A magnetic source target positioning method

Abstract

The application discloses a magnetic source target positioning method, belongs to the technical field of geophysical exploration, and is used for magnetic source target positioning, comprising the following steps: collecting plane grid magnetic anomaly data and preprocessing, constructing a simplified Euler deconvolution model under derivative characteristic constraint, segmenting observation data by using a local sliding window, solving and generating an Euler solution point cloud, converting an equivalent scale factor selection problem into a one-dimensional global optimization problem, adaptively searching for an optimal solution by using a Bayesian optimization method, identifying magnetic source high-probability solution points and noise solution points by using a density-based spatial clustering method, introducing a density penalty term to strengthen high-probability solution constraint, constructing a final positioning target function, and outputting a magnetic source optimal position solution. The application simplifies a traditional Euler deconvolution model, effectively suppresses noise interference, improves stability and robustness of an inversion process, avoids uncertainty caused by artificial selection of parameters, and improves positioning precision.

Description

TECHNICAL FIELD

[0001] The application discloses a magnetic source target positioning method and belongs to the technical field of geophysical exploration. BACKGROUND

[0002] Magnetic anomaly is a local distortion phenomenon of the geomagnetic field caused by ferromagnetic objects, has strong cross-medium detection capability, high positioning accuracy, concealment and high detection efficiency, and is widely used in the positioning of ferromagnetic targets. Existing magnetic source positioning methods mainly include an analytical positioning method based on a magnetic dipole model, a target tracking algorithm based on filtering and state estimation, and a direct positioning algorithm based on geometry and analysis. Among them, the direct positioning algorithm based on geometry and analysis has the advantages of high calculation efficiency and clear structure by using the internal mathematical characteristics of the magnetic field or the magnetic gradient to derive the analytical solution of the target position parameters. The Euler deconvolution inversion algorithm, as a typical representative of this method, is widely used because it does not require specific geological model assumptions and has significant advantages.

[0003] To further improve the positioning accuracy, an improved algorithm based on the integral form of Euler's equation is proposed, and a specially designed multi-coil sensor is combined to use the linear solution as the initial value of the nonlinear least squares optimization, realizing high-precision positioning of the magnetic source target. In addition, the improved tilted Euler inversion method avoids calculating singular points and reduces unstable factors in the inversion process, improving the robustness of the solution. In recent years, with the cross-fusion of multiple disciplines, the Euler deconvolution is combined with the deep learning target detection model to realize high-precision identification and detection of typical magnetic sources such as underwater unexploded bombs; another research based on the second-order magnetic gradient tensor system realizes high-precision single-point positioning of the magnetic source target without background magnetic field prior information by combining Euler deconvolution with magnetic gradient tensor space invariant constraint. Further, by combining Euler deconvolution automatic initialization with neural network assisted Kalman filtering, high-precision robust tracking and positioning of the position, velocity and magnetic moment of the moving magnetic source are realized without noise statistical prior and artificial initial value. SUMMARY

[0004] The purpose of the present application is to provide a magnetic source target positioning method to solve the problems of model parameters depending on artificial experience, strong subjectivity and low efficiency, divergent inversion calculation results, poor stability and weak anti-interference ability in the prior art.

[0005] A magnetic source target positioning method, comprising:

[0006] S1, collect and preprocess the planar grid magnetic anomaly data, the preprocessing includes performing local weighted regression smoothing processing according to the magnetic anomaly data, calculating the first derivative of the preprocessed magnetic anomaly data to extract a preliminary magnetic anomaly boundary, calculating the second derivative of the preprocessed magnetic anomaly data to extract a zero-crossing point constraint preliminary magnetic anomaly boundary, and taking the constrained preliminary magnetic anomaly boundary as an initial search range of an Euler deconvolution algorithm;

[0007] S2, randomly set a magnetic source target initial position in the initial search range, construct a simplified Euler deconvolution model, introduce an equivalent scale factor to represent model parameters, and construct a preliminary positioning target function by minimizing a residual sum of squares;

[0008] S3, set a local sliding window, segment the observation data based on the local sliding window, invert the magnetic source target position candidate solution in the local sliding window based on the preliminary positioning target function, aggregate the candidate solutions of all local sliding windows to construct an Euler solution point cloud, convert the selection problem of the equivalent scale factor into a one-dimensional global optimization problem, construct an observation value target function based on the trace of the covariance of the solution point cloud, introduce a Bayesian optimization to solve the observation value target function, and obtain an optimal equivalent scale factor;

[0009] S4, identify magnetic source high-density solution points and noise points using a density-based spatial clustering method, introduce a density penalty term, construct a final positioning target function based on the optimal equivalent scale factor, the density penalty term and the preliminary positioning target function, and output an optimal magnetic source target position estimate through the final positioning target function.

[0010] S1 includes S1.1, collecting and preprocessing the planar grid magnetic anomaly data, including performing neighborhood weighted regression smoothing processing according to the magnetic anomaly data;

[0011] S1 includes S1.2, calculating the first derivative of the preprocessed magnetic anomaly data and taking the absolute value, identifying the maximum value position using a peak finding function, and estimating a preliminary magnetic anomaly boundary;

[0012] S1 includes S1.3, calculating the second derivative of the preprocessed magnetic anomaly data, determining the zero-crossing point according to the sign change, and constraining the preliminary magnetic anomaly boundary using the zero-crossing point;

[0013] S1 includes S1.4, taking the constrained preliminary magnetic anomaly boundary as the initial search range of the Euler deconvolution algorithm.

[0014] S2 includes S2.1, setting the observation point coordinates as , the magnetic source target initial position as , absorbing the model parameters into the equivalent scale factor, the model parameters including a background field and constructing an index , and constructing a simplified Euler deconvolution model:

[0015] ;

[0016] ;

[0017] where, is the partial derivative symbol, is the gradient in the direction, is the gradient in the direction, is the equivalent scale factor, is the pre-processed magnetic anomaly value.

[0018] S2 includes, S2.2, for any observation point :

[0019] ;

[0020] where, is the observation point index, is the residual of the th observation point, is the gradient in the direction at the th observation point, is the gradient in the direction at the th observation point, is the pre-processed magnetic anomaly value at the th observation point; S2 includes, S2.3, constructing a preliminary positioning objective function by minimizing the sum of squares of residuals:

[0021] ;

[0022] ;

[0023] where, is the number of observation points, .

[0024] S3 includes, S3.1, setting the size of the local sliding window , dividing the observation data into , each applying the preliminary positioning objective function to invert the magnetic source target position candidate solution: ;

[0025] ;

[0026] where, is the index of the local sliding window,​​ , for Candidate solutions obtained from inversion. For a given Under the conditions, The magnetic source target inside Coordinate estimates In a given Under the conditions, The magnetic source target inside Coordinate estimates;

[0027] Summarize all candidate solutions to form an Euler solution point cloud. :

[0028] ;

[0029] In the formula, It is a two-dimensional real number space.

[0030] S3 includes S3.2, which transforms the problem of selecting the equivalent scaling factor into a one-dimensional global optimization problem, and uses the covariance trace to characterize the overall dispersion of the solution point cloud. And construct a Gaussian process proxy model:

[0031] ;

[0032] ;

[0033] In the formula, For covariance trace, The function on the left side of the sign follows the probability distribution on the right side of the sign. It is a mean function. Let covariance function be used. It is a Gaussian process.

[0034] S3 includes S3.3, constructing the acquisition function:

[0035] ;

[0036] In the formula, In order to improve, This is the current optimal observation value. For the posterior probability density, for The value of ;

[0037] Choose to Reaching the maximum value As an evaluation point for the next iteration :

[0038] ;

[0039] In the formula, To find the independent variable that maximizes the expected improvement function;

[0040] like ,renew Recalculate Iterate until The improvement amount is less than Output makes Minimum optimal equivalent scaling factor .

[0041] S4 includes, S4.1, evaluating the clustering relationships of the Eulerian solution point cloud using a density-based spatial clustering method, including setting a point density threshold. and region radius threshold ,by With the center as the center, Construct the solution set region with radius . ;

[0042] like The number of candidate solutions contained within is greater than or equal to ,definition For high-density solution sets, clustering is performed to preserve the high-density solution sets.

[0043] like The number of candidate solutions contained within is less than ,definition To identify isolated points, these isolated points are removed as noise points.

[0044] S4 includes S4.2, which uses a density penalty term to improve clustering performance:

[0045] ;

[0046] In the formula, For density penalty terms, For Let be the set of all candidate solutions within the solution set region centered at the circle. for The set of all candidate solutions in the cluster to which it belongs. This is the intersection symbol.

[0047] S4 includes S4.3, based on , Construct the final localization objective function from the initial localization objective function. :

[0048] ;

[0049] In the formula, For regularization parameters;

[0050] Solve using the least squares method Obtain the optimal magnetic source target position estimate .

[0051] Compared with existing technologies, this invention has the following advantages: By introducing derivative analysis to constrain the initial position selection of the model, this invention effectively avoids the divergence and discretization problems of solutions, ensuring the accuracy of the initial position selection. Based on this, the traditional Euler deconvolution model is simplified by reducing the dimensionality and complexity of unknown parameters, and the background field and depth, which are difficult to estimate stably, are uniformly absorbed into the equivalent scaling factor. This transforms the physically rigorous inversion model into a geometric positioning model centered on planar position determination. This simplification effectively suppresses parameter coupling and noise interference, improving the stability and robustness of the inversion process. Furthermore, the Bayesian optimization method is used to adaptively determine the equivalent scaling factor, avoiding the uncertainty caused by manual parameter selection and further improving positioning accuracy. In multi-target positioning, the algorithm constructs a density penalty term, transforming the noisy multi-magnetic-source positioning problem into a clustering and screening problem of planar geometric space solutions. Utilizing the difference between the spatial clustering of real magnetic source solutions and the random discretization of noise pseudo-solutions, the density of the solutions is used as a reliability metric. This allows for accurate identification of real targets and effective elimination of noise interference within a unified model framework, significantly enhancing the accuracy and robustness of multi-target positioning. This invention simplifies the calculation process, improves positioning efficiency, and exhibits good adaptability and scalability under complex background fields and large-scale data conditions, comprehensively improving the accuracy and reliability of magnetic anomaly source positioning. Attached Figure Description

[0052] Figure 1 This is a detailed flowchart of the present invention;

[0053] Figure 2 The results are localization results of the Euler deconvolution method under simulated noisy conditions and a single magnetic source.

[0054] Figure 3 The results are localization results of the density clustering-based Euler deconvolution method under simulated noisy conditions and a single magnetic source.

[0055] Figure 4 The results are the localization results of the method of the present invention under simulated noisy conditions and a single magnetic source.

[0056] Figure 5 The results are localization results of the Euler deconvolution method under simulated noisy conditions and multiple magnetic sources.

[0057] Figure 6 The results are localization results of the density clustering-based Euler deconvolution method under simulated noisy conditions and multiple magnetic sources.

[0058] Figure 7 The results are the localization results of the method of this invention under simulated noisy and multi-magnetic-source conditions.

[0059] Figure 8 The results are the localization results of the Euler deconvolution method under measured multi-magnetic-source conditions.

[0060] Figure 9 The results are localization results of the Euler deconvolution method based on density clustering under measured multi-magnetic-source conditions.

[0061] Figure 10 The results are the localization results of the method of this invention under actual measurement with multiple magnetic sources. Detailed Implementation

[0062] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention are described clearly and completely below. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0063] A method for locating a magnetic source target, comprising:

[0064] S1. Collect planar grid magnetic anomaly data and perform preprocessing. Preprocessing includes local weighted regression smoothing based on the magnetic anomaly data, calculating the first derivative of the preprocessed magnetic anomaly data to extract the preliminary magnetic anomaly boundary, calculating the second derivative of the preprocessed magnetic anomaly data to extract the zero intersection point constrained preliminary magnetic anomaly boundary, and using the constrained preliminary magnetic anomaly boundary as the initial search range of the Euler deconvolution algorithm.

[0065] S2. Randomly set the initial position of the magnetic source target within the initial search range, construct a simplified Euler deconvolution model, introduce an equivalent scaling factor to characterize the model parameters, and construct a preliminary positioning objective function by minimizing the sum of squared residuals.

[0066] S3. Set up a local sliding window, segment the observation data based on the local sliding window, invert candidate solutions for the magnetic source target position in the local sliding window based on the preliminary positioning objective function, summarize all candidate solutions of the local sliding window to construct the Euler solution point cloud, transform the problem of selecting the equivalent scaling factor into a one-dimensional global optimization problem, construct the observation objective function based on the covariance trace of the solution point cloud, introduce Bayesian optimization to solve the observation objective function, and obtain the optimal equivalent scaling factor.

[0067] S4. Use density-based spatial clustering to identify high-density solution points and noise points of the magnetic source, introduce a density penalty term, construct the final positioning objective function based on the optimal equivalent scaling factor, density penalty term and preliminary positioning objective function, and output the optimal magnetic source target position estimate through the final positioning objective function.

[0068] S1 includes S1.1, collecting planar grid magnetic anomaly data and performing preprocessing, including neighborhood weighted regression smoothing based on the magnetic anomaly data;

[0069] S1 includes S1.2, calculating the first derivative of the preprocessed magnetic anomaly data and taking its absolute value, using the peak-finding function to identify the location of the maximum value, and estimating the preliminary magnetic anomaly boundary;

[0070] S1 includes S1.3, calculating the second derivative of the preprocessed magnetic anomaly data, determining the zero intersection point based on the sign change, and using the zero intersection point to constrain the preliminary magnetic anomaly boundary;

[0071] S1 includes S1.4, which uses the constrained initial magnetic anomaly boundary as the initial search range for the Euler deconvolution algorithm.

[0072] S2 includes, S2.1, setting the coordinates of the observation point within the initial search range as... The initial position of the magnetic source target is The model parameters are incorporated into the equivalent scaling factor. The model parameters include the background field. and construction index Construct a simplified Euler deconvolution model:

[0073] ;

[0074] ;

[0075] In the formula, The sign of the partial derivative. for Gradient of direction, for Gradient of direction, As an equivalent scaling factor, This represents the preprocessed magnetic anomaly value.

[0076] S2 includes S2.2, for any observation point :

[0077] ;

[0078] In the formula, For the index of observation points, For the first The residuals at each observation point In the first At each observation point exist gradient in direction, In the first At each observation point exist gradient in direction, In the first Preprocessed magnetic anomaly values ​​at each observation point;

[0079] S2 includes S2.3, constructing a preliminary localization objective function by minimizing the sum of squared residuals:

[0080] ;

[0081] In the formula, For the number of observation points, .

[0082] S3 includes, S3.1, setting a partial sliding window. The size is The observation data is divided into indivual each The initial application of the objective function to invert candidate solutions for the magnetic source target location is as follows:

[0083] ;

[0084] In the formula, For the index of a local sliding window, , for Candidate solutions obtained from inversion. In a given Under the conditions, The magnetic source target inside Coordinate estimates In a given Under the conditions, The magnetic source target inside Coordinate estimates;

[0085] Summarize all candidate solutions to form an Euler solution point cloud. :

[0086] ;

[0087] In the formula, It is a two-dimensional real number space.

[0088] S3 includes S3.2, which transforms the problem of selecting the equivalent scaling factor into a one-dimensional global optimization problem, and uses the covariance trace to characterize the overall dispersion of the solution point cloud. And construct a Gaussian process proxy model:

[0089] ;

[0090] ;

[0091] In the formula, For covariance trace, The function on the left side of the sign follows the probability distribution on the right side of the sign. It is a mean function. Let covariance function be used. It is a Gaussian process.

[0092] S3 includes S3.3, constructing the acquisition function:

[0093] ;

[0094] In the formula, In order to improve, This is the current optimal observation value. For the posterior probability density, for The value of ;

[0095] Choose to Reaching the maximum value As an evaluation point for the next iteration :

[0096] ;

[0097] In the formula, To find the independent variable that maximizes the expected improvement function;

[0098] like ,renew Recalculate Iterate until The improvement amount is less than Output makes Minimum optimal equivalent scaling factor .

[0099] S4 includes, S4.1, evaluating the clustering relationships of the Eulerian solution point cloud using a density-based spatial clustering method, including setting a point density threshold. and region radius threshold ,by With the center as the center, Construct the solution set region with radius . ;

[0100] like The number of candidate solutions contained within is greater than or equal to ,definition For high-density solution sets, clustering is performed to preserve the high-density solution sets.

[0101] like The number of candidate solutions contained within is less than ,definition To identify isolated points, these isolated points are removed as noise points.

[0102] S4 includes S4.2, which uses a density penalty term to improve clustering performance:

[0103] ;

[0104] In the formula, For density penalty terms, For Let be the set of all candidate solutions within the solution set region centered at the circle. for The set of all candidate solutions in the cluster to which it belongs. This is the intersection symbol.

[0105] S4 includes S4.3, based on , Construct the final localization objective function from the initial localization objective function. :

[0106] ;

[0107] In the formula, For regularization parameters;

[0108] Solve using the least squares method Obtain the optimal magnetic source target position estimate .

[0109] The process of this invention is as follows Figure 1 As shown, the first step involves initial positional constraints on the raw magnetic anomaly data, including calculating the first and second derivatives to identify anomaly boundaries, generating initial intervals based on the anomaly boundaries, and simplifying the model using the Euler deconvolution inversion model. Specifically, this includes performing neighborhood-weighted regression smoothing on the raw magnetic anomaly data. The neighborhood-weighted regression smoothing process involves, for each survey line data... , This represents the total number of measurement points on the current survey line. For any point to be smoothed, use the index of the measurement point on the current measurement line. Select the closest Each point is used as a neighborhood subset. Calculate the neighborhood radius ;

[0110] ;

[0111] In the formula, for The first in Neighboring points, for index, ;

[0112] right Calculate normalized distance :

[0113] ;

[0114] calculate weight :

[0115] ;

[0116] right Smoothed estimate at To make an estimate, assume that it follows a first-order multinomial distribution in the neighborhood:

[0117] ;

[0118] In the formula, and These are local regression coefficients;

[0119] Solving by minimizing the weighted sum of squared residuals. and :

[0120] ;

[0121] for The original value at that location, when At that time, the smoothed estimate of that point is obtained. :

[0122] ;

[0123] In the formula, These are the optimal regression coefficients;

[0124] Calculate the first derivative of the preprocessed magnetic anomaly data and take its absolute value; then use a peak-finding function to identify the neighborhood. The location of the inner maximum is used to estimate the initial magnetic anomaly boundary. Then, the second derivative of the preprocessed magnetic anomaly data is calculated, and the zero intersection point is determined based on the sign change. The zero intersection point is used to constrain the initial magnetic anomaly boundary, and the initial magnetic anomaly boundary is used as the initial search range of the Euler deconvolution algorithm.

[0125] The second step utilizes Bayesian optimization. This includes constructing the objective function for the observed values, updating the posterior distribution using a cyclic Gaussian process surrogate model, and expecting to improve the next... The process involves three steps: evaluation, convergence, and solution selection. The Bayesian optimization results are then filtered based on a density penalty term, including density-based spatial clustering and density penalty term calculation to identify density clusters and noise points. Finally, the objective function is minimized to obtain the target location.

[0126] The principle behind using the Euler deconvolution inversion model to locate magnetic sources includes: if the function... satisfy:

[0127] ;

[0128] In the formula, Scaling factor for The homogeneous order;

[0129] So Satisfy the following partial differential equations:

[0130] ;

[0131] ;

[0132] ;

[0133] ;

[0134] In the formula, For grid points Take the value at that location. for Grid points in the direction, for Grid points in the direction, for Grid points in the direction, The difference;

[0135] In the geophysical field, Treating it as a coordinate function, for a single magnetic source anomaly field, let the position of the magnetic source be... We can obtain:

[0136] ;

[0137] Assuming the magnetic anomaly data contains One observation point, Under the condition of single magnetic source localization, in order to simplify the calculation process, the position of the single magnetic source is estimated by the global least squares method based on the Euler deconvolution equation. The linear equation system is expressed as follows:

[0138] ;

[0139] ;

[0140] ;

[0141] ;

[0142] In the formula, For the observation matrix, Let be the parameter vector to be determined. It is a data vector;

[0143] Then the optimal solution for:

[0144] ;

[0145] In the formula, This is the transpose symbol.

[0146] The pseudocode for the method of this invention is as follows: Input planar grid magnetic anomaly data; perform local weighted smoothing on the magnetic anomaly data to suppress high-frequency noise and maintain the continuity of the anomaly morphology; calculate the first derivative of the data to extract candidate positions of the anomaly boundary; calculate the zero intersection points of the second derivative of the data to constrain the geometric boundary and eliminate pseudo-boundaries caused by noise or background fluctuations; identify the anomaly boundary positions as the spatial interval where the magnetic source exists, and use them as the constraint range for the initial position of the Euler deconvolution; randomly set the initial position of the target within the constraint range to construct a simplified Euler deconvolution model and an equivalent scaling factor. And initially locate the objective function; divide the observation data into A local sliding window The target position of each local window is solved, and the Eulerian solution point cloud is obtained by summing the results. An objective function based on the observations is constructed, and Bayesian optimization is introduced to adaptively seek the optimal value. Density-based spatial clustering methods identify high-density clusters and noise points; a density penalty term based on the proportion of noise points is introduced, utilizing optimal... The final target location function is constructed by combining the density penalty term and the preliminary location objective function; the optimal magnetic source location solution is output.

[0147] This invention first utilizes the first and second derivative features of magnetic anomaly data to provide a reliable initial search region for magnetic source inversion. Then, it simplifies the Euler deconvolution inversion model by incorporating the difficult-to-estimate background field and depth parameters into an equivalent scaling factor, reducing the dimensionality and complexity of unknown parameters and improving inversion stability. Bayesian optimization is then used to adaptively determine the equivalent scaling factor. Finally, a density penalty term is introduced to further screen the Euler solution point cloud, effectively suppressing discrete misinterpretation points. The performance of the method of this invention is then evaluated.

[0148] First, the effectiveness of the proposed method is verified based on simulation data. (Settings) , , Set magnetic declination to 0 and magnetic tilt to 90° (magnetic poles), and directly generate the simulation using COMSOL software. Data in a planar coordinate system (unit: meters). In the simulation data, from... Figure 2 , Figure 3 and Figure 4 It is known that under noisy conditions and with only a single magnetic source, the traditional Eulerian deconvolution method has a large positioning error, making it difficult to effectively identify the target. Introducing a density-clustered Eulerian deconvolution method significantly improves target positioning accuracy. Based on this, the method of this invention further improves positioning accuracy and stability. (See figure...) The magnetic field strength is expressed in nanotesla (NTL). The positioning results are shown in Table 1.

[0149] Table 1. Simulation results of localization under noisy conditions and single magnetic source.

[0150] .

[0151] Depend on Figure 5 , Figure 6 and Figure 7 As can be seen, under noisy conditions and with multiple magnetic sources, the traditional Euler deconvolution method also exhibits a large positioning error and limited target recognition capability. The Euler deconvolution method that introduces density clustering can effectively improve the positioning results, while the method of this invention shows better positioning accuracy and robustness in multi-target scenarios. The positioning results are shown in Table 2.

[0152] Table 2. Simulation results of localization under noisy conditions and multiple magnetic sources.

[0153] .

[0154] Subsequently, performance evaluation was further conducted based on the measured data. The measurement area was a beach with a magnetic declination of -7°29' and a magnetic inclination of 53°44'. A [database / structure] was constructed within the measurement area. A Cartesian coordinate system was established, with the starting point of the survey line as the origin, north as the horizontal axis, and east as the vertical axis. The origin coordinates were set as (0,0), and the ending point coordinates as (20,20), with units in meters. After setting up the survey line, two hollow iron cylinders were selected as magnetic sources within the survey area and buried 0.5 meters below the sand. Experiments were conducted, and magnetic data were acquired using a cesium atomic magnetometer. To eliminate the influence of the tilted magnetization of the geomagnetic field, the collected raw magnetic anomaly data was first polarized to improve the subsequent positioning effect. The positioning performance of the method of this invention was evaluated by comparing and analyzing the distance of the positioning point relative to the center of the magnetic source (the center of the red area) in the polarized data. Figure 8 , Figure 9 andFigure 10 The results show that, under multiple magnetic source conditions, the positioning points of the traditional Euler deconvolution method deviate significantly. The method after introducing density clustering significantly improves the positioning accuracy, making the positioning points closer to the actual positions of the magnetic sources. The method of this invention further optimizes the positioning effect, with the positioning points closest to the center region of the magnetic sources. This verifies the effectiveness and superiority of this method in multi-magnetic source positioning scenarios. The positioning results are shown in Table 3.

[0155] Table 3. Measured positioning results under multiple magnetic sources

[0156] .

[0157] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for locating a magnetic source target, characterized in that, include: S1. Collect planar grid magnetic anomaly data and perform preprocessing. Preprocessing includes local weighted regression smoothing based on the magnetic anomaly data, calculating the first derivative of the preprocessed magnetic anomaly data to extract the preliminary magnetic anomaly boundary, calculating the second derivative of the preprocessed magnetic anomaly data to extract the zero intersection point constrained preliminary magnetic anomaly boundary, and using the constrained preliminary magnetic anomaly boundary as the initial search range of the Euler deconvolution algorithm. S2. Randomly set the initial position of the magnetic source target within the initial search range, construct a simplified Euler deconvolution model, introduce an equivalent scaling factor to characterize the model parameters, and construct a preliminary positioning objective function by minimizing the sum of squared residuals. S3. Set up a local sliding window, segment the observation data based on the local sliding window, invert candidate solutions for the magnetic source target position in the local sliding window based on the preliminary positioning objective function, summarize all candidate solutions of the local sliding window to construct the Euler solution point cloud, transform the problem of selecting the equivalent scaling factor into a one-dimensional global optimization problem, construct the observation objective function based on the covariance trace of the solution point cloud, introduce Bayesian optimization to solve the observation objective function, and obtain the optimal equivalent scaling factor. S4. Use density-based spatial clustering to identify high-density solution points and noise points of the magnetic source, introduce a density penalty term, construct the final positioning objective function based on the optimal equivalent scaling factor, density penalty term and preliminary positioning objective function, and output the optimal magnetic source target position estimate through the final positioning objective function. S2 includes, S2.1, setting the coordinates of the observation point within the initial search range as... The initial position of the magnetic source target is The model parameters are incorporated into the equivalent scaling factor. The model parameters include the background field. and construction index Construct a simplified Euler deconvolution model: ； ； In the formula, The sign of the partial derivative. for Gradient of direction, for Gradient of direction, As an equivalent scaling factor, These are the preprocessed magnetic anomaly values; S2 includes, S2.2, for any observation point : ； In the formula, For the observation point index, For the first The residuals at each observation point In the first At each observation point exist gradient in direction, In the first At each observation point exist gradient in direction, In the first Preprocessed magnetic anomaly values ​​at each observation point; S2 includes S2.3, constructing a preliminary localization objective function by minimizing the sum of squared residuals: ； In the formula, The number of observation points. .

2. The magnetic source target localization method according to claim 1, characterized in that, S1 includes S1.1, collecting planar grid magnetic anomaly data and performing preprocessing, including neighborhood weighted regression smoothing based on the magnetic anomaly data; S1 includes S1.2, calculating the first derivative of the preprocessed magnetic anomaly data and taking its absolute value, using the peak-finding function to identify the location of the maximum value, and estimating the preliminary magnetic anomaly boundary; S1 includes S1.3, calculating the second derivative of the preprocessed magnetic anomaly data, determining the zero intersection point based on the sign change, and using the zero intersection point to constrain the preliminary magnetic anomaly boundary; S1 includes S1.4, which uses the constrained initial magnetic anomaly boundary as the initial search range for the Euler deconvolution algorithm.

3. The magnetic source target localization method according to claim 2, characterized in that, S3 includes, S3.1, setting a partial sliding window. The size is The observation data is divided into indivual each The initial application of the objective function to invert candidate solutions for the magnetic source target location is as follows: ； In the formula, For the index of a local sliding window, , for Candidate solutions obtained from inversion. For a given Under the conditions, The magnetic source target inside Coordinate estimates For a given Under the conditions, The magnetic source target inside Coordinate estimates; Summarize all candidate solutions to form an Euler solution point cloud. : ； In the formula, It is a two-dimensional real number space.

4. The magnetic source target localization method according to claim 3, characterized in that, S3 includes S3.2, which transforms the problem of selecting the equivalent scaling factor into a one-dimensional global optimization problem, and uses the covariance trace to characterize the overall dispersion of the solution point cloud. And construct a Gaussian process proxy model: ； ； In the formula, For covariance trace, The function on the left side of the sign follows the probability distribution on the right side of the sign. It is a mean function. Let covariance function be used. It is a Gaussian process.

5. The magnetic source target localization method according to claim 4, characterized in that, S3 includes S3.3, constructing the acquisition function: ； In the formula, In order to improve, This is the current optimal observation value. For the posterior probability density, for The value of ; Choose to Reaching the maximum value As an evaluation point for the next iteration : ； In the formula, To find the independent variable that maximizes the expected improvement function; like ,renew Recalculate Iterate until The improvement amount is less than Output makes Minimum optimal equivalent scaling factor .

6. The magnetic source target localization method according to claim 5, characterized in that, S4 includes, S4.1, evaluating the clustering relationships of the Eulerian solution point cloud using a density-based spatial clustering method, including setting a point density threshold. and region radius threshold ,by With the center as the center, Construct the solution set region with radius . ; like The number of candidate solutions contained within is greater than or equal to ,definition For high-density solution sets, clustering is performed to preserve the high-density solution sets. like The number of candidate solutions contained within is less than ,definition To identify isolated points, these isolated points are removed as noise points.

7. The magnetic source target localization method according to claim 6, characterized in that, S4 includes S4.2, which uses a density penalty term to improve clustering performance: ； In the formula, For density penalty terms, For Let be the set of all candidate solutions within the solution set region centered at the circle. for The set of all candidate solutions in the cluster to which it belongs. This is the intersection symbol.

8. The magnetic source target localization method according to claim 7, characterized in that, S4 includes S4.3, based on , Construct the final localization objective function from the initial localization objective function. : ； In the formula, For regularization parameters; Solve using the least squares method Obtain the optimal magnetic source target position estimate .

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