CN107607999B - A kind of measurement method of pair of ferromagnetic target far field magnetic moment vector - Google Patents
A kind of measurement method of pair of ferromagnetic target far field magnetic moment vector Download PDFInfo
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Abstract
The present invention is to provide the measurement methods of a kind of pair of ferromagnetic target far field magnetic moment vector.With scalar Magnetic Sensor forming array, it is based on far field dipole model of magnetic, devises the measurement method with geomagnetic total field to target magnetic moment vector.Eliminate geomagnetic total field change over time with the non-uniform influence of spatial distribution, propose the criterion function of determining magnetic moment size and Orientation.Based on this criterion function and measured data, target magnetic moment size and Orientation is solved.Measurement method to ferromagnetic target far field magnetic moment proposed by the invention, only needing target once to move near array along known paths can be realized measurement.Measurement method is simple and efficient accurately.
Description
Technical field
The present invention relates to a kind of measurement method in earth's magnetic field, specifically a kind of target magnetic dipole magnetic moment vector
Measurement method.
Background technique
Earth's magnetic field is the important physical amount for reflecting the processes such as Earth evolution, geological structure differentiation.Dipole model of magnetic is very
It is multi-field to be applied, because the magnetic phenomenon of nature can be equivalent to the superposition in several magnetic dipole magnetic fields, specific
In the case of also can be equivalent to a magnetic dipole.Earth's magnetic field can be such that ferromagnetic material magnetizes, due to the presence of magnetic target,
Its induced magnetic field generated will lead to the variation of spatially Distribution of Magnetic Field, to generate magnetic anomaly within this space.Utilize magnetic anomaly
Often detection far field objects, can be approximately the magnetic field of a magnetic dipole by magnetic field of the goal.Therefore measurement target magnetic dipole magnetic
Moment vector is the premise for realizing target magnetic detection and target demagnetization, is all had great importance to magnetic detection and anti-magnetic detection.
Earth's magnetic field is formed by stacking by the magnetic field components of different changing rules.Change with time feature in consideration earth's magnetic field,
Faster earth's magnetic field, which will be changed over time, becomes the variation magnetic field of the earth, changes over time earth's magnetic field that is relatively slow or being basically unchanged
Stabilizing magnetic field as the earth.Therefore try every possible means to reduce or eliminate the influence of this variation magnetic field in magnetic survey.
Earth's magnetic field is vector field, and the magnetic survey Technical comparing based on vector sensor is mature, also popular, is had very
More advantages.Main vector Magnetic Sensor to be used includes fluxgate magnetic sensor and MEMS Magnetic Sensor in magnetic survey at present
Deng but three axis need critical alignment when vector sensor is installed, and when use also needs real-time measurement sensor posture information, sense
Device temperature drift is big.Because that its measurement accuracy will be made to decline when these complicated use conditions are not able to satisfy.And resultant field Magnetic Sensor
High resolution, detection range is remote, and temperature drift problem is not present, stringent posture information is not needed, without three axis Correction Problemss.Therefore benefit
Have the advantages that precision is high, simple and reliable with geomagnetic total field sensor measurement, this measures target magnetic moment also with geomagnetic total field
The advantages of.But target magnetic moment is vector, in addition to size, there are also directions, in addition ambient field, there is multiple unknown numbers, from algorithm
Upper theory is solved, it is necessary to which constructing multidimensional independent equation group could calculate based on geomagnetic total field, it is therefore desirable to construct geomagnetic total field measurement
Array is just able to achieve.
Summary of the invention
The purpose of the present invention is to provide a kind of measurement result is accurate, be simple and efficient to ferromagnetic target far field magnetic moment vector
Measurement method.
The object of the present invention is achieved like this:
Step 1: building array of magnetic sensors obtains geomagnetic field measuring value
Array of magnetic sensors is made of square, the distance of four scalar sensors to array center four scalar sensors
It is all D, D is known as array aperture, and target is moved along known path, and the motion profile of target and array are in same level
Interior, the position scalar sensors i is (xi,yi,zi), i=1,2,3,4, target position is (x, y, z), then scalar senses
The measured value of device i are as follows:
Wherein, T0Earth's magnetic field value, μ when for no target0It is space permeability, PmIt is the magnetic moment vector of magnetic dipole target, Pm
Size be | Pm|, PmDirection inclination angle and drift angle be respectively α, β, earth magnetism field direction inclination angle and drift angle are respectively θ,
Step 2: the influence of variation magnetic field is eliminated
In array of magnetic sensors, it is located at (xi,yi,zi) scalar sensors i in t moment measured value Ti(t,xi,yi,
zi), it is located at (xj,yj,zj) scalar sensors j t moment measured value be Tj(t,xj,yj,zj)；In t0Moment scalar sensors i
Measured value with j is respectively Ti(t0,xi,yi,zi),Tj(t0,xj,yj,zj)
Enable Δ Tij=Ti(t,xi,yi,zi)-Tj(t,xj,yj,zj)-[Ti(t0,xi,yi,zi)-Tj(t0,xj,yj,zj)] (2)
Wushu (1) substitutes into formula (2) and obtains Δ TijTheoretical value Δ Tij|Theory, Δ TijExperiment value Δ Tij|ExperimentRoot
According to (2) formula by scalar sensors i, j in t, t0Moment measured value obtains, Δ TijIt is array of magnetic sensors measured value in time and sky
Between on double gradient,
ΔTij|Theory=Δ Tij|Experiment(3)；
Step 3: separation target magnetic moment size and Orientation
It is defined as follows function:
a|TheoryAnd b |TheoryEliminated in expression formula | Pm|, a |TheoryAnd b |TheoryIt is only α, the function of β, and a
|ExperimentAnd b |ExperimentIt is known quantity as experimental measurements, first solves magnetic moment direction, then solves magnetic moment size；
Step 4: the solution of target magnetic moment direction
The motion path of known target, each measurement point coordinate is (x on pathn,yn,zn), (n=0,1,2......m),
It enables
L (α, β) indicates a in all n measurement points, the sum of absolute error between the theory and measured data of b function
Inverse, L (α, β) numerical value is bigger, and error is smaller；Suitable α, β are found, so that L (α, β) reaches maximum value, determines α, β；L(α,
It is exactly β) the criterion function for determining magnetic moment direction, thus solves the direction of target magnetic moment；
Step 5: the solution of target magnetic moment size
By fixed α, β value is updated to formula (2), definition
Ls(|Pm|) indicate absolute value error in all measurement points between each sensor measured data and theoretical value it
The inverse of sum, Ls (| Pm|) numerical value is bigger, error is smaller, and it is suitable to find | Pm|, so that Ls (| Pm|) reach maximum value, determine |
Pm|, Ls (| Pm|) it is exactly the criterion function for determining magnetic moment size.
The present invention provides the measurement methods of a kind of pair of ferromagnetic target far field magnetic moment vector.Constituted ground with scalar Magnetic Sensor
The total field measurement array of magnetic is devised and is calculated based on geomagnetic total field the measurement of target magnetic moment vector using far field dipole model of magnetic
Method.Since earth's magnetic field changes over time, there is also abnormal points in spatial distribution, pass through the design double gradient in earth's magnetic field
Algorithm eliminates the influence of influence and free air anomaly field that earth's magnetic field changes over time.Propose determining magnetic moment size and Orientation
Criterion function, and the solution to magnetic target magnetic moment direction and size is realized based on this criterion function.
The main feature of measurement method to ferromagnetic target far field magnetic moment vector of the invention is embodied in:
1, array of magnetic sensors as shown in Figure 1 is constructed, which constitutes square-shaped planar by four scalar Magnetic Sensors
Array, the motion profile with ferromagnetic target is in same level.Target is moved along known trajectory, and ferromagnetism target moves to
When each known location point, scalar Magnetic Sensor records the geomagnetic total field intensity value at each sensor position in real time.The survey is described
The principle expression formula of magnitude is shown in formula (1), after the influence for excluding various change magnetic field, is solved for formula (1) algorithm for design,
It can determine the size and Orientation of target magnetic moment vector.
2, it proposes the double gradient function of geomagnetic total field intensity measurements over time and space, sees formula (2), introduce two
Weight gradient function can eliminate influence of the earth's magnetic field at any time with spatial variations to measurement result.Ferromagnetic target is along known trajectory
Movement, array measures the geomagnetic total field intensity value of each sensor position, not total for earth magnetism when solving target magnetic moment vector
Field intensity function, that is, formula (1) direct solution, but solved for double gradient function, that is, formula (3), in such solving result
Earth's magnetic field is eliminated to change over time and the non-uniform influence of spatial distribution.
3, propose the criterion function of determining magnetic moment direction and size, using criterion function obtain target magnetic moment direction and
Size.The criterion function of magnetic moment direction is proposed, sees formula (4), target magnetic moment is obtained by the extreme-value problem of solution formula (4)
Direction.(direct solution formula (3) difficulty is too big, and the pole of solution formula (4) is converted into for the problem of this solution formula (3)
Value problem.) on the basis of obtaining target magnetic moment direction, the criterion function for proposing target magnetic moment size is shown in formula (5), passes through
The extreme-value problem of solution formula (5) obtains target magnetic moment size.The algorithm makes all measurement points on track be involved in calculating, phase
When in motion process of target complete repeatedly measurement, ensure that measurement accuracy, simplify solution difficulty, ensure that measurement
Real-time.
The method of measurement target magnetic moment vector provided by the invention, target only need to once be moved along known paths
Realize the multiple measurement of target magnetic moment, thus measurement result is accurate, method is simple and efficient, hidden for the detection of target magnetic method and target magnetic
Body provides Technical Reference.
Detailed description of the invention
Fig. 1 oriented array and target motion mode embodiment schematic diagram.
Fig. 2 target magnetic moment vector calculates process flow diagram flow chart.
The measured data of experiment and theory curve of Fig. 3 function a and position y.
The measured data of experiment and theory curve of Fig. 4 function b and position y.
The diagram of block of Fig. 5 L (α, β) and α, β.
Fig. 6 Ls (| Pm|) with | Pm| curve graph.
Specific embodiment
It illustrates below for a more detailed description to the present invention.
Step 1: building array obtains geomagnetic field measuring value
Array of magnetic sensors as shown in Figure 1 is constructed, array constitutes square by four scalar sensors, and sensor arrives
The distance of array center is all D, referred to as array aperture.Target is moved along known path, and the motion profile and battle array of target
It is listed in same level.The position sensor i is (xi,yi,zi) (i=1,2,3,4), target position be (x, y,
Z), then the measured value of sensor i are as follows:
Wherein, T0Earth's magnetic field value, μ when for no target0It is space permeability, PmIt is the magnetic moment vector of magnetic dipole target,
Middle PmSize be | Pm|, PmDirection inclination angle and drift angle be respectively α, β, earth magnetism field direction inclination angle and drift angle are respectively θ,
Step 2: the influence of variation magnetic field is eliminated
In sensor array, it is located at (xi,yi,zi) sensor i in t moment measured value Ti(t,xi,yi,zi), it is located at
(xj,yj,zj) sensor j t moment measured value be Tj(t,xj,yj,zj)；In t0The measured value of moment sensor i and j are distinguished
For Ti(t0,xi,yi,zi),Tj(t0,xj,yj,zj)
Enable Δ Tij=Ti(t,xi,yi,zi)-Tj(t,xj,yj,zj)-[Ti(t0,xi,yi,zi)-Tj(t0,xj,yj,zj)] (2)
Wushu (1), which substitutes into formula (2), can be obtained Δ TijTheoretical value Δ Tij|Theory, Δ TijExperiment value Δ Tij|Experiment
It can be by sensor i, j in t, t according to (2) formula0Moment measured value obtains.ΔTijIt is two of array measurement over time and space
Weight gradient.
ΔTij|Theory=Δ Tij|Experiment (3)
In the equation group of formula (3), the earth's magnetic field amount of changing with time and the non-uniform influence of spatial distribution are eliminated.Therefore
Target magnetic moment vector P is calculated using formula (3)m, changed over time with earth's magnetic field it is unrelated, it is also whether uniform with earth's magnetic field spatial distribution
It is unrelated.
Step 3: separation target magnetic moment size and Orientation
In order to solution formula (3) obtains [| Pm|, α, β], it is defined as follows function:
a|TheoryAnd b |TheoryEliminated in expression formula | Pm|, a |TheoryAnd b |TheoryIt is only α, the function of β.And a
|ExperimentAnd b |ExperimentIt is known quantity as experimental measurements.Thus can first solve magnetic moment direction, after solve magnetic moment again
Size.
Step 4: the solution of target magnetic moment direction
The motion path of known target, each measurement point coordinate is (x on pathn,yn,zn), (n=0,1,2......m).
It enables
L (α, β) indicates a in all n measurement points, the sum of absolute error between the theory and measured data of b function
Inverse, L (α, β) numerical value is bigger, and error is smaller.Suitable α, β are found, so that L (α, β) reaches maximum value, so that it may determine α,
β.L (α, β) is exactly the criterion function for determining magnetic moment direction.Thus the direction of target magnetic moment can be solved.
Step 5: the solution of target magnetic moment size
By fixed α, β value is updated to formula (2), definition
Ls(|Pm|) indicate absolute value error in all measurement points between each sensor measured data and theoretical value it
The inverse of sum, it is clear that Ls (| Pm|) numerical value is bigger, error is smaller.Therefore it is suitable to find | Pm|, so that Ls (| Pm|) reach maximum
Value, so that it may determine | Pm|。Ls(|Pm|) it is exactly the criterion function for determining magnetic moment size.
So far, magnetic moment vector PmDirection be determined by the maximum problem for solving (4) formula, and the size of magnetic moment | Pm|
Maximum problem by solving (5) formula provides solution.
The practicability of mentioned method is verified using experiment.Such as Fig. 1, array has 4 resultant field Magnetic Sensors, aperture D
=4m, the parallel y-axis reverse driving of measured target automobile, away from y-axis 32.02m, from y=32.8m linear uniform motion to y=-41m.
Scalar Magnetic Sensor is laid on the tripod of aluminum, and sensor is away from ground 1.43m.Local geomagnetic inclination θ=63.3 °, partially
AngleIt is transformed into measurement coordinate system, θ=63.3 °, drift anglet0Choose target be in y=32.8m when
It carves.The size of target magnetic moment is calculated by algorithm and experimental data | Pm|=476Am2, direction inclination angle size α=0.85rad, side
To drift angle β=4.21rad.
Fig. 2 is target magnetic moment vector measuring and calculating process flow diagram flow chart.
In Fig. 3, horizontal axis indicates the position of y, the value of longitudinal axis representative function a.Curve indicates the theoretical value a of a in figure |TheoryWith
The relation curve of y, the soft dot in figure represent the experiment value a of a |ExperimentWith the relationship of y, a |ExperimentWith a |TheoryCompared with
Good coincide.
In Fig. 4, horizontal axis indicates the position of y, the value of longitudinal axis representative function b.Curve indicates the theoretical value b of b in figure |TheoryWith
The relation curve of y, the soft dot in figure represent the experiment value b of b |ExperimentWith the relationship of y, b |TheoryWith b |ExperimentCompared with
Good coincide.
Fig. 5 indicates the diagram of block of L (α, β) and α, β,In the range of β ∈ (0,2 π), L (α, β)
There is maximum value L (α, β)MAX.Formula (4) is calculated, as α=0.8500, β=4.2122, L (α, β)MAX=1.81.
Fig. 6 indicates target magnetic moment size | Pm| and function Ls (| Pm|) relation curve, as | Pm|=476Am2When, Ls (| Pm
|)=4.4685, reach maximum.
Claims (1)
1. the measurement method of a kind of pair of ferromagnetic target far field magnetic moment vector, it is characterized in that including the following steps:
Step 1: building array of magnetic sensors obtains geomagnetic field measuring value
Array of magnetic sensors is made of square four scalar sensors, and the distance of four scalar sensors to array center is all
D, D are known as array aperture, and target is moved along known path, and the motion profile of target and array be in same level,
The position scalar sensors i is (xi,yi,zi), i=1,2,3,4, target position is (x, y, z), then scalar sensors i
Measured value are as follows:
Wherein, T0Earth's magnetic field value, μ when for no target0It is space permeability, PmIt is the magnetic moment vector of magnetic dipole target, PmIt is big
It is small to be | Pm|, PmDirection inclination angle and drift angle be respectively α, β, earth magnetism field direction inclination angle and drift angle are respectively θ,
Step 2: the influence of variation magnetic field is eliminated
In array of magnetic sensors, it is located at (xi,yi,zi) scalar sensors i in t moment measured value Ti(t,xi,yi,zi), it is located at
(xj,yj,zj) scalar sensors j t moment measured value be Tj(t,xj,yj,zj)；In t0The survey of moment scalar sensors i and j
Magnitude is respectively Ti(t0,xi,yi,zi),Tj(t0,xj,yj,zj)
Enable Δ Tij=Ti(t,xi,yi,zi)-Tj(t,xj,yj,zj)-[Ti(t0,xi,yi,zi)-Tj(t0,xj,yj,zj)] (2)
Wushu (1) substitutes into formula (2) and obtains Δ TijTheoretical value Δ Tij|Theory, Δ TijExperiment value Δ Tij|ExperimentAccording to
(2) formula is by scalar sensors i, j in t, t0Moment measured value obtains, Δ TijIt is array of magnetic sensors measured value in time and space
On double gradient,
ΔTij|Theory=Δ Tij|Experiment(3)；
Step 3: separation target magnetic moment size and Orientation
It is defined as follows function:
a|TheoryAnd b |TheoryEliminated in expression formula | Pm|, a |TheoryAnd b |TheoryIt is only α, the function of β, and a
|ExperimentAnd b |ExperimentIt is known quantity as experimental measurements, first solves magnetic moment direction, then solves magnetic moment size；
Step 4: the solution of target magnetic moment direction
The motion path of known target, each measurement point coordinate is (x on pathn,yn,zn), wherein n=0,1,2 ... m,
It enables
A in all n measurement points of L (α, β) expression, the inverse of the sum of absolute error between the theory and measured data of b function,
L (α, β) numerical value is bigger, and error is smaller；Suitable α, β are found, so that L (α, β) reaches maximum value, determines α, β；L (α, β) is exactly
The criterion function for determining magnetic moment direction, thus solves the direction of target magnetic moment；
Step 5: the solution of target magnetic moment size
By fixed α, β value is updated to formula (2), definition
Ls(|Pm|) indicate falling for the sum of absolute value error in all measurement points between each sensor measured data and theoretical value
Number, Ls (| Pm|) numerical value is bigger, error is smaller, and it is suitable to find | Pm|, so that Ls (| Pm|) reach maximum value, determine | Pm|, Ls
(|Pm|) it is exactly the criterion function for determining magnetic moment size.
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