read by the three axes of the magnetic sensor respectively, which is: xe=xreading-X0 ye=yreading-Y0 ze=zreading-Z0 Among them, xreading, yreading, and zreading are the data newly read by the magnetic sensor on the X-axis, Y-axis, and Z-axis respectively, and xe, ye, and ze are the data after the hard magnetic interference has been eliminated on the three axes of the magnetic sensor; Step S41. Eliminate soft magnetic interference: Carry out soft magnetic compensation calibration for X-axis-Y-axis, X-axis-Z-axis, and Y-axis-Z-axis respectively; The major axis rotation angle θx, y of the ellipse on the XOY plane of , the rotation matrix R can be obtained: Then rotate the data after removing the hard magnetic interference to the standard ellipse, specifically: Then stretch the above data to a perfect circle: specifically: If αx,y>bx,y, there are: xc=xe0 If bx,y>αx,y, there are: yc=ye0 Finally, rotate the obtained data xc, yc back, there are: Among them, xc0 and yc0 are the calibrated data of soft and hard magnetic compensation; the same is true for soft magnetic compensation of X axis-Z axis and Y axis-Z axis. After repeated calculations, six data can be obtained, which are: For the accuracy of the results, the weighted average of the six data is obtained Among them, xvalue, yvalue, and zvalue are the final data of the three-axis magnetic sensor after soft and hard magnetic calibration.