CN112284372B - Positioning precision improving method based on coil magnetic field regulation and control - Google Patents

Positioning precision improving method based on coil magnetic field regulation and control Download PDF

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CN112284372B
CN112284372B CN202011067990.2A CN202011067990A CN112284372B CN 112284372 B CN112284372 B CN 112284372B CN 202011067990 A CN202011067990 A CN 202011067990A CN 112284372 B CN112284372 B CN 112284372B
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CN112284372A (en
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林生鑫
潘东华
王矜婷
陈艳路
崔浩
李立毅
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Harbin Institute of Technology
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R33/00—Arrangements or instruments for measuring magnetic variables
    • G01R33/02—Measuring direction or magnitude of magnetic fields or magnetic flux
    • G01R33/0206—Three-component magnetometers
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R33/00—Arrangements or instruments for measuring magnetic variables
    • G01R33/02—Measuring direction or magnitude of magnetic fields or magnetic flux
    • G01R33/022—Measuring gradient
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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    • Y02A—TECHNOLOGIES FOR ADAPTATION TO CLIMATE CHANGE
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Abstract

The invention discloses a positioning accuracy improving method based on coil magnetic field regulation and control, and belongs to the technical field of magnetic positioning. Changing the included angle by regulating and controlling the magnetic moment direction of the magnetic targetThereby avoiding the positioning blind area and greatly reducing the positioning error of the tensor magnetic positioning method. In the method for avoiding the positioning blind area, the magnetic moment direction of the magnetic target is regulated and controlled by regulating and controlling the magnetic field direction of the coil, and the problem that the larger the coil axis number is, the larger the energy consumption is considered, the method for avoiding the positioning blind area of the two-axis coil and the three-axis coil is provided, and a calculation basis is provided for the selection of the coil axis number in actual use.

Description

Positioning precision improving method based on coil magnetic field regulation and control
Technical Field
The invention relates to a positioning accuracy improving method based on coil magnetic field regulation and control, and belongs to the technical field of magnetic positioning.
Background
The magnetic positioning technology is a magnetic field-based target positioning technology, has the advantages of all weather, high speed, high precision and the like, and shows specific advantages and application prospects in various fields such as geophysics, biomedical and the like. In positioning and navigating the surgical robot, magnetic positioning techniques are not affected by obstructions and are less costly than optical tracking. In tracking wireless capsule endoscopes, tongue movements, magnetic drug labeling, magnetic localization techniques are safer, lower cost, and more efficient than CT with radiation and costly MRI.
In locating certain magnetic target characteristics (magnetic moment direction of the magnetic target and direction relative to the magnetic positioning system), the positioning error is very large, called a positioning blind area, i.e. the direction of the magnetic target and the magnetic moment direction determine whether the magnetic target is located in the positioning blind area. The tensor magnetic positioning method is the next breakthrough point of the magnetic positioning technology, and the NARA method and the STAR method are widely focused in the tensor magnetic positioning method. The current tensor magnetic positioning method has the following problems:
1. NARA method has no better blind area error compensation method because of the positioning blind area existing in the singular of the full tensor matrix
The NARA method can rapidly and accurately locate magnetic targets without prior estimation of structural indexes, but when the full tensor matrix is singular, the location equation of the NARA method presents morbidity and a location blind area appears. Aiming at the pathogenicity of the positioning equation, a scholars compensates the positioning result of the positioning blind area by utilizing Newton interpolation, and the scholars calculate the inverse matrix of the full tensor matrix by utilizing Moore-Penrose generalized inverse. Both improved ideas need to firstly select a threshold to judge whether the matrix is singular or not, but the thresholds are different under different working conditions, so that an accurate threshold is difficult to select. At present, no better method is available for compensating the NARA positioning blind area.
2. The STAR method has a positioning blind area due to the existence of the aspheric coefficients, and the compensation effect of the blind area needs to be further improved
Researchers have proposed scalar triangulation and ranging (STAR) methods based on tensor invariant magnetic gradient contraction. The STAR method can position a magnetic target in real time and the positioning accuracy is not affected by the geomagnetic field. However, because of the existence of the aspheric coefficients, the STAR method has an aspheric error, i.e., a positioning blind area. The improved STAR method without aspherical coefficients, called LSM, has been proposed by the scholars, and the positioning error of LSM is reduced by 10.9% compared to STAR method. The learner compensates the direction error of the STAR method by using an iteration method, namely the WSM, and compared with the STAR method, the positioning error of the WSM is reduced by 68.5%. However, neither LSM nor WSM completely compensates for the aspheric errors, and there is room for further improvement in the compensation of STAR positioning dead zones.
3. Method for avoiding blind areas by using distribution rule of positioning blind areas without study
It has been shown that when the angle between the position vector and the magnetic moment vector isWhen the angle is close to 90 degrees, a positioning blind area appears in the NARA method; when the included angle is->Near 60 ° or 120 °, the STAR method presents a dead zone of positioning. Although the location blind area and the physical quantity are known +.>The mapping relation between the two is not studied, an avoidance method of the positioning blind area is proposed aiming at the mapping relation, and the distribution rule of the positioning blind area is not fully utilized.
Disclosure of Invention
The invention aims to provide a positioning precision improving method based on coil magnetic field regulation and control, which aims to solve the problems of insufficient error compensation and insufficient positioning precision of a tensor magnetic positioning method in the prior art.
Positioning precision improving method based on coil magnetic field regulation and control and utilizing positioning blind area and physical quantityThe mapping relation between the two magnetic targets changes the included angle by changing the magnetic moment direction of the magnetic targets so as to avoid a positioning blind area;
further, the changing of the magnetic target magnetic moment direction by using the 3-axis coil comprises the following steps:
step one: calculating a position vector of a magnetic target using tensor magnetic positioningMagnetic moment vector->And (c) angle->
Step two: judgingWhether or not it is->If yes, performing a third step, otherwise, performing a ninth step;
step three: if the adjustment times adj do not reach the limit times max, performing the step four, otherwise, performing the step nine;
step four: if the adjustment times adj is 1, the x and y axes of the three-axis coil are respectively electrified, and the magnetic gradient tensor G at the center of the tensor gradiometer is respectively calculated according to the formula (1) x 、G y ，
If the adjustment times adj are greater than 1, executing a step five;
step five: vector the positionG x Substituting formula (2) calculate magnetic moment vector when only x-axis coil is energized>Position vector +.>G y Substituting formula (2) to calculate magnetic moment vector when only y-axis circle is electrified>
Calculating the basis vector of the coil coordinate system by the method (3)
The unit vectors of the tensor gradiometer standard coordinate system in the x, y and z directions are recorded as
The coil coordinate system is obtained by rotating a standard coordinate system around a z-axis by a gamma angle, then rotating the coil coordinate system around a y-axis by a beta angle and finally rotating the coil coordinate system around an x-axis by an alpha angle:
in the formula ：
the transformation matrix T of the coil coordinate system to the tensor gradiometer coordinate system can be calculated according to equation (5):
step six: calculation ofUnit vector in standard coordinate system +.>According to the blind area distribution law, assume when +.> The positioning error is minimal if +.>Less than 90 DEG,>otherwise
Step seven: if it isIs greater than->And is less than->Then the new magnetic moment direction of the magnetic target in the standard coordinate system Satisfy the following requirements
Taking outAt->And the plane of the z axis of the standard coordinate system are:
after θ is calculated, it is obtained according to formula (7):
from the trigonometric function identity, it can be derived:
in the formula (10):
step eight: if it isIs greater than->And is less than->Triaxial coil current vector>Otherwise triaxial coil current vector +.>Adding one to the adjustment times adj, and returning to the step one;
step nine: outputting the position vector of the magnetic target in the standard coordinate systemAnd magnetic moment vector->
Further, the changing of the magnetic target magnetic moment direction by using the 2-axis coil comprises the following steps:
step one: calculating a position vector of a magnetic target using tensor magnetic positioningMagnetic moment vector->And an included angle phi;
step two: judgingWhether or not it is->If yes, performing a third step, otherwise, performing a ninth step;
step three: if the adjustment times adj do not reach the limit times max, performing the step four, otherwise, performing the step nine;
step four: if the adjustment times adj is 1, the x and y axes of the three-axis coil are respectively electrified, and the magnetic gradient tensor G at the center of the tensor gradiometer is respectively calculated according to the formula (1) x 、G y ，
If the adjustment times adj are greater than 1, executing a step five;
step five: vector the positionG x Substituting (2) calculating magnetic moment vector when only x-axis coil is electrified/>Position vector +.>G y Substituting formula (2) to calculate magnetic moment vector when only y-axis circle is electrified>
Calculating the basis vector of the coil coordinate system by the method (3)
The unit vectors of the tensor gradiometer standard coordinate system in the x, y and z directions are recorded as
The coil coordinate system is obtained by rotating a standard coordinate system around a z-axis by a gamma angle, then rotating the coil coordinate system around a y-axis by a beta angle and finally rotating the coil coordinate system around an x-axis by an alpha angle:
in the formula ：
the transformation matrix T of the coil coordinate system to the tensor gradiometer coordinate system can be calculated according to equation (5):
step six: calculation ofUnit vector in coil coordinate system>If arccosx is the 2 Less than 90 DEG,>otherwise->
Step seven: if it isIs greater than->And is less than->Then the new magnetic moment direction of the magnetic target in the coil coordinate system Satisfy the following requirements
According to formula (11):
from the trigonometric function identity, it can be derived:
in the formula (13):
if it isLess than->Or->Less than->Magnetic target new magnetic moment direction in coil coordinate system>The method comprises the following steps:
otherwise, executing the step nine;
step eight: 2-axis coil current vectorAdding one to the adjustment times adj, and executing the first step;
step nine: outputting a position vector of a magnetic targetAnd magnetic moment vector->
The invention has the main advantages that: the invention has the advantages that:
(1) Aiming at the problem of insufficient error compensation of the positioning blind area in the prior study, the positioning blind area and the physical quantity are fully utilizedThe mapping relation between the magnetic targets provides a blind area avoiding method for avoiding a positioning blind area by changing an included angle through changing the magnetic moment direction of the magnetic targets so as to improve the positioning accuracy.
(2) Specifically, the magnetic moment direction of the magnetic target is regulated and controlled by regulating and controlling the magnetic field of the multi-axis coil, the method is convenient and feasible, the problem that the more the number of coil axes is, the larger the energy consumption is considered, the positioning blind area avoidance method MC2-BAA based on the regulation and control of the magnetic field of the two-axis coil and the positioning blind area avoidance method MC3-BAA based on the regulation and control of the magnetic field of the three-axis coil are provided, and the two methods can be flexibly selected according to the provided electric energy in actual use.
(3) MC2-BAA, MC3-BAA can track can cooperate with the magnetic target in real time, and MC2-BAA reduces the root mean square error of STAR method by 49.27%, MC3-BAA reduces the root mean square error of STAR method by 95.66%, has promoted the positioning accuracy effectively.
Drawings
FIG. 1 is a schematic diagram of a regular hexahedral structure tensor gradiometer;
FIG. 2 is a schematic diagram of a positioning system based on coil magnetic field regulation;
FIG. 3 is a flow chart of steps of MC 3-BAA;
FIG. 4 is a flow chart of steps of MC 2-BAA;
fig. 5 is a map of the relative error percentage ρ and the physical quantity Φ;
FIG. 6 is a diagram of the motion profile of a wireless capsule endoscope;
fig. 7 is a diagram of the positioning error of the magnetic positioning method on the motion trajectory.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The magnetic target can be generally regarded as a magnetic dipole. The center of the tensor gradiometer is taken as an origin to establish a space rectangular coordinate system, and the magnetic gradient tensor G of the magnetic dipole is as follows:
vacuum permeability μ in (15) 0 ＝4π×10-7T·m/A，Is the magnetic moment vector, is>For the position vector, r is +.>Is of a size of (a) and (b). Delta ij Is a kronecker function, i, j=x, y, z. In the magnetic gradient tensor G, G xy ＝G yx ，G xz ＝G zx ，G yz ＝G zy ，G xx +G yy +G zz =0, only 5 elements are independent.
In practical measurement, the magnetic gradient tensor G is measured by a tensor gradiometer of a regular hexahedral structure or a "cross" structure, for example.
Using a first order taylor expansion, the magnetic gradient tensor at the center point of the upper surface of the regular hexahedron can be calculated:
wherein D is the baseline distance of the tensor gradiometer, and the magnetic gradient tensor at the center of the other five faces of the regular hexahedron can be calculated by the same methodMagnetic gradient tensor G in the center of tensor gradiometer o The calculation formula of (2) is as follows:
the relationship between the magnetic moment vector and the position vector can be obtained according to equation (1) and the least squares method:
in the formula ：
because of the dead zone and the physical quantityThere is a mapping relation, and it is known from the equation (17) that the angle +.>Thereby realizing the avoidance of the positioning blind area.
The positioning system based on coil magnetic field regulation is composed as shown in figure 2. The exciting coil is arranged in the object to generate magnetic field without changing current vectorBy varying the current vector +.>Directly modulating the direction of the magnetic moment of the magnetic target. In actual use, compared with a single-axis coil, the three-axis coil can realize magnetic moment direction regulation and control in any direction so as to optimize the avoiding effect of the positioning blind area, but the increase of the coil axis number also increases energy consumption. For applications such as wireless capsule endoscopes and the like which need a self-contained power supply system, enough electric energy can not be provided, and therefore, a positioning blind area avoiding method is respectively provided for a two-axis coil and a three-axis coil.
The main idea of the positioning blind area avoidance (MC-BAA) method based on coil magnetic field regulation is to calculate the transformation between a coil coordinate system and a tensor gradiometer coordinate system, regulate and control the coil current to change the included angle so as to avoid the positioning blind area, and accurately make the magnetic target be in a non-blind area by using an iteration method. The flow chart of the steps of the positioning blind area avoidance method (MC 3-BAA) based on the 3-axis coil is shown in fig. 3, and the specific steps are as follows:
step one: calculating a position vector of a magnetic target using tensor magnetic positioningMagnetic moment vector->And (c) angle->
Step two: if it isAt->(according to the rule of blind zone distribution, assume when +.>When the magnetic target is positioned), performing the third step, otherwise, performing the ninth step;
step three: if the adjustment times adj do not reach the limit times max, performing the step four, otherwise, performing the step nine;
step four: if the adjustment times adj is 1, the x and y axes of the three-axis coil are respectively electrified, and the magnetic gradient tensor G at the center of the tensor gradiometer is respectively calculated according to the formula (1) x 、G y If the adjustment times adj are greater than 1, executing a step five;
step five: vector the positionG x Substituting formula (2) calculate magnetic moment vector when only x-axis coil is energized>Position vector +.>G y Substituting formula (2) to calculate magnetic moment vector when only y-axis circle is electrified>Calculating the basis vector of the coil coordinate system by formula (3)>
The unit vectors of the tensor gradiometer standard coordinate system in the x, y and z directions are recorded as
The coil coordinate system can be regarded as a standard coordinate system which is obtained by rotating the standard coordinate system by an angle gamma around the z axis, then rotating the standard coordinate system by an angle beta around the y axis and finally rotating the standard coordinate system by an angle alpha around the x axis.
in the formula ：
the transformation matrix T of the coil coordinate system to the tensor gradiometer coordinate system can be calculated according to equation (5):
step six: calculation ofUnit vector in standard coordinate system +.>According to the blind area distribution law, assume when +.> The positioning error is minimal if +.>Less than 90 DEG,>otherwise
Step seven: if it isIs greater than->And is less than->Then the magnetic target is new in the standard coordinate system> Should satisfy
Taking outAt->And the plane of the z axis of the standard coordinate system are:
after θ is calculated, it can be obtained according to formula (7):
from the trigonometric function identity, it can be derived:
in the formula (10):
step eight: if it isIs greater than->And is less than->Triaxial coil current vector>Otherwise triaxial coil current vector +.>Adding one to the adjustment times adj, and executing the first step;
step nine: outputting the position vector of the magnetic target in the standard coordinate systemAnd magnetic moment vector->
The flow chart of the steps of the positioning blind area avoidance method (MC 2-BAA) based on the 2-axis coil is shown in fig. 4, and the specific steps are as follows:
step one through step five are consistent with MC3-BAA.
Step six: calculation ofUnit vector in coil coordinate system>If arccosx is the 2 Less than 90 DEG,>otherwise->
Step seven: if it isIs greater than->And is less than->Then the new magnetic moment direction of the magnetic target in the coil coordinate system Should satisfy
According to formula (11):
from the trigonometric function identity, it can be derived:
in the formula (13):
if it isLess than->Or->Less than->Magnetic target new magnetic moment direction in coil coordinate system>The method comprises the following steps:
otherwise, executing step nine.
Step eight: 2-axis coil current vectorAdding one to the adjustment times adj, and executing the first step;
step nine: outputting a position vector of a magnetic targetAnd magnetic moment vector->
The following are specific embodiments of the present invention:
the prior art provides a scalar triangulation and ranging (STAR) method based on invariants of magnetic gradient tensors, which can position a magnetic target in real time, and the positioning accuracy is not influenced by geomagnetic fields, and the STAR method is taken as an example for implementing the invention. The positioning error of the STAR method is mainly aspheric error delta, and the mapping relation between the aspheric error and the physical quantity is as follows:
from equation (18), it can be seen that the aspherical error δ is linear with distance r, and is related to the included angleIn a nonlinear relationship. Calculating the relative error percentage ρ:
percentage of relative error ρ and physical quantityThe mapping relationship between them is shown as 5, from which it can be seen when +.>Or-> When the relative error is maximum; when->Or->Or->There is no relative error. It is assumed that when the relative error percentage ρ is greater than 0.1%, the magnetic target is considered to be in the positioning blind area, at this time +.>Or 89.7 deg. or 90.3 deg. or 179.7 deg.. For convenience of regulation, take->Then in MC3-BAA In MC2-BAA, +.> and />It is necessary to calculate in real time from the position of the magnetic target.
Taking a wireless capsule endoscope as an example to position a magnetic target, the amplitude of the geomagnetic field is 55000nT, and the deflection angle and the inclination angle are respectively-10 degrees and 60 degrees. The maximum adjustment times are taken to be 10 times. The magnetic moment size M, the baseline distance D, the resolution S of the magnetic sensor, the noise level k of the magnetic sensor, and the standard deviation sigma of Gaussian white noise are shown in Table 1.
TABLE 1 simulation conditions
The cylindrical spiral line is used as the motion trail of the wireless capsule endoscope, and the mathematical expression is as follows:
where w is the angular velocity of the wireless capsule endoscope and t is the movement time. W=0.45 rad/s, t=0s, 100s,200s, … s are taken. In order to obtain a complete pathological condition, the wireless capsule endoscope needs to take pictures and video pictures in various postures, which means that the initial magnetic moment direction of the wireless capsule endoscope is arbitrary. To simulate the actual positioning conditions, the initial magnetic moment direction of the wireless capsule endoscope is random at each position. In order to obtain a calculation result with better objectivity, an average value of 100 times is taken as the calculation result.
The tensor gradiometer is placed at the origin of the coordinate system. The positioning error delta of the magnetic positioning method on the motion trail is shown in fig. 7. It can be seen that the MC2-BAA reduces the aspheric error of the STAR method by regulating the coil magnetic field, and the MC3-BAA further improves the positioning accuracy of the MC 2-BAA.
Table 2 shows that the RMS error epsilon of the magnetic positioning method on the motion track, MC2-BAA reduces the RMS error of the STAR method by 49.27%, and MC3-BAA reduces the RMS error of the STAR method by 95.66%, thereby effectively improving the positioning accuracy. In practical use, MC2-BAA or MC3-BAA can be flexibly selected according to the provided electric energy.
TABLE 2 root mean square error of magnetic positioning method on motion trajectories
The present invention is capable of other and further embodiments and its several details are capable of modification and variation in light of the present invention, as will be apparent to those skilled in the art, without departing from the spirit and scope of the invention as defined in the appended claims.

Claims (1)

1. A positioning precision improving method based on coil magnetic field regulation and control is characterized in thatIn this way, the positioning blind area and the included angle are utilizedThe mapping relation between the two magnetic targets changes the included angle by changing the magnetic moment direction of the magnetic targets so as to avoid a positioning blind area;
the changing of the magnetic target magnetic moment direction by using the 3-axis coil comprises the following steps:
step one: calculating a position vector of a magnetic target using tensor magnetic positioningMagnetic moment vector->And (c) angle->
Step two: judgingWhether or not it is->If yes, performing a third step, otherwise, performing a ninth step;
step three: if the adjustment times adj do not reach the limit times max, performing the step four, otherwise, performing the step nine;
step four: if the adjustment times adj is 1, the x and y axes of the three-axis coil are respectively electrified, and the magnetic gradient tensor G at the center of the tensor gradiometer is respectively calculated according to the formula (1) x 、G y ，G o For the magnetic gradient tensor in the center of the tensor gradiometer, the calculation formula is:
wherein ,the magnetic gradient tensor at the front surface center, the magnetic gradient tensor at the rear surface center, the magnetic gradient tensor at the right surface center, the magnetic gradient tensor at the left surface center, the magnetic gradient tensor at the upper surface center and the magnetic gradient tensor at the lower surface center in the regular hexahedral structure, respectively,
if the adjustment times adj are greater than 1, executing a step five;
step five: vector the positionG x Substituting formula (2) calculate magnetic moment vector when only x-axis coil is energized>Position vector +.>G y Substituting formula (2) to calculate magnetic moment vector when only y-axis circle is electrified>
wherein ,
x, y, z are the three-axis coordinates of the magnetic target position,
calculating a coil by the method (3)Basis vector of coordinate system
Wherein, the unit vector of the tensor gradiometer standard coordinate system in the x, y and z directions is recorded as
The coil coordinate system is obtained by rotating a standard coordinate system around a z-axis by a gamma angle, then rotating the coil coordinate system around a y-axis by a beta angle and finally rotating the coil coordinate system around an x-axis by an alpha angle:
in the formula ：
the transformation matrix T of the coil coordinate system to the tensor gradiometer coordinate system can be calculated according to equation (5):
step six: calculation ofUnit vector in standard coordinate system +.>According to the blind area distribution law, assume when +.> The positioning error is minimal if +.>Less than 90 DEG,>otherwise->
Step seven: if it isIs greater than->And is less than->Then the magnetic target is new in the standard coordinate system> Satisfy the following requirements
Taking outAt->And the plane of the z axis of the standard coordinate system are:
after θ is calculated, it is obtained according to formula (7):
from the trigonometric function identity, it can be derived:
in the formula (10):
step eight: if it isIs greater than->And is less than->Triaxial coil electricityStream vector->Otherwise triaxial coil current vector +.>Adding one to the adjustment times adj, and returning to the step one;
step nine: outputting the position vector of the magnetic target in the standard coordinate systemAnd magnetic moment vector->
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