A transient electromagnetic underground target detection and positioning method and system

Abstract

The present invention provides a method and system for detecting and positioning a transient electromagnetic underground target, which relates to the technical field of underground target positioning. The specific steps include: arranging a transient electromagnetic transmitting and receiving device in the detection area, exciting the underground medium by pulse current, collecting electromagnetic response signals, and using a high-precision GPS device to record the initial elevation model of each collection point, and correcting the electromagnetic response signal; performing spectrum analysis and filtering on the corrected signal, preliminarily estimating the underground target position and obtaining the initial value of the Gauss-Newton algorithm; inputting the initial value into the Gauss-Newton algorithm for iterative optimization, and obtaining the optimized target approximate position and eigenvector; analyzing the characteristic matrix by singular value decomposition, extracting the characteristic response related to the underground target, and using inverse calculation to deduce the precise position of the underground target. The present invention significantly improves the positioning accuracy and real-time performance under complex terrain conditions, and is suitable for efficient positioning under complex terrain conditions.

Description

Technical Field

[0001] The present invention relates to the technical field of underground target positioning, and in particular to a transient electromagnetic underground target detection and positioning method and system. Background Art

[0002] With the development and progress of science and technology, the demand for positioning underground metal objects is growing in many fields such as archeology, prospecting, geological mapping, and unexploded bomb detection. Among them, the underground metal target positioning method based on electromagnetic induction is currently a commonly used underground metal object positioning method because of its many advantages such as sensitivity to metal materials and strong penetration of low-frequency electromagnetic waves. The underground metal target positioning method based on electromagnetic induction uses electromagnetic positioning equipment to emit electromagnetic waves near underground metal objects to form a magnetic field that acts on underground metal objects. The underground metal objects induce eddy currents, which generate induction signals. Finally, the positioning device receives the induction signals. Since the information of the induction signal is related to the position of the metal, the underground metal objects can be located by analyzing the induction signals.

[0003] In the prior art, publication number CN114415246A discloses a method and system for locating underground metal objects based on machine learning, including: obtaining a data set; the i-th sample data in the data set includes multiple electromagnetic induction signals obtained from different locations in the i-th area and the position coordinates of the underground metal objects in the i-th area; constructing multiple different underground metal object positioning sub-models; obtaining multiple corresponding trained underground metal object positioning sub-models; weighting and adding each trained underground metal object positioning sub-model to obtain an integrated underground metal object positioning model, and the sum of each weighted weight is 1; using a particle swarm algorithm to adjust each weight in the integrated underground metal object positioning model to obtain a real-time positioning model for underground metal objects; using the real-time positioning model for underground metal objects to obtain the position coordinates of underground metal objects within the area to be measured. This method improves the efficiency and accuracy of positioning.

[0004] However, there are still some shortcomings. From the above statements, it can be seen that the terrain interference problem is not taken into account. Under complex terrain conditions, terrain changes will have a significant impact on the electromagnetic response signal, resulting in reduced positioning accuracy. The current method mainly relies on traditional electromagnetic signal analysis methods. The feature extraction and analysis are not in-depth enough, which limits the accuracy and reliability of the positioning results. It is not suitable for underground target positioning under complex terrain conditions.

[0005] The above information disclosed in this Background section is only for enhancement of understanding of the background of the present disclosure and therefore it may contain information that does not constitute the prior art that is already known to one of ordinary skill in the art. Summary of the invention

[0006] The purpose of the present invention is to provide a transient electromagnetic underground target detection and positioning method and system to solve the problems raised in the above background technology.

[0007] To achieve the above object, the present invention provides the following technical solutions:

[0008] A transient electromagnetic underground target detection and positioning method, the specific steps include:

[0009] S1. Arrange a transient electromagnetic transmitting device and a receiving device in the detection area, the transmitting device excites the underground medium through a pulse current to generate an electromagnetic response signal, the receiving device collects the electromagnetic response signal of the underground medium, searches for the terrain elevation data of each collection point in the digital elevation model, obtains the actual elevation data, uses a high-precision GPS device to record the initial elevation data of each collection point, performs data processing on the actual elevation data and the initial elevation data of each collection point, obtains the terrain correction factor of each collection point, uses the terrain correction factor to correct the electromagnetic response signal, and obtains the corrected electromagnetic response signal;

[0010] S2. Perform spectrum analysis and filtering on the corrected electromagnetic response signal to obtain the electromagnetic field component of the target signal, use the electromagnetic field component of the target signal to calculate the gradient of the electromagnetic field, construct a gradient tensor, preliminarily estimate the position of the underground target based on the gradient tensor, and average multiple positions to obtain the initial position value of the Gauss-Newton algorithm;

[0011] S3. Input the initial value of the preliminarily estimated position into the Gauss-Newton algorithm as the initial value of the iterative optimization, calculate the Jacobian matrix, perform approximate calculations of the gradient and the Hessian matrix, update the position parameters, obtain the optimized approximate position of the target, and use the optimized approximate position of the target to calculate the eigenvector;

[0012] S4. Using the eigenvectors obtained by optimizing the Gauss-Newton algorithm, construct a eigenmatrix, perform singular value decomposition on the eigenmatrix, obtain the product of a left singular vector matrix, a singular value diagonal matrix, and a right singular vector matrix, obtain singular values ​​and corresponding singular vectors by analyzing the left singular vector matrix, the singular value diagonal matrix, and the right singular vector matrix, and obtain characteristic responses related to underground targets according to the singular values ​​and the corresponding singular vectors;

[0013] S5. Reconstruct the feature matrix according to the feature response, extract the position feature from the reconstructed feature matrix, use the position feature and the least squares estimation algorithm to perform reverse calculation and deduce the position of the underground target.

[0014] Furthermore, the terrain correction factor of each acquisition point is calculated according to the geographic coordinates and elevation information, and the electromagnetic response signal is corrected using the terrain correction factor. The process of obtaining the corrected electromagnetic response signal is as follows:

[0015] In the elevation model, the geographic coordinates of the i-th collection point are set to , then the actual elevation data of the i-th collection point is , and the initial elevation data of the i-th collection point in the GPS record is , then the formula for obtaining the terrain correction factor is as follows:

[0016] ;

[0017] in, For the The terrain correction factor for each acquisition point is: For the The longitude of the collection point, For the The latitude of the collection point, is the index of the collection point;

[0018] Set the receiving device to The original electromagnetic response signal recorded by the acquisition points is ;

[0019] Using terrain correction factors The original electromagnetic response signal is corrected according to the following formula:

[0020] ;

[0021] in, For the The corrected electromagnetic response signal of each acquisition point is is the correction term function based on the terrain correction factor;

[0022] It is found through experiments that the relationship between the electromagnetic response signal and the change in terrain height is approximately linear, so a linear correction function is used:

[0023] ;

[0024] in, is the proportionality coefficient, , which indicates the sensitivity of terrain height changes to electromagnetic response signals.

[0025] Furthermore, the corrected electromagnetic response signal The process of spectrum analysis and filtering is as follows:

[0026] Convert the time domain signal to the frequency domain, extract different frequency components, and use fast Fourier transform for spectrum analysis. The formula is as follows:

[0027] ;

[0028] in, For the The spectrum of the corrected signal at each acquisition point is is the frequency of the response signal, is an imaginary unit, is the time variable;

[0029] Analyze the frequency components in the spectrum graph, identify the characteristic frequencies related to underground targets, determine the frequency range of target signals and noise based on the spectrum graph, separate the target signal components through a low-pass filter, combine with known geological data, compare and analyze the geological structures corresponding to the characteristic frequencies in the spectrum, and compare with known electromagnetic characteristics, including the electromagnetic response characteristics of different minerals or substances. Use this characteristic information to identify signals related to specific underground targets in the spectrum, extract characteristic parameters related to the target in the spectrum, including characteristic frequency, amplitude, and phase, and use these characteristic parameters as measurement data for the target signal.

[0030] Furthermore, the electromagnetic field component of the target signal is used to calculate the gradient of the electromagnetic field, and a gradient tensor is constructed. Based on the gradient tensor, the position of the underground target is preliminarily estimated, and multiple positions are averaged to obtain the initial position value of the Gauss-Newton algorithm. The specific process is as follows:

[0031] Through spectrum analysis and filtering processing, the filtered characteristic parameters are obtained, and the characteristic parameters in the frequency domain are converted into electromagnetic field components in the time domain. , , , using the electromagnetic field component , , , calculate the gradient of the electromagnetic field in space :

[0032] ;

[0033] in, is the electric field component of the electromagnetic field in the horizontal direction, is the electric field component in the longitudinal direction of the electromagnetic field, is the electric field component of the electromagnetic field in the depth axis direction;

[0034] Using the gradient of the electromagnetic field , construct the electromagnetic field gradient tensor :

[0035] ;

[0036] For each collection point , calculate the magnitude of the gradient vector :

[0037] ;

[0038] No. The gradient vector of the acquisition point The direction of is represented by a unit vector:

[0039] ;

[0040] in, For the The direction of the gradient vector of each acquisition point;

[0041] Use the coordinates of each collection point And the gradient vector The direction and magnitude of the gradient vector are used to estimate the position of the underground target. Pointing to the underground target, the gradient vector modulus is used As the step size, the position is estimated in the opposite direction of the gradient vector:

[0042] ;

[0043] in, For the The location of the underground target at each collection point, For the The step length of the acquisition points;

[0044] Average multiple positions to obtain the initial position value of the underground target of the Gauss-Newton algorithm :

[0045] ;

[0046] in, is the total number of collection points.

[0047] Furthermore, the initial value of the preliminarily estimated position is input into the Gauss-Newton algorithm as the initial value of the iterative optimization, the Jacobian matrix is ​​calculated, the gradient and Hessian matrix are approximated, the position is updated, and the optimized target approximate position is obtained. The optimized target approximate position is used to calculate the eigenvector. The specific process is as follows:

[0048] In the Gauss-Newton algorithm, it is necessary to calculate the Jacobian matrix of the objective function. Assuming the objective function is , then the Jacobian matrix is ​​defined as:

[0049] ;

[0050] in, is the Jacobian matrix, is the objective function vector;

[0051] The Gauss-Newton algorithm uses the Jacobian matrix to approximate the gradient and Hessian matrix of the objective function. Assume that the first error function is , then the gradient of the first error function and the approximate value of the Hessian matrix are:

[0052] ;

[0053] ;

[0054] in, is the gradient matrix of the first error function, is the Hessian matrix of the first error function, is transposed;

[0055] Update the position based on the gradient and the approximation of the Hessian matrix:

[0056] ;

[0057] in, is the position change;

[0058] The new location is:

[0059] ;

[0060] in, for the new location;

[0061] Repeat the above steps to calculate the new Jacobian matrix, gradient and Hessian matrix, and update the position until the stop condition is met to obtain the optimized target approximate position;

[0062] Using the optimized target approximate position, calculate the electromagnetic field gradient tensor The eigenvector of the electromagnetic field gradient tensor is at the optimized position Value for:

[0063] ;

[0064] The eigenvectors satisfy the following characteristic equation:

[0065] ;

[0066] in, is the characteristic value, is the feature vector;

[0067] For a given matrix , first construct the characteristic polynomial, which is represented by the following determinant:

[0068] ;

[0069] in, is the identity matrix;

[0070] Solve the characteristic polynomial and get the eigenvalue , , ;

[0071] For each eigenvalue , solve the following linear homogeneous equation to find the corresponding eigenvector :

[0072] ;

[0073] in, is the index of the eigenvalue.

[0074] Furthermore, the eigenvectors obtained by optimizing the Gauss-Newton algorithm are used to construct a characteristic matrix, and the characteristic matrix is ​​subjected to singular value decomposition to obtain the product of the left singular vector matrix, the singular value diagonal matrix, and the right singular vector matrix. The specific process is as follows:

[0075] Assume there is a nonlinear model ,in are input features, is the parameter vector, and the goal is to find the parameter vector Make the model output The actual observed value The error is minimal;

[0076] At each iteration, the Jacobian matrix is ​​calculated :

[0077] ;

[0078] Calculate the residual vector :

[0079] Update the parameter vector:

[0080] ;

[0081] in, is the index of the iteration number;

[0082] Repeat the above steps until convergence or the maximum number of iterations is reached;

[0083] Using the optimized parameter vector Construct eigenvectors and arrange them into a eigenmatrix , assuming there is feature vectors, each with a dimension of , then the feature matrix for:

[0084] ;

[0085] in, is the feature matrix The Column, representing a dimensional column vector, The value range is , is the field of real numbers, is the number of eigenvectors;

[0086] For the feature matrix Perform singular value decomposition to obtain the left singular vector matrix , singular value diagonal matrix and the right singular vector matrix ;

[0087] ;

[0088] in, is a column orthogonal matrix, whose column vectors are called left singular vectors, is a diagonal matrix whose diagonal elements are called singular values ​​and are arranged in descending order. is a column orthogonal matrix, and its column vectors are called right singular vectors.

[0089] Furthermore, by analyzing the left singular vector matrix, the singular value diagonal matrix and the right singular vector matrix, the singular values ​​and the corresponding singular vectors are obtained, and the characteristic response related to the underground target is obtained according to the singular values ​​and the corresponding singular vectors. The specific process is as follows:

[0090] The singular value diagonal matrix is The elements on the diagonal are singular values, arranged in descending order. The size of the singular value reflects the weight of different modes in the feature matrix;

[0091] ;

[0092] in, ,and ;

[0093] Left Singular Vector Matrix and the right singular vector matrix The column vectors of are called left singular vectors and right singular vectors, respectively, and are of the following form:

[0094] ;

[0095] .

[0096] Furthermore, according to the characteristic response, the characteristic matrix is ​​reconstructed, and the position features are extracted from the reconstructed characteristic matrix. The position features and the least squares estimation algorithm are used to perform reverse calculation to deduce the position of the underground target. The specific process is as follows:

[0097] Before selection Singular Values , the corresponding left singular vector is , the corresponding right singular vector is ;

[0098] Reconstructing the feature matrix , of the following form:

[0099] ;

[0100] in, It is singular values, It is left singular vectors, It is right singular vectors;

[0101] From the reconstructed feature matrix , extract row features, column features, cluster centers and high-intensity areas;

[0102] Based on the extracted features, including row features, column features, cluster centers, and high-intensity areas, the second error function is defined To measure the actual location characteristics and the features predicted by the model The difference between

[0103] ;

[0104] in, is the norm of the vector;

[0105] Optimize the second error function , calculate its relative position Gradient , based on the following formula:

[0106] ;

[0107] The precise position of the underground target is updated according to the gradient descent method. The formula is:

[0108] ;

[0109] in, is the updated location of the underground target, is the estimated position in the current iteration, For current location The gradient of the second error function at is the regulating factor;

[0110] Repeat the above steps until the second error function Reach the predetermined number of iterations.

[0111] To achieve the above object, the present invention provides the following technical solutions:

[0112] A transient electromagnetic underground target detection and positioning system, the system is used to execute any of the above-mentioned transient electromagnetic underground target detection and positioning methods, comprising:

[0113] The equipment arrangement and data acquisition module is used to arrange transient electromagnetic transmitting devices and receiving devices in the detection area. The transmitting device excites the underground medium through pulse current to generate an electromagnetic response signal. The receiving device collects the electromagnetic response signal of the underground medium, searches for the terrain elevation data of each collection point in the digital elevation model, obtains the actual elevation data, uses a high-precision GPS device to record the initial elevation data of each collection point, performs data processing on the actual elevation data and the initial elevation data of each collection point, obtains the terrain correction factor of each collection point, and uses the terrain correction factor to correct the electromagnetic response signal to obtain the corrected electromagnetic response signal;

[0114] A data processing module is used to perform spectrum analysis and filtering on the corrected electromagnetic response signal, obtain the electromagnetic field component of the target signal, calculate the gradient of the electromagnetic field using the electromagnetic field component of the target signal, construct a gradient tensor, preliminarily estimate the position of the underground target based on the gradient tensor, and average multiple positions to obtain the initial position value of the Gauss-Newton algorithm;

[0115] The optimization module is used to input the initial value of the preliminarily estimated position into the Gauss-Newton algorithm as the initial value of the iterative optimization, calculate the Jacobian matrix, perform approximate calculations of the gradient and the Hessian matrix, update the position parameters, obtain the optimized approximate position of the target, and use the optimized approximate position of the target to calculate the eigenvector;

[0116] A characteristic matrix construction module is used to construct a characteristic matrix using the characteristic vectors obtained by optimizing the Gauss-Newton algorithm, perform singular value decomposition on the characteristic matrix, obtain the product of the left singular vector matrix, the singular value diagonal matrix and the right singular vector matrix, obtain singular values ​​and corresponding singular vectors by analyzing the left singular vector matrix, the singular value diagonal matrix and the right singular vector matrix, and obtain characteristic responses related to underground targets according to the singular values ​​and the corresponding singular vectors;

[0117] The positioning module is used to reconstruct the feature matrix according to the feature response, extract the position features from the reconstructed feature matrix, and perform reverse calculation using the position features and the least squares estimation algorithm to derive the precise position of the underground target.

[0118] Compared with the prior art, the present invention has the following beneficial effects:

[0119] The present invention arranges transient electromagnetic transmitting and receiving devices in the detection area, uses high-precision GPS equipment to record the initial elevation data of each acquisition point, calculates the terrain correction factor and corrects the electromagnetic response signal, significantly reducing the interference of terrain changes on the signal; preliminarily estimates the underground target position through spectrum analysis and gradient tensor methods, and optimizes it using the Gauss-Newton algorithm to obtain a high-precision target position; through the singular value decomposition method, the eigenvector and eigenmatrix are deeply analyzed to extract the characteristic response related to the underground target, further improving the positioning accuracy. Compared with the prior art, the present invention significantly improves the accuracy and real-time performance of underground target positioning by introducing terrain correction factors and optimization algorithms, and is particularly suitable for efficient positioning under complex terrain conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0120] Figure 1 Schematic diagram of the overall method of the present invention;

[0121] Figure 2 This is a block diagram of the module composition of the present invention. DETAILED DESCRIPTION

[0122] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with specific embodiments.

[0123] It should be noted that, unless otherwise defined, the technical terms or scientific terms used in the present invention should be understood by people with ordinary skills in the field to which the present invention belongs. The words "first", "second" and similar words used in the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. "Include" or "comprise" and similar words mean that the elements or objects appearing before the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects. "Connect" or "connected" and similar words are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0124] Example:

[0125] See also Figure 1 , the present invention provides a technical solution:

[0126] A transient electromagnetic underground target detection and positioning method, the specific steps include:

[0127] S1. Arrange a transient electromagnetic transmitting device and a receiving device in the detection area, the transmitting device excites the underground medium through a pulse current to generate an electromagnetic response signal, the receiving device collects the electromagnetic response signal of the underground medium, searches for the terrain elevation data of each collection point in the digital elevation model, obtains the actual elevation data, uses a high-precision GPS device to record the initial elevation data of each collection point, performs data processing on the actual elevation data and the initial elevation data of each collection point, obtains the terrain correction factor of each collection point, uses the terrain correction factor to correct the electromagnetic response signal, and obtains the corrected electromagnetic response signal;

[0128] S2. Perform spectrum analysis and filtering on the corrected electromagnetic response signal to obtain the electromagnetic field component of the target signal, use the electromagnetic field component of the target signal to calculate the gradient of the electromagnetic field, construct a gradient tensor, preliminarily estimate the position of the underground target based on the gradient tensor, and average multiple positions to obtain the initial position value of the Gauss-Newton algorithm;

[0129] S3. Input the initial value of the preliminarily estimated position into the Gauss-Newton algorithm as the initial value of the iterative optimization, calculate the Jacobian matrix, perform approximate calculations of the gradient and the Hessian matrix, update the position parameters, obtain the optimized approximate position of the target, and use the optimized approximate position of the target to calculate the eigenvector;

[0130] S4. Using the eigenvectors obtained by optimizing the Gauss-Newton algorithm, construct a eigenmatrix, perform singular value decomposition on the eigenmatrix, obtain the product of a left singular vector matrix, a singular value diagonal matrix, and a right singular vector matrix, obtain singular values ​​and corresponding singular vectors by analyzing the left singular vector matrix, the singular value diagonal matrix, and the right singular vector matrix, and obtain characteristic responses related to underground targets according to the singular values ​​and the corresponding singular vectors;

[0131] S5. Reconstruct the feature matrix according to the feature response, extract the position features from the reconstructed feature matrix, use the position features and the least squares estimation algorithm to perform reverse calculation and deduce the precise position of the underground target.

[0132] On the basis of the above embodiment, the transient electromagnetic transmitting device and receiving device are JPMD sensors, which are sensors used for transient electromagnetic exploration, and are particularly suitable for the fields of mineral exploration, groundwater detection, and environmental geophysics;

[0133] Basic principle: The JPMD sensor is based on the transient electromagnetic method. The transmitter emits a pulse current to excite the underground medium, measures the transient electromagnetic response signal generated by the underground medium, and then the receiver collects the electromagnetic response signal of the underground medium. The signal strength and attenuation rate are related to the conductivity and other physical properties of the underground medium.

[0134] The JPMD sensor has high sensitivity and can capture weak electromagnetic response signals. The sensor can cover a wide frequency range and is suitable for detecting underground targets of different depths and types. It is designed with strong anti-electromagnetic interference capabilities to ensure the accuracy and reliability of the data.

[0135] On the basis of the above embodiment, the terrain correction factor of each acquisition point is calculated according to the actual elevation data and the initial elevation data, and the electromagnetic response signal is corrected by using the terrain correction factor to obtain the corrected electromagnetic response signal. The process is as follows:

[0136] In the elevation model, the geographic coordinates of the i-th collection point are set to , then the actual elevation data of the i-th collection point is , and the initial elevation data of a certain collection point in the GPS record is , then the formula for obtaining the terrain correction factor is as follows:

[0137] ;

[0138] in, For the The terrain correction factor for each acquisition point is: For the The longitude of the collection point, For the The latitude of the collection point, is the index of the collection point;

[0139] Find the terrain elevation data of each collection point in the digital elevation model and obtain the actual elevation data. This is the use of the digital elevation model. The digital elevation model is a data set that represents terrain elevation in the form of a raster. It is constructed through satellite remote sensing data and aerial photogrammetry data. The digital elevation model is an existing technology. The geographic coordinates of the collection point can be input to obtain the actual elevation data of the collection point.

[0140] Set the receiving device to The original electromagnetic response signal recorded by the acquisition points is ;

[0141] Using terrain correction factors The original electromagnetic response signal is corrected according to the following formula:

[0142] ;

[0143] in, For the The corrected electromagnetic response signal of each acquisition point is is the correction term function based on the terrain correction factor;

[0144] Through experiments, it is found that the relationship between the electromagnetic response signal and the change in terrain height is approximately linear, so a linear correction function is used:

[0145] ;

[0146] in, is the proportionality coefficient, , which indicates the sensitivity of terrain height changes to electromagnetic response signals.

[0147] Based on the above embodiment, the corrected electromagnetic response signal The process of spectrum analysis and filtering is as follows:

[0148] Convert the time domain signal to the frequency domain, extract different frequency components, and use fast Fourier transform for spectrum analysis. The formula is as follows:

[0149] ;

[0150] in, For the The spectrum of the corrected signal at each acquisition point is is the frequency of the response signal, is an imaginary unit, is the time variable;

[0151] Analyze the frequency components in the spectrum graph, identify the characteristic frequencies related to underground targets, determine the frequency range of target signals and noise based on the spectrum graph, separate the target signal components through a low-pass filter, combine with known geological data, compare and analyze the geological structures corresponding to the characteristic frequencies in the spectrum, and compare with known electromagnetic characteristics, such as the electromagnetic response characteristics of different minerals or substances. Use this characteristic information to identify signals related to specific underground targets in the spectrum, extract characteristic parameters related to the target in the spectrum, including characteristic frequency, amplitude, and phase, and use these characteristic parameters as measurement data for the target signal.

[0152] On the basis of the above embodiment, the electromagnetic field component of the target signal is used to calculate the gradient of the electromagnetic field, construct a gradient tensor, preliminarily estimate the position of the underground target according to the gradient tensor, and average multiple positions to obtain the initial position value of the Gauss-Newton algorithm. The specific process is as follows:

[0153] Through spectrum analysis and filtering processing, the filtered characteristic parameters are obtained, and the characteristic parameters in the frequency domain are converted into electromagnetic field components in the time domain. , , , using the filtered electromagnetic field component , , , calculate the gradient of the electromagnetic field in space :

[0154] ;

[0155] in, is the electric field component of the electromagnetic field in the horizontal direction, is the electric field component in the longitudinal direction of the electromagnetic field, is the electric field component of the electromagnetic field in the depth axis direction;

[0156] Using the gradient of the electromagnetic field , construct the electromagnetic field gradient tensor :

[0157] ;

[0158] For each collection point , calculate the magnitude of the gradient vector :

[0159] ;

[0160] No. The gradient vector of the acquisition point The direction of is represented by a unit vector:

[0161] ;

[0162] in, For the The direction of the gradient vector of each acquisition point;

[0163] Use the coordinates of each collection point And the gradient vector The direction and magnitude of the gradient vector are used to estimate the position of the underground target. Assuming the opposite direction of the gradient vector, that is, Pointing to the underground target, the gradient vector modulus is used As the step size, the position is estimated in the opposite direction of the gradient vector:

[0164] ;

[0165] in, For the The location of the underground target at each collection point, For the The step length of the acquisition points;

[0166] Average multiple positions to obtain the initial position value of the underground target of the Gauss-Newton algorithm :

[0167] ;

[0168] in, is the total number of collection points.

[0169] On the basis of the above embodiment, the initial value of the preliminarily estimated position is input into the Gauss-Newton algorithm as the initial value of the iterative optimization, the Jacobian matrix is ​​calculated, the gradient and the Hessian matrix are approximated, the position is updated, and the optimized target approximate position is obtained. The optimized target approximate position is used to calculate the eigenvector. The specific process is as follows:

[0170] In the Gauss-Newton algorithm, it is necessary to calculate the Jacobian matrix of the objective function. Assuming the objective function is , then the Jacobian matrix is ​​defined as:

[0171] ;

[0172] in, is the Jacobian matrix, is the objective function vector;

[0173] The Gauss-Newton algorithm uses the Jacobian matrix to approximate the gradient and Hessian matrix of the objective function. Assuming that the first error function is , then the gradient of the first error function and the approximate value of the Hessian matrix are:

[0174] ;

[0175] ;

[0176] in, is the gradient matrix of the first error function, is the Hessian matrix of the first error function, is transposed;

[0177] Update the position based on the gradient and the approximation of the Hessian matrix:

[0178] ;

[0179] in, is the position change;

[0180] The new location is:

[0181] ;

[0182] in, for the new location;

[0183] Repeat the above steps to calculate the new Jacobian matrix, gradient and Hessian matrix, and update the position until the stop condition is met to obtain the optimized target position. The stop condition is the position change When the time is small enough, stop iterating;

[0184] Using the optimized target approximate position, calculate the electromagnetic field gradient tensor The eigenvector of the electromagnetic field gradient tensor is at the optimized position Value for:

[0185] ;

[0186] The eigenvectors satisfy the following characteristic equation:

[0187] ;

[0188] in, is the characteristic value, is the feature vector;

[0189] Given a matrix , first construct the characteristic polynomial, which is represented by the following determinant:

[0190] ;

[0191] in, is the identity matrix;

[0192] Solve the characteristic polynomial and get the eigenvalue , , ;

[0193] For each eigenvalue , solve the following linear homogeneous equation to find the corresponding eigenvector :

[0194] ;

[0195] in, is the index of the eigenvalue.

[0196] On the basis of the above embodiment, the characteristic vector obtained by optimizing the Gauss-Newton algorithm is used to construct a characteristic matrix, and the characteristic matrix is ​​subjected to singular value decomposition to obtain the product of the left singular vector matrix, the singular value diagonal matrix and the right singular vector matrix. The specific process is as follows:

[0197] The Gauss-Newton algorithm is an iterative optimization method for nonlinear least squares problems. Assume that there is a nonlinear model ,in are input features, is the parameter vector, and the goal is to find the parameter vector Make the model output The actual observed value The error is minimal;

[0198] At each iteration, the Jacobian matrix is ​​calculated :

[0199] ;

[0200] Calculate the residual vector :

[0201] Update the parameter vector:

[0202] ;

[0203] in, is the index of the iteration number;

[0204] Repeat the above steps until convergence or the maximum number of iterations is reached;

[0205] Using the optimized parameter vector Construct eigenvectors and arrange them into a eigenmatrix , assuming there is feature vectors, each with a dimension of , then the feature matrix for:

[0206] ;

[0207] in, is the feature matrix The Column, representing a dimensional column vector, The value range is , is the field of real numbers, is the number of eigenvectors;

[0208] For the feature matrix Perform singular value decomposition to obtain the left singular vector matrix , singular value diagonal matrix and the right singular vector matrix ;

[0209] ;

[0210] in, is a column orthogonal matrix, whose column vectors are called left singular vectors, is a diagonal matrix whose diagonal elements are called singular values ​​and are arranged in descending order. Is a column orthogonal matrix, whose column vectors are called right singular vectors. Based on the above embodiment, by analyzing the left singular vector matrix, the singular value diagonal matrix and the right singular vector matrix, the singular values ​​and the corresponding singular vectors are obtained, and the characteristic response related to the underground target is obtained according to the singular values ​​and the corresponding singular vectors. The specific process is as follows:

[0211] The singular value diagonal matrix is The elements on the diagonal are singular values, arranged in descending order. The size of the singular value reflects the weight of different modes in the feature matrix;

[0212] ;

[0213] in, ,and ;

[0214] Left Singular Vector Matrix and the right singular vector matrix The column vectors of are called left singular vectors and right singular vectors, respectively, and are of the following form:

[0215] ;

[0216] ;

[0217] Identifying singular values The corresponding left singular vector , the right singular vector By analyzing There is a significant response in the direction of The distribution of underground targets in the input feature space (such as geographic coordinates, depth) is displayed. The pattern identifies the spatial location of the underground target. The distribution of underground targets in output characteristics (such as signal strength and frequency) is shown. The pattern determines the characteristic response of the underground target, and combining this information helps locate the position of the underground target.

[0218] On the basis of the above embodiment, according to the characteristic response, the characteristic matrix is ​​reconstructed, the position feature is extracted from the reconstructed characteristic matrix, and the position feature and the least squares estimation algorithm are used to perform reverse calculation to derive the precise position of the underground target. The specific process is as follows:

[0219] Before selection Large singular values , the corresponding left singular vector is , the corresponding right singular vector is ;

[0220] Reconstructing the feature matrix , of the following form:

[0221] ;

[0222] in, It is singular values, It is left singular vectors, It is right singular vectors;

[0223] From the reconstructed feature matrix In , row features, column features, cluster centers and high-intensity areas are extracted, where

[0224] Row features: Each row represents the response value of a different position. By analyzing these response values, the characteristics of the position under specific conditions can be inferred;

[0225] Column features: Each column represents the measurement value at a different time or frequency point;

[0226] Cluster centers: Analyze and reconstruct the feature matrix to find natural clusters in the data. The cluster centers correspond to potential underground target locations.

[0227] High-intensity regions: Find high-intensity regions in the reconstructed feature matrix, which correspond to the locations of underground targets;

[0228] Based on the extracted features, including row features, column features, cluster centers, and high-intensity areas, the second error function is defined To measure the actual location characteristics and the features predicted by the model The difference between

[0229] ;

[0230] in, is the norm of the vector;

[0231] Optimize the second error function , calculate its relative position Gradient , based on the following formula:

[0232] ;

[0233] Update the position of the underground target according to the gradient descent method. The formula is:

[0234] ;

[0235] in, is the updated location of the underground target, is the estimated position in the current iteration, For current location The gradient of the second error function at is the regulating factor;

[0236] Repeat the above steps until the second error function Reach the predetermined number of iterations.

[0237] In the formula and The specific value of is generally determined by those skilled in the art according to actual conditions. The essence of this formula is a comprehensive analysis by weighted summation. The technicians in this field collect multiple groups of sample data, and set corresponding regression coefficients or adjustment factors for each group of sample data. The set regression coefficients or adjustment factors and the collected sample data are substituted into the formula. Through repeated experiments and parameter adjustments, the accuracy of the model output and the rationality of the results are observed, and these regression coefficients or adjustment factors are gradually adjusted. The performance and effect of the model under different parameter settings are compared to find the optimal coefficient combination. The calculated regression coefficients or adjustment factors are screened and averaged to obtain and The value of .

[0238] In addition, the size of the regression coefficient or adjustment factor is a specific value obtained by quantifying each parameter. In order to facilitate subsequent comparison, the size of the regression coefficient or adjustment factor depends on the amount of sample data and the technical personnel in this field who initially set the corresponding regression coefficient or adjustment factor for each set of sample data. It is not unique as long as it does not affect the proportional relationship between the parameter and the quantified value.

[0239] See also Figure 2 , the present invention also provides a technical solution:

[0240] A transient electromagnetic underground target detection and positioning system, the system is used to execute any of the above-mentioned transient electromagnetic underground target detection and positioning methods, comprising:

[0241] The equipment arrangement and data acquisition module is used to arrange transient electromagnetic transmitting devices and receiving devices in the detection area. The transmitting device excites the underground medium through pulse current to generate an electromagnetic response signal. The receiving device collects the electromagnetic response signal of the underground medium, searches for the terrain elevation data of each collection point in the digital elevation model, obtains the actual elevation data, uses a high-precision GPS device to record the initial elevation data of each collection point, performs data processing on the actual elevation data and the initial elevation data of each collection point, obtains the terrain correction factor of each collection point, and uses the terrain correction factor to correct the electromagnetic response signal to obtain the corrected electromagnetic response signal;

[0242] A data processing module is used to perform spectrum analysis and filtering on the corrected electromagnetic response signal, obtain the electromagnetic field component of the target signal, calculate the gradient of the electromagnetic field using the electromagnetic field component of the target signal, construct a gradient tensor, preliminarily estimate the position of the underground target based on the gradient tensor, and average multiple positions to obtain the initial position value of the Gauss-Newton algorithm;

[0243] The optimization module is used to input the initial value of the preliminarily estimated position into the Gauss-Newton algorithm as the initial value of the iterative optimization, calculate the Jacobian matrix, perform approximate calculations of the gradient and the Hessian matrix, update the position parameters, obtain the optimized approximate position of the target, and use the optimized approximate position of the target to calculate the eigenvector;

[0244] A characteristic matrix construction module is used to construct a characteristic matrix using the characteristic vectors obtained by optimizing the Gauss-Newton algorithm, perform singular value decomposition on the characteristic matrix, obtain the product of the left singular vector matrix, the singular value diagonal matrix and the right singular vector matrix, obtain singular values ​​and corresponding singular vectors by analyzing the left singular vector matrix, the singular value diagonal matrix and the right singular vector matrix, and obtain characteristic responses related to underground targets according to the singular values ​​and the corresponding singular vectors;

[0245] The positioning module is used to reconstruct the feature matrix according to the feature response, extract the position features from the reconstructed feature matrix, and perform reverse calculation using the position features and the least squares estimation algorithm to derive the precise position of the underground target.

[0246] The above formulas are all dimensionless and numerical calculations. The formula is a formula for the most recent real situation obtained by collecting a large amount of data and performing software simulation. The preset parameters in the formula are set by technicians in this field according to actual conditions.

[0247] The above embodiments may be implemented in whole or in part by software, hardware, firmware or any other combination thereof. When implemented by software, the above embodiments may be implemented in whole or in part in the form of a computer program product. Those skilled in the art may appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein may be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed by hardware or software methods depends on the specific application and design constraints of the technical solution.

[0248] The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, and may be located in one place or distributed on multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0249] The above description is only a specific implementation manner of the present application, but the protection scope of the present application is not limited thereto. Any technician familiar with the technical field can easily think of changes or substitutions within the technical scope disclosed in the present application, which should be included in the protection scope of the present application.

Claims

1. A transient electromagnetic underground target detection and positioning method, characterized in that: The specific steps include: S1. Arrange a transient electromagnetic transmitting device and a receiving device in the detection area, the transmitting device excites the underground medium through a pulse current to generate an electromagnetic response signal, the receiving device collects the electromagnetic response signal of the underground medium, searches for the terrain elevation data of each collection point in the digital elevation model, obtains the actual elevation data, uses a high-precision GPS device to record the initial elevation data of each collection point, performs data processing on the actual elevation data and the initial elevation data of each collection point, obtains the terrain correction factor of each collection point, uses the terrain correction factor to correct the electromagnetic response signal, and obtains the corrected electromagnetic response signal; S2. Perform spectrum analysis and filtering on the corrected electromagnetic response signal to obtain the electromagnetic field component of the target signal, use the electromagnetic field component of the target signal to calculate the gradient of the electromagnetic field, construct a gradient tensor, preliminarily estimate the position of the underground target based on the gradient tensor, and average multiple positions to obtain the initial position value of the Gauss-Newton algorithm; S3. Input the initial value of the preliminarily estimated position into the Gauss-Newton algorithm as the initial value of the iterative optimization, calculate the Jacobian matrix, perform approximate calculations of the gradient and the Hessian matrix, update the position parameters, obtain the optimized approximate position of the target, and use the optimized approximate position of the target to calculate the eigenvector; S4. Using the eigenvectors obtained by optimizing the Gauss-Newton algorithm, construct a eigenmatrix, perform singular value decomposition on the eigenmatrix, obtain the product of a left singular vector matrix, a singular value diagonal matrix, and a right singular vector matrix, obtain singular values ​​and corresponding singular vectors by analyzing the left singular vector matrix, the singular value diagonal matrix, and the right singular vector matrix, and obtain characteristic responses related to underground targets according to the singular values ​​and the corresponding singular vectors; S5. Reconstruct the feature matrix according to the feature response, extract the position features from the reconstructed feature matrix, use the position features and the least squares estimation algorithm to perform reverse calculation and deduce the precise position of the underground target.

2. The transient electromagnetic underground target detection and positioning method according to claim 1 is characterized in that: According to the actual elevation data and the initial elevation data, the terrain correction factor of each acquisition point is calculated, and the electromagnetic response signal is corrected using the terrain correction factor. The process of obtaining the corrected electromagnetic response signal is as follows: In the elevation model, the geographic coordinates of the i-th collection point are set to , then the actual elevation data of the i-th collection point is , and the initial elevation data of the i-th collection point in the GPS record is , then the formula for obtaining the terrain correction factor is as follows: ； in, For the The terrain correction factor for each acquisition point is: For the The longitude of the collection point, For the The latitude of the collection point, is the index of the collection point; Set the receiving device to The original electromagnetic response signal recorded by the acquisition points is ; Using terrain correction factors The original electromagnetic response signal is corrected according to the following formula: ； in, For the The corrected electromagnetic response signal of each acquisition point is is the correction term function based on the terrain correction factor; It is found through experiments that the relationship between the electromagnetic response signal and the change in terrain height is approximately linear, so a linear correction function is used: ； in, is the proportionality coefficient, , which indicates the sensitivity of terrain height changes to electromagnetic response signals.

3. The transient electromagnetic underground target detection and positioning method according to claim 2 is characterized in that: The corrected electromagnetic response signal The process of spectrum analysis and filtering is as follows: Convert the time domain signal to the frequency domain, extract different frequency components, and use fast Fourier transform for spectrum analysis. The formula is as follows: ； in, For the The spectrum of the corrected signal at each acquisition point is is the frequency of the response signal, is an imaginary unit, is the time variable; Analyze the frequency components in the spectrum graph, identify the characteristic frequencies related to underground targets, determine the frequency range of target signals and noise based on the spectrum graph, separate the target signal components through a low-pass filter, combine with known geological data, compare and analyze the geological structures corresponding to the characteristic frequencies in the spectrum, and compare with known electromagnetic characteristics, including the electromagnetic response characteristics of different minerals or substances. Use this characteristic information to identify signals related to specific underground targets in the spectrum, extract characteristic parameters related to the target in the spectrum, including characteristic frequency, amplitude, and phase, and use these characteristic parameters as measurement data for the target signal.

4. The transient electromagnetic underground target detection and positioning method according to claim 3 is characterized in that: The electromagnetic field component of the target signal is used to calculate the gradient of the electromagnetic field and construct a gradient tensor. Based on the gradient tensor, the position of the underground target is preliminarily estimated, and multiple positions are averaged to obtain the initial position value of the Gauss-Newton algorithm. The specific process is as follows: Through spectrum analysis and filtering processing, the filtered characteristic parameters are obtained, and the characteristic parameters in the frequency domain are converted into electromagnetic field components in the time domain. , , , using the electromagnetic field component , , , calculate the gradient of the electromagnetic field in space : ； in, is the electric field component of the electromagnetic field in the horizontal direction, is the electric field component in the longitudinal direction of the electromagnetic field, is the electric field component of the electromagnetic field in the depth axis direction; Using the gradient of the electromagnetic field , construct the electromagnetic field gradient tensor : ； For each collection point , calculate the magnitude of the gradient vector : ； No. The gradient vector of the acquisition point The direction of is represented by a unit vector: ； in, For the The direction of the gradient vector of each acquisition point; Use the coordinates of each collection point And the gradient vector The direction and magnitude of the gradient vector are used to estimate the position of the underground target. Assuming the opposite direction of the gradient vector, that is, Pointing to the underground target, the gradient vector modulus is used As the step size, the position is estimated in the opposite direction of the gradient vector: ； in, For the The location of the underground target at each collection point, For the The step length of the acquisition points; Average multiple positions to obtain the initial position value of the underground target of the Gauss-Newton algorithm : ； in, is the total number of collection points.

5. The transient electromagnetic underground target detection and positioning method according to claim 4 is characterized in that: The initial value of the preliminarily estimated position is input into the Gauss-Newton algorithm as the initial value of the iterative optimization, the Jacobian matrix is ​​calculated, the gradient and Hessian matrix are approximated, the position is updated, and the optimized approximate position of the target is obtained. The optimized approximate position of the target is used to calculate the eigenvector. The specific process is as follows: In the Gauss-Newton algorithm, it is necessary to calculate the Jacobian matrix of the objective function. Assuming the objective function is , then the Jacobian matrix is ​​defined as: ； in, is the Jacobian matrix, is the objective function vector; The Gauss-Newton algorithm uses the Jacobian matrix to approximate the gradient and Hessian matrix of the objective function. Assume that the first error function is , then the gradient of the first error function and the approximate value of the Hessian matrix are: ； ； in, is the gradient matrix of the first error function, is the Hessian matrix of the first error function, is transposed; Update the position based on the gradient and the approximation of the Hessian matrix: ； in, is the position change; The new location is: ； in, for the new location; Repeat the above steps to calculate the new Jacobian matrix, gradient and Hessian matrix, and update the position until the stop condition is met to obtain the optimized target approximate position; Using the optimized target approximate position, calculate the electromagnetic field gradient tensor The eigenvector of the electromagnetic field gradient tensor is at the optimized position Value for: ； The eigenvectors satisfy the following characteristic equation: ； in, is the characteristic value, is the feature vector; For a given matrix , first construct the characteristic polynomial, which is represented by the following determinant: ； in, is the identity matrix; Solve the characteristic polynomial and get the eigenvalue , , ; For each eigenvalue , solve the following linear homogeneous equation to find the corresponding eigenvector : ； in, is the index of the eigenvalue.

6. The transient electromagnetic underground target detection and positioning method according to claim 5 is characterized in that: The eigenvectors obtained by optimizing the Gauss-Newton algorithm are used to construct the eigenmatrix, and the eigenmatrix is ​​subjected to singular value decomposition to obtain the product of the left singular vector matrix, the singular value diagonal matrix, and the right singular vector matrix. The specific process is as follows: Assume there is a nonlinear model ,in are input features, is the parameter vector, and the goal is to find the parameter vector Make the model output The actual observed value The error is minimal; At each iteration, the Jacobian matrix is ​​calculated : ； Calculate the residual vector : Update the parameter vector: ； in, is the index of the iteration number; Repeat the above steps until convergence or the maximum number of iterations is reached; Using the optimized parameter vector Construct eigenvectors and arrange them into a eigenmatrix , assuming there is feature vectors, each with a dimension of , then the feature matrix for: ； in, is the feature matrix The Column, representing a dimensional column vector, The value range is , is the field of real numbers, is the number of eigenvectors; For the feature matrix Perform singular value decomposition to obtain the left singular vector matrix , singular value diagonal matrix and the right singular vector matrix ; ； in, is a column orthogonal matrix, whose column vectors are called left singular vectors, is a diagonal matrix whose diagonal elements are called singular values ​​and are arranged in descending order. is a column orthogonal matrix, and its column vectors are called right singular vectors.

7. The transient electromagnetic underground target detection and positioning method according to claim 6 is characterized in that: By analyzing the left singular vector matrix, the singular value diagonal matrix and the right singular vector matrix, the singular values ​​and the corresponding singular vectors are obtained. According to the singular values ​​and the corresponding singular vectors, the characteristic response related to the underground target is obtained. The specific process is as follows: The singular value diagonal matrix is The elements on the diagonal are singular values, arranged in descending order. The size of the singular value reflects the weight of different modes in the feature matrix; ； in, ,and ; Left Singular Vector Matrix and the right singular vector matrix The column vectors of are called left singular vectors and right singular vectors, respectively, and are of the following form: ； 。 8. The transient electromagnetic underground target detection and positioning method according to claim 7 is characterized in that: According to the characteristic response, the characteristic matrix is ​​reconstructed, and the position features are extracted from the reconstructed characteristic matrix. The position features and the least squares estimation algorithm are used to perform reverse calculations to derive the precise position of the underground target. The specific process is as follows: Before selection Singular Values , the corresponding left singular vector is , the corresponding right singular vector is ; Reconstructing the feature matrix , of the following form: ； in, It is singular values, It is left singular vectors, It is right singular vectors; From the reconstructed feature matrix , extract row features, column features, cluster centers and high-intensity areas; Based on the extracted features, including row features, column features, cluster centers, and high-intensity areas, the second error function is defined To measure the actual location characteristics and the features predicted by the model The difference between ； in, is the norm of the vector; Optimize the second error function , calculate its relative position Gradient , based on the following formula: ； The precise position of the underground target is updated according to the gradient descent method. The formula is: ； in, The updated precise location of the underground target. is the estimated position in the current iteration, For current location The gradient of the second error function at , is the regulating factor; Repeat the above steps until the second error function Reach the predetermined number of iterations.

9. A transient electromagnetic underground target detection and positioning system, the system being used to execute a transient electromagnetic underground target detection and positioning method according to any one of claims 1 to 8, characterized in that: include: The equipment arrangement and data acquisition module is used to arrange transient electromagnetic transmitting devices and receiving devices in the detection area. The transmitting device excites the underground medium through pulse current to generate an electromagnetic response signal. The receiving device collects the electromagnetic response signal of the underground medium, searches for the terrain elevation data of each collection point in the digital elevation model, obtains the actual elevation data, uses a high-precision GPS device to record the initial elevation data of each collection point, performs data processing on the actual elevation data and the initial elevation data of each collection point, obtains the terrain correction factor of each collection point, and uses the terrain correction factor to correct the electromagnetic response signal to obtain the corrected electromagnetic response signal; A data processing module is used to perform spectrum analysis and filtering on the corrected electromagnetic response signal, obtain the electromagnetic field component of the target signal, calculate the gradient of the electromagnetic field using the electromagnetic field component of the target signal, construct a gradient tensor, preliminarily estimate the position of the underground target based on the gradient tensor, and average multiple positions to obtain the initial position value of the Gauss-Newton algorithm; The optimization module is used to input the initial value of the preliminarily estimated position into the Gauss-Newton algorithm as the initial value of the iterative optimization, calculate the Jacobian matrix, perform approximate calculations of the gradient and the Hessian matrix, update the position parameters, obtain the optimized approximate position of the target, and use the optimized approximate position of the target to calculate the eigenvector; A characteristic matrix construction module is used to construct a characteristic matrix using the characteristic vectors obtained by optimizing the Gauss-Newton algorithm, perform singular value decomposition on the characteristic matrix, obtain the product of the left singular vector matrix, the singular value diagonal matrix and the right singular vector matrix, obtain singular values ​​and corresponding singular vectors by analyzing the left singular vector matrix, the singular value diagonal matrix and the right singular vector matrix, and obtain characteristic responses related to underground targets according to the singular values ​​and the corresponding singular vectors; The positioning module is used to reconstruct the feature matrix according to the feature response, extract the position features from the reconstructed feature matrix, and perform reverse calculation using the position features and the least squares estimation algorithm to derive the precise position of the underground target.

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