Multiple magnetic source target localization method based on multi-resolution cluster matching pursuit algorithm

Abstract

The multi-magnetic source target positioning method based on the multi-resolution cluster matching pursuit algorithm has the following main steps: first, a magnetic gradient tensor meter is used to perform multi-point measurements, and the measured values ​​are used as the residual initial values; then the detection area is gridded at a lower resolution, and the grid node with the largest residual matching degree is used as the anchor point for preliminary positioning; then the anchor point and the surrounding grids are used as a new detection area, and the area is gridded at a higher resolution, and the new grid node with the largest residual matching degree is used as the target position searched this time, and the target position and the grid node set with a matching degree greater than a threshold around it are selected as candidate nodes for this target cluster, and the candidate nodes with a magnetic moment modulus value less than the magnetic moment threshold are eliminated to form the cluster for this search; finally, the target set, cluster set, residual signal and Green's matrix are updated, and the next target is positioned when the target magnetic moment is greater than the threshold, otherwise the search and positioning is completed.

Description

Technical Field

[0001] The invention relates to the field of magnetic anomaly detection and multi-magnetic dipole positioning, and in particular to a multi-magnetic source target positioning method based on a multi-resolution cluster matching pursuit algorithm. Background Art

[0002] Due to its advantages of low cost, fast response speed, and simple operation, magnetic anomaly detection and positioning has been widely used in underground metal pipeline positioning, unexploded bomb detection and other fields. Among them, compared with total anomaly field detection, the magnetic gradient tensor contains richer magnetic source information and can effectively reduce the interference of the geomagnetic field. Therefore, magnetic dipole positioning based on the magnetic gradient tensor has received more attention. However, current research is mostly focused on single magnetic target positioning. Many mature algorithms such as the Euler deconvolution method and the scalar triangulation ranging method have achieved good positioning results in practical applications. However, for multi-magnetic dipole positioning, which is more common in engineering applications, such as multiple parallel buried underground pipelines and multiple randomly distributed underground unexploded bombs, there are currently few related studies on multi-magnetic dipole positioning. Since the magnetic anomaly signals of multi-magnetic dipole targets are often aliased and the deep target signals are easily submerged by shallow targets, multi-magnetic dipole target positioning is more challenging than single magnetic dipole positioning.

[0003] The current multi-magnetic dipole target positioning methods can be roughly divided into two categories: data fitting methods and point cloud clustering methods. The data fitting method uses the least squares algorithm to fit the forward modeling data and the measured data to estimate the target position. Song Shuang et al. S. Song, C. Hu and MQ-H. Meng, "Multiple Objects Positioning and Identification Method Based on Magnetic Localization System," IEEE Trans. Magn., vol. 52, no. 10, pp. 1-4, Oct. 2016 proposed a multi-magnetic dipole positioning method that uses the Levenberg-Marquardt (LM) algorithm to fit vector magnetic field data. Since the data fitting problem of multiple magnetic dipoles is a highly ill-conditioned nonlinear problem, the above method is very easy to fall into a local optimal solution. Therefore, Lv Bowen et al., B.Lv, Y.Qin, H.Dai and S.Su, "Improving Localization Success Rate of Three Magnetic TargetsUsing Individual Memory-Based WO-LM Algorithm," IEEE Sensors J., vol.21, no.19, pp.21750-21758, Oct, 2021. proposed an improved whale optimization algorithm to estimate the initial value of the LM algorithm, thereby reducing the possibility of local optimal solutions. The above method assumes that the number of multi-magnetic dipoles is known, which is difficult to achieve in many practical applications. Therefore, Ding Xuezhen et al. [X. Ding, Y. Li, M. Luo, J. Chen, Z. Li and H. Liu, "Estimating Locations and Moments of Multiple Dipole-Like Magnetic Sources From Magnetic Gradient Tensor Data Using Differential Evolution," IEEE Trans. Geosci. Remote Sens., vol. 60, pp. 1-13, 2022.] used the magnetic dipole contour map to estimate the magnetic dipole target, and then used the differential evolution algorithm to fit the magnetic gradient tensor data. The point cloud clustering method assumes that the solution set obtained by the single magnetic dipole positioning algorithm at different measuring points tends to be distributed around the target, so the clustering algorithm can be used to perform point cloud clustering on the solution set.Yin Gang et al. [G. Yin, Y. Zhang, H. Fan, G. Ren, and Z. Li, "Automatic detection of multiple UXO-like targets using magnetic anomaly inversion and self-adaptive fuzzy c-means clustering," Explor. Geophys., vol. 48, no. 1, pp. 67-75, Dec. 2018.] first used the Euler deconvolution method to perform single-point positioning to generate a two-dimensional point cloud, and then used the adaptive fuzzy c-means clustering algorithm for clustering to estimate the position of multiple magnetic dipole targets using the centroid of the cluster. Similarly, Li Qingzhu et al. [Li Qingzhu, Li Zhining, Shi Zhiyong, Fan Hongbo. AFCM clustering and tensor invariant for multi-target positioning of magnetic sources [J]. Optics and Precision Engineering, 30 (20): 2523-2537, 2022.] improved the single-point positioning algorithm to generate a three-dimensional point cloud, and also used the adaptive fuzzy c-means clustering algorithm for clustering. However, these existing positioning methods are heavily dependent on the accuracy of pre-order assumptions and preprocessing, which will result in serious cumulative errors. Moreover, when the distance between multiple magnetic source targets is too close or there is overlap in horizontal coordinates, the existing methods cannot effectively identify multiple targets. In addition, in order to achieve higher-resolution contour maps or more accurate clustering results, the current detection methods need to spend a lot of effort to collect a large amount of measurement point data. Therefore, there is an urgent need for a method that can accurately locate highly overlapping multi-magnetic dipole targets using a small number of measurement points. Summary of the invention

[0004] The purpose of the present invention is to provide a method for addressing the problems of low positioning accuracy, the need to predict the number of targets and the large number of measuring points required in multi-magnetic dipole positioning. The method converts the multi-magnetic dipole target positioning into a sparse signal recovery problem by using compressed sensing theory, and solves the sparse signal recovery problem based on a multi-resolution cluster matching pursuit algorithm, so as to realize the identification of multiple magnetic targets with less noisy measurement data.

[0005] The objective of the present invention is achieved through the following technical solutions:

[0006] The multi-magnetic source target positioning method based on the multi-resolution cluster matching pursuit algorithm proposed in the present invention comprises the following steps:

[0007] Step 1: Use the magnetic gradient tensor to measure at p measuring points evenly distributed above the detection area. The magnetic gradient tensor signal of a single measuring point is recorded as y = [B xx B xy B xz B yy B yz] T , where B xx It represents the gradient of the magnetic field in the x direction. The meanings of the other elements are similar. The magnetic gradient tensor data of M measuring points is recorded as Y = [y1 y2…y p ] T , initialize the target set Г=φ, the residual signal ε=Y, and the cluster set Λ=φ, where φ represents the empty set.

[0008] Step 2: Divide the detection area into preliminary grids at a lower resolution. The number of grid nodes is N1. The grid nodes are numbered in the order of 1, 2, ..., N1, and the Green matrix of each grid node is established. The Green matrix of the i-th grid node can be expressed as: A i =[A i1 A i2 …A ip ] T , where A ip The Green matrix representing the i-th grid node to the p-th measurement point can be calculated using the following formula:

[0009]

[0010] Where μ0 is the vacuum magnetic permeability, r represents the distance between the ith grid node and the pth measuring point, and x, y, and z are the coordinates of the ith grid node relative to the pth measuring point.

[0011] Step 3: Calculate the matching degree ρ between each grid node and the residual signal ε using the following formula: 1i =||ρ 1i ||2:

[0012]

[0013] The grid node with the largest matching degree is used as the anchor point for preliminary positioning.

[0014] Step 4: The initially located anchor point and its adjacent K grid nodes are used as the new detection area, and the new detection area is finely gridded with a higher resolution. The number of grid nodes is N2. The grid nodes are numbered in the order of 1, 2, ..., N2, and the Green matrix of each grid node is established. The Green matrix of the i-th grid node can be expressed as: B i =[B i1 B i2 …B ip ] T , where B ip Represents the Green matrix of the i-th grid node to the p-th measurement point, and its calculation method is the same as step 2.

[0015] Step 5: Calculate the matching degree ρ between each grid node and the residual signal ε using the following formula: 2i =||ρ 2i ||2:

[0016]

[0017] The grid node number with the largest matching degree is used as the position index λ of the magnetic dipole target found this time:

[0018]

[0019] Step 6: Select the magnetic dipole target to satisfy ρ2>μ1*ρ 2max The conditional grid node set Ω is used as the candidate grid node for the magnetic dipole target cluster, where μ1 is a coefficient determined by the user and ρ 2max The maximum matching degree is obtained, and the magnetic moment modulus M of each candidate grid node is calculated using the least squares algorithm. i =||M i ||2, the calculation formula is as follows:

[0020]

[0021] M i ≤μ2*M max The grid nodes of the candidate grid nodes are removed from the set of candidate grid nodes Ω, where μ2 is the coefficient determined by the user, M max is the maximum magnetic moment modulus value, and the grid nodes corresponding to the magnetic dipole target are added to the candidate grid node set Ω to form the clustering grid node set Θ.

[0022] Step 7: Update the target set Г, cluster set Λ, residual signal ε and Green matrix A as follows:

[0023] Γ=Γ∪{λ}

[0024] Λ=Λ∪Θ

[0025]

[0026] Among them B Λ is the Green matrix corresponding to the cluster set Λ, B Г is the Green matrix corresponding to the target set Г.

[0027] Step 8: Use the least squares algorithm to calculate the magnetic moment M corresponding to the magnetic dipole target Г

[0028]

[0029] when When , δ is the preset threshold, the iterative process goes to step 3; otherwise, the iterative process goes to step 8.

[0030] Step nine: Take the searched target set Г as the multi-target positioning result and terminate the iteration.

[0031] Compared with the prior art, the present invention has the following beneficial effects:

[0032] For the first time, multi-magnetic dipole positioning is converted into a sparse signal recovery problem based on compressed sensing theory. Compared with existing methods, it can effectively reduce the number of measurement points required, thereby effectively alleviating the measurement workload of the multi-magnetic dipole positioning task and improving work efficiency. At the same time, it can effectively avoid error accumulation and improve positioning accuracy. A multi-resolution clustering matching pursuit algorithm is proposed to solve the underdetermined equation for sparse signal recovery. It can adaptively estimate the position of multi-magnetic dipole targets without a priori number of targets, reducing the dependence of the positioning task on prior information. In addition, clustering patterns and multi-resolution analysis are introduced into the matching pursuit algorithm to avoid the occurrence of false reconstructed targets. At the same time, a trade-off between computational complexity and positioning accuracy is achieved, reducing the computing resources and computing time required for target positioning and improving the practicality of the algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 This is a flowchart of a multi-magnetic source target positioning method based on a multi-resolution cluster matching pursuit algorithm of the present invention.

[0034] Figure 2 This is a schematic diagram of grid division in the multi-magnetic source target positioning method based on the multi-resolution cluster matching pursuit algorithm of the present invention. DETAILED DESCRIPTION

[0035] The present invention will be further described below in conjunction with the accompanying drawings, but the protection scope of the present invention shall not be limited thereto.

[0036] The magnetic source multi-target positioning method based on the multi-resolution cluster matching pursuit algorithm proposed in the present invention can be used for the detection of underground unexploded bombs. Multiple unexploded bombs are equivalent to multiple magnetic dipoles. The method can be used to locate the unexploded bombs before excavation, thereby improving the safety of operations.

[0037] The main steps are as follows:

[0038] Step 1: Use the magnetic gradient tensor to measure at 25 evenly distributed points above the detection area where unexploded bombs may exist. The magnetic gradient tensor data of a single point is recorded as y = [B xx B xy B xz B yy B yz ] T , where B xxIt represents the gradient of the magnetic field in the x direction. The meanings of the other elements are similar. The data of the 25 measuring points are recorded as Y = [y1 y2…y 25 ] T , initialize the target set Г=φ, the residual signal ε=Y, and the cluster set Λ=φ, where φ represents the empty set.

[0039] Step 2: Perform preliminary grid division on the detection area with a lower resolution (i.e., a larger grid size). The number of grid nodes is 125. The grid nodes are numbered in the order of 1, 2, ..., 125, and the Green matrix of each grid node is established. The Green matrix of the i-th (i is an integer between 1 and 125) grid node can be expressed as: A i =[A i1 A i2 …A i25 ] T , where A i25 The Green matrix representing the i-th grid node to the 25th measurement point can be calculated using the following formula:

[0040]

[0041] Where μ0 is the vacuum magnetic permeability, r represents the distance between the ith grid node and the 25th measuring point, and x, y, and z are the coordinates of the ith grid node relative to the 25th measuring point.

[0042] Step 3: Calculate the matching degree ρ between each grid node and the residual signal ε using the following formula: 1i =||ρ 1i ||2:

[0043]

[0044] The grid node with the largest matching degree ρ1 is used as the anchor point for preliminary positioning.

[0045] Step 4: Use the four grids adjacent to the initially located anchor point as the new detection area, such as Figure 2 As shown, the new detection area is finely divided into grids with a higher resolution (i.e., a smaller grid size). The number of grid nodes is 405. The grids are numbered in the order of 1, 2, ..., 405, and the Green matrix of each grid is established. The Green matrix of the i-th grid can be expressed as: B i =[B i1 B i2 …B i405 ] T , where B i405 represents the Green matrix of the 405th measurement point of the i-th grid, and its calculation method is the same as step 2.

[0046] Step 5: Calculate the matching degree ρ between each grid and the residual signal ε using the following formula: 2i =||ρ 2i ||2:

[0047]

[0048] The grid with the largest matching degree is taken as the location of the magnetic dipole target found in this search.

[0049] Step 6: Select the magnetic dipole target to satisfy ρ2>μ1*ρ 2max The grid set Ω of the condition is used as the candidate grid for magnetic dipole target clustering, where μ1 is equal to 0.8, ρ 2max The maximum matching degree is obtained, and the magnetic moment modulus M of each candidate grid is calculated using the least squares algorithm. i =||M i ||2, the calculation formula is as follows:

[0050]

[0051] M i ≤μ2*M max The grids are removed from the candidate grid set Ω, where μ2 is equal to 0.6, M max is the maximum magnetic moment modulus value, and the grid corresponding to the magnetic dipole target is added to the candidate grid set Ω to form the clustering grid set Θ.

[0052] Step 7: Update the target set Г, cluster set Λ, residual signal ε and Green matrix A as follows:

[0053] Γ=Γ∪{*}

[0054] Λ=Λ∪Θ

[0055]

[0056] Among them B Λ is the Green matrix corresponding to the cluster set Λ, B Г is the Green matrix corresponding to the target set Г.

[0057] Step 8: Use the least squares algorithm to calculate the magnetic moment M corresponding to the magnetic dipole target Г

[0058]

[0059] when When δ=0.1, the iterative process goes to step 3; otherwise, the iterative process goes to step 8.

[0060] Step nine: Take the searched target set Г as the multi-target positioning result and terminate the iteration.

Claims

1. A multi-magnetic source target positioning method based on a multi-resolution cluster matching pursuit algorithm, characterized in that: The following steps are involved: Step 1: evenly arrange multiple magnetic gradient tensor meters as different measuring points in the detection area, use the magnetic gradient tensor meters to collect magnetic gradient tensor data at each measuring point, and obtain an initialization target set, a residual signal and a cluster set; Step 2: Divide the detection area into preliminary grids with a lower resolution and establish the Green matrix of each grid node; Step 3: According to the Green matrix of the residual signal and each grid node, the matching degree between each grid node and the residual signal is calculated, and the grid node with the largest matching degree is used as the anchor point for preliminary positioning; Step 4: The initially located anchor point and its adjacent grids are used as a new detection area, and the area is finely divided into grids with a higher resolution, and the Green matrix of each newly divided grid node is established; Step 5: Calculate the matching degree between each newly divided grid node and the residual signal, and take the grid node with the largest matching degree as the target position of the magnetic dipole found in this search; Step 6: Select the grid node set with a matching degree greater than the threshold around the magnetic dipole target searched this time as the candidate grid node set for clustering the magnetic dipole target this time, calculate the magnetic moment modulus of each candidate grid node using the least squares algorithm, remove the grid nodes with a magnetic moment modulus less than the magnetic moment threshold from the candidate grid node set, and add the grid nodes corresponding to the magnetic dipole target searched this time to the candidate grid node set, and use the processed candidate grid node set as the clustering grid node set this time; Step 7, update the target set, cluster set, residual signal and Green matrix; use the least squares algorithm to calculate the magnetic moment modulus corresponding to the magnetic dipole target, when the magnetic moment is greater than the preset threshold, go to step 3; when the magnetic moment modulus is less than or equal to the preset threshold, go to step 8; Step eight, taking the searched target set as the multi-target positioning result.

2. The multi-magnetic source target positioning method based on the multi-resolution cluster matching pursuit algorithm according to claim 1, characterized in that: The magnetic gradient tensor data of a single measuring point in step 1 is recorded as y=[B xx B xy B xz B yy B yz ] T , where B xx represents the gradient of the magnetic field in the x direction, B xy represents the gradient of the magnetic field in the x direction in the y direction, B xz represents the gradient of the magnetic field in the x direction in the z direction, B yy represents the gradient of the magnetic field in the y direction, B yz It represents the gradient of the magnetic field in the y direction in the z direction. The data of p measuring points are recorded as Y = [y1 y2…y p ] T , initialize the target set Г=φ, the residual signal ε=Y, and the cluster set Λ=φ, where φ represents the empty set.

3. The multi-magnetic source target positioning method based on the multi-resolution cluster matching pursuit algorithm as claimed in claim 1, characterized in that: In step 2, the Green matrix of the i-th grid node is expressed as: A i =[A i1 A i2 …A ip ] T , where A ip Represents the Green matrix of the i-th grid node to the p-th measurement point. The formula is as follows: Where μ0 is the vacuum magnetic permeability, r represents the distance between the ith grid node and the pth measuring point, and x, y, and z are the coordinates of the ith grid node relative to the pth measuring point.

4. The multi-magnetic source target positioning method based on the multi-resolution cluster matching pursuit algorithm according to claim 1, characterized in that: In step 3, the matching degree ρ between each grid node and the residual signal ε i =||ρ i ||2,ρ i The calculation formula is as follows: Among them, ρ i is the matching degree between the ith grid node and the residual signal ε, A i is the Green matrix.

5. The multi-magnetic source target positioning method of the multi-resolution cluster matching pursuit algorithm according to claim 1, characterized in that: In step 5, the grid node with the largest matching degree is used as the magnetic dipole target position λ found in this search, and the formula is as follows: Among them, ρ i is the matching degree between the i-th grid node and the residual signal ε.

6. The multi-magnetic source target positioning method of the multi-resolution cluster matching pursuit algorithm according to claim 1, characterized in that: In step 6, the matching threshold is defined as μ1*ρ max , where μ1 is a coefficient determined by the user, ρ max is the maximum matching degree among all grid nodes; the magnetic moment modulus M=||M||2, and its calculation formula is as follows: Among them B i is the Green matrix of the candidate grid, which is calculated in the same way as step 2; the magnetic moment modulus threshold is defined as μ2*||M max ||2, where μ2 is a coefficient determined by the user, M max is the maximum magnetic moment modulus value corresponding to the candidate grid node; the cluster set searched this time is recorded as Θ.

7. The multi-magnetic source target positioning method using the multi-resolution cluster matching pursuit algorithm according to claim 1, wherein in step seven, it is characterized in that: The target set Г, cluster set Λ, residual signal ε and Green matrix A are updated as follows: Γ=Γ∪{λ} Λ=Λ∪Θ Among them B Λ is the Green matrix corresponding to the cluster set Λ.

8. The method for locating multiple magnetic source targets using a multi-resolution cluster matching pursuit algorithm according to claim 1, wherein in step seven, the method comprises: Calculate the magnetic moment M corresponding to the magnetic dipole target Г , the formula is as follows: Among them B Г is the Green matrix corresponding to the target set Γ.

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