CN112362048A - Practical magnetic gradient tensor high-precision single-point positioning method - Google Patents
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Abstract
Description
Technical Field
The invention belongs to the field of magnetic detection, and particularly relates to a practical magnetic gradient tensor high-precision single-point positioning method.
Background
Magnetic gradient tensor detection is a new geophysical observation means and gradually becomes a research hotspot of magnetic measurement technology, has many advantages which are not possessed by traditional magnetic total field and magnetic vector detection methods, has extremely rich magnetic target body information quantity presented by magnetic gradient tensor data in different directions, can describe characteristics of a geologic body more accurately, and is currently applied to identification and positioning of magnetic target bodies, such as hidden geologic body exploration, UXO detection, anti-latency and the like, and has wide application prospects in military, environment, resource exploration and other aspects (2008. wu wealth, liu Tian you. magnetic gradient tensor measurement and application). Conventionally, a magnetic gradient tensor detection method (2006.Nara T, Suzuki S, Ando S, a closed-form for magnetic gradient localization by means of magnetic field and spatial gradients) that uses magnetic field vectors and magnetic gradient tensor data only needs single-point observation to achieve the purpose of target localization, can reduce non-uniqueness of solutions, and does not need to increase more observation quantities.
As shown in FIG. 1, three components of the magnetic field (B)x,By,Bz) The derivatives in three directions in space xyz constitute the magnetic gradient tensor, which comprises a total of nine elements, denoted G, as follows:
in actual measurement, differentiation is often replaced by difference:
from Maxwell's equation, the divergence and rotation of the B field (magnetic field) are zero, i.e. the tensor matrix has an intangible property and symmetry, and is obtained as follows:
as can be seen from equation (3), only five of the nine elements in the magnetic gradient tensor matrix are independent. The magnetic gradient tensor matrix also has three invariants, namely rotation invariants, which are not influenced by the rotation of the three-dimensional coordinate system around the coordinate origin and are respectively expressed as
The linear relation between the magnetic dipole position information and the magnetic field vector and magnetic gradient tensor matrix of the position is deduced by Nara et al, namely, the following relation is established in the conventional single-point positioning algorithm based on the magnetic field vector and the magnetic gradient tensor:
three-component magnetic field value (B) at known magnetic gradient tensor matrix and corresponding magnetic dipolex,By,Bz) The position information of the magnetic dipole can be obtained:
but due to the magnetic field vector (B)x,By,Bz) For the magnetic field vector generated by the magnetic dipole at a certain point, it is difficult to obtain the measurement value in the presence of the earth magnetic field, and the method is usually applied to the field vector which is generated by the magnetic dipole at a certain pointKnowing the scene of the geomagnetic background field greatly limits the application range of the algorithm.
Since the gradient values of the geomagnetic field are typically much smaller than those of the magnetic extraordinary field, about 20nT/km (vertical direction) and 5nT/km (horizontal direction), they can be ignored from the measured magnetic gradient tensor. Based on the characteristic of a geomagnetic field, aiming at the defects of a conventional magnetic gradient tensor single-point positioning algorithm, Wiegert and the like (2008.R Wiegert, K Lee, Oeschager J.Improved magnetic STAR Methods for real-time, point-by-point localization of unknown and buried mines) of the U.S. naval water surface operation center, a cube array MagSTAR system comprising eight three-component flux gates is developed, and a STAR positioning method is provided, wherein the method is not influenced by a geomagnetic background field, has the advantages of good real-time performance, single-point positioning and the like, but has an elliptic coefficient, so that a positioning result has an obvious non-spherical error and cannot realize high-precision positioning; based on the same array structure, a magnetic gradient tensor positioning method based on difference is provided by the Tao et al (2014, Luwei, Liheng, Zymuo, a target positioning improvement method based on magnetic gradient tensor), and three new positioning equations are obtained by respectively solving partial differentiation on z on two sides of an equation (5):
wherein,
it can be seen that, in the equation (7), the magnetic field vector term on the right side of the equation (5) is converted into the difference of the magnetic field vectors by using a difference method, which eliminates the influence of the geomagnetic background field and other common-mode interferences to a great extent, and can realize real-time and high-precision single-point positioning. However, this method still faces two major problems in practical use: the method has the advantages that firstly, the practicability problem is solved, and under the condition that no magnetic anomaly exists or a magnetic anomaly signal is weak, due to the fact that no proper magnetic anomaly judgment standard exists, when the formula (7) is directly adopted for positioning, the square matrix of the formula (8) is a singular matrix or is close to the singular matrix, and an error positioning result is caused; secondly, the application range is limited, and the square matrix of the formula (8) only adopts the differential of the magnetic gradient tensor matrix in the z-axis direction, but does not adopt the differential of the x-axis direction and the y-axis direction, so that the magnetic anomaly of some axial magnetic moments cannot be effectively positioned.
The invention is especially provided for solving the problems of large influence by a geomagnetic background field, poor positioning precision, poor practicability, limited application range and the like of the existing magnetic gradient tensor single-point positioning algorithm.
Disclosure of Invention
The invention aims to provide a practical magnetic gradient tensor high-precision single-point positioning method which can solve the problems that the existing magnetic gradient tensor single-point positioning algorithm is greatly influenced by a geomagnetic background field, is poor in positioning precision, is poor in practicability and is limited in application range.
The technical scheme of the invention is as follows: a practical magnetic gradient tensor high-precision single-point positioning method comprises the following steps:
s100: measuring vector values of magnetic fields at eight vertexes of a cube through a cube array consisting of eight three-component magnetometers;
s200: obtaining a magnetic gradient tensor matrix G on six surfaces of a cube through calculationm，
m＝+x,-x,+y,-y,+z,-z；
S300: by calculating the invariants of each surface
m＝+x,-x,+y,-y,+z,-z；
Calculating the values of a, b and c, wherein a ═ I1+x/I1-x|，b＝|I1+y/I1-y|，c＝|I1+z/I1-z|；
S500, judging the values of a, b and c, if any value exceeds the upper and lower limit threshold values, determining that magnetic anomaly exists, adopting 12 positioning equations in the formula (12) at the moment, and realizing the positioning of the magnetic anomaly through an optimization algorithm
Further, the magnetic gradient tensor matrix G in the step S200+zAnd G-zObtained from the following equations (9) and (10),
respectively solving G in the same way-x,G+x,G-y,G+yNine tensor elements.
Further, the invariant on each plane in the step S300
m ═ x, -x, + y, -y, + z, and-z, as determined by formula (4),
further, in step S500, if none of the values a, b, and c exceeds the upper and lower threshold values, it is determined that there is no magnetic anomaly or the magnetic anomaly is far away from the threshold values, and the magnetic anomaly cannot be located.
Further, the upper and lower threshold values in step S500 are respectively: the upper threshold range is 1.05-1.50, and the lower threshold range is 0.50-0.95.
Optionally, the three-component magnetometer is a vector magnetic sensor such as a fluxgate sensor, a GMR sensor, or a TMR sensor.
Further, the cube array composed of eight three-component magnetometers is composed of magnetometers with the numbers of 1-8, the side length of the cube is d, and eight components are arrangedThe measurement value of the three-component magnetometer is represented as
Further, the magnetic gradient tensor matrix G in the six faces of the cubic arraymM ═ x, -x, + y, -y, + z, -z, is determined from measurements made by a three-component magnetometer, where G is+xDetermined by 1458 magnetometer, G-xFound by 2367 magnetometer, G+yDetermined by 3478 magnetometer, G-yDetermined by a 1256 magnetometer, G+zDetermined by 1234 magnetometer, G-zDetermined by 5678 magnetometer.
The advantages of the present invention over the prior art are as follows.
1. Under the condition of the existence of the geomagnetic field, the influence of the geomagnetic field can be effectively inhibited by adopting a magnetic gradient tensor matrix difference method, and the high-precision single-point positioning of magnetic anomaly is realized.
2. The invention makes the invariants at the central points of six surfaces of the cubic array
The m ═ x, -x, + y, -y, + z, -z are used as the basis for judging whether the magnetic anomaly exists, the problem that the magnetic anomaly exists and the positioning is carried out is effectively solved, and the practicability of the magnetic gradient tensor single-point positioning method is greatly improved.
3. The method solves partial differentiation of x, y and z by the conventional magnetic gradient tensor positioning equation to obtain 12 positioning equations, and then solves 3 position variables by the optimization algorithm.
Drawings
Figure 1 is a schematic diagram of the relationship between total magnetic field strength, magnetic vector field, and magnetic gradient tensor.
FIG. 2 is a schematic diagram of a cubic array of eight three-component magnetometers as used by the invention.
Detailed Description
The practical magnetic gradient tensor high-precision single-point positioning method of the invention is further explained below with reference to the attached drawings. It should be noted that the following examples are only for explaining the technical solution of the present invention and are not to be construed as limiting the present invention.
As shown in FIG. 2, the practical magnetic gradient tensor high-precision single-point positioning method adopts eight three-component magnetometers to form a cube array to obtain magnetic field vector values, wherein the eight three-component magnetometers are respectively 1-8 in reference number, the upper four three-component magnetometers are respectively 1-4 in reference number, the lower four three-component magnetometers are respectively 5-8 in reference number, and the side length of the cube is d. The three-component magnetometer may be one of vector magnetic sensors such as a fluxgate sensor, a GMR sensor, or a TMR sensor.
The measurement values of the eight three-component magnetometers are expressed as
The magnetic gradient tensor matrix G of the six faces of the cubic array can be obtainedmAnd m ═ x, -x, + y, -y, + z, -z. Wherein G is+xCan be determined by 1458 magnetometer, G-xCan be obtained by 2367 magnetometer, G+yCan be determined by 3478 magnetometer, G-yCan be determined by a 1256 magnetometer, G+zCan be determined by 1234 magnetometer, G-zCan be determined by 5678 magnetometer. Here, G is first determined+zNine elements of (c):
finding G-zThe nine elements of (a) are:
by the same method, G can be obtained-x,G+x,G-y,G+yNine tensor elements. After the magnetic gradient tensor matrix on the six faces of the cube is obtained, the magnetic gradient tensor matrix can be further processedEquation (4) to determine the invariants I on each side1mAnd m ═ x, -x, + y, -y, + z, -z. According to a differential equation, the gradient value of the magnetic gradient tensor at the right center point of the cube can be obtained by replacing differential with differential:
in practice, when the partial differential is obtained by the equation (5), the partial differential is obtained for x, y, and z, respectively
It can be known that when the above formula i is x, y, z respectively, 12 positioning equations can be obtained, and 3 position variables can be obtained through an optimization algorithm, which is more general and wider in application range than 3 equations obtained through derivation by billows and the like.
This patent is based on the invariant I1The characteristic that the magnetic moment and the position parameter change along with the change of the attitude angle is not used as the basis for judging whether the magnetic anomaly exists or not. When no magnetic anomaly exists, the magnetic field gradient value of the geomagnetic background field is ignored, and the following requirements are met:
in actual detection, if the above equation is not satisfied, compensation can be performed in an environment of an approximately zero gradient field. And when the magnetic anomaly exists, the equation is not satisfied, and the following conditions are satisfied:
a specific example of high precision single point localization of the magnetic gradient tensor is given here: the eight three-component fluxgate magnetometers form a cubic array, and the fluxgate array respectively measures magnetic field vector values at eight vertexes of the cube, and thenThen, magnetic gradient tensor matrix G on six surfaces of the cube is obtained by respectively calculating through an equation (9) and an equation (10)mM is + x, -x, + y, -y, + z, -z, and then the invariants on six planes are obtained
m ═ x, -x, + y, -y, + z, -z; and (3) respectively calculating the values of a, b and c by the formula (14), judging the values, if any value exceeds an upper limit threshold and a lower limit threshold, determining that magnetic anomaly exists, adopting 12 positioning equations in the formula (12) at the moment, and realizing magnetic anomaly positioning through an optimization algorithm, otherwise, determining that the magnetic anomaly does not exist or the magnetic anomaly is far in distance (namely, the magnetic anomaly signal is weak), and failing to realize the magnetic anomaly positioning.
In the invention, the threshold range can be self-defined, the upper threshold range is generally selected to be 1.05-1.50, the lower threshold range is generally selected to be 0.50-0.95, and the numerical value indicates that the abnormal body is larger or closer to the abnormal body during detection.
The embodiments in the above description are only for illustrating the present invention, and do not limit the scope of the present invention. The scope of the present invention is defined only by the appended claims, and any omissions, substitutions, or modifications made based on the embodiments disclosed herein will fall within the scope of the present invention.
Claims (8)
1. A practical magnetic gradient tensor high-precision single-point positioning method is characterized by comprising the following steps:
s100: measuring vector values of magnetic fields at eight vertexes of a cube through a cube array consisting of eight three-component magnetometers;
s200: obtaining a magnetic gradient tensor matrix G on six surfaces of a cube through calculationm，
m＝+x,-x,+y,-y,+z,-z；
S300: by calculating the invariants of each surface
S400, calculating a according to the calculation,b, c, wherein a ═ I1+x/I1-x|，b＝|I1+y/I1-y|，c＝|I1+z/I1-z|；
S500, judging the values of a, b and c, if any value exceeds the upper and lower limit threshold values, determining that magnetic anomaly exists, adopting 12 positioning equations in the formula (12) at the moment, and realizing the positioning of the magnetic anomaly through an optimization algorithm
2. The practical magnetic gradient tensor high-precision single-point positioning method as set forth in claim 1, wherein the magnetic gradient tensor matrix G in the step S200+zAnd G-zObtained from the following equations (9) and (10),
respectively solving G in the same way-x,G+x,G-y,G+yNine tensor elements.
3. The practical magnetic gradient tensor high-precision single-point positioning method as set forth in claim 1, wherein the invariant on each surface in the step S300
The compound is obtained by the following formula (4),
4. the practical magnetic gradient tensor high-precision single-point positioning method as set forth in claim 1, wherein in the step S500, if none of the values of a, b and c exceeds the upper and lower threshold values, it is determined that there is no magnetic anomaly or the magnetic anomaly is far away from the threshold values, and the magnetic anomaly positioning cannot be realized.
5. The practical high-precision single-point positioning method of magnetic gradient tensor according to claim 4, wherein the upper and lower threshold values are respectively: the upper threshold range is 1.05-1.50, and the lower threshold range is 0.50-0.95.
6. The method as claimed in claim 1, wherein the three-component magnetometer is a vector magnetic sensor such as a fluxgate sensor, a GMR sensor or a TMR sensor.
7. The practical high-precision single-point positioning method of magnetic gradient tensor as set forth in claim 1, wherein the cubic array consisting of eight three-component magnetometers consists of magnetometers with the numbers 1-8, the side length of the cube is d, and the measurement values of the eight three-component magnetometers are expressed as
8. The practical magnetic gradient tensor high-precision single-point positioning method as set forth in claim 7, wherein the magnetic gradient tensor matrix G in the six faces of the cubic arraymM ═ x, -x, + y, -y, + z, -z, is determined from measurements made by a three-component magnetometer, where G is+xDetermined by 1458 magnetometer, G-xFound by 2367 magnetometer, G+yDetermined by 3478 magnetometer, G-yDetermined by a 1256 magnetometer, G+zDetermined by 1234 magnetometer, G-zDetermined by 5678 magnetometer.
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