CN110333536A - A kind of linear location algorithm of ranging - Google Patents
A kind of linear location algorithm of ranging Download PDFInfo
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- CN110333536A CN110333536A CN201910660147.6A CN201910660147A CN110333536A CN 110333536 A CN110333536 A CN 110333536A CN 201910660147 A CN201910660147 A CN 201910660147A CN 110333536 A CN110333536 A CN 110333536A
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
- G01V3/00—Electric or magnetic prospecting or detecting; Measuring magnetic field characteristics of the earth, e.g. declination, deviation
- G01V3/08—Electric or magnetic prospecting or detecting; Measuring magnetic field characteristics of the earth, e.g. declination, deviation operating with magnetic or electric fields produced or modified by objects or geological structures or by detecting devices
Abstract
The present invention provides a kind of linear location algorithm of ranging, according to the eight of array three axis magnetometers to the measured value of Magnetic Field of Magnetic Body, calculates the measured value of 5 isolated components of magnetic substance magnetic gradient tensor at tested point；Calculate the measured value of magnetic gradient tensor at tested point；Magnetic gradient Tensor measuring value is divided into three groups, calculates separately the distance between different and magnetic substance；System of linear equations is formed by the distance between tested point and magnetic substance, the position coordinate value of magnetic substance is calculated by system of linear equations.The present invention can calculate random magnetism body in the magnetic gradient tensor of array body-centered and the center of area simultaneously by the single measurement result of array；The present invention is a kind of fast locating algorithm, the position of single non-magnetic dipole magnetic substance can be uniquely finally inversed by, location algorithm speed is fast and does not limit the magnetic field model of this magnetic substance, enhances the anti-interference ability and stability of this single magnetic substance linear orientation algorithm.
Description
Technical field
The invention belongs to magnetic detection and field of locating technology, and in particular to a kind of linear location algorithm of ranging.
Background technique
Different from information sources such as sound field, light field and electromagnetic waves, the detection of passive type magnetic substance and location technology based on magnetic field
Have many advantages, such as good concealment, can continuously detect, is high-efficient, using it is simple and reliable, be swift in response, also not by astronomical, meteorological and
The influence of the hydrology etc.；Its detection and positioning in submarine, submarine mine, submarine communication cable, biochemical nuke rubbish and not quick-fried explosive, body
Noninvasive positioning of interior medical micro device etc. has important application value.
Mcfee et al. is fitted two-dimensional grid magnetic-field measurement data using least square method, estimates magnetic substance parameter, gives
A kind of portable resultant field magnetic spy system (Mcfee J E, Ellingson R, Das Y.A total-field that can be positioned on line
magnetometer system for location and identification of compact ferrous
objects[J].IEEE Transactions on Instrumentation and Measurement,1994,43(4):
613-619).Kasatkin et al. analyzes the Uniqueness of the magnetic dipole positioning of known two o'clock magnetic vector value, shows
Two dimension or three-dimensional magnetic dipole can more accurately be positioned using two three axis magnetometers (Kasatkin S I,
Polyakov O P,Rusakova N E,et al.On uniqueness of solution of a reverse
problem of magnetic location[J].Journal of Magnetism and Magnetic Materials,
2006,305(2):361-364).Callmer et al. uses the cooperation ship of three axis magnetometer and a known dipole model of magnetic
Passive magnetic orientation is only carried out, estimates the track and the position of magnetometer of cooperating ship simultaneously by extended Kalman filter
(Callmer J,Martin S koglund,G Fredrik.Silent Localization of Underwater
Sensors Using Magnetometer[J].EURASIP Journal on Advances in Signal
Processing,2010,2010:709318).Domestic naval engineering university also studied based on movement scalar or vector magnetic strength
The parameter Estimation and magnetic substance localization method of meter.Most of this kind of magnetic substance localization method is by the measurement data of the multiple points in space
Magnetic substance parameter or some preconditions of setting are solved come what is realized by optimization algorithm, and which results in the algorithms of localization method
It is computationally intensive, real-time is poor and can not achieve single measurement positioning.Filtering localization method needs to know the characteristics of motion of magnetic substance,
The inaccurate motion model of magnetic substance will lead to filtering failure, therefore it is applied to cooperate the positioning occasion of magnetic substance more.
Different from resultant field and its gradiometry, magnetic gradient Tensor measuring is a kind of difference that can be conjugated inhibition background magnetic field noise
Point measurement, result influenced by the inclination angle in earth's magnetic field and drift angle it is small, the tensor invariant constituted without specially treated can
Magnetic field sources are described well.Therefore, the localization method based on magnetic gradient tensor arouses great concern.By Eulerian equation
Integrated form, Nara etc. derived magnetic flux density cube face integral magnetic dipole position between linear equation,
And closed solutions (Nara T, Watanabe H, the Ito W.Properties of the linear of position is obtained
equations derived from Euler’s equation and its application to magnetic
dipole localization[J].IEEE Transactions on Magnetics,2012,48(11):4444-4447)。
Wiegert et al. proposes the magnetic substance localization method of tensor contraction amount STAR, and the basis of tensor contraction amount is a contour surface
For invariant (the Wiegert R F.Magnetic STAR technology for real-time of spherical surface
localization and classification of unexploded ordnance and buried mines[C]
.Proceedings of SPIE-The International Society for Optical Engineering,2009)。
For the aspherical error problem of STAR method, it is lost et al. with sun and proposes to reduce positioning by its baseline results of iterative processing and calculate
Systematic error (Sui Y, Li G, Wang S, the Lin J.Asphericity errors correction of of method
magnetic gradient tensor invariants method for magnetic dipole localization
[J].IEEE Transactions on Magnetics,2012,48(12):4701-4706).Lv Junwei et al. proposes one
One-Point Location improved method of the kind based on regular hexahedron magnetic gradient tensor system, the system for eliminating tensor contraction amount STAR method are missed
(the oval error cancelling method of Lv Junwei, Chi Cheng, Yu Zhentao, Bi Bo, Song Qingshan magnetic gradient tensor invariant studies [J] to difference
Acta Physica Sinica, 2015,64 (19): 52-59).The geometrical invariants of magnetic dipole gradient tensor are applied to by engineering university, ground force
Real-time tracking (Gang Y.I.N., Yingtang Z, Zhining L, the Hongbo F and Guoquan of magnetic substance
R.Detection of ferromagnetic target based on mobile magnetic gradient tensor
System [J] .Journal of Magnetism and Magnetic Material, 2016,402 (6): 1-7, Yin Gang,
English hall, Li Zhining, Zhang Guang, the geometrical invariants and its application [J] Chinese Journal of Geophysics of Fan Hongbo magnetic dipole gradient tensor,
2016,59(2):749-756)。
But general magnetic gradient tensor system can only obtain the magnetic gradient tensor of single spatial point through single measurement, use
It is the location algorithm based on single-point magnetic gradient tensor.This location algorithm is not only more sensitive to magnetic noise, but also needs to measure
It is superimposed on the Magnetic Field of Magnetic Body vector in earth's magnetic field, but Magnetic Field of Magnetic Body vector is difficult accurately to isolate from magnetic-field measurement data
Come.Though the magnetic gradient tensor positioning based on space two o'clock does not need measurement Magnetic Field of Magnetic Body vector, magnetic gradient tensor system is
The value of another point is measured by move mode, and there are more Xie Wenti for location algorithm.
The method of three axis magnetometer regular hexahedron array measurement multiple spot magnetic gradient tensor proposed by the present invention can be by array
Single measurement result calculates magnetic gradient tensor of the magnetic substance at array body-centered and the center of area.It is proposed by the present invention to be based on array surface
The linear location algorithm of the ranging of magnetic gradient tensor at the heart can be used for carrying out single measurement positioning to single magnetic substance, magnetic substance
Magnetic field model can be a non-magnetic dipole；It calculates this six center of areas to magnetism by array center of area magnetic gradient tensor value
The distance between body, then the linear side about magnetic substance position coordinates is formed by the difference of two squares of the distance value of three pairs of parallel surface center of areas
Journey group is finally inversed by magnetic substance position coordinate value；This location algorithm need not optimization Nonlinear System of Equations, therefore position fast
Speed.
Summary of the invention
The object of the present invention is to provide a kind of linear location algorithms of ranging, are calculated by the single measurement result of array
Magnetic gradient tensor of the magnetic substance at array body-centered and the center of area.
The object of the present invention is achieved like this:
A kind of linear location algorithm of ranging, concrete implementation step are as follows:
Step 1., to the measured value of Magnetic Field of Magnetic Body, calculates point P according to eight three axis magnetometers of arraynLocate magnetic substance magnetic
The measured value of 5 isolated components of gradient tensor
Wherein Bxx(Pn)、Byy(Pn)、Bxy(Pn)、Byz(Pn)、Bxz(Pn) it is respectively magnetic substance in point Pn(n=0,1 ..., 6)
5 isolated components of the magnetic gradient tensor at place,For angle matrix,For relative measurement value matrix；
Step 2. is by point PnThe measured value for locating 5 isolated components of magnetic substance magnetic gradient tensor calculates point PnLocate magnetic gradient
The measured value of amount
Step 3. is by magnetic gradient Tensor measuring valueWithIt is divided into three
A group, i.e.,WithIt is calculated separately by three groups of magnetic gradient Tensor measuring values
Point P1And P2、P3And P4、P5And P6The distance between magnetic substance；
Step 4. is by point PnThe distance between (n ≠ 0) and magnetic substanceSystem of linear equations is formed,
In formula,WithFor the position coordinates of magnetic substance, the regular hexahedron side length on the direction x, y and z is respectively Lx、
LyAnd Lz, point PnThe distance between (n ≠ 0) and magnetic substance are respectively
Step 5. is calculated the position coordinate value of magnetic substance by system of linear equations
The specific steps of the step 3 are as follows:
Step 3.1. is calculatedEigenvalue λiWith feature vector vi, calculateEigenvalue λjAnd feature vector
vj, i ≠ j；
Step 3.2. calculates cosine value
In formula, λik(k=1,2,3) it indicatesK-th of characteristic value, λjkIt indicatesK-th of characteristic value；
The unit vector of step 3.3. calculating magnetic substance magnetic moment
In formula, cij=(vi22vj23-vi23vj22)/(vi21vj22-vi22vj21), dij=(vi21vj23-vi23vj21)/
(vi21vj22-vi22vj21), vi2kForThe 2nd characteristic value k-th of component, vj2kForThe 2nd characteristic value
K-th of component；
Step 3.4. calculates point PiPosition vector relative to magnetic substanceUnit vector
Step 3.5.WithRespectively position vectorX, y and z-component, calculateWithPoint P is calculated againi
The distance between point Q
In formula, dijx、dijyAnd dijzRespectively PjRelative to PiPosition vectorX, y and z-component.
The array of the step 1 are as follows: on upper layer, mounting plate and lower layer's mounting plate install four three axis magnetometers respectively, and eight
The corresponding sensitive axes of three axis magnetometer are mutually aligned, and constitute regular hexahedron array.
The beneficial effects of the present invention are: compared to the array measurement method of existing magnetic gradient tensor, the present invention is proposed
Three axis magnetometer front volume array measurement multiple spot magnetic gradient tensor method can be counted simultaneously by the single measurement result of array
Magnetic gradient tensor of the calculating random magnetism body at array body-centered and the center of area, and the array measurement method of existing magnetic gradient tensor
Magnetic gradient tensor at computing array center；Compared to the existing location algorithm based on two o'clock magnetic gradient tensor, it is based on battle array
The magnetic substance linear orientation algorithm of magnetic gradient tensor is a kind of fast locating algorithm at the column center of area, can be uniquely finally inversed by single non-
The position of magnetic dipole magnetic substance；It calculates this six center of areas to magnetic substance by array center of area magnetic gradient tensor value
Distance, then the system of linear equations about magnetic substance position coordinates is formed by the difference of two squares of the distance value of three pairs of parallel surface center of areas, instead
Magnetic substance position coordinate value is performed, location algorithm speed is fast and does not limit the magnetic field model of this magnetic substance；By magnetic substance with
The distance between regular hexahedron array center of area value resolves the position coordinates of magnetic substance, enhances this single magnetic substance linear orientation
The anti-interference ability and stability of algorithm.
Detailed description of the invention
Fig. 1 is the structural diagram of the present invention.
Fig. 2 is the linear location algorithm flow chart of ranging based on magnetic gradient tensor at six center of areas.
Fig. 3 is the relative error of magnetic gradient component of tensor at array body-centered and the center of area with three axis magnetometer noise criteria difference
Point P0The change curve at place.
Fig. 4 is the relative error of magnetic gradient component of tensor at array body-centered and the center of area with three axis magnetometer noise criteria difference
Point P1The change curve at place.
Fig. 5 is the relative error of magnetic gradient component of tensor at array body-centered and the center of area with three axis magnetometer noise criteria difference
Point P2The change curve at place.
Fig. 6 is the relative error of magnetic gradient component of tensor at array body-centered and the center of area with three axis magnetometer noise criteria difference
Point P3The change curve at place.
Fig. 7 is the relative error of magnetic gradient component of tensor at array body-centered and the center of area with three axis magnetometer noise criteria difference
Point P4The change curve at place.
Fig. 8 is the relative error of magnetic gradient component of tensor at array body-centered and the center of area with three axis magnetometer noise criteria difference
Point P5The change curve at place.
Fig. 9 is the relative error of magnetic gradient component of tensor at array body-centered and the center of area with three axis magnetometer noise criteria difference
Point P6The change curve at place.
Figure 10 is the absolute error of magnetic substance positioning with the change curve of three axis magnetometer noise criteria difference.
Figure 11 is the absolute error of orientation distance with the change curve of three axis magnetometer noise criteria difference.
Specific embodiment
The present invention will be further described with reference to the accompanying drawing:
Embodiment 1
A kind of ranging linear orientation based on magnetic gradient tensor at the three axis magnetometer regular hexahedron array center of area of the invention
The realization process of algorithm is as described below.
As shown in Figure 1, a kind of three axis magnetometer regular hexahedron array is made of eight three axis magnetometers, on each plane layer
There are four three axis magnetometers for distribution, share two layers.Array is regular hexahedron configuration, i.e. eight three axis magnetometers are located at positive six
On the vertex of face body, the regular hexahedron side length on the direction x, y and z is respectively Lx、LyAnd Lz.Regular hexahedron body-centered point is P0, with P0
Rectangular coordinate system P is established for origin0The spatial position of xyz, Q expression magnetic substance.Face A1B1C1D1、A2B2C2D2、A1D1D2A2、
B1C1C2B2、C1C2D2D1And B1B2A2A1Central point be respectively P1、P2、P3、P4、P5And P6.By eight three axis magnetometers to magnetism
The measured value in body magnetic field can calculate magnetic substance in point PnMagnetic gradient tensor at (n=0,1 ..., 6).
Magnetic Field of Magnetic Body is passive irrotational field, therefore the magnetic gradient tensor matrix of magnetic substance is the symmetrical matrix that mark is 0, i.e. magnetic substance
Magnetic gradient tensor there was only 5 isolated components, B can be selected as respectivelyxx、Byy、Bxy、ByzAnd Bxz。
Respectively point AmX, y of Magnetic Field of Magnetic Body and the measured value of z-component at (m=1,2),Point
It Wei not point BmLocate x, y of Magnetic Field of Magnetic Body and the measured value of z-component,Respectively point CmLocate magnetic
Property x, the y in body magnetic field and the measured value of z-component,Respectively point DmLocate Magnetic Field of Magnetic Body
X, the measured value of y and z-component.In point PnThe measured value of 5 isolated components for locating magnetic gradient tensor is
In formula, symbol T indicates transposition.
In formula
WithRespectively vectorWith the angle of x, y and z axes,WithRespectively
VectorWith the angle of x, y and z axes,WithRespectively vectorWith the angle of x, y and z axes, WithRespectively vectorWith the angle of x, y and z axes.
In formula, With
WithRespectively vectorWith the angle of x, y and z axes,WithRespectively vectorWith x, y and z axes
Angle.
In formula, With
WithRespectively vectorWith the angle of x, y and z axes,WithRespectively vectorWith x, y and z
The angle of axis.
In formula, With
WithRespectively vectorWith the angle of x, y and z axes,WithRespectively vectorWith x, y and z
The angle of axis.
In formula, With
WithRespectively vectorWith the angle of x, y and z axes,WithRespectively vectorWith x, y and z axes
Angle.
In formula, With
WithRespectively vectorWith the angle of x, y and z axes,WithRespectively vectorWith x, y and z
The angle of axis.
In formula, With
WithRespectively vectorWith the angle of x, y and z axes,WithRespectively vectorWith x, y and z axes
Angle.
Magnetic gradient tensor value and based on magnetic at the array center of area at three axis magnetometer regular hexahedron array measurement body-centered and the center of area
Steps are as follows for the linear location algorithm of the ranging of gradient tensor:
Step 1: point P being calculated by formula (16) to the measured value of Magnetic Field of Magnetic Body by eight three axis magnetometers of arraynLocate magnetic
The measured value of 5 isolated components of property body magnetic gradient tensor.
Step 2: by point PnThe measured value for locating 5 isolated components of magnetic substance magnetic gradient tensor calculates point P by formula (17)nPlace
The measured value of magnetic gradient tensor
Step 3: by magnetic gradient Tensor measuring valueWithIt is divided into three
A group, i.e.,WithStep is repeated 1) extremely to walk 5), by three groups of magnetic gradient tensors
Measured value calculates separately point P1And P2、P3And P4、P5And P6The distance between magnetic substance.
1) step calculatesEigenvalue λiWith feature vector vi, calculateEigenvalue λjWith feature vector vj, i ≠
j。
2) step calculates following cosine value,
In formula, λik(k=1,2,3) it indicatesK-th of characteristic value, λjkIt indicatesK-th of characteristic value.
3) step calculates the unit vector of magnetic substance magnetic moment
In formula, cij=(vi22vj23-vi23vj22)/(vi21vj22-vi22vj21), dij=(vi21vj23-vi23vj21)/
(vi21vj22-vi22vj21), vi2kForThe 2nd characteristic value k-th of component, vj2kForThe 2nd characteristic value
K-th of component.
4) step calculates point P by formula (21)iPosition vector relative to magnetic substanceUnit vector
Step is 5)WithRespectively position vectorX, y and z-component, according to formula (22) andIt calculatesWith
Point P is calculated againiThe distance between point Q
In formula, dijx、dijyAnd dijzRespectively PjRelative to PiPosition vectorX, y and z-component.
Step 4: by point PnThe distance between (n ≠ 0) and magnetic substanceSystem of linear equations shown in composition formula (23),
In formula,WithFor the position coordinates of magnetic substance.
Step 5: calculating the position coordinate value of magnetic substance by formula (24) by system of linear equations.
It is worth noting that, being solved using formula (21)OrOrWhen obtain is quadratic equation with one unknown, therefore
OrOrThere are two solutions；Factor (22) has sign again, thereforeWithThere are four groups of solutions.It can be proved that this four
Group solution be it is symmetrical about point Q, institute it is calculatedIt is identical.
Embodiment 2
Embodiments of the present invention are described in detail with reference to the accompanying drawing:
The corresponding sensitive axes of eight three axis magnetometers are mutually aligned by step 1, and configuration mode difference as shown in Figure 1
It is placed on the regular hexahedron array that three axis magnetometer is constituted on two layers of mounting plate.
Step 2 is counted respectively according to the spatial position of eight three axis magnetometers of this three axis magnetometer regular hexahedron array
Calculate angle WithCosine value.
Step 3 is exported by the measurement of collected eight three axis magnetometers of multichannel data actuation With
Point P is calculated by formula (1)nLocate the measured value of 5 isolated components of magnetic substance magnetic gradient tensor With
In formula
As n ≠ 0,
As n ≠ 0,
With
Step 4, byWithPoint P is calculated by formula (2)nLocate magnetic ladder
Spend the measured value of tensor
Step 5: by magnetic gradient Tensor measuring valueWithIt is divided into three
A group, i.e.,WithStep is repeated 1) extremely to walk 6), by three groups of magnetic gradient tensors
Measured value calculates separately point P1And P2、P3And P4、P5And P6The distance between point Q.
1) step calculatesEigenvalue λiWith feature vector vi, calculateEigenvalue λjWith feature vector vj, i ≠
j。
2) step calculates following cosine value,
In formula, λik(k=1,2,3) it indicatesK-th of characteristic value, λjkIt indicatesK-th of characteristic value.
3) step calculates the unit vector of magnetic substance magnetic moment
In formula, cij=(vi22vj23-vi23vj22)/(vi21vj22-vi22vj21), dij=(vi21vj23-vi23vj21)/
(vi21vj22-vi22vj21), vi2kForThe 2nd characteristic value k-th of component, vj2kForThe 2nd characteristic value
K component.
4) step is successively calculated by formula (6), formula (7) and formula (8)With
In formula, ± it is any selection,
ByWithObtain point PiPosition vector relative to magnetic substanceUnit vector
Step is 5)WithRespectively position vectorX, y and z-component, according to formula (9) andIt calculatesWith
In formula, ± it is any selection, dijx、dijyAnd dijzRespectively PjRelative to PiPosition vectorX, y and z-component.
Step 6) byWithCalculate point PiThe distance between point Q
Step 6: the position coordinate value of magnetic substance is calculated by formula (11)With
In order to characterize the precision of three axis magnetometer regular hexahedron array measurement magnetic gradient tensor isolated component, magnetic gradient is defined
The relative error of tensor isolated component is
In formula,And Bμν(Pi) it is respectively magnetic gradient tensor isolated component BμνIn point PiThe measured value and true value at place.
In order to characterize three axis magnetometer regular hexahedron array to the positioning accuracy of magnetic substance, the absolute of magnetic substance positioning is defined
Error is respectivelyWithThe absolute error δ r that definition distance resolves
ForWherein xQ、yQAnd zQFor the position coordinates true value of magnetic substance.
The magnetic field model of magnetic substance is represented by a magnetic dipole magnetic field multiplied by coefficient ρ.Magnetic substance magnetic moment three-component point
It Wei not mx=6.8 × 108A·m、my=3.9 × 108Am and mz=13.6 × 108Am, position coordinates true value are xQ=
8m、yQ=20m and zQThree side lengths of=- 5m, ρ=1.3, the regular hexahedron of three axis magnetometer array are respectively Lx=0.05m,
Ly=0.05m and Lz=0.05m.Three axis magnetometer is independent from each other Gaussian process, mean value 0, mark in the noise of each axis
Quasi- difference is σmagnetometer, in the case where different three axis magnetometer noise criterias is poor, it is only to carry out array measurement magnetic gradient tensor
50 Monte Carlo simulations experiment of vertical component and magnetic substance positioning.
The relative error of array measurement magnetic gradient tensor isolated component with three axis magnetometer noise criteria difference change curve
As shown in figs. 3 to 9, wherein Fig. 3 is σmagnetometerP when increasing to 0.5nT from 0.004nT0Locate the opposite of each isolated component to miss
Poor curve, Fig. 4 σmagnetometerP when increasing to 0.5nT from 0.004nT1Locate the relative error curve of each isolated component, Fig. 5 is
σmagnetometerP when increasing to 0.5nT from 0.004nT2Locate the relative error curve of each isolated component, Fig. 6 σmagnetometerFrom
P when 0.004nT increases to 0.5nT3Locate the relative error curve of each isolated component, Fig. 7 σmagnetometerIncrease from 0.004nT
P when to 0.5nT4Locate the relative error curve of each isolated component, Fig. 8 σmagnetometerP when increasing to 0.5nT from 0.004nT5Place
The relative error curve of each isolated component, Fig. 9 σmagnetometerP when increasing to 0.5nT from 0.004nT6Locate each isolated component
Relative error curve.By Fig. 3 to Fig. 9 it is found that the relative error of each isolated component is with σmagnetometerIncrease and near-linear increase
Add.
Work as σmagnetometerWhen increasing to 0.5nT from 0.004nT, the absolute error of magnetic substance positioning is made an uproar with three axis magnetometer
The change curve of sound standard deviation is as shown in Figure 10, and as shown in Figure 10, the absolute error of magnetic substance positioning is with σmagnetometerIncrease
And increase.Work as σmagnetometerWhen increasing to 0.5nT from 0.004nT, the magnetic substance and array body-centered P that are finally inversed by0Point between away from
From absolute error Δ rQChange curve with three axis magnetometer noise criteria difference is as shown in figure 11, as shown in Figure 11, Δ rQWith
σmagnetometerIncrease and in increase trend；σmagnetometerWhen=0.5nT apart from absolute error be about 0.4m.
Use a non-magnetic dipole as the magnetic field model of single magnetic substance, carries out magnetic gradient Tensor measuring and magnetism
The Monte Carlo simulation experiment of body positioning, provides three axis magnetometer regular hexahedron array measurement this magnetic substance in array cube
The center of area and body-centered at the magnetic gradient tensor that generates with the change curve between three axis magnetometer noise criteria difference, give magnetism
Body positioning absolute error and apart from absolute error with the change curve of three axis magnetometer noise criteria difference.Simulation result shows this
Inventing the multiple spot magnetic gradient Tensor measuring method based on three axis magnetometer regular hexahedron array proposed can be by single measurement simultaneously
Obtain the magnetic substance magnetic gradient tensor at array body-centered and six center of areas；What the present invention was mentioned is opened based on magnetic gradient at the array center of area
The linear orientation algorithm of amount can position any one magnetic substance.
Claims (3)
1. a kind of linear location algorithm of ranging, which is characterized in that concrete implementation step are as follows:
Step 1., to the measured value of Magnetic Field of Magnetic Body, calculates point P according to eight three axis magnetometers of arraynLocate magnetic substance magnetic gradient
The measured value of 5 isolated components of tensor
Wherein Bxx(Pn)、Byy(Pn)、Bxy(Pn)、Byz(Pn)、Bxz(Pn) it is respectively magnetic substance in point Pn(n=0,1 ..., 6) at
5 isolated components of magnetic gradient tensor,For angle matrix,For relative measurement value matrix；
Step 2. is by point PnThe measured value for locating 5 isolated components of magnetic substance magnetic gradient tensor calculates point PnLocate magnetic gradient tensor
Measured value
Step 3. is by magnetic gradient Tensor measuring valueWithIt is divided into three
Group, i.e.,WithPoint P is calculated separately by three groups of magnetic gradient Tensor measuring values1
And P2、P3And P4、P5And P6The distance between magnetic substance；
Step 4. is by point PnThe distance between (n ≠ 0) and magnetic substanceSystem of linear equations is formed,
In formula,WithFor the position coordinates of magnetic substance, the regular hexahedron side length on the direction x, y and z is respectively Lx、LyWith
Lz, point PnThe distance between (n ≠ 0) and magnetic substance are respectively
Step 5. is calculated the position coordinate value of magnetic substance by system of linear equations
2. the linear location algorithm of a kind of ranging according to claim 1, which is characterized in that the specific steps of the step 3
Are as follows:
Step 3.1. is calculatedEigenvalue λiWith feature vector vi, calculateEigenvalue λjWith feature vector vj, i ≠
j；
Step 3.2. calculates cosine value
In formula, λik(k=1,2,3) it indicatesK-th of characteristic value, λjkIt indicatesK-th of characteristic value；
The unit vector of step 3.3. calculating magnetic substance magnetic moment
In formula, cij=(vi22vj23-vi23vj22)/(vi21vj22-vi22vj21), dij=(vi21vj23-vi23vj21)/(vi21vj22-
vi22vj21), vi2kForThe 2nd characteristic value k-th of component, vj2kForThe 2nd characteristic value k-th of component；
Step 3.4. calculates point PiPosition vector relative to magnetic substanceUnit vector
Step 3.5.WithRespectively position vectorX, y and z-component, calculateWithPoint P is calculated againiWith point Q
The distance between
In formula, dijx、dijyAnd dijzRespectively PjRelative to PiPosition vectorX, y and z-component.
3. the linear location algorithm of a kind of ranging according to claim 1, which is characterized in that the array of the step 1 are as follows:
Upper layer mounting plate and lower layer's mounting plate install four three axis magnetometers respectively, and the corresponding sensitive axes of eight three axis magnetometers are mutually right
Together, regular hexahedron array is constituted.
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Cited By (6)
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|---|---|---|---|---|
| CN111190230A (en) * | 2020-01-16 | 2020-05-22 | 哈尔滨工业大学 | Detection method based on magnetic gradient tensor |
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| CN112050799A (en) * | 2020-08-19 | 2020-12-08 | 哈尔滨工程大学 | Distance measurement positioning method based on magnetic gradient tensor shrinkage ratio |
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| CN112362048A (en) * | 2020-11-12 | 2021-02-12 | 中国电子科技集团公司第三研究所 | Practical magnetic gradient tensor high-precision single-point positioning method |
| CN112611310A (en) * | 2020-12-11 | 2021-04-06 | 哈尔滨工程大学 | Magnetic dipole target distance and direction measuring method |
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