CN113866688A - Error calibration method for three-axis magnetic sensor under condition of small attitude angle - Google Patents

Error calibration method for three-axis magnetic sensor under condition of small attitude angle Download PDF

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CN113866688A
CN113866688A CN202111104574.XA CN202111104574A CN113866688A CN 113866688 A CN113866688 A CN 113866688A CN 202111104574 A CN202111104574 A CN 202111104574A CN 113866688 A CN113866688 A CN 113866688A
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CN113866688B (en
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刘建国
严有玉
严胜刚
李先刚
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Northwestern Polytechnical University
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    • G01R33/0206—Three-component magnetometers
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Abstract

The invention discloses an error calibration method of a triaxial magnetic sensor under the condition of a small attitude angle, wherein the triaxial magnetic sensor has three errors of triaxial nonorthogonal, inconsistent sensitivity and zero drift due to the imperfect current manufacturing process; the traditional scalar calibration method needs to rotate a sensor along three sensitive axes in a large range of angles, record output values of the sensor under each posture in real time, and then use collected data and an established model to finish calibration. However, when the range of the attitude change of the sensor is limited, it is difficult to achieve a desired calibration effect using the conventional method. The invention establishes an error joint calibration model based on the geomagnetic horizontal total quantity and the vertical component by combining the attitude information of the sensor, and adopts an optimization algorithm, so that when the attitude of the sensor is variable in a small range, error parameters can be accurately solved, and the error calibration of the sensor is completed.

Description

Error calibration method for three-axis magnetic sensor under condition of small attitude angle
Technical Field
The invention belongs to the technical field of sensors, and particularly relates to an error calibration method for a three-axis magnetic sensor.
Background
The currently more common error calibration method for the three-axis magnetic sensor in practice is based on the principle that the modulus of the magnetic field vector at one point in space is not changed, i.e. scalar calibration. This method requires, when executed, a number of extensive changes in the attitude of the sensor (specifically operative to rotate the sensor along its three sensitive axes) and recording the magnetic field data of the sensor at each attitude. And then, estimating error parameters by using the data and the established error model, and finally, compensating the acquired data by using the solved error parameters to finish calibration. However, when the magnetic sensor is installed on a large-scale motion platform such as a ship, an airplane or an aircraft, it is particularly difficult to change the attitude angle of the carrier, particularly the pitch angle and the roll angle, in a large range, and only a small range of change can be performed. This results in a large correlation of the acquired magnetic field data, and if the estimated parameters are trained using these strongly correlated data, the calibration effect will deviate significantly from the ideal. For the problems existing in the method, the general solution idea is to project the acquired data to a horizontal plane in combination with the attitude information of the magnetic sensor, and then obtain error parameters by ellipse fitting, and the calibration model is called a two-dimensional total quantity model. However, since the measured magnetic field value contains noise and changes with the change of the yaw angle, the combination of the measured magnetic field value and the zero offset cannot be regarded as a constant in the model, and therefore, even if the roll and the yaw angle are fixed by the training sample, the LM or PSO method adopted by the model cannot achieve a good effect for the two-dimensional total quantity model.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides an error calibration method of a three-axis magnetic sensor under the condition of a small attitude angle, wherein three errors of three-axis non-orthogonality, inconsistent sensitivity and zero drift exist in the three-axis magnetic sensor due to the imperfect current manufacturing process; the traditional scalar calibration method needs to rotate a sensor along three sensitive axes in a large range of angles, record output values of the sensor under each posture in real time, and then use collected data and an established model to finish calibration. However, when the range of the attitude change of the sensor is limited, it is difficult to achieve a desired calibration effect using the conventional method. The invention establishes an error joint calibration model based on the geomagnetic horizontal total quantity and the vertical component by combining the attitude information of the sensor, and adopts an optimization algorithm, so that when the attitude of the sensor is variable in a small range, error parameters can be accurately solved, and the error calibration of the sensor is completed.
The technical scheme adopted by the invention for solving the technical problem comprises the following steps:
step 1: establishing an error model:
factors influencing the measurement accuracy of the three-axis magnetic sensor comprise three errors of three-axis non-orthogonality, inconsistent scale factors and zero offset;
step 1-1: the non-orthogonal error is expressed in that the actual sensitive axes of the three-axis magnetic sensor are not completely orthogonal in pairs due to the limitation of the manufacturing process;
defining O-XYZ to represent an ideal orthogonal coordinate system; defining O-X ' Y ' Z ' as a coordinate system where three sensitive axes of the actual three-axis magnetic sensor are located, and the coordinate system is called as a sensor coordinate system;
suppose that: (1) the OZ' axis of the sensor coordinate system is coincident with the OZ axis of the ideal orthogonal coordinate system; (2) a Z ' OY ' plane of a sensor coordinate system is coplanar with a ZOY plane of an ideal orthogonal coordinate system, and an included angle between an OY ' axis and an OY axis is alpha; (3) the OX ' axis of the sensor coordinate system deviates downwards from the XOY plane, OX ' is defined as the projection of OX ' on the XOY plane, the included angle between the OX ' axis and the sensor coordinate system is beta, and the included angle between the OX ' axis and the OX axis of the ideal orthogonal coordinate system is gamma;
the relationship between the ideal orthogonal coordinate system and the sensor coordinate system is expressed as:
Figure BDA0003271607320000021
step 1-2: the inconsistent scale factors show that when the three components of the magnetic field are the same, the magnetic field values output by the three shafts of the three-shaft magnetic sensor are different in size and can be represented by a theoretical value multiplied by a diagonal matrix;
step 1-3: the zero offset is represented by that the three axes have zero offset due to the residual magnetism of the magnetic core, the drift of the amplifying and conditioning part of the internal circuit and the external temperature change factors, so that different magnetic fields can be superposed and fixed in the three-axis direction when the three-axis magnetic sensor is used for measurement;
step 1-4: when the three errors are comprehensively considered, the relationship between the actual output value and the theoretical value of the three-axis magnetic sensor is expressed as follows:
Bm＝RB+bp (2)
wherein B ═ Bx,By,Bz]For an ideal magnetic field value, Bm＝[Bmx,Bmy,Bmz]Magnetic field values, error matrix for actual three-axis magnetic sensor output
Figure BDA0003271607320000022
kx kyAnd kzScale factors representing three axes, respectively, bp＝[bx by bz]TZero offset error for a three-axis magnetic sensor;
further derivation yields a true error-free magnetic field representation as:
B＝R'(Bm-bp) (3)
wherein R' is the inverse of the error matrix R and is an upper triangular matrix;
step 2: establishing a geomagnetic model;
establishing a geographic coordinate system: the coordinate origin is located at the intersection point of a connecting line of a carrier provided with the three-axis magnetic sensor and the earth center and the earth surface, the x axis points to the geographical north, the y axis points to the geographical east, and the z axis points to the earth center vertically; the projections of the earth magnetic field intensity T on the x, y and z axes are respectively north components BNEast component BEAnd a vertical component BD，BHD and I are respectively a geomagnetic declination angle and a geomagnetic inclination angle; t, BN、BE、BD、BHD, I are collectively called seven elements of the earth's magnetic field and the magnetic field value at any point on the earth's surface is described and expressed by seven elements of earth's magnetism;
the relationship between seven elements of geomagnetism is expressed as:
Figure BDA0003271607320000031
and step 3: establishing an error calibration model of a three-axis magnetic sensor;
when using the geomagnetic field to perform error calibration of the three-axis magnetic sensor, equation (3) is written as:
Figure BDA0003271607320000032
in the formula (I), the compound is shown in the specification,
Figure BDA0003271607320000033
is the geomagnetic field value in the sensor coordinate system;
the conversion relation between the geographical coordinate system and the sensor coordinate system is described by the connected multiplication of the attitude matrix, so that
Figure BDA0003271607320000034
Expressed as:
Figure BDA0003271607320000035
wherein
Figure BDA0003271607320000036
Gamma, theta and psi are roll, pitch and yaw, respectively; .
Continuing with the derivation formula (6) to obtain:
Figure BDA0003271607320000041
wherein psi' ═ psi-D,
Figure BDA0003271607320000042
k11，k12…k33the matrix K is an element of the matrix K, and the matrix K can change along with the change of the roll angle and the pitch angle and is not an upper triangular or symmetrical matrix any more;
when the output values of N ≧ 12 groups of sensors under different postures are known, equation (7) is converted into a multi-objective function problem:
Figure BDA0003271607320000043
wherein the variable having the superscript ^' represents the geomagnetic field component represented by the formula (8), BHAnd BDRespectively representing the horizontal component modulus and the vertical component of the local real geomagnetic field;
and 4, step 4: estimating parameters;
estimating error parameters by adopting an optimization algorithm according to the established error estimation model formula (8);
and 5: and (4) compensating the magnetic field value with the error by using the parameter solved in the step (4) to finish calibration.
Preferably, the horizontal component module and the vertical component of the local real geomagnetic field in the step 3 can be obtained according to a world magnetic field model, and the average value of the measured values is used as a substitute in the experiment.
Preferably, the optimization algorithm in the step 5 is a Levenberg Marquardt algorithm or a particle swarm algorithm.
The invention has the following beneficial effects:
1. under the condition of a small range of attitude angles (the variation range of the pitch angle and the roll angle is less than +/-15 degrees), the method can still accurately estimate error parameters, and is more suitable for error correction of airborne or shipborne triaxial magnetic sensors compared with the existing large-scale calibration method based on the total magnetic field.
2. Compared with a two-dimensional total amount calibration method (magnetic field values are projected to a horizontal plane by using a known attitude angle, and then ellipse fitting is carried out to solve error parameters), the method provided by the invention has a better calibration effect.
Drawings
Fig. 1 is a non-orthogonal error model of a three-axis fluxgate sensor.
FIG. 2 is a diagram of geomagnetic elements in accordance with the present invention.
FIG. 3 is a diagram comparing a conventional method with the method of the present invention.
Detailed Description
The invention is further illustrated with reference to the following figures and examples.
In order to solve the problem that error parameters cannot be accurately estimated due to strong correlation among data when the change range of an attitude angle is limited by the conventional magnetic field total amount calibration method based on the total amount, the invention provides a mixed calibration method based on the horizontal total amount and the vertical component of a magnetic field by combining pitch and roll information.
A method for calibrating errors of a three-axis magnetic sensor under the condition of a small attitude angle comprises the following steps:
step 1: establishing an error model:
factors influencing the measurement accuracy of the three-axis magnetic sensor comprise three errors of three-axis non-orthogonality, inconsistent scale factors and zero offset;
step 1-1: the non-orthogonal error is expressed in that the actual sensitive axes of the three-axis magnetic sensor are not completely orthogonal in pairs due to the limitation of the manufacturing process;
FIG. 1 shows a model diagram of non-orthogonal errors of a three-axis fluxgate sensor, defining O-XYZ to represent an ideal orthogonal coordinate system; defining O-X ' Y ' Z ' as a coordinate system where three sensitive axes of the actual three-axis magnetic sensor are located, and the coordinate system is called as a sensor coordinate system;
suppose that: (1) the OZ' axis of the sensor coordinate system is coincident with the OZ axis of the ideal orthogonal coordinate system; (2) a Z ' OY ' plane of a sensor coordinate system is coplanar with a ZOY plane of an ideal orthogonal coordinate system, and an included angle between an OY ' axis and an OY axis is alpha; (3) the OX ' axis of the sensor coordinate system deviates downwards from the XOY plane, OX ' is defined as the projection of OX ' on the XOY plane, the included angle between the OX ' axis and the sensor coordinate system is beta, and the included angle between the OX ' axis and the OX axis of the ideal orthogonal coordinate system is gamma;
the relationship between the ideal orthogonal coordinate system and the sensor coordinate system is expressed as:
Figure BDA0003271607320000051
step 1-2: the inconsistent scale factors show that when the three components of the magnetic field are the same, the magnetic field values output by the three shafts of the three-shaft magnetic sensor are different in size and can be represented by a theoretical value multiplied by a diagonal matrix;
step 1-3: the zero offset is represented by that the three axes have zero offset due to the residual magnetism of the magnetic core, the drift of the amplifying and conditioning part of the internal circuit and the external temperature change factors, so that different magnetic fields can be superposed and fixed in the three-axis direction when the three-axis magnetic sensor is used for measurement;
step 1-4: when the three errors are comprehensively considered, the relationship between the actual output value and the theoretical value of the three-axis magnetic sensor is expressed as follows:
Bm＝RB+bp (2)
wherein B ═ Bx,By,Bz]For an ideal magnetic field value, Bm＝[Bmx,Bmy,Bmz]Magnetic field values, error matrix for actual three-axis magnetic sensor output
Figure BDA0003271607320000061
kx kyAnd kzScale factors representing three axes, respectively, bp＝[bx by bz]TZero offset error for a three-axis magnetic sensor;
further derivation yields a true error-free magnetic field representation as:
B＝R'(Bm-bp) (3)
wherein R' is the inverse of the error matrix R and is an upper triangular matrix; 6 elements for solving R' accurately and bpThe 3 elements of the vector are the key to the magnetic sensor error calibration problem. The invention establishes a new error solving model, so that the 9 parameters can be accurately estimated even under the condition of a small range of attitude angles.
Step 2: establishing a geomagnetic model;
the invention utilizes the earth magnetic field to carry out error calibration. As shown in fig. 2, a geographical coordinate system is established: the origin of coordinates is located at the intersection of the connecting line of the carrier and the earth center and the earth surfaceAt the point, the x axis points to the geographical north, the y axis points to the geographical east, and the z axis points to the geocentric vertically; the projections of the earth magnetic field intensity T on the x, y and z axes are respectively north components BNEast component BEAnd a vertical component BD，BHD and I are respectively a geomagnetic declination angle and a geomagnetic inclination angle; t, BN、BE、BD、BHD, I are collectively called seven elements of the earth's magnetic field and the magnetic field value at any point on the earth's surface is described and expressed by seven elements of earth's magnetism;
the relationship between seven elements of geomagnetism is expressed as:
Figure BDA0003271607320000062
and step 3: establishing an error calibration model of a three-axis magnetic sensor;
when using the geomagnetic field to perform error calibration of the three-axis magnetic sensor, equation (3) is written as:
Figure BDA0003271607320000071
in the formula (I), the compound is shown in the specification,
Figure BDA0003271607320000072
is the geomagnetic field value in the sensor coordinate system;
the conversion relation between the geographical coordinate system and the sensor coordinate system is described by the connected multiplication of the attitude matrix, so that
Figure BDA0003271607320000073
Expressed as:
Figure BDA0003271607320000074
wherein
Figure BDA0003271607320000075
Gamma, theta and psi are roll, pitch and yaw, respectively;。
continuing with the derivation formula (6) to obtain:
Figure BDA0003271607320000076
wherein psi' ═ psi-D,
Figure BDA0003271607320000077
k11，k12…k33the matrix K is an element of the matrix K, and the matrix K can change along with the change of the roll angle and the pitch angle and is not an upper triangular or symmetrical matrix any more;
when the output values of N ≧ 12 groups of sensors under different postures are known, equation (7) is converted into a multi-objective function problem:
Figure BDA0003271607320000078
wherein the variable having the superscript ^' represents the geomagnetic field component represented by the formula (8), BHAnd BDThe horizontal and vertical components, respectively, representing the local true earth magnetic field, can be obtained from the World Magnetic Model (WMM), and the average of the measurements is used as a substitute in the experiment.
And 4, step 4: estimating parameters;
according to the established error estimation model formula (8), selecting a proper optimization algorithm (such as Levenberg Marquardt algorithm, particle swarm algorithm and the like) to estimate error parameters (6 elements of R' and b)p3 elements of the vector).
And 5: and (4) compensating the magnetic field value with the error by using the parameter solved in the step (4) to finish calibration.
The specific embodiment is as follows:
1. example data preparation
The present embodiment considers a scenario in which errors of a three-axis magnetic sensor are calibrated in the context of a geomagnetic field, assuming that the total geomagnetic field is 48000nT, and the geomagnetic declination angle D and the inclination angle I are-5 ° and 5 °, respectively. Containing quadrature error and scale factorError matrix of
Figure BDA0003271607320000081
Zero offset is set as bp＝[2000 3000 4000]T. And (3) according to the set parameters, simulating and generating 20 groups of geomagnetic field values with no theoretical error and actually measured errors under different postures of the sensors, wherein the variation ranges of the pitch angles and the roll angles of the sensors are limited within +/-15 degrees so as to simulate the condition of a small-range posture angle. The structure formula of the earth magnetic field component theoretical value is as follows:
Figure BDA0003271607320000082
the output value of the actual magnetic sensor is constructed by the formula:
Figure BDA0003271607320000085
2. estimating error parameters according to the model provided by the invention;
the generated magnetic field data is brought into the well established objective function,
Figure BDA0003271607320000083
the 6 elements of R' and b are estimated by using Levenberg Marquardt algorithm p3 elements of the vector. In order to show that the method provided by the invention has better calibration effect than the total amount-based method, the generated magnetic field data is simultaneously brought into the three-dimensional total amount method, and the error parameters are estimated and compared by adopting a communicated parameter solving algorithm. To quantitatively compare the merits of the two methods, the error parameters estimated by the two methods are averaged for absolute deviation (MAD), which is defined as:
Figure BDA0003271607320000084
wherein xiRepresents the set R' and bpValue, ciRepresenting the values estimated by both models. Table 1 gives the MAD values for both methods.
TABLE 1 comparison of error calibration results for two methods
Figure BDA0003271607320000091
As can be seen from table 1, the MAD of the error parameters obtained by the method proposed by the present invention is small, while the large MAD of the parameters obtained by the total-amount-based calibration method indicates that the estimated parameters deviate significantly from the true values.
3. Test data error calibration
And (3) according to the simulation data set in the step 1, constructing 360 groups of test data under any posture, and correcting the 360 groups of test data by using the error parameters estimated by the two methods in the step 2. The correction formula is as follows: b ═ R' (B)m-bp). The data before and after correction are plotted as a comparative calibration effect (as shown in fig. 3). As can be seen from the figure, the magnetic field values (indicated by the lines marked with an "x" in the figure) actually output by the magnetic sensor deviate significantly from the true values (indicated by the straight lines in the figure) when the attitude of the sensor changes due to the presence of errors. The fluctuation range of the magnetic field component calibrated by the two methods is reduced, particularly, the magnetic field component (shown by a line with an "o" mark in the figure) calibrated by the method provided by the invention is very close to a theoretical value, and the calibration effect of the traditional method based on the total amount under the condition of a small range of attitude angles is obviously reduced. The result of the embodiment shows that the calibration method provided by the invention still has good capability of calibrating errors under the condition that the change range of the attitude angle of the sensor is limited.

Claims (3)

1. A method for calibrating errors of a three-axis magnetic sensor under the condition of a small attitude angle is characterized by comprising the following steps:
step 1: establishing an error model:
factors influencing the measurement accuracy of the three-axis magnetic sensor comprise three errors of three-axis non-orthogonality, inconsistent scale factors and zero offset;
step 1-1: the non-orthogonal error is expressed in that the actual sensitive axes of the three-axis magnetic sensor are not completely orthogonal in pairs due to the limitation of the manufacturing process;
defining O-XYZ to represent an ideal orthogonal coordinate system; defining O-X ' Y ' Z ' as a coordinate system where three sensitive axes of the actual three-axis magnetic sensor are located, and the coordinate system is called as a sensor coordinate system;
suppose that: (1) the OZ' axis of the sensor coordinate system is coincident with the OZ axis of the ideal orthogonal coordinate system; (2) a Z ' OY ' plane of a sensor coordinate system is coplanar with a ZOY plane of an ideal orthogonal coordinate system, and an included angle between an OY ' axis and an OY axis is alpha; (3) the OX ' axis of the sensor coordinate system deviates downwards from the XOY plane, OX ' is defined as the projection of OX ' on the XOY plane, the included angle between the OX ' axis and the sensor coordinate system is beta, and the included angle between the OX ' axis and the OX axis of the ideal orthogonal coordinate system is gamma;
the relationship between the ideal orthogonal coordinate system and the sensor coordinate system is expressed as:
Figure FDA0003271607310000011
step 1-2: the inconsistent scale factors show that when the three components of the magnetic field are the same, the magnetic field values output by the three shafts of the three-shaft magnetic sensor are different in size and can be represented by a theoretical value multiplied by a diagonal matrix;
step 1-3: the zero offset is represented by that the three axes have zero offset due to the residual magnetism of the magnetic core, the drift of the amplifying and conditioning part of the internal circuit and the external temperature change factors, so that different magnetic fields can be superposed and fixed in the three-axis direction when the three-axis magnetic sensor is used for measurement;
step 1-4: when the three errors are comprehensively considered, the relationship between the actual output value and the theoretical value of the three-axis magnetic sensor is expressed as follows:
Bm＝RB+bp (2)
wherein B ═ Bx,By,Bz]For an ideal magnetic field value, Bm＝[Bmx,Bmy,Bmz]Magnetic field values, error matrix for actual three-axis magnetic sensor output
Figure FDA0003271607310000021
kxkyAnd kzScale factors representing three axes, respectively, bp＝[bx by bz]TZero offset error for a three-axis magnetic sensor;
further derivation yields a true error-free magnetic field representation as:
B＝R'(Bm-bp) (3)
wherein R' is the inverse of the error matrix R and is an upper triangular matrix;
step 2: establishing a geomagnetic model;
establishing a geographic coordinate system: the coordinate origin is located at the intersection point of a connecting line of a carrier provided with the three-axis magnetic sensor and the earth center and the earth surface, the x axis points to the geographical north, the y axis points to the geographical east, and the z axis points to the earth center vertically; the projections of the earth magnetic field intensity T on the x, y and z axes are respectively north components BNEast component BEAnd a vertical component BD，BHD and I are respectively a geomagnetic declination angle and a geomagnetic inclination angle; t, BN、BE、BD、BHD, I are collectively called seven elements of the earth's magnetic field and the magnetic field value at any point on the earth's surface is described and expressed by seven elements of earth's magnetism;
the relationship between seven elements of geomagnetism is expressed as:
Figure FDA0003271607310000022
and step 3: establishing an error calibration model of a three-axis magnetic sensor;
when using the geomagnetic field to perform error calibration of the three-axis magnetic sensor, equation (3) is written as:
Figure FDA0003271607310000023
in the formula (I), the compound is shown in the specification,
Figure FDA0003271607310000024
is the geomagnetic field value in the sensor coordinate system;
the conversion relation between the geographical coordinate system and the sensor coordinate system is described by the connected multiplication of the attitude matrix, so that
Figure FDA0003271607310000025
Expressed as:
Figure FDA0003271607310000026
wherein
Figure FDA0003271607310000027
Gamma, theta and psi are roll, pitch and yaw, respectively;
continuing with the derivation formula (6) to obtain:
Figure FDA0003271607310000031
wherein psi' ═ psi-D,
Figure FDA0003271607310000032
k11，k12…k33the matrix K is an element of the matrix K, and the matrix K can change along with the change of the roll angle and the pitch angle and is not an upper triangular or symmetrical matrix any more;
when the output values of N ≧ 12 groups of sensors under different postures are known, equation (7) is converted into a multi-objective function problem:
Figure FDA0003271607310000033
wherein the variable having the superscript ^' represents the geomagnetic field component represented by the formula (8), BHAnd BDRespectively representing the horizontal component modulus and the vertical component of the local real geomagnetic field;
and 4, step 4: estimating parameters;
estimating error parameters by adopting an optimization algorithm according to the established error estimation model formula (8);
and 5: and (4) compensating the magnetic field value with the error by using the parameter solved in the step (4) to finish calibration.
2. The method for calibrating errors of a three-axis magnetic sensor under the condition of small attitude angle as claimed in claim 1, wherein the horizontal component module and the vertical component of the local real geomagnetic field in the step 3 can be obtained according to a world magnetic field model, and the average value of the measured values is used as a substitute in the experiment.
3. The method for calibrating the error of the three-axis magnetic sensor under the condition of small attitude angle according to claim 1, wherein the optimization algorithm in the step 5 is a Levenberg Marquardt algorithm or a particle swarm algorithm.
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CN115507849A (en) * 2022-11-22 2022-12-23 北京理工大学前沿技术研究院 Magnetic sensor correction method and system based on INS/GNSS combined navigation assistance
CN117686952A (en) * 2024-02-02 2024-03-12 北京理工大学前沿技术研究院 Method and system for carrying out plane correction based on combination of multiple magnetic sensors
CN117686952B (en) * 2024-02-02 2024-05-03 北京理工大学前沿技术研究院 Method and system for carrying out plane correction based on combination of multiple magnetic sensors

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