CN112254732A - Space four-point magnetic field positioning method and device based on rotating magnetic dipole - Google Patents

Space four-point magnetic field positioning method and device based on rotating magnetic dipole Download PDF

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CN112254732A
CN112254732A CN202011106014.3A CN202011106014A CN112254732A CN 112254732 A CN112254732 A CN 112254732A CN 202011106014 A CN202011106014 A CN 202011106014A CN 112254732 A CN112254732 A CN 112254732A
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magnetic field
dipole
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CN112254732B (en
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张宁
林朋飞
常明
林春生
徐磊
程锦房
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Naval University of Engineering PLA
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    • G01—MEASURING; TESTING
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Abstract

The invention relates to a space four-point magnetic field positioning method and device based on a rotating magnetic dipole. The invention realizes the positioning of the magnetic source target under the condition of unknown magnetic source information, and has small influence of noise and high positioning precision.

Description

Space four-point magnetic field positioning method and device based on rotating magnetic dipole
Technical Field
The invention relates to the field of magnetic field positioning, in particular to a space four-point magnetic field positioning method and device based on a rotating magnetic dipole.
Background
The realization of magnetic target positioning by using magnetic field signals is always a research hotspot at home and abroad. The magnetic positioning technology is widely applied in the fields of medical equipment, geomagnetic matching, military target identification, well drilling exploration and the like. Sheinker et al propose an indoor positioning method based on the quasi-static magnetic field of the rotating magnetic dipole source, and verify through experiments that the positioning accuracy of the algorithm is high, the calculated amount is small, and the real-time is strong. Christian et al propose a Jacobian matrix-based magnetic gradient positioning algorithm for a robotic capsule endoscope, which positions the capsule in real time, thereby achieving real-time control of the endoscope capsule. The characteristic analysis is carried out on the magnetic field signal of the alternating magnetic dipole radiation source in the geomagnetic environment by the high-flying mode, and an optimal solving algorithm combining a gauss-newton method and a particle swarm method is provided. Fan et al propose a fast linear real-time positioning algorithm for targets based on total magnetic field gradients, and verify that the positioning accuracy of the algorithm is very high through simulation and a large amount of test data.
However, most magnetic field localization is mainly directed to static magnetic field signals, and localization studies for harmonic magnetic fields are few. The static magnetic field signal is greatly affected by environmental noise and geomagnetic disturbance, which limits the positioning distance and requires many sensors. And the low-frequency harmonic signals generated by the low-frequency rotating magnetic dipole have the characteristics of long propagation distance and high anti-interference capability, and are favorable for improving the positioning distance and precision.
Disclosure of Invention
The invention provides a space four-point magnetic field positioning method based on a rotating magnetic dipole, aiming at the technical problem that the existing magnetic positioning technology is easy to be interfered by environmental noise and geomagnetism, and the method comprises the following steps: constructing a magnetic source coordinate system, an observation coordinate system and a magnetic field model of the rotating magnetic dipole; determining the relationship between the coordinates of the observation point on the magnetic source coordinate system and the magnetic field distribution of the rotating magnetic dipole according to the magnetic source coordinate system and the magnetic field model; determining the relationship between the rotating magnetic dipole and the coordinate of the observation point in the observation coordinate system and the induced magnetic field intensity of the observation point in the observation coordinate system according to the equivalent relationship between the rotating magnetic dipole and the magnetic source coordinate system and the magnetic field distribution of the rotating magnetic dipole; and obtaining the induced magnetic field intensity and the coordinates of the observation point in the observation coordinate system, and solving the coordinates of the rotating magnetic dipole in the observation coordinate system by a Newton iteration method according to the induced magnetic field intensity and the coordinates of the observation point in the observation coordinate system and the equivalent relation of the rotating magnetic dipole in the observation coordinate system and the magnetic source coordinate system.
In some embodiments of the present invention, the determining a relationship between coordinates of the observation point on the source coordinate system and a magnetic field distribution of the rotating magnetic dipole according to the source coordinate system and the magnetic field model includes: to rotate the magnetic moment of the magnetic dipole
Figure BDA0002726981490000021
The rotating shaft of the magnetic source is a z-axis, and a magnetic source coordinate system xyz is established; determining the magnetic moment of a rotating magnetic dipole from a magnetic field model
Figure BDA0002726981490000022
The components m in the x, y and z axes of the coordinate system xyzp、mf、ml：
Figure BDA0002726981490000023
Equation (1); in which the magnetic moment
Figure BDA0002726981490000024
Projection on the z-axis is
Figure BDA0002726981490000025
The projection on the xy plane is
Figure BDA0002726981490000026
Omega is the rotation angular velocity of the rotating magnetic dipole, alpha0Being magnetic moment
Figure BDA0002726981490000027
An initial angle with the x-axis;
obtaining the magnetic moment according to the Biao-Saval law, the coefficient matrix and the equation (1)
Figure BDA0002726981490000028
And
Figure BDA0002726981490000029
magnetic field strength generated on three axes of the coordinate system xyz:
Figure BDA00027269814900000210
equation (2); wherein
Figure BDA00027269814900000211
Indicating sensed magnetic moment at observation point
Figure BDA00027269814900000212
And
Figure BDA00027269814900000213
the magnetic field component corresponding to three axes on the magnetic source coordinate system, omega is the rotation angular velocity of the rotating magnetic dipole, alpha0Being magnetic moment
Figure BDA00027269814900000214
An initial angle with the x-axis;
determining the rotating magnetic dipole moment from equation (2) and the coefficient matrix A
Figure BDA00027269814900000216
And
Figure BDA00027269814900000217
the relationship of three components of magnetic induction intensity generated at an observation point in a coordinate system xyz is as follows:
Figure BDA0002726981490000031
equation (3); the coefficient matrix a is defined as:
Figure BDA0002726981490000032
wherein r is2＝(x-x0)2+(y-y0)2+(z-z0)2，μ0Is magnetic permeability; x, y and z respectively represent x-axis coordinate, y-axis coordinate and z-axis coordinate of the observation point in a coordinate system xyz, and x0、y0、z0Are respectively provided withAnd the x-axis coordinate, the y-axis coordinate and the z-axis coordinate of the rotating magnetic dipole in a coordinate system xyz are shown.
Further, the determining the relationship between the rotating magnetic dipole and the coordinate of the observation point in the observation coordinate system and the induced magnetic field strength of the observation point in the observation coordinate system according to the equivalent relationship between the rotating magnetic dipole and the magnetic source coordinate system and the magnetic field distribution comprises the following steps:
according to the initial angle alpha of the rotating magnetic dipole0Determining a rotation matrix K according to the rotation equivalent relation between the observed coordinate system uvw and the magnetic source coordinate system xyz, wherein
Figure BDA0002726981490000033
According to said magnetic moment
Figure BDA0002726981490000034
And
Figure BDA0002726981490000035
determining the relation between the coordinates of an observation point in an observation coordinate system and the magnetic field component by the magnetic field intensity generated by three axes of the magnetic source coordinate system xyz and the rotation matrix K:
Figure BDA0002726981490000036
equation (4); wherein u, v and w are corresponding three-axis coordinates of the observation point in an observation coordinate system uvw, and u0、v0、w0Is the corresponding three-axis coordinate of the rotating magnetic dipole in the observation coordinate system uvw, omega is the rotation angular velocity of the rotating magnetic dipole,
Figure BDA0002726981490000037
is the component of the magnetic field strength of the observation point in the observation coordinate system uvw.
Furthermore, the magnetic field intensity component B of the rotating magnetic dipole in the observed coordinate system uvw is obtained according to the magnetic field model of the rotating magnetic dipole in the source coordinate system xyz and the equivalent relationship between the observed coordinate system uvw and the source coordinate system xyzu、Bv、Bw、：
Figure BDA0002726981490000041
Equation (5); wherein
Figure BDA00027269814900000410
Respectively represent the magnetic moments
Figure BDA0002726981490000042
Figure BDA0002726981490000043
And
Figure BDA0002726981490000044
the magnetic field strength on the three axes of the observation coordinate system uvw,
Figure BDA0002726981490000045
respectively representing magnetic moments
Figure BDA0002726981490000046
And
Figure BDA0002726981490000047
the magnetic field intensity on three axes of a magnetic source coordinate system xyz;
and (3) determining the relation between the coordinates of the rotating magnetic dipole and the observation point in the observation coordinate system and the rotation matrix K according to the equation (5) and the equation (2) and the coefficient matrix B:
Figure BDA0002726981490000048
equation (6); wherein the coefficient matrix B is defined as:
Figure BDA0002726981490000049
in some embodiments of the present invention, the obtaining of the induced magnetic field strength and the coordinates of the observation point in the observation coordinate system, and solving the coordinates of the rotating magnetic dipole in the observation coordinate system by a newton iteration method according to the induced magnetic field strength and the coordinates of the observation point in the observation coordinate system and the equivalent relationship between the rotating magnetic dipole in the observation coordinate system and the magnetic source coordinate system includes the following steps:
acquiring magnetic field strengths of the four observation points and coordinates of the four observation points in an observation point coordinate system;
determining the relation between a coefficient matrix B and a rotation matrix K according to the relation between the magnetic field intensity, the coordinate of the observation point coordinate system, the rotary magnetic dipole and the coordinate of the observation point in the observation coordinate system and the rotation matrix K:
Figure BDA0002726981490000051
solving the coordinates of the rotating magnetic dipole in the observation coordinate system according to the constraint condition of the rotating matrix K and an equation (7), wherein the constraint condition of the rotating matrix K is as follows:
Figure BDA0002726981490000052
equation (8).
Further, the solving of the coordinates of the rotating magnetic dipole in the observation coordinate system according to the constraint condition of the rotation matrix K and equation (7) includes the following steps:
obtaining P1 and P2 of two observation points, the P1、P2The coordinates in the observation coordinate system are respectively P1(0,0,0)、P2(u2,v2,w2)；
Will P1、P2Substituting into equation (6), we get from newton's iteration:
Figure BDA0002726981490000053
equation (9);
and (5) calculating the coordinates of the rotating magnetic dipole observation coordinate system according to the equation (8) and the equation (9).
In a second aspect of the invention, a space four-point magnetic field positioning device based on a rotating magnetic dipole is provided, which comprises a construction module, a first determination module, a second determination module and an iteration module, wherein the construction module is used for respectively establishing a magnetic field model for the rotating magnetic dipole in a magnetic source coordinate system and an observation coordinate system; the first determining module is used for determining the relationship between the coordinates of the observation point on the magnetic source coordinate system and the magnetic field distribution of the rotating magnetic dipole according to the magnetic source coordinate system and the magnetic field model; the second determining module is used for determining the relationship between the rotating magnetic dipole and the coordinate of the observation point in the observation coordinate system and the induced magnetic field intensity of the observation point in the observation coordinate system according to the equivalent relationship between the rotating magnetic dipole and the magnetic source coordinate system and the magnetic field distribution of the rotating magnetic dipole; and the iteration module is used for solving the coordinates of the rotating magnetic dipole in the observation coordinate system by a Newton iteration method according to the magnetic field intensity and the coordinates detected by the observation point in the observation coordinate system and the equivalent relationship of the rotating magnetic dipole in the observation coordinate system and the magnetic source coordinate system.
Further, the iteration module comprises an acquisition module and a calculation module, wherein the acquisition module is used for acquiring the coordinates and the magnetic field intensity of the observation point in the observation coordinate system;
and the calculation module is used for solving the coordinates of the rotating magnetic dipole in the observation coordinate system by a Newton iteration method according to the magnetic field intensity and the coordinates detected by the observation point in the observation coordinate system and the equivalent relationship of the rotating magnetic dipole in the observation coordinate system and the magnetic source coordinate system.
In a third aspect of the present invention, there is provided an electronic device comprising: one or more processors; storage means for storing one or more programs which, when executed by the one or more processors, cause the one or more processors to carry out the method provided by the first aspect of the invention.
In a fourth aspect of the invention, a computer-readable medium is provided, on which a computer program is stored, wherein the computer program, when executed by a processor, implements the method provided by the first aspect of the invention.
The invention has the beneficial effects that:
1. modeling the magnetic field distribution of rotating magnetic dipoles in a magnetic source coordinate system and an observation coordinate system, and solving the magnetic field component of an observation point and the nonlinear equation set of the magnetic source in the observation coordinate system by a Newton iteration method under the condition of unknown target information of the magnetic source;
2. the invention is little influenced by measurement noise, and meanwhile, the magnetic moment can move in a certain range due to uneven magnetic distribution, and the size of a magnetic target can show that the movement range of the general magnetic moment is limited, and the influence on the positioning precision is also in a reasonable range;
3. the influence of measurement noise on the positioning precision is small, and the magnitude of triaxial absolute error is 10-12With a relative error of the order of 10-14. And the motion range of the magnetic moment in the z-axis direction is [ z ]0-0.5,z0+0.5]The motion radius r' in the xy plane is less than 1.5m, the absolute error of the three axes is less than 0.2m, and the relative error is less than 4%.
Drawings
FIG. 1 is a schematic diagram of a magnetic source coordinate system in some embodiments of the invention;
FIG. 2 is a schematic diagram of a measurement coordinate system and a magnetic source coordinate system in some embodiments of the invention;
FIG. 3 is a basic flow diagram of a method for spatial four-point magnetic field localization based on rotating magnetic dipoles in some embodiments of the present invention;
FIG. 4 is a basic block diagram of a rotating magnetic dipole based spatial four-point magnetic field positioning device in some embodiments of the present invention;
FIG. 5 is a primary block diagram of an electronic device in some of the several embodiments of the present invention;
FIG. 6 is P in some embodiments of the invention1Point magnetic field intensity three components and total intensity distribution thereof;
FIG. 7 is P in some embodiments of the invention2Point magnetic field intensity three components and total intensity distribution thereof;
FIG. 8 illustrates u in an observation coordinate system according to some embodiments of the inventions0、v0、w0And r0Along with magnetic source coordinate system x0A change in (c);
FIG. 9 is an absolute error of three axis coordinates in some embodiments of the invention;
FIG. 10 is a graph of the relative error of three-axis coordinates in some embodiments of the invention;
FIG. 11 is a graph of the absolute error of three-axis coordinates at a measurement noise of 1nT in some embodiments of the present invention;
FIG. 12 is a graph of the relative error of three axis coordinates with a measurement noise of 1nT in some embodiments of the invention;
FIG. 13 is a schematic diagram of the magnetic moment movement of a rotating magnetic dipole in some embodiments of the invention;
FIG. 14 is a graph of absolute error of three axis coordinates at different radii of motion in some embodiments of the invention;
FIG. 15 illustrates the relative error of three axis coordinates at different radii of motion in some embodiments of the invention.
Detailed Description
The principles and features of this invention are described below in conjunction with the following drawings, which are set forth by way of illustration only and are not intended to limit the scope of the invention.
Referring to fig. 1 to 3, a method for positioning a spatial four-point magnetic field based on a rotating magnetic dipole includes: s101, constructing a magnetic source coordinate system, an observation coordinate system and a magnetic field model of a rotating magnetic dipole; s102, determining the relation between the coordinate of an observation point on a magnetic source coordinate system and the magnetic field distribution of the rotating magnetic dipole according to the magnetic source coordinate system and a magnetic field model; s103, determining the relationship between the rotating magnetic dipole and the coordinate of the observation point in the observation coordinate system and the induced magnetic field intensity of the observation point in the observation coordinate system according to the equivalent relationship between the rotating magnetic dipole and the magnetic source coordinate system and the magnetic field distribution of the rotating magnetic dipole; s104, acquiring the induced magnetic field intensity and the coordinates of the observation point in the observation coordinate system, and solving the coordinates of the rotating magnetic dipole in the observation coordinate system through a Newton iteration method according to the induced magnetic field intensity and the coordinates of the observation point in the observation coordinate system and the equivalent relation of the rotating magnetic dipole in the observation coordinate system and the magnetic source coordinate system.
In step S102 of some embodiments of the invention, the magnetic field is appliedThe source coordinate system and the magnetic field model determine the relationship between the coordinates of the observation point on the magnetic source coordinate system and the magnetic field distribution of the rotating magnetic dipole, and the method comprises the following steps: to rotate the magnetic moment of the magnetic dipole
Figure BDA0002726981490000081
The rotating shaft of the magnetic source is a z-axis, and a magnetic source coordinate system xyz is established; determining the magnetic moment of a rotating magnetic dipole from a magnetic field model
Figure BDA0002726981490000082
The components m in the x, y and z axes of the coordinate system xyzp、mf、ml：
Figure BDA0002726981490000083
Equation (1); in which the magnetic moment
Figure BDA0002726981490000084
Projection on the z-axis is
Figure BDA0002726981490000085
The projection on the xy plane is
Figure BDA0002726981490000086
Omega is the rotation angular velocity of the rotating magnetic dipole, alpha0Being magnetic moment
Figure BDA0002726981490000087
An initial angle with the x-axis; obtaining the magnetic moment according to the Biao-Saval law, the coefficient matrix and the equation (1)
Figure BDA0002726981490000088
And
Figure BDA0002726981490000089
magnetic field strength generated on three axes of the coordinate system xyz:
Figure BDA00027269814900000810
equation (2); wherein
Figure BDA00027269814900000811
Indicating sensed magnetic moment at observation point
Figure BDA00027269814900000812
And
Figure BDA00027269814900000813
the component of the magnetic field corresponding to three axes in the magnetic source coordinate system is the rotation angular velocity of the rotating magnetic dipole, alpha0Being magnetic moment
Figure BDA00027269814900000814
An initial angle with the x-axis; determining the rotating magnetic dipole moment from equation (2) and the coefficient matrix A
Figure BDA00027269814900000815
And
Figure BDA00027269814900000816
the relationship of three components of magnetic induction intensity generated at an observation point in a coordinate system xyz is as follows:
Figure BDA0002726981490000091
equation (3); the coefficient matrix a is defined as:
Figure BDA0002726981490000092
wherein r is2＝(x-x0)2+(y-y0)2+(z-z0)2，μ0Is magnetic permeability; x, y and z respectively represent x-axis coordinate, y-axis coordinate and z-axis coordinate of the observation point in a coordinate system xyz, and x0、y0、z0Respectively representing the x-axis coordinate, the y-axis coordinate and the z-axis coordinate of the rotating magnetic dipole in a coordinate system xyz.
Further, the determining the relationship between the rotating magnetic dipole and the coordinate of the observation point in the observation coordinate system and the induced magnetic field strength of the observation point in the observation coordinate system according to the equivalent relationship between the rotating magnetic dipole and the magnetic source coordinate system and the magnetic field distribution comprises the following steps:
according to the initial angle alpha of the rotating magnetic dipole0Determining a rotation matrix K according to the rotation equivalent relation between the observed coordinate system uvw and the magnetic source coordinate system xyz, wherein
Figure BDA0002726981490000093
According to said magnetic moment
Figure BDA0002726981490000094
And
Figure BDA0002726981490000095
determining the relation between the coordinates of an observation point in an observation coordinate system and the magnetic field component by the magnetic field intensity generated by three axes of the magnetic source coordinate system xyz and the rotation matrix K:
Figure BDA0002726981490000096
equation (4); wherein u, v and w are corresponding three-axis coordinates of the observation point in an observation coordinate system uvw, and u0、v0、w0Is the corresponding three-axis coordinate of the rotating magnetic dipole in the observation coordinate system uvw, omega is the rotation angular velocity of the rotating magnetic dipole,
Figure BDA0002726981490000097
is the component of the magnetic field strength of the observation point in the observation coordinate system uvw.
Furthermore, the magnetic field intensity component B of the rotating magnetic dipole in the observed coordinate system uvw is obtained according to the magnetic field model of the rotating magnetic dipole in the source coordinate system xyz and the equivalent relationship between the observed coordinate system uvw and the source coordinate system xyzu、Bv、Bw、：
Figure BDA0002726981490000101
Equation (5); wherein
Figure BDA0002726981490000102
Respectively representThe magnetic moment
Figure BDA0002726981490000103
Figure BDA0002726981490000104
And
Figure BDA0002726981490000105
the magnetic field strength on the three axes of the observation coordinate system uvw,
Figure BDA0002726981490000106
respectively representing magnetic moments
Figure BDA0002726981490000107
And
Figure BDA0002726981490000108
the magnetic field intensity on three axes of a magnetic source coordinate system xyz; and (3) determining the relation between the coordinates of the rotating magnetic dipole and the observation point in the observation coordinate system and the rotation matrix K according to the equation (5) and the equation (2) and the coefficient matrix B:
Figure BDA0002726981490000109
equation (6); wherein the coefficient matrix B is defined as:
Figure BDA00027269814900001010
in step S104 of some embodiments of the present invention, the obtaining of the induced magnetic field strength and the coordinates of the observation point in the observation coordinate system, and solving the coordinates of the rotating magnetic dipole in the observation coordinate system by using a newton iteration method according to the induced magnetic field strength and the coordinates of the observation point in the observation coordinate system and the equivalent relationship between the observation coordinate system and the magnetic source coordinate system of the observation point and the magnetic source coordinate system includes the following steps: acquiring magnetic field strengths of the four observation points and coordinates of the four observation points in an observation point coordinate system; determining the relation between a coefficient matrix B and a rotation matrix K according to the relation between the magnetic field intensity, the coordinate of the observation point coordinate system, the rotary magnetic dipole and the coordinate of the observation point in the observation coordinate system and the rotation matrix K:
Figure BDA0002726981490000111
equation (7);
solving the coordinates of the rotating magnetic dipole in the observation coordinate system according to the constraint condition of the rotating matrix K and an equation (7), wherein the constraint condition of the rotating matrix K is as follows:
Figure BDA0002726981490000112
equation (8).
Further, the solving of the coordinates of the rotating magnetic dipole in the observation coordinate system according to the constraint condition of the rotation matrix K and equation (7) includes the following steps: obtaining P1 and P2 of two observation points, the P1、P2The coordinates in the observation coordinate system are respectively P1(0,0,0)、P2(u2,v2,w2) (ii) a Will P1、P2Substituting into equation (6), we get from newton's iteration:
Figure BDA0002726981490000113
equation (9);
and (5) calculating the coordinates of the rotating magnetic dipole observation coordinate system according to the equation (8) and the equation (9).
Referring to fig. 4, the present invention provides a space four-point magnetic field positioning apparatus 1 based on a rotating magnetic dipole, including a construction module 11, a first determination module 12, a second determination module 13, and an iteration module 14, where the construction module 11 is configured to respectively establish a magnetic field model in a magnetic source coordinate system and an observation coordinate system for the rotating magnetic dipole; the first determining module 12 is configured to determine, according to the magnetic source coordinate system and the magnetic field model, a relationship between coordinates of the observation point on the magnetic source coordinate system and magnetic field distribution of the rotating magnetic dipole; the second determining module 13 is configured to determine, according to an equivalent relationship between the rotating magnetic dipole and the magnetic source coordinate system in the observation coordinate system and the magnetic field distribution thereof, a relationship between the rotating magnetic dipole and a coordinate of the observation point in the observation coordinate system and an induced magnetic field strength of the observation point in the observation coordinate system; the iteration module 14 is configured to solve the coordinates of the rotating magnetic dipole in the observation coordinate system by a newton iteration method according to the magnetic field strength and the coordinates detected by the observation point in the observation coordinate system and the equivalent relationship between the rotating magnetic dipole in the observation coordinate system and the magnetic source coordinate system.
Further, the iteration module 14 includes an obtaining module and a calculating module, where the obtaining module is configured to obtain coordinates and magnetic field strength of the observation point in the observation coordinate system; and the calculation module is used for solving the coordinates of the rotating magnetic dipole in the observation coordinate system by a Newton iteration method according to the magnetic field intensity and the coordinates detected by the observation point in the observation coordinate system and the equivalent relationship of the rotating magnetic dipole in the observation coordinate system and the magnetic source coordinate system.
The following further explains the implementation effect of the present invention by combining with simulation experiments: in the magnetic source coordinate system, let the magnetic source coordinate be (x)0,y0,z0) The coordinates of the observation point P are (x, y, z) ((15, 4, 10)), (15,20,27), the observation coordinate system uvw is obtained by sequentially rotating the magnetic source xyz coordinate system by an angle α around the x-axis, an angle β around the y-axis, and an angle γ around the z-axis, where α is pi/3, β is pi/5, γ is 2 pi/7, and the magnetic moment m isxy＝1000，ml100, 5Hz, 2 pi f 10 pi, and magnetic permeability0＝4π×10-7H/m, the variation of the magnetic field strength at the observation point with time in the magnetic source coordinate system is shown in FIG. 6.
From fig. 6 and 7, it can be seen that the three components of the magnetic field of the magnetic dipole in the magnetic source coordinate system and the observation coordinate system are harmonic signals, and the magnitude and the phase of the three components of the magnetic field are changed, but the frequency of the three components and the total magnetic field strength are unchanged.
Referring to FIG. 8, let the magnetic dipole be in the magnetic source coordinate system, the x coordinate is represented by x0Taking 50 points at 11m intervals of 1m, y coordinate y 05, Z coordinate Z0Taking four points in the observation coordinate system as 12m, and the coordinates are P1(0,0,0)，P2(2.1132,5.9744,5.0834)，P3(0.3419,4.8697,11.8393)，P4(1.7043,12.3164,5.8652), magnetic dipole coordinate (x)0,y0,z0) The coordinate corresponding to the observation coordinate system is (u)0,v0,w0) Then observe u in the coordinate system0,v0,w0And distance of its origin of coordinates
Figure BDA0002726981490000121
It can be seen that with x0Increase of (2) the distance r of the magnetic source (magnetic dipole) from the origin of the observation coordinate system0Gradually increase u0,w0Is also gradually increased, v0The three coordinate components of the magnetic dipole in the observation coordinate system are accompanied by x0By using the calculated u in the positioning error simulation0,v0,w0And theory u0,v0,w0Determining absolute and relative error function r0The trend of change of (c) is shown in fig. 9 and 10. As can be seen, with distance r0The absolute error and the relative error are increased, but the positioning error is still very small and the order of magnitude is very small, and the error is mainly caused by the error of a computing system.
Referring to fig. 6, a magnetic field distribution simulation of the magnetic dipole, it can be seen that the magnetic field signal generated by rotating the magnetic dipole is a harmonic signal having a certain frequency. Through the interference of signals such as the environmental static magnetic field noise and the power frequency magnetic field of filtering that band-pass filtering can be fine, the magnetic field interference that it received is less, and it is about 1nT to establish the measurement noise, then the positioning error simulation is like fig. 11 and fig. 12: the positioning error shows that the influence of the measurement noise on the positioning error is very small, and the influence of the noise in the measurement magnetic field on the calculation result is greatly reduced because the positioning algorithm adopts the Newton iteration method to solve the nonlinear equation set.
Referring to fig. 13, in an actual magnetic target, the magnetic distribution is not uniform, the magnetic dipole moment cannot strictly rotate around a fixed point but moves within a certain range, and the magnetic dipole moment is set to swing around a ring with radius r' in the xy plane, which is [ z ] in the z-axis direction0-z',z0+z']Within the range ofShaking, wherein z' is a movement radius on a z-axis; if the magnetic moment of the magnetic dipole source shakes on a circle with the point D as the origin of coordinates and the radius r', the coordinates of the magnetic dipole source become:
Figure BDA0002726981490000131
let the magnetic source target coordinate be D (x)0,y0,z0) (20,5,12), observation point P1,P2,P3,P4The coordinates are unchanged. The motion radius r 'in the xy plane is 0.05, and the values are sequentially spaced by 0.05m, and 50 values are obtained in total, z' is 0.5m, the simulation calculates the variation of the positioning error along with the motion radius, and the simulation of the positioning error is shown in fig. 14 and fig. 15: as can be seen from fig. 14 and 15, the absolute error and the relative error gradually increase as the movement radius r' increases. When the shaking radius r' is less than 1.5m, u0,v0,w0The absolute error of the three axes is less than 0.2m, and the relative error is less than 4%. When r' is more than 1.5m, the error is increased rapidly along with the increase of the shaking radius, and when the shaking radius is 2.5m, the relative error reaches about 9 percent.
Referring to fig. 5, an electronic device 500 may include a processing means (e.g., central processing unit, graphics processor, etc.) 501 that may perform various appropriate actions and processes in accordance with a program stored in a Read Only Memory (ROM)502 or a program loaded from a storage means 508 into a Random Access Memory (RAM) 503. In the RAM 503, various programs and data necessary for the operation of the electronic apparatus 500 are also stored. The processing device 501, the ROM502, and the RAM 503 are connected to each other through a bus 504. An input/output (I/O) interface 505 is also connected to bus 504. The following devices may be connected to the I/O interface 505 in general: input devices 506 including, for example, a touch screen, touch pad, keyboard, mouse, camera, microphone, accelerometer, gyroscope, etc.; output devices 507 including, for example, a Liquid Crystal Display (LCD), speakers, vibrators, and the like; a storage device 508 including, for example, a hard disk; and a communication device 509. The communication means 509 may allow the electronic device 500 to communicate with other devices wirelessly or by wire to exchange data. While fig. 5 illustrates an electronic device 500 having various means, it is to be understood that not all illustrated means are required to be implemented or provided. More or fewer devices may alternatively be implemented or provided. Each block shown in fig. 5 may represent one device or may represent multiple devices as desired.
In particular, according to an embodiment of the present disclosure, the processes described above with reference to the flowcharts may be implemented as computer software programs. For example, embodiments of the present disclosure include a computer program product comprising a computer program embodied on a computer readable medium, the computer program comprising program code for performing the method illustrated in the flow chart. In such an embodiment, the computer program may be downloaded and installed from a network via the communication means 509, or installed from the storage means 508, or installed from the ROM 502. The computer program, when executed by the processing device 501, performs the above-described functions defined in the methods of embodiments of the present disclosure.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims (10)

1. A space four-point magnetic field positioning method based on a rotating magnetic dipole is characterized by comprising the following steps:
constructing a magnetic source coordinate system, an observation coordinate system and a magnetic field model of the rotating magnetic dipole;
determining the relationship between the coordinates of the observation point on the magnetic source coordinate system and the magnetic field distribution of the rotating magnetic dipole according to the magnetic source coordinate system and the magnetic field model;
determining the relationship between the rotating magnetic dipole and the coordinate of the observation point in the observation coordinate system and the induced magnetic field intensity of the observation point in the observation coordinate system according to the equivalent relationship between the rotating magnetic dipole and the magnetic source coordinate system and the magnetic field distribution of the rotating magnetic dipole;
and obtaining the induced magnetic field intensity and the coordinates of the observation point in the observation coordinate system, and solving the coordinates of the rotating magnetic dipole in the observation coordinate system by a Newton iteration method according to the induced magnetic field intensity and the coordinates of the observation point in the observation coordinate system and the equivalent relation of the rotating magnetic dipole in the observation coordinate system and the magnetic source coordinate system.
2. The method for positioning the spatial four-point magnetic field based on the rotating magnetic dipole according to claim 1, wherein the step of determining the relationship between the coordinates of the observation point on the magnetic source coordinate system and the magnetic field distribution of the rotating magnetic dipole according to the magnetic source coordinate system and the magnetic field model comprises the following steps:
to rotate the magnetic moment of the magnetic dipole
Figure FDA0002726981480000011
The rotating shaft of the magnetic source is a z-axis, and a magnetic source coordinate system xyz is established;
determining the magnetic moment of a rotating magnetic dipole from a magnetic field model
Figure FDA0002726981480000012
The components m in the x, y and z axes of the coordinate system xyzp、mf、ml：
Figure FDA0002726981480000013
In which the magnetic moment
Figure FDA0002726981480000014
Projection on the z-axis is
Figure FDA0002726981480000015
The projection on the xy plane is
Figure FDA0002726981480000016
Omega is the rotation angular velocity of the rotating magnetic dipole, alpha0Being magnetic moment
Figure FDA0002726981480000017
An initial angle with the x-axis;
according to the Biao-Saval law, coefficient matrixA and equation (1) give the magnetic moment
Figure FDA0002726981480000018
And
Figure FDA0002726981480000019
magnetic field strength generated on three axes of the coordinate system xyz:
Figure FDA00027269814800000110
wherein
Figure FDA0002726981480000021
Indicating sensed magnetic moment at observation point
Figure FDA0002726981480000022
And
Figure FDA0002726981480000023
the magnetic field component corresponding to three axes on the magnetic source coordinate system, omega is the rotation angular velocity of the rotating magnetic dipole, alpha0Being magnetic moment
Figure FDA0002726981480000024
An initial angle with the x-axis;
determining the rotating magnetic dipole moment from equation (2) and the coefficient matrix A
Figure FDA0002726981480000025
And
Figure FDA0002726981480000026
the relationship of three components of magnetic induction intensity generated at an observation point in a coordinate system xyz is as follows:
Figure FDA0002726981480000027
the coefficient matrix a is defined as:
Figure FDA0002726981480000028
wherein r is2＝(x-x0)2+(y-y0)2+(z-z0)2，μ0Is magnetic permeability; x, y and z respectively represent x-axis coordinate, y-axis coordinate and z-axis coordinate of the observation point in a coordinate system xyz, and x0、y0、z0Respectively representing the x-axis coordinate, the y-axis coordinate and the z-axis coordinate of the rotating magnetic dipole in a coordinate system xyz.
3. The method for positioning the spatial four-point magnetic field based on the rotating magnetic dipole according to claim 2, wherein the step of determining the relationship between the rotating magnetic dipole and the coordinates of the observation point in the observation coordinate system and the induced magnetic field strength of the observation point in the observation coordinate system according to the equivalent relationship between the observation coordinate system and the magnetic source coordinate system and the magnetic field distribution of the rotating magnetic dipole comprises the following steps:
according to the initial angle alpha of the rotating magnetic dipole0Determining a rotation matrix K according to the rotation equivalent relation between the observed coordinate system uvw and the magnetic source coordinate system xyz, wherein
Figure FDA0002726981480000029
According to said magnetic moment
Figure FDA00027269814800000210
And
Figure FDA00027269814800000211
determining the relation between the coordinates of an observation point in an observation coordinate system and the magnetic field component by the magnetic field intensity generated by three axes of the magnetic source coordinate system xyz and the rotation matrix K:
Figure FDA0002726981480000031
wherein u, v and w are corresponding three-axis coordinates of the observation point in an observation coordinate system uvw, and u0、v0、w0Is the corresponding three-axis coordinate of the rotating magnetic dipole in the observation coordinate system uvw, omega is the rotation angular velocity of the rotating magnetic dipole,
Figure FDA0002726981480000032
is the component of the magnetic field strength of the observation point in the observation coordinate system uvw.
4. The method for positioning the spatial four-point magnetic field based on the rotating magnetic dipole according to claim 3, wherein the magnetic field intensity component B of the rotating magnetic dipole in the observed coordinate system uvw is obtained according to the magnetic field model of the rotating magnetic dipole in the source coordinate system xyz and the equivalent relationship between the observed coordinate system uvw and the source coordinate system xyzu、Bv、Bw、：
Figure FDA0002726981480000033
Figure FDA0002726981480000034
Wherein
Figure FDA0002726981480000035
Respectively represent the magnetic moments
Figure FDA0002726981480000036
Figure FDA0002726981480000037
And
Figure FDA0002726981480000038
the magnetic field strength on the three axes of the observation coordinate system uvw,
Figure FDA0002726981480000039
respectively representing magnetic moments
Figure FDA00027269814800000310
And
Figure FDA00027269814800000311
the magnetic field intensity on three axes of a magnetic source coordinate system xyz;
and (3) determining the relation between the coordinates of the rotating magnetic dipole and the observation point in the observation coordinate system and the rotation matrix K according to the equation (5) and the equation (2) and the coefficient matrix B:
Figure FDA00027269814800000312
wherein the coefficient matrix B is defined as:
Figure FDA0002726981480000041
5. the method for positioning the spatial four-point magnetic field based on the rotating magnetic dipole according to claim 4, wherein the step of obtaining the induced magnetic field strength and the coordinates of the observation point in the observation coordinate system, and the step of solving the coordinates of the rotating magnetic dipole in the observation coordinate system by a Newton iteration method according to the induced magnetic field strength and the coordinates of the observation point in the observation coordinate system and the equivalent relationship between the observation coordinate system and the magnetic source coordinate system comprises the following steps:
acquiring magnetic field strengths of the four observation points and coordinates of the four observation points in an observation point coordinate system;
determining the relation between a coefficient matrix B and a rotation matrix K according to the relation between the magnetic field intensity, the coordinate of the observation point coordinate system, the rotary magnetic dipole and the coordinate of the observation point in the observation coordinate system and the rotation matrix K:
Figure FDA0002726981480000042
solving the coordinates of the rotating magnetic dipole in the observation coordinate system according to the constraint condition of the rotation matrix K and the equation (7), wherein the coordinates of the rotating magnetic dipole in the observation coordinate system are obtainedThe constraint conditions of the rotation matrix K are as follows:
Figure FDA0002726981480000043
6. the method for positioning the spatial four-point magnetic field based on the rotating magnetic dipole according to claim 5, wherein the step of solving the coordinates of the rotating magnetic dipole in the observation coordinate system according to the constraint condition of the rotation matrix K and the equation (7) comprises the following steps:
obtaining P of two observation points1And P2Said P is1、P2The coordinates in the observation coordinate system are respectively P1(0,0,0)、P2(u2,v2,w2)；
Will P1、P2Substituting into equation (6), we get from newton's iteration:
Figure FDA0002726981480000051
and (5) calculating the coordinates of the rotating magnetic dipole observation coordinate system according to the equation (8) and the equation (9).
7. A space four-point magnetic field positioning device based on a rotating magnetic dipole is characterized by comprising a construction module, a first determination module, a second determination module and an iteration module,
the construction module is used for respectively establishing a magnetic field model for the rotating magnetic dipole in a magnetic source coordinate system and an observation coordinate system;
the first determining module is used for determining the relationship between the coordinates of the observation point on the magnetic source coordinate system and the magnetic field distribution of the rotating magnetic dipole according to the magnetic source coordinate system and the magnetic field model;
the second determining module is used for determining the relationship between the rotating magnetic dipole and the coordinate of the observation point in the observation coordinate system and the induced magnetic field intensity of the observation point in the observation coordinate system according to the equivalent relationship between the rotating magnetic dipole and the magnetic source coordinate system and the magnetic field distribution of the rotating magnetic dipole;
and the iteration module is used for solving the coordinates of the rotating magnetic dipole in the observation coordinate system by a Newton iteration method according to the magnetic field intensity and the coordinates detected by the observation point in the observation coordinate system and the equivalent relationship of the rotating magnetic dipole in the observation coordinate system and the magnetic source coordinate system.
8. The rotating magnetic dipole-based spatial four-point magnetic field positioning device of claim 7, wherein said iteration module comprises an acquisition module, a calculation module,
the acquisition module is used for acquiring the coordinates and the magnetic field intensity of the observation point in an observation coordinate system;
and the calculation module is used for solving the coordinates of the rotating magnetic dipole in the observation coordinate system by a Newton iteration method according to the magnetic field intensity and the coordinates detected by the observation point in the observation coordinate system and the equivalent relationship of the rotating magnetic dipole in the observation coordinate system and the magnetic source coordinate system.
9. An electronic device, comprising: one or more processors; storage means for storing one or more programs which, when executed by the one or more processors, cause the one or more processors to carry out the method according to any one of claims 1-6.
10. A computer-readable medium, on which a computer program is stored, wherein the computer program, when being executed by a processor, carries out the method according to any one of claims 1-6.
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