CN106990451A - Earth magnetism vector measurement system error calibration method based on lagrange's method of multipliers - Google Patents
Earth magnetism vector measurement system error calibration method based on lagrange's method of multipliers Download PDFInfo
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Abstract
The invention belongs to magnetic measurement field, and in particular to a kind of earth magnetism vector measurement system error calibrating method based on lagrange's method of multipliers, comprise the following steps：(S1) calibration region is chosen, heart position sets one without magnetic recording level platform in the zone, with proton magnetometer measurement without the earth's magnetic field total amount above magnetic recording level platform；(S2) earth magnetism vector measurement system is encapsulated in one without in the casing of magnetic L faces, casing is placed on no magnetic recording level face；(S3) upset makes each face of casing be placed on as bottom surface on no magnetic recording level platform successively without magnetic L faces casing；When each face is as bottom surface, making L faces casing, angularly difference rotates R posture around the vertical axle without magnetic recording level platform, records the magnetic sensor at each posture moment and the output valve of inertial navigation system；(S4) system of linear equations is set up, using earth's magnetic field total amount as constraints, joint is solved, and obtains composition error model parameter；The earth magnetism vector value under geographic coordinate system and Magnetic Sensor coordinate system after further being calibrated.
Description
Technical field
The invention belongs to magnetic measurement field, and in particular to a kind of earth magnetism vector measurement system based on lagrange's method of multipliers
Error calibrating method, mainly for the interference of magnetic sensor constant error, the soft magnetism of measuring system and Hard Magnetic and three axle magnetic
The non-aligned error of sensitive axes between sensor and inertial navigation system.
Background technology
Earth's magnetic field is a vector field, under geographic coordinate system, and its three components are respectively north component X, east component Y
With vertical component Z, general described ground magnetic vector is exactly to refer to these three components.Therefore in actually measurement, sensed with three axle magnetic
Device measures projection components of the earth's magnetic field in the sensitive direction of principal axis of Magnetic Sensor, is carried by the inertial navigation system with magnetic sensor strapdown
For its Eulerian angles between geographic coordinate system, so that magnetic sensor is exported to the projection be converted under geographic coordinate system,
Just earth magnetism vector measurement can be realized.The measurement error main source of earth magnetism vector measurement system based on the principle has：Three axle magnetic
Sensor constant error, the soft magnetism of measuring system and Hard Magnetic interference and the sensitive axes between magnetic sensor and inertial navigation system
Non-aligned error etc..For this three classes main error, most research is all to set up error model according to the characteristics of respective, is led to
Cross evaluated error model parameter and calibrated for error so as to realize.
For magnetic sensor constant error (zero offset error, scale factor error and three axle non-orthogonal errors),
J.M.G.Merayo (J.M.G.Merayo.Scalar calibration of vector magnetometers,
Meas.Sci.Technol.2000,11(1):Earth's magnetic field modulus value invariance principle 20-32) is based on, sensor three-axis measurement is derived
Linear parameter model between value and magnetic field scalar value, carries out least-squares estimation and obtains sensor error parameter, so that real
Existing error correction.C.C.Foster(C.C.Foster.Extension of a two-step calibration
methodology to include nonorthogonal sensor axes[J].IEEE Transactions on
Aerospace and Electronic Systems,2008,44(3):1070-1078.) passed using ellipse fitting method
Sensor error model parameters are estimated and error correction.
For interference magnetic field, P.Leliak. (P.Leliak.Identification and evaluation of
Magnetic field sources of mag-netic airborne detector equipped aircraft, IRE
TRANSACTIONS ON AEROSPACE AND NAVIGATIONAL ELECTRONICS, 1961,95-105) it is based on
Tolles-Lawson equations, have carried out the research of magnetic air interference compensation.(Zhang Xiaoming, Zhao Yan are based on ellipse restriction for Zhang Xiaoming
Novel carriers magnetic field is demarcated and compensation technique, Chinese journal of scientific instrument, 2009,30 (11):2438~2443.) according to ellipse hypothesis,
Approximately regard magnetic-field measurement track as an ellipse, parameter identification is carried out using least square method.Above two method can only
Magnetic field modulus value error is compensated, magnetic-field component error compensation is cannot be used for.
For the non-aligned error of sensitive axes, using perpendicular type table top and positive six face casing, (such as Pang Hongfeng is used for ground to Pang Hongfeng
The non-aligned error calibration method of magnetic key element measuring system, national inventing patent, the patent No.：201210355541.7), at right angle
Repeatedly upset is without magnetic hexahedron on type table top, using gravitational vectors consistency, sets up Nonlinear System of Equations, solve Magnetic Sensor with
Non-aligned angle between inertance element, so as to obtain the euler rotation matrix between two sensitive axis coordinate systems, is realized non-aligned
Error correction.This method requires that the flatness and perpendicularity of perpendicular type table top are very high, and upset requires table top and case every time
Body closely agrees with.
The studies above is that a certain item error for being directed to earth magnetism vector measurement system is corrected.Individual error separates school
Just, not only program is complicated, and error propagation can reduce correction accuracy.If setting up the composition error mould of earth magnetism vector measurement system
Type, carries out error synthesis correction, not only simple flow, and can improve precision.
And in terms of error synthesis calibration, (a kind of earth magnetism vector measurement errors based on linear model of such as fine jade are comprehensive by Zhang Qi
Close compensation method, national inventing patent, application number：201410477818.2), pilot region is calculated according to global geomagnetic model
Geomagnetic fieldvector value；Earth magnetism vector measurement model is set up with magnetic sensor and inertial navigation system output valve；Solve equation group
Afterwards, it just can obtain the earth's magnetic field value vector after error model parameters and compensation.But sweared by the earth's magnetic field that global geomagnetic model is obtained
Amount also has error, meeting affecting parameters estimated accuracy, so as to reduce the precision that calibrates for error in itself.
In summary, the method for existing individual error separation correction can not contentedly magnetic vector measurement accuracy demand,
And the error synthesis bearing calibration based on global geomagnetic model also has inherent shortcoming, therefore, a kind of ground magnetic vector that is used for of research is surveyed
The composition error calibration method of amount system has certain theory significance and practical value.
The content of the invention
In order to solve the above technical problems, the present invention proposes a kind of earth magnetism vector measurement system based on lagrange's method of multipliers
Error calibration method, comprises the following steps：
(S1) calibration region is chosen, heart position sets one without magnetic recording level platform in the zone, with proton magnetometer measurement without magnetic
Earth's magnetic field total amount above platform, is denoted as：Te；
(S2) earth magnetism vector measurement system is encapsulated in one without in the casing of magnetic L faces, casing is placed in L >=4 and round numbers
On without magnetic recording level face；The earth magnetism vector measurement system includes magnetic sensor and inertial navigation system；The inertial navigation system is by top
Spiral shell instrument and accelerometer composition.
(S3) upset makes each face of casing be placed on as bottom surface on no magnetic recording level platform successively without magnetic L faces casing；When each
When face is as bottom surface, making L faces casing, angularly difference rotates R posture, R >=4, and round numbers, note around the vertical axle without magnetic recording level platform
Record the magnetic sensor output valve at each posture moment and the output valve of inertial navigation system；
(S4) according to the magnetic sensor and inertial navigation system output valve under all postures in step (S3), linear side is set up
Journey group, using earth's magnetic field total amount in step (S1) as constraints, joint is solved, and obtains composition error model parameter；Further
The earth magnetism vector value under geographic coordinate system and Magnetic Sensor coordinate system after being calibrated.
Further, the step (S4) is specially：
(a) set up system of linear equations and be designated as ATAX=λ DX, seek system of linear equations ATAX=λ DX generalized eigenvalue λiAnd spy
Levy vectorial aiObtain (λi,ai), (i=1,2 ..., 15), wherein matrix A is magnetic sensor and inertial navigation system output valve structure
Into the matrix of 3N × 15；N=L × R is flipping gesture number；
(b) generalized eigenvalue λ is choseni(i=1,2 ..., 15) in correspond to minimum positive eigenvalue λkThat group of characteristic vector
ak, orderT represents transposition symbol, then optimal estimation vector is μkak；
(c) following earth magnetism vector composition error model parameter is calculated according to optimal estimation vector respectively：
Its
InProjection vector estimate of the geomagnetic fieldvector under geographic coordinate system is represented,It is integrated interference coefficient,It is comprehensive inclined
Put magnetic field；Representing matrixInverse matrix.The composition error model parameter includes integrated interference coefficient and comprehensive biasing
Magnetic field；
(d) according to the composition error model parameter, calculated according to following formula：
The magnetic field value that magnetic vector measuring system is measured over the ground is carried out under real time calibration, the geographic coordinate system after being calibrated
Earth magnetism vector valueWith the earth magnetism vector value under Magnetic Sensor coordinate systemWherein TinIt is inertial navigation coordinate system to geographical coordinate
The euler rotation matrix of system, is made up of, B inertial navigation system output datat1For the measured value of magnetic sensor,Representing matrix
TinInverse matrix.
Further, the earth's magnetic field in step (S1) the alignment region is uniform and stable, and magnetic field gradient is less than
5nT/m。
Further, the posture number value R=6 or 8.
Further, the L values are 6.
In order to be best understood from technical scheme, now its principle and formula proving are described below in detail：
The present invention proposes a kind of geomagnetic fieldvector measurement system error bearing calibration low for equipment requirements, easy to operate.
Earth magnetism vector measurement system is made up of magnetic sensor and inertial navigation system, and wherein inertial navigation system provides attitude information for system.
Measuring system is placed on one without on magnetic recording level platform, some posture upsets is carried out, obtains multigroup attitude value and three-component magnetic field value, build
Vertical system of linear equations；Using proton magnetometer measurement without the earth's magnetic field total amount above magnetic recording level platform, as constraints, combine and ask
Solution, can not only obtain error model parameters, with can also obtaining the region magnetic vector., can using errors model parameter
To realize the error correction of magnetic vector measuring system over the ground.Detailed process：
(1) an earth's magnetic field stabilization and more uniform calibration region (magnetic field gradient are chosen<5nT/m), in central area
One is set without magnetic recording level platform；
(2) it is denoted as T without the earth's magnetic field total amount above magnetic recording level platform with proton magnetometer measuremente；
(3) magnetic sensor and inertial navigation system that constitute geomagnetic fieldvector measuring system are encapsulated in one without magnetic L faces
In casing, magnetic sensor accurately need not be aligned and demarcate with the sensitive axes of inertial navigation system；
(4) coordinate system 1 is set up：Using measuring system central point as the origin of coordinates, using magnetic sensor sensitive axes as coordinate
The coordinate system that axle is constituted, also referred to as Magnetic Sensor coordinate system；
(5) coordinate system 2 is set up：Using measuring system central point as the origin of coordinates, using inertial navigation system sensitive axes as reference axis structure
Into coordinate system, also referred to as inertial navigation coordinate system；
(6) coordinate system 3 is set up：Using measuring system central point as the origin of coordinates, respectively with geographical north orientation, geographical east orientation and
The coordinate system constituted vertically downward for x, y, z axle, also referred to as geographic coordinate system；
(7) projection vector of the geomagnetic fieldvector under geographic coordinate system is Be=[Bex Bey Bez], it is amount to be solved；
(8) Eulerian angles (non-aligned angle) between Magnetic Sensor coordinate system and inertial navigation coordinate system are α0,β0,γ0, it is size
Unknown constant, then the euler rotation matrix T between two coordinate systemsmiFor：
(9) Eulerian angles between inertial navigation coordinate system and geographic coordinate system are exported by inertial navigation system, its course angle, the angle of pitch,
Roll angle is designated as respectively：α, beta, gamma, then the euler rotation matrix T between two coordinate systemsinFor：
(10) projection vector of the geomagnetic fieldvector under Magnetic Sensor coordinate system is Bep=[Bepx Bepy Bepz]T, then BeWith
BepMeet relational expression (3)：
Bep=TmiTinBe (3)
(11) under Magnetic Sensor coordinate system, magnetic sensor measurement model can be expressed as：
Wherein Bt=[Btx,Bty,Btz]TFor the measured value of magnetic sensor, C is calibration factor inconsistency error and non-
The constant coefficient matrix of quadrature error synthesis, AsFor system soft magnetism coefficient matrix, I3×3For 3 rank unit matrixs, BbOften sweared for Hard Magnetic
Amount, B0To characterize the normal vector that Magnetic Sensor zero is inclined, Bd=CBb+B0=[Bdx,Bdy,Bdz]TFor composition error vector, (this is often arrow
Amount),For magnetic sensor constant error, the soft magnetism of measuring system and hard
Magnetic disturbance synthesizes composition error coefficient matrix, and the matrix is constant coefficient matrix；
(12) can be expressed as by relational expression (3), the measurement model of magnetic sensor：
Bt=AtTmiTinBe+Bd=MTinBe+Bd (5)
Wherein M=AtTmiFor the interference of magnetic sensor constant error, the soft magnetism of measuring system and Hard Magnetic and three axle magnetic
The integrated interference coefficient matrix of the class error estimate formula of non-aligned error of sensitive axes between sensor and inertial navigation system etc. three.
(13) further, obtain the expression formula of ground magnetic vector：
TinBe=M-1(Bt-Bd) (6)
Wherein
After (14) are further arranged, component equation form is obtained：
Measured by N groups, specific measurement process is：This sentences six face casings and illustrated, by six faces of six face casings
No. 1 to No. 6 is respectively labeled as, six face casings are placed on no magnetic recording level platform, first, bottom surface is No. 1 face；By hexahedron around without magnetic
Angularly difference rotates M posture to the vertical axle of plane, records the output valve of magnetic sensor and inertial navigation system；Successively the bottom of according to
Face is 2,3,4,5,6 order, repeats above-mentioned way, and the defeated of N=6 × R groups magnetic sensor and inertial navigation system is always obtained
Go out value, following system of linear equations can be set up：
AX=0 (8)
Wherein
b1=m11Bd1+m12Bd2+m13Bd3
b2=m21Bd1+m22Bd2+m23Bd3
b3=m31Bd1+m32Bd2+m33Bd3
Obviously
(15) undetermined multiplier λ is introduced, then constructing Lagrangian is：
It can be obtained by L (X) extreme value necessary condition：
Wherein ATA and D are known 15 rank square formations, and D is irreversible, therefore Generalized-grads Theory ATAX=λ DX have solution (λi,
ai), (i=1,2 ..., 15), and for any non-zero constant μ, (λi,μai) be still the generalized eigenvalue problem solution.If
MeetThen to haveSet mark j represent to refer in particular to some features for meeting equation requirement to
Amount, the matrix A being made up of experimental dataTA is positive definite matrix, so havingCan
See, meet the eigenvalue λ of equality constraintj＞ 0, nowAnd (λj,μjaj) it is full
Whole extreme values of the Lagrangian of sufficient equality constraint.
(16) due to
Therefore take (λj,μjaj) in minimal eigenvalue corresponding to that group of characteristic vector akIt is multiplied by coefficient μkThe vectorial μ of gainedkakIt is optimal solution, is obtained according to each parameter definition of optimal estimation vector：
WhereinIt is the ground magnetic vector obtained by estimation,It is integrated interference coefficient,It is comprehensive bias magnetic field.On letter
Band wedge angle symbolRepresent the corresponding estimate of the variable；After error parameter is obtained, according to following formula：
Can magnetic vector measuring system is measured over the ground magnetic field carry out real time calibration.Geographic coordinate system and magnetic after being calibrated
Earth magnetism vector value under sensor coordinate systemWherein TinIt is transition matrix of the inertial navigation coordinate system to geographic coordinate system,
It is made up of inertial navigation system data.
The beneficial effect obtained using the present invention：The main output information using inertial navigation system and magnetic sensor, builds
The vertical composition error model for including interference magnetic field, Magnetic Sensor constant error and the non-aligned error of sensitive axes, with earth's magnetic field total amount
As constraints, geomagnetic fieldvector and error model parameters are estimated based on lagrange's method of multipliers, then by having tried to achieve
Error parameter real time correction earth magnetism vector measurement system error.The present invention sets up magnetic-field component mathematical modeling, and magnetic field is introduced again
Modulus value is constrained, and can improve the degree of accuracy of error model parameters estimation and the precision of error correction.The present invention is a kind of to equipment
It is required that the small earth magnetism vector measurement system error calibration method of low, easy to operate, operand.
Brief description of the drawings
Fig. 1 is steps flow chart schematic diagram of the present invention.
Fig. 2 is compensation device arrangement schematic diagram in the present invention；
Embodiment
Below, with reference to the drawings and specific embodiments, the invention will be further described.
The 1st, simulated conditions are set, l-G simulation test is carried out to the present invention.
1) pilot region geomagnetic fieldvector is set as Be=[35200-33155-2000] nT (under geographic coordinate system,
According to global geomagnetic model, projection vector value of this geomagnetic fieldvector under geographic coordinate system can be calculated)；Proton magnetometer
Measurement is T without the earth magnetism total amount above magnetic recording level platforme=48397nT.
2) according to priori, the numerical value (under Magnetic Sensor coordinate system) of the parameter of some in measuring system is preset,
Specially：
3) Eulerian angles between magnetic coordinate system and inertial navigation coordinate system are respectively：[α0 β0 γ0]=[8-5 3] degree.
4) measurement noise for setting Magnetic Sensor is standard deviation as 5nT white Gaussian noise, the measurement noise of inertial navigation system
It is the white Gaussian noise that standard deviation is 0.5 degree.
2nd, as shown in figure 1, for the inventive method workflow diagram, the positive six faces casing of no magnetic is selected in embodiment, according to hair
Bright step, obtains measurement data.
1) positive six face casing is placed on no magnetic recording level face, bottom surface is No. 1 face, as shown in Figure 2；
2) by positive six face casing around the vertical axle without magnetic horizontal plane, angularly difference rotates 4 postures to level, records three axle magnetic
The output valve of sensor and inertial navigation system；
3) successively according to the order that bottom surface is No. 2 to No. 6, upper one is repeated suddenly, obtained measurement data is as shown in table 1.
The measurement data (being used for parameter Estimation) of the inertial navigation system of table 1 and magnetic sensor
3rd, formula (11) equation group is set up, composition error model parameter and ground magnetic vector is solved.
WhereinIt is the inverse matrix estimation of three class composition error coefficient matrixes,It is comprehensive offset vector estimation,It is
Ground magnetic vector estimation.
4th, required composition error model parameter and ground magnetic vector are assessed.
It is to be obtained according to simulation parameter
Integrated interference coefficient inverse matrix and comprehensive bias magnetic field matrix, the ground magnetic vector with reference to setting is visible：
1) estimate of integrated interference coefficient matrix and preset value are basically identical；
2) error between the actual value and estimate of comprehensive bias magnetic field is less than 2nT；
3) the equal error between geomagnetic fieldvector and the actual value and estimate of modulus value is less than 1nT.
5th, the effect that calibrates for error based on required error model parameters is assessed.
Again one group of data of simulation generation are used for Compensation estimating, as shown in table 2.Then formula (11) is utilized, to Magnetic Sensor
Measured value is compensated, and table 3 is earth magnetism vector compensation value and the error of actual value, and each component error average is less than 4nT, is respectively
X-component 1.18nT, Y-component 0.19nT, Z component 3.85nT, total amount 0.83nT；Error to standard deviation is less than 12nT, respectively X points
9.23nT is measured, Y-component 9.25nT, Z component 11.32nT, total amount 8.87nT.
The measurement data (being used for Compensation estimating) of the inertial navigation system of table 2 and magnetic sensor
After table 3 is compensated, the error (nT) of geomagnetic fieldvector and total amount
| X-component | Y-component | Z component | Total amount |
| 7.43 | 13.20 | -1.53 | -3.58 |
| -0.57 | -3.64 | 10.61 | 1.64 |
| -28.33 | 5.10 | 6.29 | -24.35 |
| 15.94 | 2.71 | -0.25 | 9.75 |
| 3.77 | -8.01 | -22.34 | 9.16 |
| -7.43 | 1.50 | 11.20 | -6.89 |
| 3.28 | -13.20 | 8.00 | 11.10 |
| 7.63 | -1.41 | 0.08 | 6.52 |
| -1.69 | 14.18 | -13.02 | -10.41 |
| 8.34 | -11.70 | 0.39 | 14.06 |
| -3.24 | 9.06 | 4.49 | -8.75 |
| -3.89 | -2.89 | 2.72 | -0.96 |
| 1.05 | 14.20 | -13.21 | -8.41 |
| -12.12 | -10.35 | -9.81 | -1.32 |
| -5.62 | 2.92 | -0.39 | -6.07 |
| 2.80 | 11.24 | -12.35 | -5.15 |
| 3.41 | 12.04 | -3.80 | -5.60 |
| -4.56 | 9.52 | -6.94 | -9.55 |
| -12.70 | -11.78 | -27.82 | -0.01 |
| -10.46 | -13.09 | 7.09 | 1.07 |
| -0.68 | -3.93 | -30.36 | 3.46 |
| -5.69 | -2.99 | -3.71 | -1.94 |
| 5.84 | 0.01 | -1.57 | 4.30 |
| 9.27 | -8.06 | 3.78 | 12.11 |
It will be further noted that, the invention is not limited in specific embodiments above, those skilled in the art can be
Any deformation or improvement are made in the range of claim.
Claims (4)
1. a kind of earth magnetism vector measurement system error calibration method based on lagrange's method of multipliers, it is characterised in that including with
Lower step：
(S1) calibration region is chosen, heart position sets one without magnetic recording level platform in the zone, with proton magnetometer measurement without magnetic recording level platform
The earth's magnetic field total amount of top, is denoted as：Te；
(S2) earth magnetism vector measurement system is encapsulated in one without in the casing of magnetic L faces, casing is placed on nothing by L >=4 and round numbers
On magnetic recording level face；The earth magnetism vector measurement system includes magnetic sensor and inertial navigation system；The inertial navigation system is by gyroscope
With accelerometer composition；
(S3) upset makes each face of casing be placed on as bottom surface on no magnetic recording level platform successively without magnetic L faces casing；When each face is made
During for bottom surface, making six face casings, angularly difference rotates R posture, R >=4, and round numbers around the vertical axle without magnetic recording level platform, and record is every
The magnetic sensor output valve at individual posture moment and the output valve of inertial navigation system；
(S4) according to the magnetic sensor and inertial navigation system output valve under all postures in step (S3), linear equation is set up
Group, using earth's magnetic field total amount in step (S1) as constraints, joint is solved, and obtains composition error model parameter；Further
The earth magnetism vector value under geographic coordinate system and Magnetic Sensor coordinate system after to calibration；Concretely comprise the following steps：
(S41) set up system of linear equations and be designated as ATAX=λ DX, seek system of linear equations ATAX=λ DX generalized eigenvalue λiAnd feature
Vectorial aiObtain (λi,ai), (i=1,2 ..., 15), wherein matrix A is magnetic sensor and three axle inertance element output valves
The matrix of the 3N of composition × 15；N=L × R is flipping gesture number；
(S42) generalized eigenvalue λ is choseni(i=1,2 ..., 15) in correspond to minimum positive eigenvalue λkThat group of characteristic vector
ak, orderT represents transposition symbol, then optimal estimation vector is μkak；
(S43) following earth magnetism vector composition error model parameter is calculated according to optimal estimation vector respectively：
WhereinProjection vector estimate of the geomagnetic fieldvector under geographic coordinate system is represented,It is integrated interference coefficient,It is
Comprehensive bias magnetic field；Representing matrixInverse matrix；
(S44) according to the composition error model parameter, calculated according to following formula：
The magnetic field value that magnetic vector measuring system is measured over the ground carries out real time calibration, the earth magnetism under geographic coordinate system after being calibrated
Vector valueWith the earth magnetism vector value under Magnetic Sensor coordinate systemWherein Tin1It is inertial navigation coordinate system to geographic coordinate system
Euler rotation matrix, be made up of inertial navigation system output data, Bt1For the measured value of magnetic sensor,Representing matrix Tin
Inverse matrix.
2. a kind of earth magnetism vector measurement system error calibration method based on lagrange's method of multipliers as claimed in claim 1,
Characterized in that, the earth's magnetic field in step (S1) the alignment region is uniform and stable, and magnetic field gradient is less than 5nT/m.
3. a kind of earth magnetism vector measurement system error calibration method based on lagrange's method of multipliers as claimed in claim 1,
It is characterized in that：The posture number value R=6 or 8.
4. a kind of earth magnetism vector measurement system error calibration method based on lagrange's method of multipliers as claimed in claim 1,
It is characterized in that：The L values are 6.
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