CN105466458A - Direct error correction method for regular-hexahedron magnetic gradient tensor system - Google Patents

Abstract

The invention belongs to the technical field of magnetic measurement technologies, and particularly relates to a direct error correction method for a regular-hexahedron magnetic gradient tensor system. According to the technical scheme, the method includes the following steps that firstly, the regular-hexahedron magnetic gradient tensor system is placed in a uniform magnetic field and is rotated, and output values of all flux-gate magnetometers are recorded; secondly, one magnetometer in the system is selected as a reference magnetometer, and single magnetometer system error correction parameters of the reference magnetometer are worked out through a linearized correction method; thirdly, according to the relation between the output values of the rest of the magnetometers in the system and the output value of the reference magnetometer, the output values of the rest of the magnetometers are converted to the output value of the reference magnetometer, and then correction is carried out through the single magnetometer error coefficient of the reference magnetometer; fourthly, error correction can be carried out on the regular-hexahedron magnetic gradient tensor system through the obtained error correction parameters. By means of the method, direct error correction can be carried out on the regular-hexahedron magnetic gradient tensor system, the correction process is simple, the number of the correction parameters is reduced, and the correction efficiency is improved.

Description

The direct bearing calibration of regular hexahedron magnetic gradient tensor systematic error

Technical field

The present invention relates to the regular hexahedron magnetic gradient tensor system be made up of fluxgate sensor, particularly a kind of direct bearing calibration of systematic error of regular hexahedron magnetic gradient tensor system.

Background technology

Magnetic gradient tensor system is a kind of important magnetic target detection system.Magnetic gradient tensor system is made up of three or multiple flux-gate magnetometer usually, difference is asked to obtain the Grad of target by the measured value of magnetometer, because the gradient of terrestrial magnetic field is less than 0.02nT/m usually, therefore magnetic gradient tensor system effectively can overcome the interference of terrestrial magnetic field.There are non-orthogonal errors, three axle sensitivity variations, zero drift error etc. in single fluxgate sensor, exist between magnetometer and install error in pointing, these errors can affect the measurement of magnetic gradient tensor, will cause the increase of target location error.

For the systematic error problem of magnetic gradient tensor system, current Chinese scholars has carried out large quantifier elimination.The Liu Limin of Jilin University utilizes nine of magnetic gradient tensor component corresponding relation algorithm for designs to correct cross measurement system error, but the method hypothesis sensor z-axis do not exist alignment error (Liu Limin. the structural design of fluxgate tensor, error analysis and Underwater Target Detection [D]. Changchun: Jilin University, 2012).The Chen Jin of the National University of Defense technology flies first to utilize least square method to correct single magnetometer, then utilize the method that solves Nonlinear System of Equations to the installation error in pointing between magnetometer correct (Chen Jinfei. the magnetic anomaly object localization method based on gradient tensor studies [D]. Changsha: the National University of Defense Technology, 2012).First the Zhang Guang of Ordnance Engineering College utilizes linear error model to correct single magnetometer error, then the installation error in pointing of linear model to cross measuring system is utilized to correct (Zhang Guang, Zhang Yingtang, Yin Gang, Deng. based on magnetic tensor system compensation method [J] of linear error model. Jilin University's journal (engineering version), 2013,43 (10): 2683-2690).The Yin Gang of Ordnance Engineering College obtains the linear model of single magnetometer error correction by two nonlinear transformations, then (YinG is corrected to the installation error in pointing of cross measuring system, ZhangYT, FanHBetal..Linearcalibrationmethodofmagneticgradienttens orsystem [J] .Measurment, 2014,18 (8): 8-18).The Y.H.Pei of Singapore DSO International Laboratory proposes the error compensating method of positive tetrahedron magnetic gradient tensor system, specific practice is set to by a magnetometer with reference to magnetometer, single magnetometer is carried out to remaining three magnetometers and Pointing Calibration is installed, three magnetometers after correcting finally are adopted to carry out the calculating (Y.H.PEI of magnetic gradient tensor, H.G.YEO.UXOSurveyusingvectormagneticgradiometeronautonom ousunderwatervehicle [C] .MTS/IEEEOceans2009, Biloxi, 2009:1-8).The Yu Zhentao of naval aviation engineering college adds the constraint of magnetic gradient tensor itself for positive tetrahedron measuring system, compensation method (the Yu Zhentao of systematic error is proposed, Lv Junwei, Guo Ning, Deng. the error compensation [J] of tetrahedron magnetic gradient tensor system. optical precision engineering, 2014,22 (10): 2683-2690).

The bearing calibration of the magnetic gradient tensor systematic error of current employing is: be positioned in the environment of uniform magnetic field by magnetic gradient tensor system, the measured value of different attitude is obtained by rotary magnetic gradient tensor system, then single magnetometer error correction parameters of each fluxgate sensor is obtained by measured value, after obtaining single magnetometer error correction parameters, first error correction is carried out to single magnetometer, then utilize the value after correcting to calculate the installation error in pointing between fluxgate sensor, obtain error in pointing parameter is installed.

There is the problems such as correction coefficient is more, trimming process is complicated in the bearing calibration of the magnetic gradient tensor system of current employing.For regular hexahedron magnetic gradient tensor system, system is made up of 8 flux-gate magnetometer magnetometers, the parameter corrected is needed to have 135 (8 single magnetometer error parameter 8 × 9, the installation error in pointing parameter 7 × 9 of 7 magnetometers) in systematic error.

Summary of the invention

For the bearing calibration Problems existing of the magnetic gradient tensor systematic error adopted at present, technical matters to be solved by this invention is to provide a kind of direct bearing calibration of systematic error of regular hexahedron magnetic gradient tensor system, first direct bearing calibration in the present invention sets one with reference to magnetometer, by rotating the single magnetometer error correction parameters obtained with reference to magnetometer in uniform magnetic field, then by the relation between the real output value that remains magnetometer in computing reference magnetometer and system, convert the output valve of residue magnetometer to output valve with reference to magnetometer, the single magnetometer error parameter with reference to magnetometer is utilized to carry out error correction, realize the residue installation error in pointing of magnetometer and the correction of single magnetometer error, thus complete the correction of regular hexahedron magnetic gradient tensor system.Method of the present invention can reduce the correction parameter of the bearing calibration adopted at present, improves and corrects efficiency, improves the precision corrected.

The present invention is achieved by the following technical solutions:

Adopt rotation in uniform magnetic field to ask for error parameter, because the mould of magnetic field value true in uniform magnetic field is constant, single magnetometer error mathematic model therefore can be utilized to ask for error parameter.As follows according to single magnetometer error formula:

Wherein, B ^mfor the measured value of magnetometer, B ^rfor the actual value in magnetic field, k _x, k _y, k _zfor the sensitivity coefficient of axle measured by magnetometer three, (O _x, O _y, O _z) ^tfor the zero drift error of magnetometer, θ, ψ are the non-orthogonal errors angle of magnetometer three axles.

According to (1) formula, abbreviation can obtain the relation between real magnetic field value and measured value:

Order wherein E is 3 × 3 unit matrixs, then $C^{\′}=\left(\begin{array}{ccc}{c}_{11}^{\′}& c_{12}^{\′}& c_{13}^{\′}\\ 0& c_{22}^{\′}& c_{11}^{\′}\\ 0& 0& c_{33}^{\′}\end{array}\right)$ In nonzero element be all in a small amount.

Then (2) formula can be write as:

B ^r＝(E+C′)(B ^m-O)(3)

＝B ^m+C′B ^m-(E+C′)O

Make O '=(E+C ') O, then above formula can be written as:

B ^r＝B ^m+C′B ^m-O′(4)

To the above formula left and right sides squared and, the Final finishing casting out second order a small amount of obtains:

$\begin{array}{c}\frac{1}{2}\left(\left|\right|B^r|{|}^2-B^m|{|}^2\right)=c_{11}^{\′}{\left(B_x^m\right)}^2+c_{22}^{\′}{\left(B_y^m\right)}^2+c_{33}^{\′}{\left(B_z^m\right)}^2\\ +c_{12}^{\′}{B}_x^m{B}_y^m+c_{13}^{\′}{B}_x^m{B}_z^m+c_{23}^{\′}{B}_y^m{B}_z^m\\ -O_x^{\′}{B}_x^m-O_y^{\′}{B}_y^m-O_z^{\′}{B}_z^m\end{array}---\left(5\right)$

Above formula is form linearly, the multi-pose measured value of magnetometer can be utilized to ask for generalized inverse form and ask for single magnetometer error correction parameters.

The present invention sets No. 1 magnetometer as reference magnetometer, if the measured value of magnetometer is B ^m, the amount after single magnetometer systematic features is B ', and the measured value after all error term corrections is B ^r, have B for No. 1 magnetometer ₁'=B ₁ ^r, then single magnetometer error formula of No. 1 reference magnetometer is as follows:

$\left(\begin{array}{c}{B}_{1x}^r\\ B_{1y}^r\\ B_{1z}^r\end{array}\right)=\left(\begin{array}{ccc}{a}_{11}^1& a_{12}^1& a_{13}^1\\ 0& a_{22}^1& a_{23}^1\\ 0& 0& a_{33}^1\end{array}\right)\left(\begin{array}{c}{B}_{1x}^m-O_{1x}\\ B_{1y}^m-O_{1y}\\ B_{1z}^m-O_{1z}\end{array}\right)---\left(7\right)$

Be abbreviated as 2 ~ No. 8 magnetometers are had simultaneously:

$B_i^{\′}=A_i(B_i^m-O_i)---\left(8\right)$

With No. 1 magnetometer for correcting the installation error in pointing of 2 ~ No. 8 magnetometers with reference to magnetometer, then the amount of four magnetometers after single magnetometer Systematic Error Correction has following relational expression:

$\left(\begin{array}{c}{B}_{1x}^r\\ B_{1y}^r\\ B_{1z}^r\end{array}\right)=\left(\begin{array}{c}{B}_{ix}^r\\ B_{iy}^r\\ B_{iz}^r\end{array}\right)=\left(\begin{array}{ccc}{r}_{11}^i& r_{12}^i& r_{13}^i\\ r_{21}^i& r_{22}^i& r_{23}^i\\ r_{31}^i& r_{32}^i& r_{33}^i\end{array}\right)\left(\begin{array}{c}{B}_{ix}^{\′}\\ B_{iy}^{\′}\\ B_{iz}^{\′}\end{array}\right)---\left(9\right)$

Can be obtained fom the above equation, the installation error in pointing parameter of i magnetometer has 9 parameters.(9) formula can be abbreviated as:

$B_1^r=B_i^r=R_i{B}_i^{\′}=R_i{A}_i(B_i^m-O_i)---\left(10\right)$

Bring (7), (8) formula into (10) Shi Ke get:

$B_1^r=A_1(B_1^m-O_1)=R_i{B}_i^{\′}=R_i{A}_i(B_i^m-O_i)---\left(11\right)$

Above formula abbreviation is obtained:

$\begin{array}{c}{B}_1^m=A_1^{-1}{R}_i{A}_i\left(R_i^m-O_i\right)+O_1\\ =A_1^{-1}{R}_i{A}_i{B}_i^m+O_1-A_1^{-1}{R}_i{A}_i{O}_i\\ =X_i{B}_i^m+C_i\end{array}---\left(12\right)$

X in formula _ibe 3 × 3 matrixes, C _ibe 3 × 1 matrixes, then comprise altogether 12 unknown numbers in this equation.Then according to (12) formula, rotate in uniform magnetic field by regular hexahedron magnetic gradient tensor system and obtain different measured values to ask for parameter.

The direct bearing calibration of systematic error provided by the present invention, is not limited to and carries out Systematic Error Correction to regular hexahedron magnetic gradient tensor, also may be used for other the magnetic gradient tensor system be made up of flux-gate magnetometer.

Adopt the useful effect that the present invention obtains: apply bearing calibration of the present invention, the direct correction of the systematic error to regular hexahedron magnetic gradient tensor system can be realized, in the present invention, direct bearing calibration needs correction parameter 93 (with reference to magnetometer list magnetometer error parameter 9, conversion coefficient 7 × 12 between residue magnetometer and reference magnetometer), relative to original universal method for correcting, correction parameter 42 can be reduced, direct bearing calibration correction parameter in the present invention reduces, correcting process is simple, corrects efficiency and improves.

Accompanying drawing explanation

Fig. 1 is schematic flow sheet of the present invention.

Fig. 2 is regular hexahedron magnetic gradient tensor system construction drawing.

Fig. 3 is the direct calibration result figure of systematic error of the present invention.

Embodiment

Be described further the specific embodiment of the present invention below in conjunction with accompanying drawing, in order to better understand technical scheme of the present invention, the existing specifically correction example that its principle and computing formula combined describes in detail as follows:

First regular hexahedron magnetic gradient tensor system is positioned over three axles without on magnetic rotation platform, rotary system in uniform magnetic field, record the output valve of each fluxgate sensor, because the mould of magnetic field value true in uniform magnetic field is constant, single magnetometer error mathematic model therefore can be utilized to ask for error parameter.The present invention chooses No. 1 magnetometer for reference magnetometer, and regular hexahedron magnetic gradient tensor system construction drawing as shown in Figure 2.As follows according to single magnetometer error formula:

Wherein, B ^mfor the measured value of magnetometer, B ^rfor the actual value in magnetic field, k _x, k _y, k _zfor the sensitivity coefficient of axle measured by magnetometer three, (O _x, O _y, O _z) ^tfor the zero drift error of magnetometer, θ, ψ are the non-orthogonal errors angle of magnetometer three axles.

According to (13) formula, abbreviation can obtain the relation between real magnetic field value and measured value:

Order wherein E is 3 × 3 unit matrixs, then $C^{\′}=\left(\begin{array}{ccc}{c}_{11}^{\′}& c_{12}^{\′}& c_{13}^{\′}\\ 0& c_{22}^{\′}& c_{23}^{\′}\\ 0& 0& c_{33}^{\′}\end{array}\right)$ In nonzero element be all in a small amount.Then (14) formula can be write as:

B ^r＝(E+C′)(B ^m-O)(15)

＝B ^m+C′B ^m-(E+C′)O

Make O '=(E+C ') O, then above formula can be written as:

B ^r＝B ^m+C′B ^m-O′(16)

To the above formula left and right sides squared and, the Final finishing casting out second order a small amount of obtains:

$\begin{array}{c}\frac{1}{2}\left(\left|\right|B^r|{|}^2-|\left|B^m\right|{|}^2\right)=c_{11}^{\′}{\left(B_x^m\right)}^2+c_{22}^{\′}{\left(B_y^m\right)}^2+c_{33}^{\′}{\left(B_z^m\right)}^2\\ +c_{12}^{\′}{B}_x^m{B}_y^m+c_{13}^{\′}{B}_x^m{B}_z^m+c_{23}^{\′}{B}_y^m{B}_z^m\\ -O_x^{\′}{B}_x^m-O_y^{\′}{B}_y^m-O_z^{\′}{B}_z^m\end{array}---\left(17\right)$

Above formula is form linearly, the multi-pose measured value of magnetometer can be utilized to ask for generalized inverse form and ask for error correction parameters.The expression formula of error parameter as shown in the formula:

Ask for the installation error in pointing of residue magnetometer and single magnetometer error coefficient below, the present invention converts the output valve of residue magnetometer to output valve with reference to magnetometer, then utilizes the single magnetometer error coefficient with reference to magnetometer to correct.If the measured value of magnetometer is B ^m, the amount after single magnetometer systematic features is B ', and the measuring amount after all error term corrections is B ^r, have B for No. 1 magnetometer ₁'=B ₁ ^r, then the single magnetometer error formula with reference to magnetometer is as follows:

$\left(\begin{array}{c}{B}_{1x}^r\\ B_{1y}^r\\ B_{1z}^r\end{array}\right)=\left(\begin{array}{ccc}{a}_{11}^1& a_{12}^1& a_{13}^1\\ 0& a_{22}^1& a_{23}^1\\ 0& 0& a_{33}^1\end{array}\right)\left(\begin{array}{c}{B}_{1x}^m-O_{1x}\\ B_{1y}^m-O_{1y}\\ B_{1z}^m-O_{1z}\end{array}\right)---\left(19\right)$

Be abbreviated as 2 ~ No. 8 magnetometers are had simultaneously:

$B_i^{\′}=A_i(B_i^m-O_i)---\left(20\right)$

With No. 1 magnetometer for correcting the alignment error of 2 ~ No. 8 magnetometers with reference to magnetometer, then the amount of four magnetometers after single magnetometer Systematic Error Correction has following relational expression:

$\left(\begin{array}{c}{B}_{1x}^r\\ B_{1y}^r\\ B_{1z}^r\end{array}\right)=\left(\begin{array}{c}{B}_{ix}^r\\ B_{iy}^r\\ B_{iz}^r\end{array}\right)=\left(\begin{array}{ccc}{r}_{11}^i& r_{12}^i& r_{13}^i\\ r_{21}^i& r_{22}^i& r_{23}^i\\ r_{31}^i& r_{32}^i& r_{33}^i\end{array}\right)\left(\begin{array}{c}{B}_{ix}^{\′}\\ B_{iy}^{\′}\\ B_{iz}^{\′}\end{array}\right)---\left(21\right)$

Above formula is the installation error in pointing relation between residue magnetometer and reference magnetometer, can be obtained by formula (21), and the installation error in pointing of residue magnetometer has 9 parameters.(21) formula is write a Chinese character in simplified form as follows:

$B_1^r=B_i^r=R_i{B}_i^{\′}=R_i{A}_i(B_i^m-O_i)---\left(22\right)$

Bring (19), (20) formula into (22) Shi Ke get:

$B_1^r=A_1(B_1^m-O_1)=R_i{B}_i^{\′}=R_i{A}_i(B_i^m-O_i)---\left(23\right)$

Above formula abbreviation is obtained:

$\begin{array}{c}{R}_1^m=A_1^{-1}{R}_i{A}_i\left(B_i^m-O_i\right)+O_1\\ =A_1^{-1}{R}_i{A}_i{B}_i^m+O_1-A_1^{-1}{R}_i{A}_i{O}_i\\ =X_i{B}_i^m+C_i\end{array}---\left(24\right)$

X in formula _ibe 3 × 3 matrixes, C _ibe 3 × 1 matrixes, then comprise altogether 12 unknown numbers in this equation.(24) formula rotates by regular hexahedron magnetic gradient tensor system and obtains different measured values to ask for parameter in uniform magnetic field.

Corresponding relation can be there is with reference between the output valve of magnetometer and the output valve of residue magnetometer by formula (24), the output valve of residue magnetometer can be converted to the output valve with reference to magnetometer, then utilize the single magnetometer error parameter with reference to magnetometer to correct, list the error correction formula of each magnetometer in regular hexahedron magnetic gradient tensor system below.For reference magnetometer:

For remaining magnetometer:

Single magnetometer error that direct bearing calibration of the present invention can realize remaining magnetometer directly corrects with a step of installing error in pointing, method simple practical.

Utilize the calibration result of Simulation experiments validate direct bearing calibration of the present invention below.Emulation experiment adopts the magnetic gradient tensor around regular hexahedron magnetic gradient tensor systematic survey magnetic target, comparative analysis measured value and the relation between corrected value and theoretical value, suppose that magnetic target can regard a magnetic dipole as, the magnetic moment m=(-400 of target, 600,200) Am ²the coordinate system set up as shown in Figure 2, true origin is positioned at the central point of regular hexahedron magnetic gradient tensor, parallax range is taken as 0.5m, suppose that magnetic target moves along the intersection of y=0m plane and z=15m plane, analyze the change of the magnetic gradient tensor F norm of systematic survey when the x component variation of magnetic target, measurement result as shown in Figure 3.

Definition error statistics formula is as follows:

In formula || G _theoretical|| _ffor the F norm of magnetic gradient tensor theories value, || G _{actual measurement}|| _fwith || G _correct|| _fbe respectively the F norm of the magnetic gradient tensor after actual measurement and error correction.

Calculate according to error statistics formula (27), the method can compensate the systematic error of in magnetic gradient Tensor measuring value 99.86%.

Claims (6)

1. a direct bearing calibration for regular hexahedron magnetic gradient tensor system, is characterized in that, comprise the following steps:

Step S1, regular hexahedron magnetic gradient tensor system is positioned over three axles without on magnetic rotation platform, and rotary system in uniform magnetic field, records the output valve of each fluxgate sensor;

Step S2, in selecting system, certain flux-gate magnetometer is as with reference to magnetometer, utilizes linearization rectify methods to obtain single magnetometer Systematic Error Correction parameter of reference magnetometer;

Step S3, according to the corresponding relation between flux-gate magnetometer remaining in system and the output valve of reference magnetometer, first the output valve of residue magnetometer is changed into reference to magnetometer output valve, then utilize the single magnetometer error calibration method with reference to magnetometer, thus realize the residue alignment error of magnetometer and the correction of single magnetometer error;

Step S4, utilizes the corresponding relation between reference magnetometer error correction parameters and remanence open gate magnetometer and the output valve of reference magnetometer obtained can realize the error correction of regular hexahedron magnetic gradient tensor system.

2. the direct bearing calibration of regular hexahedron magnetic gradient tensor system as claimed in claim 1, it is characterized in that, in described step S1, three axles are without magnetic rotation platform, comprise horizontal azimuth adjustment, roll angle regulates, the angle of pitch regulates three parts, be positioned in uniform magnetic field, the motion in three directions can be realized.

3. the direct bearing calibration of regular hexahedron magnetic gradient tensor system as claimed in claim 1, is characterized in that, the single magnetometer Systematic Error Correction parameter equation with reference to magnetometer in described step S2 is as follows:

Wherein, B ^mfor the measured value of magnetometer, B ^rfor the actual value in magnetic field, k _x, k _y, k _zfor the sensitivity coefficient of axle measured by magnetometer three, (O _x, O _y, O _z) ^tfor the zero drift error of magnetometer, θ, ψ are the non-orthogonal errors angle of magnetometer three axles, then for the magnetometer being numbered i in system, its single magnetometer error correction formula can be expressed as following formula:

In formula, O _ifor the zero drift error of i magnetometer, A _ifor comprising the parameter matrix at sensitivity coefficient and non-orthogonal errors angle.

4. the direct bearing calibration of regular hexahedron magnetic gradient tensor system as claimed in claim 1, is characterized in that, in described step S3 remaining flux-gate magnetometer and with reference to magnetometer output valve between corresponding relation as follows:

In formula, B _ifor the measured value of i magnetometer, R _ierror matrix is not aligned, X for i magnetometer and with reference to the installation between magnetometer _ibe 3 × 3 matrixes, C _ibe 3 × 1 matrixes, then comprise altogether 12 unknown numbers in this equation.

5. the direct bearing calibration of regular hexahedron magnetic gradient tensor system as claimed in claim 1, it is characterized in that, in described step S4, the error correction of regular hexahedron magnetic gradient tensor system is as follows, for reference magnetometer:

For remaining magnetometer:

。

6. the direct bearing calibration of regular hexahedron magnetic gradient tensor system as claimed in claim 1, it is characterized in that, the magnetometer in described step S1 and step S4 in regular hexahedron magnetic gradient tensor system is flux-gate magnetometer.