CN114280523A - Correction alignment method of flux gate magnetometer array - Google Patents
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Abstract
The invention discloses a correction alignment method of a fluxgate magnetometer array, which aligns a plurality of fluxgate magnetometers by using a genetic algorithm based on a measurement coordinate system of one of the fluxgate magnetometers, defines an average difference modulus as a fitness function of the genetic algorithm in an alignment process, and provides a correction alignment method which does not need to measure a rotation angle and does not need a positive angle of a platform mechanical coordinate system. The method effectively solves the problem that the prior method needs a three-axis rotating non-magnetic turntable for auxiliary measurement, simplifies the parameter solving process of correction and alignment of the fluxgate magnetometer array, and has practical significance.
Description
Technical Field
The invention belongs to the technical field of magnetic measurement and the field of flux gate magnetometer calibration, and particularly relates to a correction alignment method of a flux gate magnetometer array.
Background
The measurement of the magnetic gradient tensor is seriously influenced by the output error of a single fluxgate magnetometer and the installation error between the fluxgate magnetometers in the magnetic gradient tensor measurement system. The error of the single fluxgate magnetometer comprises calibration factors of three axes, non-orthogonal error and hard magnetic interference. When a plurality of fluxgate magnetometers are assembled into a magnetometer array, misalignment errors may exist between each magnetometer. It is often necessary to calibrate each magnetometer individually and then align the different magnetometers of the overall system.
The correction of a single fluxgate magnetometer mainly includes direct correction and indirect correction (Liqing bamboo, Lishining, Zhang Yingtang, etc.. magnetic gradient tensor system development and its error correction study status [ J ]. proceedings of the institute of Engineers engineering, 2017, 031(006): 72-81.). Direct correction is to model the error parameters through ideal and actual measurement data, directly calculate specific error parameters by using relevant mathematical tools, and correct the output of the magnetometer. The indirect correction does not consider the specific error parameters of the magnetometer, and the output is ideally corrected by using methods such as a neural network and the like. Thereby indirectly finding the replacement correction parameters. The correction of a single fluxgate magnetometer belongs to a direct correction method, and the error parameters of the fluxgate magnetometer are directly calculated by using ellipsoid fitting and a genetic algorithm, so that the problem of larger calculation amount during indirect correction by using a neural network and the like is solved.
The cross fluxgate magnetometer array based on ellipsoid fitting is researched, and the Lizhu cyan researches the application of ellipsoid fitting in the correction and alignment of the cross fluxgate sensor array (Lizhu, Lishining, Zhang Yingtang, etc.. magnetic gradient tensor system integrated correction based on ellipsoid fitting [ J ] China inertial technical report, 2018,026(002):187 plus 195.). Constructing a linear equation set of the system error of the single-flux-gate magnetometer by using two nonlinear variable conversions, performing least square estimation on error parameters, and correcting actual outputs of the sensors into respective ideal orthogonal outputs; and constructing a linear equation set of the non-alignment error between the ideal orthogonal axes of each sensor by using the rotation matrix, solving a least square solution, and correcting the output of each sensor to the orthogonal coordinate system of the reference platform frame. The three-axis nonmagnetic turntable is required for auxiliary measurement of the rotation angle in the alignment correction process, and the orthogonality of a platform frame coordinate system is required to be high when the coordinate of the platform frame is aligned.
In summary, the calibration and alignment method of the fluxgate magnetometer array based on the ellipsoid fitting is practical, but it requires a three-axis non-magnetic turntable and an accurate measurement of the rotation angle. In addition, the fluxgate magnetometer may still have a deviation after its final alignment due to the possible non-orthogonal angle of the orthogonal coordinate system of the reference platform frame.
Disclosure of Invention
The invention aims to provide a correction alignment method of a fluxgate magnetometer array without measuring a rotation angle and requiring orthogonality of a platform mechanical coordinate system, wherein a measurement coordinate system of one fluxgate magnetometer is taken as a reference, a genetic algorithm is adopted to align a plurality of fluxgate magnetometers, and an average differential mode is defined as a fitness function in the genetic algorithm in an alignment process.
The technical scheme for realizing the purpose of the invention is as follows: a correction alignment method of a fluxgate magnetometer array comprises the following steps:
step 1, firstly, selecting a space area with stable magnetic field intensity and gradient smaller than a set threshold value, and recording the magnetic field intensity value Gm；
Step 2, the fluxgate sensor array rotates around the center of the array at the center of the selected space area;
step 3, respectively recording the magnetic field component measurement values of the fluxgate magnetometer array in the rotation process as Bjix、Bjiy、BjizJ represents the jth fluxgate magnetometer, j is 0, 1, 2, 3 … P-1; i represents the ith data point collected, i is 1, 2, 3 … N;
wherein P is the number of the flux gate magnetometers, and N is the number of data points;
step 4, fitting the data acquired in the rotation motion to an ellipsoid surface for a single fluxgate magnetometer to obtain the hard magnetic interference hjAnd a scale factor kj；
Step 5, obtaining a model parameter k according to an ellipsoid fitting algorithmj、hjIn root mean square error
Computing a non-orthogonal matrix R of a fluxgate magnetometer for a genetic algorithm of a fitness functionjObtaining a corrected output of each fluxgate magnetometer:
Bjis the magnetic field three-component value of the jth fluxgate magnetometer;
and 6, randomly selecting one fluxgate magnetometer as a reference, marking the fluxgate magnetometer as the 0 th fluxgate magnetometer, and averaging the differential modulus value according to the corrected output of the fluxgate magnetometer
Solving the rotational alignment matrix M of the remaining P-1 fluxgate magnetometers for the fitness function genetic algorithm0jJ is 1, 2, 3 … P-1; and finally obtaining the corrected and aligned output of each fluxgate magnetometer:
wherein M is0jRepresenting the rotation matrix between the jth fluxgate magnetometer and the 0 th fluxgate magnetometer,
is the corrected aligned output of the fluxgate magnetometer.
Compared with the prior art, the invention has the beneficial effects that: the correction and alignment of the fluxgate magnetometer array do not need auxiliary measurement of a triaxial rotation non-magnetic turntable, the solution of the model parameters is completed by combining ellipsoid fitting and a genetic algorithm, and a root mean square error value and an average difference mode value are respectively selected as fitness function values of single fluxgate correction and alignment among different fluxgates when the genetic algorithm is used for solving the parameters. The method effectively solves the problem that the prior method needs a three-axis rotating non-magnetic turntable for auxiliary measurement, simplifies the parameter solving process of correction and alignment of the fluxgate magnetometer array, and has practical significance.
Drawings
FIG. 1 is a schematic diagram of a non-quadrature error model of a single fluxgate magnetometer.
FIG. 2 is a schematic view of a non-alignment error model of a fluxgate magnetometer array.
FIG. 3 is a schematic view of an in-line fluxgate magnetometer array.
FIG. 4 is a schematic diagram of the calibration alignment effect of a simulated in-line fluxgate magnetometer array.
Detailed Description
A fluxgate magnetometer array correction alignment method based on ellipsoid fitting and genetic algorithm comprises the following steps:
step 1, selecting a space area with stable magnetic field intensity and gradient smaller than a set threshold value, and recording the magnetic field intensity value Gm. Assume its vector value S0，S0＝[Sx Sy Sz]T。
The stable magnetic field strength means that the fluctuation of the measured value of the magnetic field strength in the center of the space region is less than 1nT, and the set threshold value is 1 nT/m; the magnetic field strength value GmRefers to the time average of the measurements at the center of a spatial region.
Step 2, the fluxgate sensor array rotates around the center of the array at the center of the selected space area;
the fluxgate sensor array comprises a linear fluxgate sensor array, a cross fluxgate sensor array and a regular rectangular pyramid fluxgate sensor array;
the rotation motion is space rotation, the rotation angle is larger than or equal to 360 degrees, and the rotation track can form a spherical surface.
And 3, respectively recording the measured values of the fluxgate magnetometer array in the rotating process as Bjix、Bjiy、BjizJ represents the jth fluxgate magnetometer, j is 0, 1, 2, 3 … P-1; i represents the ith data point collected, i is 1, 2, 3 … N.
Wherein P is the number of the flux gate magnetometers, and N is the number of data points;
step 4, setting an ideal orthogonal measurement coordinate system as OXXYZ, and an actual measurement coordinate system as OX ' Y ' Z ', as shown in FIG. 1, wherein OZ and O ' Z ' are coincident, YOZ and Y ' O ' Z ' are coplanar, an included angle between OY and OY ' is alpha, an included angle between OX ' and an XOZ plane is beta, and an included angle between a projection of OX ' on the XOZ plane and OX is gamma; k is a radical ofx、ky、kzIs the three-axis calibration coefficient, hx、hy、hzIs a hard magnetic disturbance.
Error model for the jth fluxgate magnetometer:
since the values of α, β, γ are small, the model can be approximated as:
Bj＝kj*Rj*S0+hj (3)
kjscale factor matrix, R, representing the jth fluxgate magnetometerjA non-orthogonal matrix representing the jth fluxgate magnetometer.
And 5, ideally outputting data of the fluxgate magnetometer in the rotating motion process on a spherical surface with a sphere center at an origin and a radius of a magnetic field value, namely:
however, due to the error of the fluxgate magnetometer, the output data is distorted from a spherical surface with a radius of a magnetic field value to an ellipsoidal surface with a spherical center deviated from the origin:
wherein x0、y0、z0Denotes the center of the ellipsoid, D, E, F denotes the three half-axis lengths of the ellipsoid;
the value of the deviation of the center of the sphere from the origin represents the value of the hard magnetic interference, and the ratio of the three semi-axial lengths of the ellipsoid to the geomagnetic field represents the scale factor.
Namely:
fitting the data obtained in the rotation motion to an ellipsoid for a fluxgate magnetometer to obtain the hard magnetic interference hjAnd a scale factor kj. And the data acquired in the rotating motion is a magnetic field vector measurement value of the corresponding fluxgate magnetometer in the rotating process.
Step 6, for the flux gate magnetometer data obtained in the rotary motion, the h solved in the step 5j、kjSubstituting into formula 3, calculating the values of non-orthogonal angles alpha, beta and gamma by using genetic algorithm, namely Rj. The root mean square error is used as the fitness function value in the genetic algorithm.
Root mean square error
And 7, correcting the single fluxgate magnetometer to ensure that the three axes are vertical to each other, but the measurement coordinate systems of each fluxgate magnetometer are not parallel. One fluxgate magnetometer is arbitrarily selected as a reference, and is marked as the 0 th fluxgate magnetometer. Then a, b, c are rotational euler angles between the fluxgate magnetometer 1 and the reference fluxgate magnetometer 0 as shown in fig. 2. Alignment between different fluxgate magnetometers is then performed. Rotating the matrix:
due to c1、c2、c3The values are small, and the above formula is simply written as:
fluxgate magnetometer 1 to reference fluxgate magnetometer 0 alignment required rotation matrix M01
Namely: b is0＝M01B1(10)
Step 8, after error parameters of each fluxgate magnetometer are obtained in the steps 5 and 6, correcting the output of a single fluxgate magnetometer; corrected flux gate magnetometer output
Step 9, defining an average differential mode:
and solving the values of the non-orthogonal angles a, b and c by utilizing a genetic algorithm for the data of the fluxgate magnetometer acquired in the rotary motion. I.e. the matrix M0jJ is 1, 2, 3 … P-1; the average difference mode is adopted as a fitness function value in the genetic algorithm.
wherein M is0jRepresenting the rotation matrix between the jth fluxgate magnetometer and the 0 th fluxgate magnetometer,
is the corrected aligned output of the fluxgate magnetometer.
The invention is further described below with reference to the accompanying drawings and examples.
Examples
Selecting a space region and measuring the central magnetic field intensity of the space region by using an optical pump magnetometer, wherein the gradient is required to be less than 1nT/m, and the fluctuation of the measured value of the magnetic field intensity is required to be less than 1 nT. Record the average value of the measurement as Gm. Assume its vector value S0，S0＝[Sx Sy Sz]T。
The fluxgate magnetometer array performs a rotational movement around the centre of the array in the selected area. And the rotation angle is not less than 360 degrees, so that the rotation track can form a spherical surface.
The measured values of the fluxgate magnetometer array in the rotating process are respectively recorded as Bjix、Bjiy、BjizJ denotes the jth fluxgate magnetometer, j is 0, 1, 2, 3 … P-1. i represents the ith data point collected, i is 1, 2, 3 … N.
Obtaining a model parameter k according to an ellipsoid fitting algorithmj、hjCalculating the model parameter R of the genetic algorithm by taking the root mean square error as the fitness functionj. Obtaining a corrected output for each fluxgate magnetometer:
arbitrarily selecting one fluxgate magnetometer as a reference, marking the fluxgate magnetometer as the 0 th fluxgate magnetometer, and solving the rotation alignment matrix M of the rest fluxgate magnetometers by using a genetic algorithm taking an average differential mode as a fitness function according to the corrected output of the fluxgate magnetometer0jJ is 1, 2, 3 … P-1. And finally obtaining the corrected and aligned output of each fluxgate magnetometer:
M0jrepresenting a rotation matrix between the jth fluxgate magnetometer and the 0 th fluxgate magnetometer;
is the corrected aligned output of the fluxgate magnetometer.
The correction alignment does not need a three-axis nonmagnetic turntable to assist in measuring the rotation angle, and a measurement coordinate system of a corrected fluxgate magnetometer is arbitrarily selected as a reference in the alignment process.
The correction parameters of the single fluxgate magnetometer are solved by sequentially using an ellipsoid fitting algorithm and a genetic algorithm taking a root mean square error value as a fitness function.
The alignment parameters of different fluxgate magnetometers are solved by a genetic algorithm with the mean mode of difference as a fitness function.
The effect of the method is simulated and analyzed through a simulation experiment.
A line array of two fluxgate magnetometers is shown in figure 3.
Error parameters of the fluxgate magnetometers 0 and 1 are set to
Rotation matrix between fluxgate magnetometers 0 and 1
Geomagnetic field Gm＝50000nT。
The simulation result of fig. 4 shows that the correction alignment effect of the method is that the average differential mode between the original data fluxgate magnetometers 0 and 1 is 68nT, which is reduced to 1nT after the correction alignment by the method. Can well meet the requirements of practical application.
Claims (8)
1. A method of correcting alignment of a fluxgate magnetometer array comprising the steps of:
step 1, firstly, selecting a space area with stable magnetic field intensity and gradient smaller than a set threshold value, and recording the magnetic field intensity value Gm；
Step 2, the fluxgate sensor array rotates around the center of the array at the center of the selected space area;
step 3, respectively recording the magnetic field component measurement values of the fluxgate magnetometer array in the rotation process as Bjix、Bjiy、BjizJ represents the jth fluxgate magnetometer, j is 0, 1, 2, 3 … P-1; i represents the ith data point collected, i is 1, 2, 3 … N;
wherein P is the number of the flux gate magnetometers, and N is the number of data points;
step 4, fitting the data acquired in the rotation motion to an ellipsoid surface for a single fluxgate magnetometer to obtain the hard magnetic interference hjAnd a scale factor kj；
Step 5, obtaining a model parameter k according to an ellipsoid fitting algorithmj、hjIn root mean square error
Computing a non-orthogonal matrix R of a fluxgate magnetometer for a genetic algorithm of a fitness functionjObtaining a corrected output of each fluxgate magnetometer:
Bjis the magnetic field three-component value of the jth fluxgate magnetometer;
and 6, randomly selecting one fluxgate magnetometer as a reference, marking the fluxgate magnetometer as the 0 th fluxgate magnetometer, and averaging the differential modulus value according to the corrected output of the fluxgate magnetometer
Solving the rotational alignment matrix M of the remaining P-1 fluxgate magnetometers for the fitness function genetic algorithm0jJ is 1, 2, 3 … P-1; and finally obtaining the corrected and aligned output of each fluxgate magnetometer:
wherein M is0jRepresenting the rotation matrix between the jth fluxgate magnetometer and the 0 th fluxgate magnetometer,
is the corrected aligned output of the fluxgate magnetometer.
2. The method of claim 1, wherein the steady state of magnetic field strength in step 1 is a fluctuation of less than 1nT in the measured value of magnetic field strength at the center of the area of space.
3. The method of claim 1, wherein the set threshold in step 1 is 1 nT/m.
4. The method of claim 1, wherein the field strength value G is determined in step 1mRefers to the time average of the measurements at the center of a spatial region.
5. The method of claim 1, wherein the array of fluxgate sensors comprises an in-line fluxgate sensor array, a cross fluxgate sensor array, a regular rectangular pyramid fluxgate sensor array.
6. The method of claim 1, wherein the rotation in step 2 is a spatial rotation and the rotation angle is greater than or equal to 360 ° so that the rotation trajectory forms a spherical surface.
7. The method of claim 1, wherein the data acquired during the rotational movement in step 4 is a magnetic field vector measurement of the corresponding fluxgate magnetometer during the rotation.
8. A method of aligning a fluxgate magnetometer array according to claim 1 wherein the data acquired in the rotary motion for a single fluxgate magnetometer of step 4 is fitted on an ellipsoid:
wherein x0、y0、z0Denotes the center of the ellipsoid, D, E, F denotes the three half-axis lengths of the ellipsoid;
obtaining parameters:
where h denotes hard magnetic interference and k denotes a scale factor.
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