CN112294437B - Positioning based on magnetic gradiometer array and design method thereof - Google Patents

Positioning based on magnetic gradiometer array and design method thereof Download PDF

Info

Publication number
CN112294437B
CN112294437B CN202011067995.5A CN202011067995A CN112294437B CN 112294437 B CN112294437 B CN 112294437B CN 202011067995 A CN202011067995 A CN 202011067995A CN 112294437 B CN112294437 B CN 112294437B
Authority
CN
China
Prior art keywords
magnetic
positioning
array
gradiometer
blind area
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN202011067995.5A
Other languages
Chinese (zh)
Other versions
CN112294437A (en
Inventor
林生鑫
潘东华
靳崇渝
王矜婷
李立毅
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Harbin Institute of Technology
Original Assignee
Harbin Institute of Technology
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Harbin Institute of Technology filed Critical Harbin Institute of Technology
Priority to CN202011067995.5A priority Critical patent/CN112294437B/en
Publication of CN112294437A publication Critical patent/CN112294437A/en
Application granted granted Critical
Publication of CN112294437B publication Critical patent/CN112294437B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B34/00—Computer-aided surgery; Manipulators or robots specially adapted for use in surgery
    • A61B34/20—Surgical navigation systems; Devices for tracking or guiding surgical instruments, e.g. for frameless stereotaxis
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B1/00—Instruments for performing medical examinations of the interior of cavities or tubes of the body by visual or photographical inspection, e.g. endoscopes; Illuminating arrangements therefor
    • A61B1/00147—Holding or positioning arrangements
    • A61B1/00158—Holding or positioning arrangements using magnetic field
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B1/00—Instruments for performing medical examinations of the interior of cavities or tubes of the body by visual or photographical inspection, e.g. endoscopes; Illuminating arrangements therefor
    • A61B1/04—Instruments for performing medical examinations of the interior of cavities or tubes of the body by visual or photographical inspection, e.g. endoscopes; Illuminating arrangements therefor combined with photographic or television appliances
    • A61B1/041—Capsule endoscopes for imaging
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B5/00—Measuring for diagnostic purposes; Identification of persons
    • A61B5/06—Devices, other than using radiation, for detecting or locating foreign bodies ; determining position of probes within or on the body of the patient
    • A61B5/061—Determining position of a probe within the body employing means separate from the probe, e.g. sensing internal probe position employing impedance electrodes on the surface of the body
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B5/00—Measuring for diagnostic purposes; Identification of persons
    • A61B5/06—Devices, other than using radiation, for detecting or locating foreign bodies ; determining position of probes within or on the body of the patient
    • A61B5/061—Determining position of a probe within the body employing means separate from the probe, e.g. sensing internal probe position employing impedance electrodes on the surface of the body
    • A61B5/062—Determining position of a probe within the body employing means separate from the probe, e.g. sensing internal probe position employing impedance electrodes on the surface of the body using magnetic field
    • 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
    • G01R33/022—Measuring gradient
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B34/00—Computer-aided surgery; Manipulators or robots specially adapted for use in surgery
    • A61B34/20—Surgical navigation systems; Devices for tracking or guiding surgical instruments, e.g. for frameless stereotaxis
    • A61B2034/2046—Tracking techniques
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B34/00—Computer-aided surgery; Manipulators or robots specially adapted for use in surgery
    • A61B34/20—Surgical navigation systems; Devices for tracking or guiding surgical instruments, e.g. for frameless stereotaxis
    • A61B2034/2068—Surgical navigation systems; Devices for tracking or guiding surgical instruments, e.g. for frameless stereotaxis using pointers, e.g. pointers having reference marks for determining coordinates of body points

Abstract

The invention discloses positioning based on a magnetic gradiometer array and a design method thereof, belonging to the technical field of magnetic positioning. The positioning and design method comprises the following steps: s000, designing a topological structure of the magnetic gradiometer array; s100, calculating magnetic gradient tensors G (i ═ 1,2, …, N) at all magnetic gradiometer positions according to equation (1), where N is the number of magnetic gradiometers: s200, calculating the positions of all magnetic gradiometers by using the formula (2)
Figure DDA0002714403860000015
(i ═ 1,2, …, N): s300, according to the positioning blind area and the included angle
Figure DDA0002714403860000011
The mapping relation of (A) obtains an included angle which can minimize the positioning error
Figure DDA0002714403860000012
S400, calculating a position vector by using the magnetic gradient tensor of the magnetic gradiometer with the number j
Figure DDA0002714403860000013
And magnetic moment vector
Figure DDA0002714403860000014
Based on the distribution rule of the positioning blind area, the invention provides a method for changing the included angle by forming an array by a plurality of magnetic gradiometers
Figure DDA0002714403860000016
And furthermore, a method for avoiding a positioning blind area greatly reduces the positioning error of the tensor magnetic positioning method.

Description

Positioning based on magnetic gradiometer array and design method thereof
Technical Field
The invention relates to positioning based on a magnetic gradiometer array and a design method thereof, belonging to the technical field of magnetic positioning.
Background
The magnetic positioning technology is a target positioning technology based on a magnetic field, has the advantages of all weather, high speed, high precision and the like, and has specific advantages and application prospects in numerous fields such as geophysical and biomedical fields. In locating and navigating a surgical robot, magnetic location techniques are not affected by obstructions and are less costly than optical tracking. Magnetic localization techniques are safer, less costly, and more efficient when tracking wireless capsule endoscopes, tongue motion, and magnetic drug markers than CT with radiation and expensive MRI.
When locating certain magnetic target characteristics (the magnetic moment direction of the magnetic target and the direction relative to the magnetic locating system), the locating error is very large, called a locating dead zone, i.e. the direction and the magnetic moment direction of the magnetic target determine whether the magnetic target is located in the locating dead zone. 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 concerned in the tensor magnetic positioning method. The current tensor magnetic positioning method has the following problems:
1. NARA method has positioning blind area due to singular full tensor matrix and does not have good blind area error compensation method
The NARA method does not need prior estimation of structural indexes, can quickly and accurately position magnetic targets, but when the full tensor matrix is odd, the positioning equation of the NARA method presents ill-condition and generates a positioning blind area. For the ill-conditioned nature of the positioning equation, a learner compensates the positioning result of the positioning blind area by utilizing Newton interpolation, and the learner also calculates the inverse matrix of the full tensor matrix by utilizing Moore-Penrose generalized inverse. Both of the two improved ideas need to select a threshold value to judge whether the matrix is singular or not, but the threshold values are different under different working conditions, so that the accurate threshold value is difficult to select. Currently, there is no good way to compensate for the location blind area of NARA.
2. The STAR method has a positioning blind area due to the aspheric coefficient, and the compensation effect of the blind area needs to be further improved
Researchers have proposed a scalar triangulation and ranging (STAR) method based on tensor invariant magnetic gradient contraction. The STAR method can position magnetic targets in real time and the positioning accuracy is not affected by the earth magnetic field. However, due to the existence of aspheric coefficients, the STAR method has aspheric errors, i.e. dead zones. The scholars have proposed an improved STAR method without aspheric coefficients, called LSM, which reduces the localization error of LSM by 10.9% compared to the STAR method. The learners compensate the direction error of the STAR method by using an iterative method, called WSM, and the positioning error of the WSM is reduced by 68.5% compared with the STAR method. However, neither LSM nor WSM fully compensates for aspheric errors, and there is room for further improvement in the compensation of STAR-method dead-zone localization.
3. Method for avoiding blind area by utilizing positioning blind area distribution rule without research
It has been shown that when the angle between the position vector and the magnetic moment vector is measured
Figure BDA0002714403840000029
When the temperature approaches 90 ℃, a positioning blind area appears in the NARA method; when the angle is included
Figure BDA00027144038400000210
Near 60 ° or 120 °, the STAR method has a dead zone of orientation. Although the dead zone and physical quantity of the location are known
Figure BDA00027144038400000211
However, no research is made on the mapping relationship to provide a method for avoiding the positioning blind area, and the distribution rule of the positioning blind area is not fully utilized.
Disclosure of Invention
The invention aims to provide a positioning method based on a magnetic gradiometer array and a design method thereof, and solves the problems that the tensor magnetic positioning method in the prior art has a positioning blind area, and is insufficient in error compensation of the positioning blind area and insufficient in positioning precision.
Positioning based on magnetic gradiometer array and design method thereof, positioning blind area and physical quantity are utilized
Figure BDA00027144038400000212
The mapping relation between the magnetic gradient meter and the magnetic gradient meter, and the topology of the magnetic gradient meter array is determined by designThe structure is that the optimal magnetic gradiometer in the magnetic gradiometer array is selected to change the included angle
Figure BDA00027144038400000213
To avoid the positioning blind area;
further, the selection of the optimal magnetic gradiometer in the array of magnetic gradiometers comprises the following steps:
s100, calculating magnetic gradient tensors G (i ═ 1,2, …, N) at all magnetic gradiometer positions according to equation (1), where N is the number of magnetic gradiometers:
Figure BDA0002714403840000021
b is magnetic induction, BabRepresents the gradient of the a component of B in the B direction;
s200, calculating the positions of all magnetic gradiometers by using the formula (2)
Figure BDA0002714403840000022
Figure BDA0002714403840000023
S300, according to the positioning blind area and the included angle
Figure BDA0002714403840000024
The mapping relation of (A) obtains an included angle which can minimize the positioning error
Figure BDA0002714403840000025
S400, calculating a position vector by using the magnetic gradient tensor of the magnetic gradiometer with the number j
Figure BDA0002714403840000026
And magnetic moment vector
Figure BDA0002714403840000027
Further, the design of the magnetic sensor array topology specifically comprises the following steps:
s010, average positioning distance in positioning working condition
Figure BDA0002714403840000028
Evaluating the magnetic moment M, the environmental noise standard deviation delta, the resolution S of the magnetic sensor and the noise level l of the magnetic sensor;
s020, substituting evaluation results of various factors in the positioning working condition into the full-attitude magnetic positioning model, and averaging the positioning results of the full-attitude magnetic positioning model to obtain a full-attitude error expectation epsilonpAs an evaluation index of positioning accuracy,. epsilonpThe smaller the positioning accuracy is, the higher the positioning accuracy is;
s030, recording the expected full attitude error as epsilon obtained by carrying out magnetic positioning by using a single magnetic gradiometerp0And the expected full attitude error of magnetic positioning by using the expanded positive N-edge heart-shaped array structure is recorded as epsilonp1Calculating the positioning accuracy improvement percentage rho,
Figure BDA0002714403840000031
s040, designing and expanding the edge number N, the expanded layer number m and the array radius L of the positive N-edge heart-shaped array structure by taking the positioning precision lifting percentage rho as an optimization index0Radius ratio ki；
And S050, obtaining the corresponding relation between the positioning precision lifting percentage rho and the number of the magnetic gradient meters, and selecting and expanding a parameter design scheme of the positive N-edge heart-shaped array structure according to the cost.
The main advantages of the invention are: the invention has the following advantages:
(1) aiming at the problem of insufficient error compensation of the existing research on the positioning blind area, the positioning blind area and the physical quantity are fully utilized
Figure BDA0002714403840000032
The mapping relationship between the magnetic gradient meters provides a method for changing the clips by selecting different magnetic gradient meters in the magnetic gradient meter arrayA blind area avoiding method for avoiding the positioning blind area by an angle so as to improve the positioning precision;
(2) specifically, the method for designing the array topological structure parameters is provided aiming at the problem that the more the number of the magnetic gradient meters is, the higher the cost is, the more the number of the magnetic gradient meters is, the more the position vectors can be regulated and controlled, the convenience and the feasibility are realized, the method for designing the array topological structure parameters is provided, the corresponding relation between the positioning precision and the number of the magnetic gradient meters is obtained, and the array topological structure parameters can be flexibly designed by combining the cost according to the corresponding relation in the practical use;
(3) compared with the magnetic positioning by using a single magnetic gradiometer, when the number m of the expansion layers is equal to 0, the positioning precision can be improved by 72.5 percent and is 0.0058 m; when the number of expansion layers m is equal to 1, the positioning accuracy can be improved by 82.6%, the positioning accuracy is 0.0037m, and the positioning accuracy is effectively improved.
Drawings
FIG. 1 is a schematic diagram of a magnetic gradiometer array based positioning system;
FIG. 2 is a diagram of a positive N-sided cardioid array structure;
FIG. 3 is a diagram of an expanded positive N-edge cardioid array structure;
FIG. 4 is a full-attitude magnetic positioning model;
FIG. 5 is a graph of percentage of relative error ω versus physical quantity
Figure BDA0002714403840000049
A map of the mapping relationship between;
fig. 6 is a graph of the design results when m is 0;
fig. 7 is a design result when m is 1;
FIG. 8 shows the positioning accuracy εp1The number of magnetic gradiometers.
Detailed Description
The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Because the positioning blind area has a mapping relation with the physical quantity phi, the position vector can be changed according to the formula (4)
Figure BDA00027144038400000410
Can change the included angle
Figure BDA00027144038400000411
Thereby realizing the avoidance of the positioning blind area. In magnetic positioning, it is difficult to move the magnetic target to the exact position without determining the position of the target, but the position vector can be changed by changing the position of the magnetic gradiometer. If the magnetic gradiometer is moved manually, the accuracy is insufficient, and if the magnetic gradiometer is moved by using a driving control system, hard magnetic and soft magnetic interference is introduced, so that the magnetic gradiometer array is formed by a plurality of magnetic gradiometers, the optimal magnetic gradiometer is selected for magnetic positioning by using the mapping relation between the positioning dead zone and the physical quantity, and the positioning system based on the magnetic gradiometer array is composed as shown in figure 1.
Figure BDA0002714403840000041
In the position vector
Figure BDA0002714403840000042
And magnetic moment vector
Figure BDA0002714403840000043
Under the unknown condition, the included angle can be accurately calculated by the formula (2)
Figure BDA0002714403840000044
Figure BDA0002714403840000045
In the formula of1、λ2、λ3Three features of the magnetic gradient tensor G ordered from large to smallThe eigenvalue, the magnetic gradient tensor, is the rate of change of the magnetic field vector in space, and contains 9 elements in total:
Figure BDA0002714403840000046
the main idea of a positioning blind area avoidance (GA-BAA) method based on a magnetic gradiometer array is to firstly utilize magnetic gradient tensor to calculate an included angle
Figure BDA0002714403840000047
According to the positioning blind area and the included angle
Figure BDA0002714403840000048
The mapping relation is that an optimal magnetic gradiometer is selected for magnetic positioning, and the avoidance of a positioning blind area is realized, and the specific steps are as follows:
the method comprises the following steps: calculating a magnetic gradient tensor G (i ═ 1,2, …, N) at all magnetic gradient meter (number of magnetic gradient meters N) positions according to equation (1);
step two: calculating the position of all magnetic gradiometers using equation (2)
Figure BDA0002714403840000051
Step three: according to the positioning blind area and the included angle
Figure BDA0002714403840000052
The mapping relation of (A) obtains an included angle which can minimize the positioning error
Figure BDA0002714403840000053
Step four: computing a position vector using a magnetic gradient tensor of a numbered j magnetic gradiometer
Figure BDA0002714403840000054
And magnetic moment vector
Figure BDA0002714403840000055
In GA-BAA, the topology of the magnetic gradiometer array is crucial. In order to ensure effectiveness and convenient implementation, the array topology should be designed according to the principles of "plane distribution" and "uniform distribution", and for this purpose, the invention proposes a positive N-edge heart-shaped array structure, as shown in fig. 2. Assuming that the array of magnetic gradiometers is located in the yoz plane, the square frame in the figure represents the magnetic gradiometers, N +1 magnetic gradiometers are at the original point except the magnetic gradiometer No. 0, the rest of the magnetic gradiometers are respectively on each vertex of the regular N polygon, the radius of the circumscribed circle of the regular N polygon is L, and L is called as the array radius.
The position coordinates of the other magnetic gradiometers except the magnetic gradiometer No. 0 are as follows:
Figure BDA0002714403840000056
meanwhile, the regular N-edge heart-shaped array structure is expanded outwards to obtain an expanded regular N-edge heart-shaped array structure, as shown in FIG. 3, m is called an expanded layer number Lj( j 1,2, …, m) extends the array radius of the array for j layers.
In the expanded positive N-edge heart-shaped array structure, the position coordinates of the other magnetic gradiometers except the magnetic gradiometer 0 are as follows:
Figure BDA0002714403840000057
in the expanded regular N-edge heart-shaped array structure, the number of edges N and the expanded layer number m of a regular polygon determine the number of magnetic gradiometer arrays, and the more the number is, the greater the probability of regulating and controlling the included angle to an ideal included angle is, but the corresponding cost is increased; array radius LmDetermines the regulation range of the included angle, LmToo small to effectively avoid the blind zone, LmToo large results in the outer magnetic gradient meter being too far away from the magnetic target, and the positioning error is increased, so that the outer magnetic gradient meter cannot be effectively utilized. Therefore, the number of opposite sides N, the number of expanding layers m, and the array radius L are requiredmAnd (5) designing. For design convenience, the radius ratio k is definedi：
Figure BDA0002714403840000061
In actual positioning, the attitude of the magnetic target is often arbitrary and uncontrolled, while the magnetic moment vector is made to be complete in order to make the change of the angle φ complete
Figure BDA0002714403840000062
A full-attitude magnetic localization model is established covering the whole sphere, as shown in fig. 4.
Therefore, the specific design steps for expanding the positive N-edge heart-shaped array structure are as follows:
the method comprises the following steps: for average positioning distance in positioning working condition
Figure BDA0002714403840000063
Evaluating the magnetic moment M, the environmental noise standard deviation sigma, the resolution S of the magnetic sensor and the noise level l of the magnetic sensor;
step two: substituting the evaluation results of various factors in the positioning working condition into the full-attitude magnetic positioning model, and averaging the positioning results of the full-attitude magnetic positioning model to obtain the expected full-attitude error epsilonpAs an evaluation index of positioning accuracy,. epsilonpThe smaller the positioning accuracy is;
step three: the expected full attitude error obtained by magnetic positioning by using a single magnetic gradiometer is recorded as epsilonp0And the expected full attitude error of magnetic positioning by using the expanded positive N-edge heart-shaped array structure is recorded as epsilonp1Calculating the positioning precision improvement percentage rho;
Figure BDA0002714403840000064
step four: designing and expanding the edge number N, the expanded layer number m and the array radius L of the positive N-edge heart-shaped array structure by taking the positioning precision lifting percentage rho as an optimization index0Radius ratio ki；
Step five: and obtaining the corresponding relation between the positioning precision improvement percentage rho and the number of the magnetic gradiometers, and selecting and expanding a parameter design scheme of the positive N-edge heart-shaped array structure according to the cost.
The following are specific embodiments of the present invention:
in the prior art, a scalar triangulation and ranging (STAR) method is provided based on an invariant of a magnetic gradient tensor, a magnetic target can be positioned in real time, positioning accuracy is not influenced by a geomagnetic field, and the STAR method is taken as an example to carry out implementation description of the invention. The positioning error of the STAR method is mainly an aspheric error δ, and the mapping relation between the aspheric error and the physical quantity is as follows:
Figure BDA0002714403840000065
from the equation (8), it can be seen that the aspheric error delta is linear with the distance r and is linear with the included angle
Figure BDA0002714403840000066
In a non-linear relationship. Calculating the relative error percentage ω:
Figure BDA0002714403840000071
percentage of relative error ω and physical quantity
Figure BDA0002714403840000079
The mapping relationship between the two is shown as 5, and it can be seen from the figure that when the two are combined
Figure BDA0002714403840000072
Or
Figure BDA0002714403840000073
The relative error is maximum; when in use
Figure BDA0002714403840000074
Or
Figure BDA0002714403840000075
Or
Figure BDA0002714403840000076
There is no relative error. Thus, in GA-BAA, the included angle is calculated
Figure BDA0002714403840000077
And then selecting the optimal magnetic gradiometer number according to the formula (9).
The amplitude of the geomagnetic field is 55000nT, the declination angle and the inclination angle are-10 degrees and 60 degrees respectively, the magnetic moment size M, the baseline distance D, the resolution S of the magnetic sensor, the noise level l of the magnetic sensor and the standard deviation sigma of Gaussian white noise are shown in Table 1.
Figure BDA0002714403840000078
TABLE 1 simulation conditions
When the number of expansion layers m is 0, the calculation result is shown in fig. 6. At this time, the array radius L is taken0The positioning precision can be improved to the maximum to reach 72.5 percent by the edge number N of 0.14m and the expected epsilon of the full attitude errorp1It was 0.0058 m.
When the number of expansion layers m is 1, the calculation result is shown in fig. 7. At this time, the array radius L is taken00.10m, radius ratio k11.7 is the array radius L1The positioning precision can be improved to the maximum by 0.17m and 10 edges N, and reaches 82.6%, and the expected epsilon of the full attitude errorp1It was 0.0037 m. The user can design for more layers of expansion according to the method of the present invention, and does not show too many in this example.
The highest positioning accuracy obtained by expanding different sides of the positive N-side heart-shaped array structure is calculated, as shown in FIG. 8. In the figure, the number of edges is the number of the magnetic gradient meters when the expansion layer number m is equal to 0, the number of edges is twice the number of the magnetic gradient meters when the expansion layer number m is equal to 1, and the rest of the expansion layer numbers can be analogized. Therefore, fig. 8 is a corresponding relationship between the positioning accuracy and the magnetic gradient meter, and parameters for flexibly designing and expanding the positive N-edge heart-shaped array structure can be combined with the corresponding relationship and the cost.
The present invention is capable of other embodiments and its several details are capable of modifications in various obvious respects, all without departing from the spirit and scope of the present invention.

Claims (1)

1. A positioning and design method based on magnetic gradiometer array is characterized by using positioning blind area and physical quantity
Figure FDA00031883127600000110
The mapping relation between the magnetic gradient meters is determined by designing the topological structure of the magnetic gradient meter array, and the optimal magnetic gradient meter in the magnetic gradient meter array is selected to change the included angle
Figure FDA00031883127600000111
To avoid the positioning blind area;
the selection of the optimal magnetic gradiometer in the array of magnetic gradiometers comprises the steps of:
s100, calculating magnetic gradient tensors G at the positions of all the magnetic gradiometers according to an equation (1), wherein N is the number of the magnetic gradiometers:
Figure FDA0003188312760000011
b is magnetic induction, BabRepresents the gradient of the a component of B in the B direction;
s200, calculating the positions of all magnetic gradiometers by using the formula (2)
Figure FDA0003188312760000012
Figure FDA0003188312760000013
S300, according to the positioning blind area and the included angle
Figure FDA0003188312760000014
The mapping relation of (A) obtains an included angle which can minimize the positioning error
Figure FDA0003188312760000015
S400, calculating a position vector by using the magnetic gradient tensor of the magnetic gradiometer with the number j
Figure FDA0003188312760000016
Magnetic moment vector
Figure FDA0003188312760000017
The design of the magnetic sensor array topology specifically comprises the following steps:
s010, average positioning distance in positioning working condition
Figure FDA0003188312760000018
Evaluating the magnetic moment M, the environmental noise standard deviation delta, the resolution S of the magnetic sensor and the noise level l of the magnetic sensor;
s020, substituting evaluation results of various factors in the positioning working condition into the full-attitude magnetic positioning model, and averaging the positioning results of the full-attitude magnetic positioning model to obtain a full-attitude error expectation epsilonpAs an evaluation index of positioning accuracy,. epsilonpThe smaller the positioning accuracy is, the higher the positioning accuracy is;
s030, recording the expected full attitude error as epsilon obtained by carrying out magnetic positioning by using a single magnetic gradiometerp0And the expected full attitude error of magnetic positioning by using the expanded positive N-edge heart-shaped array structure is recorded as epsilonp1Calculating the positioning accuracy improvement percentage rho,
Figure FDA0003188312760000019
s040, designing and expanding the edge number N, the expanded layer number m and the array radius L of the positive N-edge heart-shaped array structure by taking the positioning precision lifting percentage rho as an optimization index0Radius ratio ki；
And S050, obtaining the corresponding relation between the positioning precision lifting percentage rho and the number of the magnetic gradient meters, and selecting and expanding a parameter design scheme of the positive N-edge heart-shaped array structure according to the cost.
CN202011067995.5A 2020-10-08 2020-10-08 Positioning based on magnetic gradiometer array and design method thereof Active CN112294437B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202011067995.5A CN112294437B (en) 2020-10-08 2020-10-08 Positioning based on magnetic gradiometer array and design method thereof

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202011067995.5A CN112294437B (en) 2020-10-08 2020-10-08 Positioning based on magnetic gradiometer array and design method thereof

Publications (2)

Publication Number Publication Date
CN112294437A CN112294437A (en) 2021-02-02
CN112294437B true CN112294437B (en) 2021-09-14

Family

ID=74488716

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202011067995.5A Active CN112294437B (en) 2020-10-08 2020-10-08 Positioning based on magnetic gradiometer array and design method thereof

Country Status (1)

Country Link
CN (1) CN112294437B (en)

Families Citing this family (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114137447B (en) * 2022-02-07 2022-07-12 西南民族大学 Method and device for compensating swing noise of magnetic gradiometer, electronic device and storage medium
CN114413884B (en) * 2022-03-29 2022-07-15 西南民族大学 Positioning method and device based on magnetic gradiometer array and storage medium

Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US6562019B1 (en) * 1999-09-20 2003-05-13 Stereotaxis, Inc. Method of utilizing a magnetically guided myocardial treatment system
CN110095738A (en) * 2019-04-15 2019-08-06 哈尔滨工业大学 Magnetic gradiometer Parameters design

Family Cites Families (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
DE202005007918U1 (en) * 2005-05-20 2005-07-14 Böllhoff Verbindungstechnik GmbH Structural components` distance tolerance compensating unit, has base and compensating parts with stepped supporting and counter surfaces, respectively, where surfaces fit together so that parts rotate to change axial dimension of unit
KR20090040695A (en) * 2007-10-22 2009-04-27 주식회사 이노터치테크놀로지 Touch screen
CN102826166B (en) * 2012-07-28 2014-03-26 成都宽和科技有限责任公司 Sensor with unevenly distributed magnetic blocks inside shell
CN106595670B (en) * 2016-12-30 2019-11-05 北京航空航天大学 A method of using generalized inverse matrix dead zone-eliminating
WO2018172881A1 (en) * 2017-03-24 2018-09-27 株式会社半導体エネルギー研究所 Semiconductor device, display system, and electronic device
CN110044321B (en) * 2019-03-22 2021-01-29 北京理工大学 Method for resolving aircraft attitude by using geomagnetic information and angular rate gyroscope
CN110007350B (en) * 2019-04-15 2020-08-25 哈尔滨工业大学 Analysis method for magnetic detection method blind area

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US6562019B1 (en) * 1999-09-20 2003-05-13 Stereotaxis, Inc. Method of utilizing a magnetically guided myocardial treatment system
CN110095738A (en) * 2019-04-15 2019-08-06 哈尔滨工业大学 Magnetic gradiometer Parameters design

Also Published As

Publication number Publication date
CN112294437A (en) 2021-02-02

Similar Documents

Publication Publication Date Title
CN112294437B (en) Positioning based on magnetic gradiometer array and design method thereof
CN110007350B (en) Analysis method for magnetic detection method blind area
CN111190230B (en) Detection method based on magnetic gradient tensor
CN108413988B (en) Method for quickly calibrating coordinate system of theodolite at tail end of robot
CN111551895B (en) Method for positioning TDOA and FDOA of motion source based on weighted multidimensional scale and Lagrange multiplier
CN109211246B (en) Planet landing trajectory planning method under uncertain environment
Chen et al. A new geomagnetic matching navigation method based on multidimensional vector elements of earth’s magnetic field
CN109917333A (en) Merge the passive location method of AOA observed quantity and TDOA observed quantity
CN110849355B (en) Bionic navigation method for geomagnetic multi-parameter multi-target rapid convergence
CN112986906B (en) RSS-TOA joint positioning method for semi-positive definite programming
CN111190229B (en) Magnetic target detection method
CN114063614B (en) Multi-small robot system mixed formation rapid convergence method based on airborne monocular vision perception
CN116661469A (en) Robot track error correction method and system
CN103307968A (en) Method for detecting posture of robot carrying platform
CN114527786A (en) Improved dynamic planning method for complex terrain low-altitude penetration flight path planning
CN112284372B (en) Positioning precision improving method based on coil magnetic field regulation and control
CN112386209B (en) Positioning precision improving method based on movable magnetic gradiometer
CN108061922B (en) A kind of distribution magnetic anomaly detection system dynamic magnetic compensation method
CN109375160A (en) A kind of angle error estimation method in Pure orientation passive location
CN108595373A (en) It is a kind of without control DEM method for registering
Wang et al. High precision and fast estimation of position and attitude measurement for space targets
CN110687502B (en) Short wave direction finding data set labeling method based on least square positioning
CN105259564B (en) A kind of spaceborne and poor amplitude-comparison monopulse DF and location method, apparatus and system
Pargmann et al. Enhancing heliostat calibration on low data by fusing robotic rigid body kinematics with neural networks
Wan et al. Joint Rigid Body Localization and Wireless Signal Transmission Parameter Estimation Under NLOS Environment

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant