A magnetic target positioning method based on magnetic gradient full tensor

Abstract

The application belongs to the technical field of magnetic field measurement, and particularly relates to a magnetic target positioning method based on a magnetic gradient full tensor, which comprises the following steps: step 1, measuring the magnetic gradient full tensor at two observation points; step 2, solving the characteristic polynomial of the magnetic gradient tensor matrix at the two observation points, and calculating the corresponding real characteristic value and the corresponding unit eigenvector; step 3, calculating the normalized magnetic source intensity corresponding to the two observation points, the cosine of the angle between the relative position vector and the magnetic moment vector, and the cosine of the angle between the plane P1 and the plane P2; step 4, calculating the cosine value of the angle between the relative position vectors at the two observation points, and the modulus value of the relative position vector; step 5, establishing an equation group, and solving the unit direction vector of the relative position vector; and step 6, determining the magnetic source position. The application is convenient to measure, simple to calculate, and high in accuracy.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of magnetic field measurement, and particularly relates to a magnetic target positioning method based on a magnetic gradient full tensor. BACKGROUND

[0002] The magnetic field generated by the magnetization of ferromagnetic substances to the geomagnetic field will cause disturbance to the geomagnetic field, and further affect the geomagnetic field distribution, resulting in geomagnetic anomaly. Based on this phenomenon, the additional magnetic field generated by the ferromagnetic substances in the geomagnetic space is measured, and the position information of the magnetic anomaly body is obtained through inversion, so as to realize the magnetic anomaly target detection.

[0003] The traditional magnetic anomaly target positioning method mainly includes a positioning method based on total amount, a positioning method based on vector, and a positioning method based on gradient, and mainly has the following problems: (1) The positioning method based on total amount mainly compares and identifies the magnetic anomaly target body according to the data collection of a large number of existing magnetized objects (circular, square, cylindrical, linear, etc.). This principle requires a large amount of prior calculation, which is large in calculation amount and poor in real-time performance. (2) The solving method based on vector has high requirements for the orientation of the sensitive axis due to the directionality of each component, and is greatly affected by the space attitude of the sensor platform. (3) The inversion positioning method based on vector gradient or total amount gradient is inevitably incomplete in information because it is only the projection of the total magnetic field in a certain direction or plane.

[0004] With the development of magnetic measurement technology, the magnetic anomaly target detection has experienced magnetic total amount detection, magnetic gradient detection, and now magnetic gradient full tensor detection. Compared with the total amount and vector detection technology, the magnetic gradient full tensor detection technology has small influence on the geomagnetic field, can provide more abundant magnetic field information, and realize more accurate positioning. The existing magnetic anomaly target positioning method based on single-point magnetic gradient full tensor includes Euler method, eigenvalue and eigenvector method, and STAR (Scalar Triangulation and Ranging) method, which has the following problems: (1) The Euler method needs to measure the magnetic gradient tensor and the magnetic field vector three components of any point in the magnetic field. However, due to the existence of the background geomagnetic field, the magnetic field vector three components are difficult to separate from the geomagnetic field, and the measurement will cause large positioning error. (2) The existence of inherent asphericity error in the STAR method will cause large positioning error, and the measurement system is complex, which needs more sensors and increases the hardware manufacturing cost. (3) The eigenvalue and eigenvector method is simple, has high inversion positioning accuracy, but has inherent fourfold ambiguity, and the positioning result is not unique, so some additional information needs to be added to obtain a unique solution, such as adding the components of the magnetic field vector or However, due to the influence of the geomagnetic field, the measurement of the magnetic field vector is difficult, which will introduce large error.

[0005] In addition, the improved method of the existing single-point magnetic gradient full tensor magnetic anomaly target positioning method includes multi-point measurement positioning and high-order tensor positioning. The improved multi-point measurement positioning method mostly uses a large number of points to obtain an approximate solution, and is easily affected by the distance between observation points, or uses an optimization algorithm such as a genetic algorithm or a particle swarm algorithm, and has high algorithm complexity. The high-order tensor positioning method is easily affected by instrument measurement noise due to the small high-order magnetic gradient, and thus has high requirements for instrument accuracy. SUMMARY

[0006] The present application overcomes the key technical problems of low accuracy and susceptibility to geomagnetic field interference in the prior art magnetic target positioning method, and provides a magnetic target positioning method based on two-point magnetic gradient full tensor to simplify the positioning algorithm and improve positioning accuracy.

[0007] To solve the above technical problems, the technical scheme adopted by the present application is as follows: a magnetic target positioning method based on magnetic gradient full tensor, comprising the following steps:

[0008] Step 1, measuring the magnetic gradient full tensor at two observation points;

[0009] Step 2, solving the characteristic polynomial of the magnetic gradient tensor matrix at the two observation points, and calculating the corresponding real eigenvalues and corresponding unit eigenvectors;

[0010] Step 3, calculating the normalized magnetic source intensity and of the two observation points and , and the cosine of the angle between the relative position vector and and the magnetic moment vector ; ;

[0011] Step 4, calculating the cosine value of the angle between the relative position vectors and , and the modulus of the relative position vectors and ; ;

[0012] Step 5, using the unit eigenvector corresponding to the eigenvalue with the smallest absolute value to be perpendicular to the relative position vector between the observation point and the target, establishing the cosine of the angle between the first relative position vector​​​​ corresponding unit direction vector corresponding equation group, and the solution is ;

[0013] Step 6, the first relative position vector calculated according to step 4 the modulus value and the unit direction vector obtained in step 5 , and the position of the first observation point, determine the magnetic source position.

[0014] In the step 2, the calculated real eigenvalues include: λ min1 , λ med1 , λ max1 , λ min2 , λ med2 , λ max2 , wherein λ min1 , λ med1 , λ max1 respectively represent three real eigenvalues corresponding to the magnetic gradient tensor matrix corresponding to the first observation point, λ min2 , λ med2 , λ max2 respectively represent three real eigenvalues corresponding to the magnetic gradient tensor matrix corresponding to the second observation point, λ min1 < λ med1 < λ max1 , λ min2 < λ med2 < λ max2 .

[0015] In the step 3, the calculation formula of the normalized magnetic source intensity corresponding to the first observation point and the normalized magnetic source intensity corresponding to the second observation point respectively are:

[0016] ;

[0017] ;

[0018] The cosine of the angle between the relative position vector and the magnetic moment vector is calculated as:

[0019] ;

[0020] ;

[0021] The cosine value of the angle between the plane P1 and the plane P2 is:

[0022] ;

[0023] wherein, and λ med1 λ med2 corresponding unit eigenvectors.

[0024] the cosine value of the included angle between the relative position vector and The calculation formula is:

[0025] ;

[0026] and the modulus value of the relative position vector and and The calculation formula is:

[0027] , ;

[0028] , ;

[0029] dr represents the distance between the two observation points.

[0030] In step 5, the equation group related to the unit direction vector corresponding to the first relative position vector is established:

[0031] ;

[0032] ;

[0033] ;

[0034] and λ med1 and λ med2 corresponding unit eigenvectors, represent the relative position vector between the two observation points.

[0035] In step 3, it also includes the step of calculating the value of and If the calculation results are the same, ; if the signs are opposite, .

[0036] In step 6, the position calculation formula of the magnetic source is:

[0037] ​​ ;

[0038] wherein, represents a magnetic source position vector, represents a position vector of the first observation point.

[0039] In the step 1, the magnetic gradient tensor at the observation point is obtained by a cross-shaped magnetic gradient full tensor measurement array.

[0040] Compared with the prior art, the present application has the following beneficial effects:

[0041] 1. The present application provides a magnetic anomaly target detection and positioning method based on two-point magnetic gradient full tensor, which measures the magnetic gradient tensor of two points, constructs the simple spatial relationship between the observation point and the magnetic source, establishes the equation set, and solves to realize the accurate positioning of the magnetic anomaly source. This inversion method does not need to measure the magnetic field vector component, so it is not affected by the geomagnetic field; there is no approximation calculation in the inversion process, so there is no inherent error; the inversion result is unique; it is not affected by the distance between the observation points, and realizes the randomness of the moving direction and position of the observation point.

[0042] 2. Compared with the traditional magnetic anomaly target positioning algorithm, the present application is simpler, faster, more accurate, and has lower implementation cost, solving the technical problems of the traditional magnetic anomaly positioning algorithm, such as being easily affected by the geomagnetic interference, inherent error being difficult to remove, and positioning result not being unique.

[0043] 3. Compared with other multi-point positioning algorithms, the present application overcomes the technical problem that the positioning result is affected by the distance between the observation points, realizes the randomness of the moving trajectory and measurement interval of the observation point, and is suitable for sensor platforms with arbitrary space and arbitrary trajectory.

[0044] 4. The present application has high implementability, and in the positioning process, the moving trajectory and measurement interval of the observation point are not constrained, and the unique positioning of the magnetic anomaly target of the sensor platform with arbitrary space, arbitrary trajectory and arbitrary measurement interval can be realized, and if multi-point measurement is performed, any two observation points can be combined and then the present method is used to realize the accurate positioning of the magnetic anomaly source. Using a small number of observation points in arbitrary combination, multiple inversion solutions can be obtained, the positioning result is more accurate according to the aggregation of the solutions, and the information obtained by each observation point is fully utilized. In the future, it can be applied to metal unexploded ordnance detection, underwater target detection, nondestructive testing, mineral resource exploration, biomagnetic measurement (magnetocardiography, magnetoencephalography, etc.) and many other aspects. BRIEF DESCRIPTION OF DRAWINGS

[0045] Figure 1 A flowchart of a magnetic target positioning method based on magnetic gradient full tensor provided for the embodiments of the present application;

[0046] Figure 2This is a schematic diagram illustrating the principle of the cross-shaped magnetic gradient full tensor measurement array used in this embodiment of the invention.

[0047] Figure 3 This is a schematic diagram of the positioning principle of the present invention;

[0048] Figure 4 This is a schematic diagram of the experiment during algorithm verification in an embodiment of the present invention;

[0049] Figure 5 This is a diagram of the experimental setup used for algorithm verification.

[0050] Figure 6 This is a schematic diagram of a measurement device used in a magnetic target localization method based on the full magnetic gradient tensor provided in an embodiment of the present invention. Detailed Implementation

[0051] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0052] like Figure 1 As shown, Embodiment 1 of the present invention provides a magnetic target localization method based on the full magnetic gradient tensor, comprising the following steps:

[0053] Step 1: Measure the full magnetic gradient tensor at the two observation points.

[0054] In this embodiment, a cross-shaped magnetic gradient full tensor measurement array is used to measure the magnetic gradient tensor. According to magnetic gradient tensor theory, only five independent components are needed to obtain the first-order magnetic gradient full tensor. In engineering practice, planar magnetic gradient full tensor measurement arrays are easy to implement, and the center point of the structure is easier to find. Among them, the planar cross-shaped measurement array has smaller structural errors, higher measurement accuracy, and the best overall performance. Figure 2 The diagram shows a cross-shaped magnetic gradient full tensor measurement array model. Four triaxial magnetic sensors are positioned in a single plane, with sensors 1 and 3, and sensors 2 and 4 arranged symmetrically. The baseline distance between each sensor is d. The center point of the cross-shaped structure can be obtained based on the principle of coaxial difference with the same baseline. O The tensor matrix expression corresponding to the full tensor at position 1 is as follows:

[0055] (1)

[0056] in,( , , ) represents the magnetic field intensity value measured by the No. 1 three-axis magnetic sensor, , , ) represents the magnetic field intensity value measured by the No. 2 three-axis magnetic sensor, , , ) represents the magnetic field intensity value measured by the No. 3 three-axis magnetic sensor, , , ) represents the magnetic field intensity value measured by the No. 4 three-axis magnetic sensor.

[0057] Step 2, solve the characteristic polynomial of the magnetic gradient tensor matrix at two observation points, and calculate the corresponding real eigenvalues and corresponding unit eigenvectors.

[0058] The earth as a huge magnet can magnetize the ferromagnetic objects placed in it to generate its own magnetic field. Compared with other methods such as sonar, which need to actively emit signals to realize positioning by using specific equipment, the magnetic positioning method has natural advantages as a "non-contact" passive positioning technology. When the distance between the magnetic target and the observation point is greater than 2.5 times the maximum size of the magnetic target, the magnetic target can be equivalent to a magnetic dipole. According to the Biot-Savart law, the magnetic field vector generated by the magnetic dipole at a point can be obtained by the following formula:

[0059] (2)

[0060] where, is the relative position vector between the observation point and the magnetic target, . is the magnetic moment vector of the magnetic dipole, is the vacuum permeability.

[0061] The spatial variation rate of the three components of the magnetic field vector in three mutually orthogonal directions is called the first-order magnetic gradient tensor, denoted as

[0062] (3)

[0063] According to Maxwell's equations, in a passive static magnetic field, the divergence and curl of the magnetic field vector are both 0, that is, , , where, is the Hamiltonian operator. According to the operation rules of dot product and cross product, it can be deduced that

[0064] (4)

[0065] This shows that the tensor matrix Given a real symmetric matrix with no trace, its nine components contain only five independent elements. Solving for the characteristic polynomial of the tensor matrix yields three real eigenvalues. , , ( , , The three mutually orthogonal unit eigenvectors corresponding to the real eigenvalues. , , The eigenvalues ​​of the magnetic gradient tensor matrix are independent of the choice of coordinate system and are fundamental invariants of the tensor. Other combinations formed by it are also tensor invariants.

[0066] Figure 3 This illustrates the positioning principle of this embodiment. (Choose any point in space.) O Establish a Cartesian coordinate system with the origin as the origin, and let the relative position vector between observation point 1 and the magnetic source be . , The relative position vector between observation point 2 and the magnetic source is , The relative position vector between the two observation points is .

[0067] Therefore, in step 1, by solving the characteristic polynomial of the magnetic gradient tensor matrix at the two observation points, the real eigenvalues ​​that can be calculated include: , , , , , ,in, , , These represent the three real eigenvalues ​​of the magnetic gradient tensor matrix corresponding to the first observation point. , , These represent the three real eigenvalues ​​of the magnetic gradient tensor matrix corresponding to the second observation point. , And there is: , Furthermore, it can also obtain eigenvalues ​​related to real numbers. , , The three corresponding mutually orthogonal unit eigenvectors , , , and with real eigenvalues , , The three corresponding mutually orthogonal unit eigenvectors , , .

[0068] Step 3, calculating the normalized magnetic source strength corresponding to two observation points and ; calculating the cosine of the angle between the relative position vector and and the magnetic dipole moment vector and ; calculating the cosine of the angle between the relative position vector of the first observation point and the magnetic dipole moment vector and the relative position vector of the second observation point and the magnetic dipole moment vector .

[0069] Clark gives the expression of the eigenvalue of the tensor matrix , , , as follows:

[0070] (5)

[0071] wherein is the magnitude of the magnetic dipole moment vector, is the angle between the relative position vector and the magnetic moment vector.

[0072] From equation (5), we have:

[0073] (6)

[0074] which is also a tensor invariant.

[0075] Define the normalized magnetic source strength (Normalized Source Strength, NSS) as:

[0076] (7)

[0077] Obviously, the NSS can be completely calculated from the eigenvalue, and it also belongs to the tensor invariant, and has the advantage of complete isotropy around the magnetic dipole source.

[0078] Therefore, in step 3, the calculation formula of the normalized magnetic source strength corresponding to the first observation point and the normalized magnetic source strength corresponding to the second observation point are respectively:

[0079] ​​(8)

[0080] (9)

[0081] Since the magnetic field information at two observation points is generated by the same magnetic source, according to equation (7), we have

[0082] (10)

[0083] According to the relationship of tensor geometric invariants, the unit eigenvector corresponding to the smallest absolute value of the eigenvalue is perpendicular to the plane formed by the magnetic moment vector and the position vector of the magnetic dipole, i.e., the unit eigenvector of the tensor matrix at the first observation point is the normal vector of the plane formed by and , and the unit eigenvector of the tensor matrix at the second observation point is the normal vector of the plane formed by and , and the cosine of the angle between the two planes is

[0084] (11)

[0085] where and represent the unit eigenvectors corresponding to the eigenvalues and of the tensor matrix at the first observation point and the second observation point, respectively.

[0086] In step 3, the values of and are also calculated, and if the calculation results are of the same sign, ; if the signs are opposite, .

[0087] The angle between and the magnetic moment of the magnetic dipole is defined as , and the angle between and the magnetic moment of the magnetic dipole is defined as , according to equation (6), , the cosine values of and can be obtained from the eigenvalues of the magnetic gradient tensor matrix at the observation points: i.e.,

[0088] (12)

[0089] (13)

[0090] Step 4, calculate the relative position vector and cosine value of the included angle , and the relative position vector and the modulus value and .

[0091] The space relationship can be derived and the cosine value of the included angle between them :

[0092] ; (14)

[0093] According to the cosine law:

[0094] ; (15)

[0095] denotes the distance between two observation points. Substitute (10) (14) into equation (15) to solve the modulus value of , and through equation (10) the modulus value of .

[0096] Step 5, use the unit eigenvector corresponding to the smallest absolute value eigenvalue to be perpendicular to the relative position vector between the observation point and the target, establish the equation group related to the unit direction vector corresponding to the first relative position vector , and solve to obtain .

[0097] According to the definition of vector included angle cosine, and the cosine of the included angle between them can also be expressed as

[0098] ; (16)

[0099] where is the unit direction vector of . According to the tensor geometric invariant relationship, , , and , simplifying can get:

[0100] ; (17)

[0101] ; (18)

[0102] and These represent the eigenvalues ​​of the tensor matrix at the first observation point. eigenvalues ​​of the tensor matrix at the second observation point The corresponding unit eigenvector, This represents the relative position vector between two observation points. unit direction vector There are three components, namely Therefore, by solving the system of equations (16), (17), and (18) simultaneously, we can obtain the result. unit direction vector .

[0103] Step 6: Calculate the first relative position vector based on Step 4. modulus and the unit direction vector obtained in step 5 The location of the magnetic source is determined by the location of the first observation point and the location of the first observation point.

[0104] The formula for calculating the position of the magnetic source is:

[0105] (19)

[0106] in, Represents the magnetic source position vector. This represents the position vector of the first observation point.

[0107] To verify the performance and localization effect of the proposed algorithm, a magnetic gradient full tensor measurement system was built based on a cross-shaped magnetic gradient full tensor measurement array, and a straight-line trajectory was selected for localization experiments. The experimental principle diagram is shown below. Figure 4 As shown in the diagram, the experimental setup is as follows: Figure 5 As shown, during implementation, the measurement array is based on Figure 2The cross-shaped structure design, wherein the cross-shaped structure middle position also provided a sensor is used to measure the magnetic field vector three components, the center sensor measured magnetic field vector three components can be used for traditional single point positioning method measurement, with the positioning results of the embodiment of the present application are compared. The baseline distance of the measurement array is 40 cm. The support platform is made of wood, the cross-shaped support is made of non-magnetic acrylic plate, and the lower part has a pulley for easy movement on the track of the support platform. The sensor uses a three-axis fluxgate magnetometer (Mag890) produced by Bartington Company. The sensor array outputs 15 analog signals, to ensure the consistency of the acquisition accuracy, all fluxgate digitization is completed by using the same set of data acquisition module. In order to reduce the influence of geomagnetic diurnal variation, the experiment is carried out at 0-3 o'clock at night, and the environmental temperature is 18℃. Due to the continuous work of electrical equipment (such as incandescent lamp) at night, the environmental gradient in the room cannot be ignored. Therefore, before placing the magnetic target, the background gradient in the environment needs to be measured. The gradient value measured at each point in the formal measurement needs to be subtracted from the background gradient value. Figure 6 As shown in the figure, it is a schematic diagram of a measuring device used by a magnetic anomaly target detection and positioning method based on two-point magnetic gradient full tensor proposed by the embodiment of the present application, which includes four three-axis magnetic sensors arranged in a cross shape in the same plane, and also includes power supply and acquisition module, which supplies power to the four three-axis magnetic sensors and collects data at the same time.

[0108] A coordinate system was established with an arbitrary point as the origin, and the ferromagnetic target was located at (-82.14, -51.6, 88.91) cm. The measurement array moved along the z=x straight trajectory, and the total length of the movement trajectory was 180 cm. The observation points were spaced at 30 cm intervals. Therefore, a total of seven groups of measurement data were obtained in the experiment. The observation data were processed using two methods, respectively, to verify the actual positioning effect of the embodiment of the application, and compared with the traditional single-point positioning algorithm (Nara, T.; Suzuki, S.; Ando, S. A Closed-Form Formula for Magnetic Dipole Localization by Measurement of Its Magnetic Field and Spatial Gradients. IEEE Transactions on Magnetics 2006, 42, 3291-3293, doi:10.1109 / tmag.2006.879151.) and the two-point positioning algorithm proposed by Xu (Xu, L.; Gu, H.; Chang, M.; Fang, L.; Lin, P.; Lin, C. Magnetic Target Linear Location Method Using Two-Point Gradient Full Tensor. IEEE Transactions on Instrumentation and Measurement 2021, 70, 1-8, doi:10.1109 / tim.2021.3084283).

[0109] A. Observation points are equally spaced

[0110] First, two-point magnetic gradient tensor positioning was realized using any adjacent observation points, which means that the distance between the observation points is fixed at a minimum of 30 cm. Therefore, there are a total of 6 groups of two-point positioning solutions and 7 groups of single-point positioning solutions. Table 1 shows the relative error percentages in three directions and the average relative error of the three methods. Among them, the relative error (%) = (|estimated value - true value| / |true value|) 100.

[0111] Table 1 Positioning relative error (%) of three algorithms

[0112]

[0113] By comparison, it can be found firstly that the positioning method of the present application and Xu's two-point positioning method are less affected by the geomagnetic field, and the positioning accuracy is better than that of the traditional single-point positioning method. The minimum error of the traditional single-point positioning method is 14.78%, and the minimum errors of Xu's two-point positioning method and the positioning method of the present application are 0.13% and 0.15% respectively. In addition, the maximum errors of the positioning method of the present application and Xu's two-point positioning method in the x-axis direction are 13.01% and 14.59% respectively, which are smaller than the minimum error of the single-point method in this direction. The maximum error of the single-point positioning method is 44.31%, which is increased by 28.18% and 26.78% respectively than the maximum errors of Xu's two-point positioning method and the positioning method of the present application. And the average errors of Xu's two-point positioning method and the positioning method of the present application in three directions are all smaller than the average error of the single-point positioning method, and the maximum difference of the average errors is 17.53% and 21.26% respectively.

[0114] Secondly, it can be found that when the distance between the observation points is 30 cm, the positioning accuracy of the positioning method of the present application is slightly higher than that of Xu's two-point positioning method, and the average relative errors in the x, y and z directions are reduced by 0.28%, 1.02% and 3.73% respectively than those of Xu's two-point positioning method. The maximum error of the positioning method of the present application is 16.13% in the z direction, while that of Xu's two-point positioning method is 17.52% in the y direction. The positioning results of the two-point method will be analyzed and compared according to the change of the distance between the two observation points.

[0115] B. Distance change between observation points

[0116] Suppose the starting point is the position of the first observation point and is fixed, and the second observation point moves along the z=x straight line trajectory. In this case, the measurement data of the starting point is taken as the data of observation point 1, and the rest of the observation points are taken in turn as the data of observation point 2 for two-point positioning, a total of 6 groups of two-point positioning solutions. With the change of observation point 2, the distance between the two observation points becomes larger and larger. The positioning relative error of the two-point method is shown in Table 2.

[0117] Table 2 Positioning relative error of two-point method (%)

[0118]

[0119] It can be seen that, compared with the two-point distance fixed at 30 cm (adjacent two points realize positioning), the positioning error of Xu's two-point positioning method in x, y and z directions increases significantly. Although the point error in x direction is not too obvious, the average error only increases by 4%, but the positioning error in y and z directions increases exponentially with the distance between the two observation points, and the average error increases by 40.71% and 48.29% respectively; further, when the distance exceeds 90 cm, the positioning error in z direction reaches more than 53.99%, and the positioning algorithm can be considered invalid. In summary, as the two-point interval increases, the positioning error increases. However, the positioning method of the present application is not affected by the distance between the two points, and the point error only appears slight fluctuation due to the influence of random noise. The average error of the present application in three directions is much smaller than that of Xu's two-point positioning method, the maximum positioning error is reduced, and the minimum positioning error is reduced.

[0120] In summary, the algorithm proposed in the present application is not affected by the distance between the observation points, and is fully adapted to the arbitrary change between the positions of the two observation points. Any two positions can form two points, and a small number of observation points can be arbitrarily combined to obtain multiple inversion solutions, and more accurate positioning can be achieved according to the solution aggregation, and the information obtained by each observation point is fully utilized.

[0121] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present application, and are not limited thereto; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: it can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement to part or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present application.

Claims

1. A magnetic target localization method based on the full magnetic gradient tensor, characterized in that, Includes the following steps: Step 1: Measure the total magnetic gradient tensor at the two observation points; Step 2: Solve for the characteristic polynomial of the magnetic gradient tensor matrix at the two observation points, and calculate the corresponding real eigenvalues ​​and the corresponding unit eigenvectors. Step 3: Calculate the normalized magnetic source intensity corresponding to the two observation points. and ; Calculate the relative position vector and cosine of the angle with the magnetic moment vector and ; Calculate the relative position vector of the first observation point and magnetic dipole magnetic moment vector The relative position vector between the plane P1 and the second observation point and magnetic dipole magnetic moment vector The cosine of the angle between the planes P2 and P2 ; Step 4: Calculate the relative position vector and cosine of the included angle and relative position vector and modulus and ; Step 5: Using the unit eigenvector corresponding to the real eigenvalue with the smallest absolute value, which is perpendicular to the relative position vector between the observation point and the target, establish a relationship with the first relative position vector. The corresponding unit direction vector The relevant system of equations was solved to obtain ; Step 6: Calculate the first relative position vector based on Step 4. modulus and the unit direction vector obtained in step 5 The location of the magnetic source is determined by the location of the first observation point and the location of the first observation point.

2. The magnetic target localization method based on the full magnetic gradient tensor according to claim 1, characterized in that, In step 2, the calculated real eigenvalues ​​include: λ min1 , λ med1 , λ max1 , λ min2 , λ med2 , λ max2 , where λ min1 , λ med1 , λ max1 Let λ represent the three real eigenvalues ​​of the magnetic gradient tensor matrix corresponding to the first observation point. min2 , λ med2 , λ max2 These represent the three real eigenvalues ​​of the magnetic gradient tensor matrix corresponding to the second observation point. , .

3. The magnetic target localization method based on the full magnetic gradient tensor according to claim 1, characterized in that, In step 3, the normalized magnetic source intensity corresponding to the first observation point Normalized magnetic source intensity corresponding to the second observation point The calculation formulas are as follows: ； ； The formula for calculating the cosine of the angle between the relative position vector and the magnetic moment vector is: ； ； The cosine of the angle between plane P1 and plane P2 is: ； in, and Let λ represent the real eigenvalues ​​of the magnetic gradient tensor matrix at the first observation point. med1 The real eigenvalues ​​λ of the magnetic gradient tensor matrix at the second observation point med2 The corresponding unit eigenvector.

4. The magnetic target localization method based on the full magnetic gradient tensor according to claim 1, characterized in that, In step 4, the relative position vector and cosine of the included angle The calculation formula is: ； and relative position vector and modulus and The calculation formula is: ， ； ， ； dr represents the distance between two observation points.

5. The magnetic target localization method based on the full magnetic gradient tensor according to claim 1, characterized in that, In step 5, the established relative position vector with the first position vector is... The corresponding unit direction vector The relevant system of equations is as follows: ； ； ； and Let λ represent the real eigenvalues ​​of the magnetic gradient tensor matrix at the first observation point. med1 The real eigenvalues ​​λ of the magnetic gradient tensor matrix at the second observation point med2 The corresponding unit eigenvector, This represents the relative position vector between two observation points.

6. The magnetic target localization method based on the full magnetic gradient tensor according to claim 3, characterized in that, Step 3 also includes calculation. and The steps for calculating the value, if the calculation results have the same sign, If the signs are opposite, .

7. The magnetic target localization method based on the full magnetic gradient tensor according to claim 1, characterized in that, In step 6, the formula for calculating the position of the magnetic source is: ； in, Represents the magnetic source position vector. This represents the position vector of the first observation point.

8. The magnetic target localization method based on the full magnetic gradient tensor according to claim 1, characterized in that, In step 1, the magnetic gradient tensor at the observation point is obtained through a cross-shaped magnetic gradient full tensor measurement array.

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