CN108333551B - Correction method of magnetometer - Google Patents
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Abstract
The invention provides a correction method of a magnetometer, which comprises the following steps: step one, error modeling is carried out on a magnetometer array; step two, calculating invariants in the magnetic field; and step three, searching a correlation optimization algorithm to determine a correction coefficient of the magnetometer array by using the invariant in the magnetic field. The correction method of the invention can be applied to non-uniform fields and uniform field environments, and has strong real-time performance and good correction effect.
Description
Technical Field
The invention belongs to the technical field of magnetic anomaly measurement, and particularly relates to a correction method of a magnetometer.
Background
Magnetometers are classified into scalar magnetometers and vector magnetometers by measurement target. Compared with a scalar magnetometer for measuring a magnetic field modulus, the vector magnetometer can measure three components of a magnetic field, obtains more information quantity, and plays an important role in the fields of underwater magnetic target detection, UXO detection, mineral exploration and navigation. However, due to the limitations of the processing technology and the installation level, the output error of the three-axis vector magnetometer mainly has a zero offset error, a scale factor of three axes and a non-orthogonal error of three axes. In addition, for the vector magnetometer array, besides the output error of a single magnetometer, the output error of the magnetometer array is affected by the mismatch error between the magnetometers and the soft iron and hard iron error caused by the support structure of the magnetometer array, so that the correction work of the magnetometer array is indispensable.
Conventional magnetometer correction methods are divided into scalar corrections and vector corrections. The basic principle of both correction methods is to use invariants in the correction process. Scalar correction is based on that under the condition of uniform field, the modulus value of the magnetic field measured by the vector magnetometer in the correction process is kept unchanged; the vector correction is to use the measurement values of a plurality of vector magnetometers in the correction process to be equal under the uniform field environment. The existing correction methods are all based on the assumed condition of a uniform field, but in practical application, the ideal uniform field does not exist due to the daily change of a geomagnetic field, the existence of peripheral power transmission lines, vehicles, underground unknown ferromagnetic targets and the like. At this time, the existing correction method has failed, and a magnetometer correction method simulating a non-uniform field in a real environment needs to be provided to solve the problem.
Disclosure of Invention
In view of the above technical problems, an object of the present invention is to provide a correction method of a magnetometer. The correction method of the invention can be applied to non-uniform fields and uniform field environments, and has strong real-time performance and good correction effect.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
a method of calibrating a magnetometer, comprising the steps of:
step one, error modeling is carried out on a magnetometer array;
step two, calculating invariants in the magnetic field;
and step three, searching a correlation optimization algorithm to determine a correction coefficient of the magnetometer array by using the invariant in the magnetic field.
According to the technical scheme, the correction method of the magnetometer has at least one of the following beneficial effects:
(1) the correction method of the invention does not need additional equipment;
(2) the correction method of the invention can be applied to non-uniform fields and can also be applied to uniform field environments;
(3) the correction method of the invention has simple correction operation, strong real-time performance and good correction effect, and is a universal method.
Drawings
FIG. 1 is a flow chart of a method for calibrating a magnetometer in a non-uniform field according to an embodiment of the invention.
FIG. 2 is a schematic diagram of a magnetometer array structure in the calibration system according to the embodiment of the invention.
FIG. 3 shows a system measurement value I before calibration according to an embodiment of the present invention1Schematic representation of (a).
FIG. 4 is I1Theoretical measurement of (1), after correction of the uniform field (I)1And corrected by the invention I1Schematic diagram of comparative analysis of (1).
[ Main element ]
1. A first magnetometer;
2. a second magnetometer;
3. a third magnetometer;
4. a fourth magnetometer.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to specific embodiments and the accompanying drawings.
The invention provides a correction method of a magnetometer, and FIG. 1 is a flow chart of the correction method of the magnetometer in a non-uniform field according to the embodiment of the invention. As shown in fig. 1, the method for calibrating a magnetometer in an inhomogeneous field according to the present invention comprises the following steps:
step one, error modeling is carried out on a magnetometer array; step two, calculating invariant in the inhomogeneous field; and step three, searching a correlation optimization algorithm to determine a correction coefficient of the magnetometer array by using the invariant in the inhomogeneous field.
In step one, three errors are mainly involved when error modeling is performed on the magnetometer array, which are respectively: single magnetometer errors, magnetometer support structures cause soft iron and hard errors, magnetometer to magnetometer mismatch errors.
Sources of deviation of individual magnetometer measurements from true values for individual magnetometer errors include: 1) a three-axis scale factor error; 2) zero bias factor error; 3) a non-quadrature error; 4) temperature drift; 5) a non-linear error; 6) observing noise, etc. When the temperature changes slowly and the influence of nonlinearity is neglected, the output of the magnetometer is:
Bout＝MkMoHe+e+n＝MFHe+e+n (1)
wherein HeRepresenting a true magnetic field vector; b isoutRepresenting a magnetometer measuring a magnetic field vector; mkIs a third-order diagonal matrix which represents the error of the three-axis scale factor; moIs a three-order upper triangular matrix which represents the three-axis non-orthogonal error; e, representing zero offset factor error; n is magnetometer observation noise. MF＝MKMoAnd characterizing the integrated three-axis scale factor error and the non-orthogonal error.
For soft iron and hard body errors caused by the magnetometer support structure, the rotation of the support structure can generate induced magnetic field errors and residual magnetic field errors, which are respectively expressed as soft iron errors and hard body errors, and a coefficient matrix M is usedsAnd a bias vector h.
Bout＝MsMkMo(He-h)+e+n＝MHe+b+n (2)
Wherein M is MsMkMoCharacterization of integrated soft errors, three-axis scaleFactor error and non-quadrature error. b is-MsMkMoh + e, characterizing the integrated hard iron error and zero offset factor error. n is magnetometer observation noise.
For the mismatch error between magnetometers, the mismatch error between magnetometers is mainly caused by two components. Taking the coordinate system where one magnetometer in the magnetometer array is located as a standard coordinate system, and taking the standard coordinate system as a reference, the mismatch error between the coordinate systems of other magnetometers and the reference coordinate system can be represented by an Euler rotation matrix.
Bnew＝REulerBout＝REuler(MHe+b)+n＝QHe+teff+n (3)
Wherein R isEulerCharacterization of mismatch errors between magnetometers for Euler rotation matrix, BoutIs the output magnetic field of equation (2). Q ═ REulerM, characterization of integrated magnetometer mismatch error and soft body error, three-axis scale factor error and non-orthogonal error, teff＝REulerAnd b, characterizing the mismatch error of the integrated magnetometer, the hard iron error and the zero bias factor error. n is magnetometer observation noise. Thus, Q, teffTwo matrix parameters characterize the influence of three large types of errors of integration on the measurement result.
In step two, a single vector magnetometer can measure three components of a magnetic field vector, differences are used to replace differentiation, and a magnetometer array with a specific structure formed by the vector magnetometers can measure magnetic gradient tensor, namely, the spatial change rate of the magnetic field vector is marked as G. G is a second order tensor, calculated as:
in a passive magnetic field, both the divergence and the curl of the magnetic field are 0. The magnetic gradient tensor matrix is a symmetric matrix with a sum of 0 for the diagonal elements of the matrix, i.e., only 5 out of 9 elements in the tensor matrix are independent, including two diagonal elements and three off-diagonal elements.
The magnetic gradient tensor matrix G corresponds to three tensor invariants, which are recorded asI0,I1,I2：
In the homogeneous field, the 3 tensor invariants are all 0, while in the inhomogeneous field, except I0Always equal to 0 and the two remaining invariants are both constants other than 0.
In step three, tensor invariant I is used1Correction coefficients for the magnetometer array are determined. As a specific embodiment, the magnetometer array includes four vector magnetometers, and the four vector magnetometers form a cross-shaped structure, wherein the first magnetometer 1 and the third magnetometer 3 are fixed on the x axis, and the second magnetometer 2 and the fourth magnetometer 4 are fixed on the y axis, as shown in fig. 2. Using the difference instead of the differential, the elements of the magnetic gradient tensor matrix can be obtained:
wherein Q is3×3，E3×1Are respectively equivalent to Q and t in formula (3)effThe influence of three major types of errors on the measurement of the magnetometer 3 is characterized. Also, P3×3，R3×1Is equivalent to Q, t in the formula (3)effThe influence of three major types of errors on the measurement of the magnetometer 4 is characterized.
During correction, the magnetometer array rotates around the center position of the correction system, and the tensor invariant I1Is a constant other than 0.
I1＝f(Bxx,Byx,Bzx,Bxy,Byy,Bzy)＝const (9)
Substituting equations (6), (7), and (8) into equation (9) can yield:
I1＝f(Q3×3,E3×1,P3×3,R3×1)＝const (10)
the above formula contains 24 correction coefficients and an unknown constant, and 25 unknown parameters are introduced into the tensor invariant I1The left side in equation (10) is a binary non-linear function of the unknown coefficients, so that the objective function is established by considering the determination of the unknown parameters by using a non-linear optimization method Levenberg-Marquardt (LM):
i represents a sampling point, each sampling point can establish an equation, 25 unknown parameters are required to be solved, and therefore, measurement values of a plurality of sampling points are required. In the process of rotating around the center of the correction system, n (n >25) sampling points are used in total, n equations can be established, and 25 unknown parameters are determined by using an LM algorithm, wherein the unknown parameters comprise 24 correction coefficients to be solved.
Specifically, the correction method of the present invention further includes the steps of:
firstly, constructing a vector magnetometer array, and installing the vector magnetometer array on a nonmagnetic rotating platform to ensure that the central position of a correction system is fixed;
and secondly, the correction system rotates around the central position at will, and data are collected to obtain n (n >25) sampling points.
In a specific embodiment, the output result of the magnetometer array is a gradient field in three directions, and the magnetometer array can be a triangular array, a quadrilateral array, a tetrahedral array, an octahedral array, a cube, a pentagonal frustum, a hexagonal frustum, an irregular array and the like besides a cross-shaped array.
The magnetometer may specifically be a giant magneto-impedance sensor, a tunneling magneto-impedance sensor, a hall sensor, a fluxgate magnetometer, a superconducting quantum interference magnetometer, or the like.
The algorithm for determining the 25 unknown parameters is as follows: Levenberg-Marquardt algorithm, gaussian-newton method, Tikhonov regularization method, confidence domain method, steepest descent method, bi-conjugate gradient method, newton-conjugate gradient method, truncated conjugate gradient method, gradient operator method, genetic algorithm, simulated annealing, or least squares method.
The simulation experiment is as follows:
as shown in FIG. 2, the calibration system comprises four vector magnetometers forming a cross magnetometer array, the base line length is 0.5m, and the installation position is shown in FIG. 2. Fig. 3 and 4 show simulation experiment results, which are designed as follows: the simulation produced a geomagnetic field with a total field of 55000nT, a declination of 60 degrees and a declination of 5 degrees, while the magnetometer array was placed at a magnetic moment of (6, 10, 12) Am2In the non-uniform field environment generated by the magnetic dipole, the system respectively rotates for a circle around an x axis, a y axis and a z axis to obtain 360 sampling points. The correction coefficient of the magnetometer is determined by using the correction method provided by the invention, and the correction effect of the correction method is analyzed. Tensor invariant I corrected by using traditional uniform field correction method1Still a variable amount, the method has failed. The system RMS error before correction was 149393.88 and after correction was 0.04269 using the non-uniform field correction method. Experimental results show that the correction method is good in correction effect and small in calculation amount.
Up to this point, the present embodiment has been described in detail with reference to the accompanying drawings. From the above description, the person skilled in the art will have a clear understanding of the method of correction of a magnetometer in an inhomogeneous field according to the invention.
It should be understood that the above calibration method can also be used in a uniform field environment, and the calibration process for the magnetometer in the uniform field is not described herein again.
It is to be noted that, in the attached drawings or in the description, the implementation modes not shown or described are all the modes known by the ordinary skilled person in the field of technology, and are not described in detail. Further, the above definitions of the various elements and methods are not limited to the various specific structures, shapes or arrangements of parts mentioned in the examples, which may be easily modified or substituted by those of ordinary skill in the art.
It is also noted that the illustrations herein may provide examples of parameters that include particular values, but that these parameters need not be exactly equal to the corresponding values, but may be approximated to the corresponding values within acceptable error tolerances or design constraints. Directional phrases used in the embodiments, such as "upper", "lower", "front", "rear", "left", "right", etc., refer only to the direction of the attached drawings and are not intended to limit the scope of the present invention. In addition, unless steps are specifically described or must occur in sequence, the order of the steps is not limited to that listed above and may be changed or rearranged as desired by the desired design. The embodiments described above may be mixed and matched with each other or with other embodiments based on design and reliability considerations, i.e., technical features in different embodiments may be freely combined to form further embodiments.
In summary, the present invention provides a magnetometer calibration method, where a conventional calibration method is suitable for an ideal uniform field environment, and has a high requirement on a system working environment, and the calibration method provided by the present invention can be applied not only to calibration in a non-uniform field, but also in a uniform field environment, and is simple in calibration operation, small in computation amount, and good in calibration effect, and is a universal method.
The algorithms and displays presented herein are not inherently related to any particular computer, virtual machine, or other apparatus. Various general purpose systems may also be used with the teachings herein. The required structure for constructing such a system will be apparent from the description above. Moreover, the present invention is not directed to any particular programming language. It is appreciated that a variety of programming languages may be used to implement the teachings of the present invention as described herein, and any descriptions of specific languages are provided above to disclose the best mode of the invention.
Furthermore, the use of ordinal numbers such as "first," "second," "third," etc., in the specification and claims to modify a corresponding element is not intended to imply any ordinal numbers for the element, nor the order in which an element is sequenced or methods of manufacture, but are used to distinguish one element having a certain name from another element having a same name.
It should be noted that throughout the drawings, like elements are represented by like or similar reference numerals. In the following description, some specific embodiments are for illustrative purposes only and should not be construed as limiting the present invention in any way, but merely as exemplifications of embodiments of the invention. Conventional structures or constructions will be omitted when they may obscure the understanding of the present invention. It should be noted that the shapes and sizes of the respective components in the drawings do not reflect actual sizes and proportions, but merely illustrate the contents of the embodiments of the present invention.
The above-mentioned embodiments are intended to illustrate the objects, technical solutions and advantages of the present invention in further detail, and it should be understood that the above-mentioned embodiments are only exemplary embodiments of the present invention, and are not intended to limit the present invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (11)
1. A method of calibrating a magnetometer, comprising the steps of:
step one, error modeling is carried out on a magnetometer array;
step two, calculating invariants in the magnetic field;
thirdly, searching a correlation optimization algorithm to determine a correction coefficient of the magnetometer array by using invariant in the magnetic field;
wherein, in the third step, the tensor invariant I is used1Determining correction coefficients of the magnetometer array, and replacing differentiation with difference to obtain each element of the magnetic gradient tensor matrix:
Bzx＝Bxz
Bzy＝Byz
Bzz＝-Bxx-Byy，
and I1＝f(Bxx，Byx，Bzx，Bxy，Byy，Bzy) Substituting each element of the magnetic gradient tensor matrix into the I ═ const1In the formula (2), it can be obtained:
I1＝f(Q3×3，E3×1，P3×3，R3×1)＝const。
2. the correction method according to claim 1, further comprising the steps of:
firstly, constructing a vector magnetometer array, and installing the vector magnetometer array on a nonmagnetic rotating platform to ensure that the central position of a correction system is fixed;
and secondly, the correction system rotates around the central position at will, and data are collected to obtain n sampling points, wherein n is more than or equal to 25.
3. The calibration method of claim 2, wherein, in step one, the errors involved in error modeling the magnetometer array comprise: single magnetometer error, soft iron error and hard error caused by magnetometer support structure, and mismatching error between magnetometers.
4. The correction method according to claim 3,
for a single magnetometer error, the output of the magnetometer is:
Bout1＝MkMoHe+e+n＝MFHe+e+n，
wherein HeRepresenting a true magnetic field vector; b isout1Representing a magnetometer measuring a magnetic field vector; mkIs a third-order diagonal matrix which represents the error of the three-axis scale factor; moIs a three-order upper triangular matrix which represents the three-axis non-orthogonal error; mF＝MKMOCharacterizing the integrated three-axis scale factor error and non-orthogonal error; e, representing zero offset factor error; n is magnetometer observation noise;
for soft iron errors and hard errors caused by the magnetometer support structure, the output of the magnetometer is:
Bout2＝MsMkMo(He-h)+e+n＝MHe+b+n，
wherein M is MsMkMoRepresenting integrated soft errors, three-axis scale factor errors and non-orthogonal errors; b is-MsMkMoh + e, representing the integrated hard iron error and zero offset factor error; soft iron error and hard error, using a coefficient matrix MsAnd an offset vector h;
for the mismatch error between magnetometers, which can be represented by euler rotation matrices,
Bnew＝REuler(MHe+b+n)＝QHe+teff+REulern，
wherein R isEulerThe mismatch error between the magnetometers is characterized for the Euler rotation matrix, Q ═ REulerM, characterization of integrated magnetometer mismatch error and soft body error, three-axis scale factor error and non-orthogonal error, teff＝REulerAnd b, characterizing the mismatch error of the integrated magnetometer, the hard iron error and the zero bias factor error.
5. The correction method according to claim 4, wherein in step two, a single vector magnetometer measures the three components of the magnetic field vector, and a magnetometer array measures a magnetic gradient tensor matrix G using differences instead of differentials, the magnetic gradient tensor matrix G corresponding to the three tensor invariants.
6. The correction method of claim 5, wherein G is a second order tensor calculated as:
I0＝Bxx+Byy+Bzz＝0
7. The correction method according to claim 6, wherein in step three, the correction coefficients are determined using a nonlinear optimization method Levenberg-Marquardt, establishing an objective function:
i represents a sampling point, each sampling point can establish an equation, 25 unknown parameters are required to be solved, and therefore measurement values of a plurality of sampling points are required; during the rotation process around the center of the correction system, n sampling points are used in total, n equations can be established, and 25 unknown parameters are determined, wherein the 25 unknown parameters comprise 24 correction coefficients to be solved.
8. The calibration method of claim 1, wherein the magnetometer is a giant magneto-impedance sensor, a tunneling magneto-impedance sensor, a hall sensor, a flux gate magnetometer, or a superconducting quantum interference magnetometer.
9. The calibration method of claim 7, wherein the algorithm used to determine the 25 unknown parameters is: Levenberg-Marquardt algorithm, gaussian-newton method, Tikhonov regularization method, confidence domain method, steepest descent method, bi-conjugate gradient method, newton-conjugate gradient method, truncated conjugate gradient method, gradient operator method, genetic algorithm, simulated annealing, or least squares method.
10. The calibration method according to claim 6, wherein the output result of the magnetometer array is a gradient field of three directions, and the magnetometer array structure is one of a cross, a planar quadrilateral, an equilateral triangle, a regular tetrahedron, a cube, a pentagonal terrace and a hexagonal terrace.
11. The correction method of claim 6, the invariant of the tensor in step three is I1，I2Any of the above.
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| CN109061770B (en) * | 2018-10-16 | 2019-10-25 | 吉林大学 | A kind of differential type rotates full tensor instrument bearing calibration and device |
| CN111504318B (en) * | 2020-04-02 | 2022-02-01 | 天津大学 | Ocean navigation auxiliary method based on multi-magnetic dipole inversion |
| CN112363099B (en) * | 2020-10-30 | 2023-05-09 | 天津大学 | TMR current sensor temperature drift and geomagnetic field correction device and method |
| CN112362048A (en) * | 2020-11-12 | 2021-02-12 | 中国电子科技集团公司第三研究所 | Practical magnetic gradient tensor high-precision single-point positioning method |
| CN112964278B (en) * | 2021-03-25 | 2022-04-22 | 北京三快在线科技有限公司 | Method, device, electronic equipment and storage medium for determining calibration parameters of magnetometer |
| CN113176529B (en) * | 2021-03-31 | 2023-10-24 | 西南民族大学 | Magnetic gradiometer correction method, magnetic gradiometer correction device and storage medium |
| CN113720904B (en) * | 2021-09-08 | 2024-05-10 | 中国人民解放军国防科技大学 | Hall magnetic gradient tensor structure design method and Hall magnetic gradient tensor structure |
| WO2023092392A1 (en) * | 2021-11-25 | 2023-06-01 | 上海健康医学院 | Magnetometer sensor experimental positioning device and method |
| CN114660511B (en) * | 2021-11-30 | 2024-05-31 | 哈尔滨工业大学 | Calibration method of magnetic sensor array |
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