A variable structure underwater ferromagnetic anomaly positioning method based on magnetic gradient tensor

Abstract

The present invention relates to a variable-structure underwater ferromagnetic anomaly location method based on magnetic gradient tensors, comprising the following steps: first, placing eight three-axis magnetometer sensors in a hexahedral array and aligning their three coordinate axes; second, using an improved scalar triangulation and ranging method to calculate the rough position of the underwater target relative to the sensor array as an initial value; then, establishing a multi-point positioning objective function based on the magnetic dipole single-point positioning principle, and using a particle swarm optimization algorithm to calculate the optimal sensor array baseline length and height; finally, recalculating the precise position of the underwater ferromagnetic anomaly based on the optimal baseline length and height. The present invention can adaptively adjust the baseline length and height of the sensor array according to the target location, obtaining a more accurate positioning result, and can also be combined with a variety of different positioning methods, thus providing a highly universal and generalizable underwater ferromagnetic anomaly location system.

Description

Technical Field

[0001] The present invention relates to a variable structure underwater ferromagnetic anomaly positioning method based on magnetic gradient tensor, which is mainly used for accurate positioning of underwater ferromagnetic anomalies and belongs to the technical field of magnetic detection and positioning. Background Art

[0002] Because magnetic objects buried underwater or shallowly beneath the surface distort the surrounding geomagnetic field, magnetic targets can be detected and located using a variety of methods, including magnetic, electromagnetic, and ground-penetrating radar. Magnetic methods are widely used due to their high sensitivity, low cost, and rapid response. Magnetic detection, a magnetic field-based target detection technology, offers advantages such as all-weather, rapidity, and high precision, and holds great potential in geophysics and biomedicine. Because magnetic gradient tensor measurements can measure both vector and total field gradients, they can provide more information about field sources while also eliminating the influence of the geomagnetic field. The magnetic gradient tensor invariant, an extension of the magnetic gradient tensor, possesses the advantageous property of rotational invariance; it depends only on the sensor's position vector and is independent of its placement angle. Currently, most research on magnetic gradient tensor-based localization algorithms focuses on eliminating the inherent orientation error (ellipticity) and range error inherent in the tensor invariant, while little attention has been paid to the mechanical design of the sensor array. On this basis, the present invention fully considers the requirement of variable sensor array structure and carries out research on variable structure underwater ferromagnetic anomaly positioning system based on magnetic gradient tensor, aiming to achieve adaptive and adjustable precise positioning of underwater ferromagnetic anomalies. Summary of the Invention

[0003] The technology of the present invention solves the problem that the traditional underwater ferromagnetic anomaly positioning accuracy is low, and a variable structure underwater ferromagnetic anomaly positioning system based on magnetic gradient tensor is provided. It can significantly improve the positioning accuracy of underwater magnetic targets. Moreover, the multi-sensor array structure designed by the present invention can also be combined with a variety of other detection methods, and has certain universality and generalization.

[0004] The technical solution of the present invention is a variable structure underwater ferromagnetic anomaly positioning method based on magnetic gradient tensor, which is implemented in the following steps:

[0005] In the first step, an improved Scalar Triangulation and Ranging (STAR) algorithm for locating underwater ferromagnetic anomalies is proposed.

[0006] An underwater ferromagnetic anomaly far from the sensor array is modeled as a magnetic dipole, expressed as:

[0007]

[0008] Where μ0 = 4π × 10 -7 H / m represents the vacuum magnetic permeability, r=[r x ,r y ,r z ] T represents the position vector from the underwater ferromagnetic anomaly to the sensor array, r = |r| represents the modulus of the vector r, and m = [m x ,m y ,m z ] T represents the magnetic dipole moment vector, and the magnetic gradient tensor is defined as the rate of change of the three components of magnetic induction along the three coordinate axes, expressed as:

[0009]

[0010] In addition, considering that the magnetic field is a passive field and there is no conduction current in the static magnetic field, the divergence and curl of the magnetic field are both zero, so:

[0011]

[0012] Therefore, the magnetic gradient tensor matrix G is a symmetric matrix, and its 9 elements can be represented by 5 of them, namely:

[0013]

[0014] and the magnetic gradient tensor invariant C T Defined as the Frobenius norm of the matrix G is different. Taking into account the existence of elliptic errors, a new magnetic gradient tensor invariant is defined as:

[0015]

[0016] in, is the ellipticity coefficient, θ is the angle between the magnetic moment direction and the position direction of the anomaly, and the gradient of the invariant C is obtained:

[0017]

[0018] Among them, x0 represents the unit vector along the positive direction of the x-axis, y0 represents the unit vector along the positive direction of the y-axis, z0 represents the unit vector along the positive direction of the z-axis, C x+ ,C x- ,...,C z- They represent the tensor invariants at the center points of the sensor array, where C at each point can be solved by the following formula:

[0019]

[0020] in, λ2=3Ccosθ, are the three eigenvalues ​​of the magnetic gradient tensor matrix G, and satisfy λ1>λ2>λ3,|λ1|>|λ2|,|λ3|>|λ2|, G ij is the element in the i-th row and j-th column of the gradient tensor matrix;

[0021] In addition, it can be seen from the gradient formula of the tensor invariant C that the gradient direction of C is the same as the direction of the position vector of the underwater ferromagnetic anomaly. Therefore, the unit vector U0 of the rate of change of the tensor invariant C in the three directions of the coordinate axis can be used to approximate the unit vector r0 of the position of the underwater ferromagnetic anomaly, that is:

[0022]

[0023] Next, the distance between the underwater ferromagnetic anomaly and the sensor array is calculated, which is obtained from the position relationship:

[0024]

[0025] Among them, r z+ represents the position vector of the underwater ferromagnetic anomaly to the center point of the plane in the positive direction of the z-axis, and d represents the baseline length of the initial sensor array. Modulo the above equation and approximate it using the Maclaurin formula, we have:

[0026]

[0027] Similarly, we can get:

[0028]

[0029]

[0030]

[0031]

[0032]

[0033] Then we have:

[0034]

[0035]

[0036]

[0037] Where k is the ellipticity coefficient at the six center points of the measurement array. Solving the above equations separately, the distance between the sensor array and the underwater ferromagnetic anomaly can be calculated as:

[0038]

[0039] At this point, the position vector of the underwater ferromagnetic anomaly can be roughly obtained:

[0040] r=r·r0

[0041] And it is used as the initial value for locating underwater ferromagnetic anomalies.

[0042] The second step is to design an objective function based on multi-point positioning and use the particle swarm optimization algorithm to solve the optimal baseline length and height problem of the sensor array. From the ideal single-point positioning algorithm, we can know that:

[0043] r=-3G -1 B

[0044] Then the center points of the six faces of the sensor array cube are:

[0045]

[0046]

[0047]

[0048] Because the magnetic induction intensity generated by the underwater ferromagnetic anomaly modeled as a magnetic dipole can also be expressed as:

[0049]

[0050] So for the center points of the six faces of the sensor array:

[0051]

[0052]

[0053]

[0054] Since the magnetic moment of underwater ferromagnetic anomalies is fixed and unique, the above equations can be combined to obtain:

[0055]

[0056] So the objective function can be designed as:

[0057]

[0058] Next, the baseline length and height of the sensor array are set as unknown variables. The particle swarm optimization algorithm can be used to obtain the optimal baseline length d' and height h' of the sensor array under the premise of knowing the rough location of the underwater ferromagnetic anomaly.

[0059] The third step is to calculate the precise position of the underwater ferromagnetic anomaly again. First, the slide rails of the sensor array are controlled to control the length and height between the sensors to the optimized baseline length d' and height h' obtained by the particle swarm optimization algorithm. Figure 2 (bd) shown, Figure 2 (b) for Figure 2 (a) Schematic diagram of adjusting the horizontal baseline length d' based on the initial conditions. Figure 2 (c) for Figure 2 (a) Schematic diagram of adjusting the vertical baseline height h' based on the initial conditions. Figure 2 (d) Figure 2 (a) Schematic diagram of adjusting the horizontal baseline length d' and the vertical baseline height h' simultaneously based on the initial conditions.

[0060] Next, the precise position of the underwater ferromagnetic anomaly is calculated again based on the method in the first step, where the new unit vector r0′ of the underwater ferromagnetic anomaly orientation is:

[0061]

[0062] The distance r′ between the new sensor array and the underwater ferromagnetic anomaly is:

[0063]

[0064] In summary, the position vector r′ of the new underwater ferromagnetic anomaly can be accurately calculated as:

[0065] r′=r′·r′0.

[0066] The advantages of the variable structure underwater ferromagnetic anomaly positioning system based on magnetic gradient tensor designed by the present invention compared with the existing technology are as follows:

[0067] (1) The present invention fully considers the orientation error (elliptical error) and distance error in three directions during the initial positioning process, and derives a more accurate distance formula.

[0068] (2) The present invention designs an objective function based on multi-point positioning and uses a particle swarm optimization algorithm to solve the optimal sensor array baseline length and height for locating underwater ferromagnetic anomalies with known rough positions.

[0069] (3) The variable structure underwater ferromagnetic anomaly positioning system designed by the present invention has strong generalization and can be used in combination with different existing positioning algorithms to effectively improve positioning accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1This is a flow chart of a variable structure underwater ferromagnetic anomaly positioning method based on magnetic gradient tensor according to the present invention;

[0071] Figure 2 Schematic diagram of the baseline length and height adjustment of the positioning sensor array mechanical structure designed for the present invention;

[0072] Figure 3 A comparison chart of the positioning accuracy of ferromagnetic targets at different positions of the present invention and other methods;

[0073] Figure 4 This is a comparison chart of the positioning accuracy of ferromagnetic targets at different positions in the O-xy plane of the present invention and other methods;

[0074] Figure 5 This is a comparison chart of the positioning accuracy of ferromagnetic targets at different positions in the z-axis direction of the present invention and other methods. DETAILED DESCRIPTION

[0075] like Figure 1 As shown, the variable structure underwater ferromagnetic anomaly positioning system based on magnetic gradient tensor of the present invention includes the following steps: first, eight three-axis magnetometer sensors are placed in a hexahedron array and their three coordinate axes are aligned; second, the improved STAR method is used to calculate the rough position of the underwater ferromagnetic anomaly relative to the sensor array as the initial value; then, a multi-point positioning objective function is established based on the magnetic dipole single-point positioning principle, and the particle swarm optimization algorithm is used to calculate the optimal sensor array baseline length and height; finally, the precise position of the underwater ferromagnetic anomaly is calculated again based on the optimal baseline length and height. The principle block diagram of the entire system is shown in FIG. Figure 1 The specific implementation steps are as follows:

[0076] The first step is to propose an improved STAR magnetic underwater ferromagnetic anomaly location algorithm. The underwater ferromagnetic anomaly far away from the sensor array is modeled as a magnetic dipole, expressed as:

[0077]

[0078] Where μ0 = 4π × 10 -7 H / m represents the vacuum magnetic permeability, r=[r x ,r y ,r z ] T represents the position vector from the underwater ferromagnetic anomaly to the sensor, r = |r| represents the modulus of the vector r, m = [m x ,m y ,m z ] Trepresents the magnetic dipole moment vector, and the magnetic gradient tensor is defined as the rate of change of the three components of magnetic induction along the three coordinate axes, expressed as:

[0079]

[0080] In addition, considering that the magnetic field is a passive field and there is no conduction current in the static magnetic field, the divergence and curl of the magnetic field are both zero, so:

[0081]

[0082] Therefore, the magnetic gradient tensor matrix G is a symmetric matrix, and its 9 elements can be represented by 5 of them, namely:

[0083]

[0084] and the magnetic gradient tensor invariant C T Defined as the Frobenius norm of the matrix G is different. Taking into account the existence of elliptic errors, a new magnetic gradient tensor invariant is defined as:

[0085]

[0086] in, is the ellipticity coefficient, θ is the angle between the magnetic moment direction and the position direction of the anomaly, and the gradient of the invariant C is obtained:

[0087]

[0088] Among them, x0 represents the unit vector along the positive direction of the x-axis, y0 represents the unit vector along the positive direction of the y-axis, z0 represents the unit vector along the positive direction of the z-axis, C x+ ,C x- ,...,C z- They represent the tensor invariants at the center points of the sensor array, where C at each point can be solved by the following formula:

[0089]

[0090] in, λ2=3Ccosθ, are the three eigenvalues ​​of the magnetic gradient tensor matrix G, and satisfy λ1>λ2>λ3,|λ1|>|λ2|,|λ3|>|λ2|, G ij is the element in the i-th row and j-th column of the gradient tensor matrix,

[0091] In addition, it can be seen from the gradient formula of the tensor invariant C that the gradient direction of C is the same as the direction of the position vector of the underwater ferromagnetic anomaly. Therefore, the unit vector U0 of the rate of change of the tensor invariant C in the three directions of the coordinate axis can be used to approximate the unit vector r0 of the position of the underwater ferromagnetic anomaly, that is:

[0092]

[0093] Next, the distance between the underwater ferromagnetic anomaly and the sensor array is calculated, which is obtained from the position relationship:

[0094]

[0095] Among them, r z+ represents the position vector of the underwater ferromagnetic anomaly to the center point of the plane in the positive direction of the z-axis, and d represents the baseline length of the initial sensor array. Modulo the above equation and approximate it using the Maclaurin formula, we have:

[0096]

[0097] Similarly, we can get:

[0098]

[0099]

[0100]

[0101]

[0102]

[0103] Then we have:

[0104]

[0105]

[0106]

[0107] Where k is the ellipticity coefficient at the six center points of the measurement array. Solving the above equations separately, the distance between the sensor array and the underwater ferromagnetic anomaly can be calculated as:

[0108]

[0109] At this point, the position vector of the underwater ferromagnetic anomaly can be roughly obtained:

[0110] r=r·r0

[0111] And it is used as the initial value for locating underwater ferromagnetic anomalies.

[0112] The second step is to design an objective function based on multi-point positioning and use the particle swarm optimization algorithm to solve the optimal baseline length and height problem of the sensor array. From the ideal single-point positioning algorithm, we can know that:

[0113] r=-3G -1 B

[0114] Then the center points of the six faces of the sensor array cube are:

[0115]

[0116]

[0117]

[0118] Because the magnetic induction intensity generated by the underwater ferromagnetic anomaly modeled as a magnetic dipole can also be expressed as:

[0119]

[0120] So for the center points of the six faces of the sensor array:

[0121]

[0122]

[0123]

[0124] Since the magnetic moment of underwater ferromagnetic anomalies is fixed and unique, the above equations can be combined to obtain:

[0125]

[0126] So the objective function can be designed as:

[0127]

[0128] Next, the baseline length and height of the sensor array are set as unknown variables. The particle swarm optimization algorithm can be used to obtain the optimal baseline length d' and height h' of the sensor array under the premise of knowing the rough location of the underwater ferromagnetic anomaly.

[0129] The third step is to calculate the precise position of the underwater ferromagnetic anomaly again. First, the slide rails of the sensor array are controlled to control the length and height between the sensors to the optimized baseline length d' and height h' obtained by the particle swarm optimization algorithm. Figure 2 (bd) shown, Figure 2 (b) for Figure 2 (a) Schematic diagram of adjusting the horizontal baseline length d' based on the initial conditions. Figure 2 (c) for Figure 2 (a) Schematic diagram of adjusting the vertical baseline height h' based on the initial conditions. Figure 2 (d) Figure 2 (a) Schematic diagram of adjusting the horizontal baseline length d' and the vertical baseline height h' simultaneously based on the initial conditions.

[0130] Next, the precise position of the underwater ferromagnetic anomaly is calculated again based on the method in the first step, where the new unit vector r0′ of the underwater ferromagnetic anomaly orientation is:

[0131]

[0132] The distance r′ between the new sensor array and the underwater ferromagnetic anomaly is:

[0133]

[0134] In summary, the position vector r′ of the new underwater ferromagnetic anomaly can be accurately calculated as:

[0135] r′=r′·r′0.

[0136] Matlab is used for simulation verification. The magnetic moment vector of the underwater ferromagnetic anomaly is set to m = [0, 0, 50] T A.m 2 The position vectors are 18 points on a circle with a radius of 0.55m and a height of -0.325m around the z-axis. The initial baseline length of the sensor array is set to d = 0.07m, and the accuracy of the three-axis magnetometer is set to 0.01nT. Without considering the geomagnetic field and sensor measurement noise, the simulation results are compared with various classic positioning methods (such as STAR, Lv-STAR, Wang-STAR, etc.). Figure 3-5 As shown in the figure, the curve labeled "ChenSTAR traj" represents the positioning results of the positioning system proposed in this invention. It is obvious that the positioning accuracy achieved by the variable structure underwater ferromagnetic anomaly positioning system based on magnetic gradient tensor proposed in this invention is far higher than that of other existing algorithms.

[0137] The contents not described in detail in the specification of the present invention belong to the prior art known to professional and technical personnel in this field. Although exemplary embodiments of the present invention have been described for illustrative purposes, it will be understood by those skilled in the art that various modifications, additions and substitutions can be made in form and detail without departing from the scope and spirit of the invention disclosed in the appended claims, and all such changes should fall within the scope of protection of the appended claims of the present invention, and the various departments of the product and the various steps in the method claimed in the present invention can be combined together in any combination. Therefore, the description of the embodiments disclosed in the present invention is not intended to limit the scope of the present invention, but is used to describe the present invention. Accordingly, the scope of the present invention is not limited by the above embodiments, but is defined by the claims or their equivalents.

Claims

1. A variable structure underwater ferromagnetic anomaly positioning method based on magnetic gradient tensor, characterized in that: The following steps are involved: Step (1) Place eight three-axis magnetometer sensors in a hexahedral array and align their three coordinate axes; Step (2) based on step (1), the rough position of the underwater ferromagnetic anomaly relative to the sensor array is calculated using the improved scalar triangulation and ranging method as the initial value; Step (3) Based on step (2), a multi-point positioning objective function is established using the magnetic dipole single-point positioning principle, and the particle swarm optimization algorithm is used to calculate the optimal sensor array baseline length and height; Step (4) calculates the precise position of the underwater ferromagnetic anomaly again based on the optimal baseline length and height in step (3).

2. The method for locating underwater ferromagnetic anomalies based on magnetic gradient tensor and variable structure according to claim 1 is characterized in that: In step (2), the improved scalar triangulation and ranging method is used to calculate the magnetic target positioning algorithm as follows, An underwater ferromagnetic anomaly far from the sensor array is modeled as a magnetic dipole, expressed as: ； in, represents the vacuum permeability, represents the position vector from the underwater ferromagnetic anomaly to the sensor, Represents a vector The model, represents the magnetic dipole moment vector; The magnetic gradient tensor is defined as the rate of change of the three components of magnetic induction along the three coordinate axes, expressed as: ； In addition, considering that the magnetic field is a passive field and there is no conduction current in the static magnetic field, the divergence and curl of the magnetic field are both zero, so: ； Therefore, the magnetic gradient tensor matrix It is a symmetric matrix, and its 9 elements are represented by 5 of them, namely: ； and the magnetic gradient tensor invariant Defined as a matrix The Frobenius norm is different. Considering the existence of elliptic error, a new magnetic gradient tensor invariant is defined as: ； in, is the ellipticity coefficient, is the angle between the direction of the magnetic moment of the anomaly and the direction of its position, and the invariant Finding the gradient, we can get: ； in, represents the unit vector along the positive x-axis, represents the unit vector along the positive y-axis, represents the unit vector along the positive z-axis, Represents the tensor invariant at the center point of the sensor array, where each point All can be solved by the following formula: ； in, is the magnetic gradient tensor matrix The three eigenvalues ​​of , is the first in the gradient tensor matrix Rank Elements of the column; In addition, by the tensor invariant The gradient formula shows that The gradient direction of is the same as the direction of the position vector of the underwater ferromagnetic anomaly. Therefore, the tensor invariants in the three directions of the coordinate axis can be used. The unit vector of the rate of change of To approximate the unit vector of the underwater ferromagnetic anomaly ,Right now: ； Next, the distance between the underwater ferromagnetic anomaly and the sensor array is calculated, which is obtained from the position relationship: ； in, Represents the position vector of the underwater ferromagnetic anomaly to the center point of the plane in the positive direction of the z axis, represents the baseline length of the initial sensor array. Modulo the above equation and approximate it using the Maclaurin formula, we have: ； Similarly, we can get: ； Then we have: ； in, is the ellipticity coefficient at the six center points of the measurement array; by solving the above equations separately, the distance between the sensor array and the underwater ferromagnetic anomaly can be calculated as: ； At this point, the position vector of the underwater ferromagnetic anomaly can be roughly obtained: ； And it is used as the initial value for locating underwater ferromagnetic anomalies.

3. The method for locating underwater ferromagnetic anomalies based on magnetic gradient tensor and variable structure according to claim 2 is characterized in that: In step (3), the method for calculating the optimal sensor array baseline length and height is as follows, From the ideal single point positioning algorithm, we can know that: ； Then the center points of the six faces of the sensor array cube are: ； Because the magnetic induction intensity generated by the underwater ferromagnetic anomaly modeled as a magnetic dipole can also be expressed as: ； So for the center points of the six faces of the sensor array: ； Since the magnetic moment of underwater ferromagnetic anomalies is fixed and unique, the above equations can be combined to obtain: ； So the objective function is designed as: ； Next, the baseline length and height of the sensor array are set as unknown variables. The particle swarm optimization algorithm can be used to obtain the optimal baseline length of the sensor array under the premise of knowing the rough location of the underwater ferromagnetic anomaly. and height .

4. The method for locating underwater ferromagnetic anomalies based on magnetic gradient tensor and variable structure according to claim 3 is characterized by: In step (4), the method for calculating the precise position of the underwater ferromagnetic anomaly again is to first control the slide rail of the sensor array to control the length and height between the sensors to the optimized baseline length obtained by the particle swarm optimization algorithm. and height ; Next, the precise position of the underwater ferromagnetic anomaly is calculated again based on the algorithm in step (2), where the unit vector of the new underwater ferromagnetic anomaly orientation is for: ； New sensor array to underwater ferromagnetic anomalies distance for: ； In summary, the position vector of the new underwater ferromagnetic anomaly can be accurately obtained for: 。

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