Magnetic detection method based on scalar gradient

Abstract

The invention provides a magnetic detection method based on scalar gradient, relates to the technical field of magnetic positioning, and solves the problems that the traditional scalar magnetic detection is large in positioning error, the effective detection distance of tensor magnetic detection is short, and the traditional scalar gradient method requires that the magnetic moment direction is strictly overlapped with the geomagnetic field direction. A magnetic sensor array is adopted to collect magnetic field scalar intensity and obtain a scalar gradient, a long-distance magnetic target is equivalent to a magnetic dipole to derive modeling, a unit direction vector of a target pointing sensor is solved, a distance is solved through a double-measuring-point simultaneous geometric equation, a target position is determined through pseudo-solution screening, and the same direction of a magnetic moment and a geomagnetic field is not needed. And the detection distance and the positioning precision are considered. The effective distance and positioning precision of magnetic detection are effectively considered, the contradiction that a traditional scalar method is large in error and a tensor method is short in detection distance is overcome, the magnetic moment and the geomagnetic field do not need to be strictly in the same direction, positioning precision is guaranteed by means of pseudo-solution screening, and robustness and actual detection applicability in a complex magnetic field environment are improved.

Description

Technical Field

[0001] This invention relates to the field of magnetic positioning technology, and in particular to a magnetic detection method based on scalar gradient. Background Technology

[0002] Magnetic detection is a target detection technology based on magnetic field measurement. It boasts advantages such as high sensitivity, fast response, and non-contact measurement, demonstrating unique value and application potential in various fields including national defense, resource exploration, and environmental monitoring. When detecting underwater vehicles or unexploded ordnance underground, magnetic detection is less susceptible to interference from media and offers greater concealment compared to acoustic and optical methods. In exploring mineral distribution or archaeological remains, magnetic detection is more efficient, lower in cost, and less damaging to the target compared to traditional drilling and magnetotelluric methods.

[0003] As a core component of a magnetic detection system, the magnetic detection algorithm is crucial to the accuracy and reliability of the system's detection results. An efficient magnetic detection system requires not only excellent signal acquisition and noise filtering capabilities but also appropriate and logically rigorous computational methods. These three aspects complement each other and jointly determine the quality of the detection performance. Signal acquisition capability determines the system's effectiveness in capturing weak magnetic field signals under different environmental conditions. If signal acquisition is insufficient or subject to severe noise interference, even the most advanced algorithm will struggle to provide accurate results. Simultaneously, noise filtering capability effectively suppresses background noise, improves signal clarity, and lays a solid foundation for subsequent data processing. Magnetic detection methods bear the important responsibility of extracting magnetic anomaly information from complex interference signals and establishing a connection with the detection target. Rounding and truncation errors in numerical calculations within the detection method, as well as the inevitable simplification and approximation of physical models to complex realities, all result in nonlinear transmission and amplification during the algorithm's iterative inversion process, leading to a decrease in the reliability and accuracy of the positioning results.

[0004] Current methods of magnetic detection have the following problems: 1. Scalar-based magnetic detection methods have larger positioning errors, while magnetic tensor-based magnetic detection methods have higher accuracy but shorter detection distances.

[0005] Scalar-based magnetic detection methods detect targets by acquiring the modulus information of the magnetic field vector, thus proving effective detection range over long distances due to their relatively simple measurement principle, strong system robustness, and slow signal attenuation with distance in a uniform magnetic field background. This makes them suitable for large-scale, rapid scanning. However, a limitation is that a single scalar observation cannot uniquely determine the vector characteristics of the magnetic field source, leading to severe non-uniqueness in the inversion problem and ultimately resulting in significant positioning errors. In contrast, magnetic gradient tensor detection acquires higher-dimensional magnetic field structure information by simultaneously measuring the rate of change of the magnetic field in spatially orthogonal directions. A significant advantage of this method is its background field suppression capability: since the spatial gradient of a uniform background magnetic field is zero, tensor measurements can directly extract local anomalous gradients caused by the target, greatly improving the signal-to-noise ratio. However, the trade-off is that the magnetic gradient field attenuates much faster with distance than the total field strength. This rapid signal attenuation severely limits its effective range, typically maintaining a high signal-to-noise ratio only within a range several times the target's feature size, thus limiting its application in long-range detection.

[0006] 2. Traditional magnetic detection methods based on scalar gradients require that the direction of the magnetic moment must strictly coincide with the direction of the geomagnetic field.

[0007] To establish an analytical relationship between the total magnetic field strength and the gradient, the most common method is to derive it based on an ideal model of a magnetic dipole. When the target's magnetic moment direction is aligned with the geomagnetic field direction, the perturbation magnetic field vector generated by the target and the geomagnetic field vector remain parallel in space. Under this condition, a relatively simple mathematical correspondence can be established between the total magnetic field strength and the gradient, allowing for improved positioning accuracy through joint inversion. However, in real-world detection scenarios, the equivalent magnetic moment direction of most actual targets, such as unexploded ordnance and man-made ferromagnetic components, is not determined by a single mechanism, but rather by the vector sum of their inherent remanence and the induced magnetization generated by the external geomagnetic field. This composite direction is difficult to keep strictly aligned with the geomagnetic field direction. Currently, magnetic detection methods based on scalar gradient information lack a complete methodological framework for systematically analyzing the equivalent magnetic moment under the combined effects of remanence and induced magnetization, significantly increasing the difficulty in practical applications. Summary of the Invention

[0008] The purpose of this invention is to provide a magnetic detection method based on scalar gradient. This method uses a magnetic sensor array to collect the scalar intensity of the magnetic field and obtain scalar gradient information. It then calculates the unit direction vector of the magnetic target pointing to the sensor, solves the target distance by solving the geometric equations of the two measurement points, and completes the spatial positioning. At the same time, it filters out false solutions to solve the problems of large positioning error, short effective detection distance of tensor magnetic detection, and the requirement that the magnetic moment direction must be strictly coincident with the geomagnetic field direction in the traditional scalar magnetic detection method.

[0009] A magnetic detection method based on scalar gradient includes the following steps: S1. Use a magnetic sensor array to collect the scalar intensity of the magnetic field at multiple points on the coordinate axis, and use the difference instead of the derivative to obtain the scalar gradient information of the magnetic field. S2. Based on the magnetic field scalar gradient information, the position information of the magnetic target is decomposed into direction information and distance information, and the unit direction vector from the magnetic target to the magnetic sensor array is calculated. S3. Move the magnetic sensor array to another measuring point and repeat S2 to obtain two sets of unit direction vectors. Solve the geometric equations to find the distance between the magnetic target and the sensor array. Combine the unit direction vectors and the distance to determine the spatial coordinates of the magnetic target. S4. After filtering out the false solutions generated by the calculation and obtaining the true and valid solutions, the location is completed.

[0010] Furthermore, in S1, when the detection distance is greater than three times the size of the magnetic target itself, the magnetic target is equivalent to a magnetic dipole. A spatial rectangular coordinate system is established with the magnetic dipole as the origin, and the magnetic induction intensity of the magnetic target is calculated based on the magnetic dipole model. B o : (1) in, B o This represents the magnetic flux density vector generated at the detection point by the magnetic dipole model. m 0 represents the free permeability, with a value of 4π × 10⁻⁶. -7 H / m, M The magnetic moment vector of the magnetic dipole. r Let be the position vector pointing from the magnetic dipole to the probe point. r The distance from the magnetic dipole to the detection point is denoted as . Taking the modulus of equation (1) yields: (2) in, M magnetic moment vector M The magnitude of the vector and the included angle. f magnetic moment vector M and position vector r The angle between them.

[0011] Furthermore, in S1, during the detection of magnetic targets under the background of the Earth's magnetic field, the total magnetic field measured by the magnetic sensor array... B t It is composed of the magnetic field vector of the magnetic dipole. B o With the geomagnetic field vector B e The result of superposition (3) Simultaneously, the modulo values ​​from both sides are obtained as follows: (4) Taylor expansion of equation (4) yields: (5) Among them, the geomagnetic field vector B e Its magnitude is approximately 0.5 to 0.6 Gauss, which is much greater than the magnetic field strength of a magnetic dipole.

[0012] Furthermore, in S1, ignoring the third term in equation (5) and expanding the second term, we get: (6) in, r 0=( r x , r y , r z ) T , m 0=( m x , m y , m z ) T , e 0=( e x , e y , e z ) T These are the unit vectors of the probe position vector, the magnetic dipole moment, and the geomagnetic field, respectively. Approximating the direction of the magnetic moment in equation (6) to the direction of the Earth's magnetic field, it simplifies to: (7) make: (8) in, i It is the angle between the direction of the magnetic target and the direction of the geomagnetic field.

[0013] Furthermore, in S2, combining equations (7) and (8), and differentiating equation (7), we obtain: (9) (10) in, T The magnetic field gradient representing the spatial location of a magnetic target. The direction vector is obtained by transforming equation (10). r 0: (11).

[0014] Furthermore, in S3, both sides of equation (11) are multiplied by the unit vector of the geomagnetic field direction. e 0 yields: (12) Equation (12) contains only one unknown quantity, cos i The nonlinear equation, where, α Gradient vector T and geomagnetic field vector e The angle between the two sides, cos α The value range of cos is [-1, 1]. α When the value changes, this nonlinear equation has exactly three solutions within the range, corresponding to three different cosine values. i Substituting these values ​​back into equation (11) yields three corresponding direction vectors pointing towards the magnetic sensor array. r 0. Among these, two solutions have no practical significance in physics and are considered pseudo-solutions. They need to be eliminated through appropriate mathematical or physical constraints. Furthermore, the direction vector of the magnetic target is obtained by solving for a single measuring point. By moving the magnetic sensor to another measuring point in space and repeating the above calculation process, another set of direction vectors corresponding to that measuring point is obtained. Then, the following system of equations is constructed: (13) Based on the two sets of direction vectors, construct the geometric relationship shown in equation (13), solve the distance between the magnetic target and the sensor array, and combine the distance with the corresponding direction vector to determine the spatial coordinates of the magnetic target with the magnetic sensor array as the origin. r 1: (14) in, r 1 is the distance from the first measuring point to the magnetic target obtained from equation (13). u 10 Let be the unit direction vector from the magnetic target to the first measuring point of the sensor in equation (11).

[0015] Furthermore, in S4, regarding the problem of spurious solutions in equation (11), the spurious solution elimination mechanism is as follows: First, substitute the three results obtained from equation (12) back into equation (11) to obtain the three unit direction vectors. r 0, and extract the values ​​of each vector. z Coordinate components; at this time, zNumber of vectors with coordinates less than 0 N There are only two possible values, namely N =1 or N =2, if N =1, then the unit direction vector is directly determined as a valid solution; if N =2, the two-point positioning method needs to be extended to the trajectory positioning method first, and a distance data set needs to be constructed. A and B Then calculate the standard deviation of the two sets of data respectively. s 1 and s 2. Select the unit direction vector corresponding to the dataset with the smaller standard deviation as the correct solution; Finally, based on the correct direction vector obtained through screening, equations (13) and (14) are combined to complete the final positioning calculation; Among them, data group A , B ={ r 12 , r 23 , r 34 ,…, r ij ; j = i +1}, i Indicates the first i A magnetic sensor array measuring points, j Indicates the first i +1 magnetic sensor array measurement points, r ij Indicates the first i The magnetic sensor array measurement points and the first j The distance to the magnetic target is obtained by joint measurement of the measurement points of the magnetic sensor array.

[0016] A computer program product includes a computer program / instructions that, when executed by a processor, implement the aforementioned scalar gradient-based magnetic detection method.

[0017] A storage medium storing a computer program that, when executed by a processor, implements the above-described scalar gradient-based magnetic detection method.

[0018] A computer device includes: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the above-described scalar gradient-based magnetic detection method.

[0019] Compared with the prior art, the present invention achieves significant beneficial effects through the above technical solution: 1. By keeping the distance between the magnetic target and the magnetic sensor array constant, and comparing the positioning errors of traditional scalar-based and tensor-based magnetic detection methods with the proposed scalar gradient method, it can be seen that this invention effectively overcomes the contradiction between accuracy and distance in magnetic positioning technology. By calculating the spatial gradient information of the magnetic field scalar, this method improves positioning performance by approximately 82% while maintaining an effective detection range comparable to the traditional scalar method. Compared to the smaller detection range of the tensor method, this method outperforms the tensor method in positioning performance beyond 550m from the magnetic target, maintaining good positioning accuracy over a wider range.

[0020] 2. This invention successfully avoids the requirement that the direction of the geomagnetic field must be strictly aligned with the direction of the target magnetic moment. Even when the magnetic target contains an unknown residual magnetic moment, this method can still maintain stable positioning performance with a small reduction in positioning error. Compared with traditional methods, it enhances robustness and practicality in actual complex magnetic field environments. Attached Figure Description

[0021] Figure 1 A schematic diagram illustrating the use of the scalar gradient method to detect magnetic targets; Figure 2 Flowchart of the spurious solution elimination mechanism; Figure 3 It is a magnetic sensor array structure; Figure 4 A schematic diagram to verify the scheme; Figure 5 To determine the positioning accuracy of different detection methods at different distances. Detailed Implementation

[0022] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0023] Reference Figure 1-Figure 5 As shown, a magnetic detection method based on scalar gradient includes the following steps: S1. Use a magnetic sensor array to collect the scalar intensity of the magnetic field at multiple points on the coordinate axis, and use the difference instead of the derivative to obtain the scalar gradient information of the magnetic field. S2. Based on the magnetic field scalar gradient information, the position information of the magnetic target is decomposed into direction information and distance information, and the unit direction vector from the magnetic target to the magnetic sensor array is calculated. S3. Move the magnetic sensor array to another measuring point and repeat S2 to obtain two sets of unit direction vectors. Solve the geometric equations to find the distance between the magnetic target and the sensor array. Combine the unit direction vectors and the distance to determine the spatial coordinates of the magnetic target. S4. After filtering out the false solutions generated by the calculation and obtaining the true and valid solutions, the location is completed.

[0024] Specifically, the objectives of this invention include: 1. In magnetic positioning technology, there is often a trade-off between positioning accuracy and effective detection range. The purpose of this invention is to propose a magnetic detection method based on the scalar gradient method to improve the accuracy limitations of traditional scalar methods in magnetic positioning technology. This method aims to improve target positioning accuracy without sacrificing effective detection range by utilizing the spatial gradient of magnetic field scalar information, thereby achieving a balance between positioning performance and detection range over medium to long distances.

[0025] 2. Traditional magnetic positioning methods using scalar gradients require strict alignment of the geomagnetic field direction with the magnetic target. However, in practical applications, not only is strict alignment of the geomagnetic field direction with the magnetic moment direction difficult to achieve, but the magnetic moment direction of the magnetic target and the geomagnetic field direction are often also unknown. This invention provides a magnetic positioning method based on the scalar gradient method, aiming to solve the dependence of existing technologies on the strict alignment of the geomagnetic field and the target magnetic moment direction. Even in practical applications where there is a certain angular deviation between the geomagnetic field direction and the target magnetic moment direction, this method can still maintain stable positioning accuracy, effectively overcoming the performance degradation problem caused by misalignment.

[0026] This invention collects the scalar intensity of the magnetic field at multiple points on the coordinate axis using a magnetic sensor array and obtains the scalar gradient information of the magnetic field by substituting the difference for the derivative. Based on the scalar gradient information, it calculates the unit direction vector of the magnetic target pointing to the sensor array. Then, it obtains two sets of direction vectors through dual measurement points and solves the distance between the magnetic target and the sensor array by solving the geometric equations. Combining the direction and distance, it determines the spatial coordinates of the magnetic target. At the same time, it filters out the false solutions generated by the calculation to obtain the true and effective solution. This invention effectively overcomes the contradiction between positioning accuracy and effective detection distance in magnetic positioning technology. It does not require the magnetic moment direction to be strictly coincident with the geomagnetic field direction. It can still maintain stable positioning performance in actual complex magnetic field environments, and greatly improves the reliability, accuracy, practicality and robustness of magnetic detection positioning results.

[0027] Furthermore, in S1, when the detection distance is greater than three times the size of the magnetic target itself, the magnetic target can generally be considered as a magnetic dipole. A spatial rectangular coordinate system is established with the magnetic dipole as the origin, and the magnetic flux density of the magnetic target can be calculated based on the magnetic dipole model. B o : (1) in, B o This represents the magnetic flux density vector generated at the detection point by the magnetic dipole model. m 0 represents the free permeability, with a value of 4π × 10⁻⁶. -7 H / m, M The magnetic moment vector of the magnetic dipole. r Let be the position vector pointing from the magnetic dipole to the probe point. r The distance from the magnetic dipole to the detection point is denoted as . Taking the modulus of equation (1) yields: (2) in, M magnetic moment vector M The magnitude of the vector and the included angle. f magnetic moment vector M and position vector r The angle between them.

[0028] Specifically, when the detection distance is greater than three times the size of the magnetic target itself, this invention treats the magnetic target as a magnetic dipole. Based on the magnetic dipole model, it accurately calculates the magnetic induction intensity vector of the magnetic target and obtains its magnitude, which simplifies the physical calculation model of magnetic detection and effectively avoids calculation errors caused by improper simplification of the physical model.

[0029] Furthermore, in S1, during the detection of magnetic targets under the background of the Earth's magnetic field, the total magnetic field measured by the magnetic sensor array... B t It is composed of the magnetic field vector of the magnetic dipole. B o With the geomagnetic field vector B e The result of superposition (3) Simultaneously, the modulo values ​​from both sides are obtained as follows: (4) Taylor expansion of equation (4) yields: (5) Among them, the geomagnetic field vector B e Its magnitude is approximately 0.5~0.6 Gauss (50000~60000 nT), which is much greater than the magnetic field strength of a magnetic dipole.

[0030] Furthermore, in S1, ignoring the third term in equation (5) and expanding the second term, we get: (6) in,r 0=( r x , r y , r z ) T , m 0=( m x , m y , m z ) T , e 0=( e x , e y , e z ) T These are the unit vectors of the probe position vector, the magnetic dipole moment, and the Earth's magnetic field, respectively. Magnetic moment M It is composed of the superposition of induced magnetic field and intrinsic magnetic field. The induced magnetic field is generated by the magnetization of the target material in the Earth's background magnetic field, and its direction is roughly the same as the direction of the geomagnetic field. The intrinsic magnetic field is the inherent permanent magnetism of the target, which is independent of the current external field. Considering that the intrinsic magnetic field of the magnetic target is relatively weak, its value is generally 10% of the magnitude of the induced magnetic moment, while the induced magnetic field generated by the influence of the geomagnetic field is often regarded as an absolute factor, the direction of the magnetic moment in equation (6) is approximated to the direction of the geomagnetic field, and then it is simplified to: (7) make: (8) in, i It is the angle between the direction of the magnetic target and the direction of the geomagnetic field.

[0031] Furthermore, in S2, combining equations (7) and (8), and differentiating equation (7), we obtain: (9) (10) in, T The magnetic field gradient representing the spatial location of a magnetic target. The direction vector is obtained by transforming equation (10). r 0: (11).

[0032] Specifically, this invention constructs a vector superposition and magnitude expression of the total magnetic field under the background of geomagnetic field and performs a Taylor expansion on it. Considering the actual detection conditions where the magnitude of the geomagnetic field is much greater than the magnetic field strength of the magnetic dipole, the expansion is reasonably ignored and expanded. Then, the magnetic moment direction is approximated as the geomagnetic field direction to simplify the formula. Furthermore, the magnetic field gradient is obtained by differentiation and the direction vector of the magnetic target pointing to the sensor array is derived. Finally, a nonlinear equation containing only a single unknown is established, forming a complete mathematical derivation link adapted to the actual detection conditions, thus getting rid of the dependence of the traditional scalar gradient method on the strict coincidence of the magnetic moment direction and the geomagnetic field direction.

[0033] Furthermore, in S3, both sides of equation (11) are multiplied by the unit vector of the geomagnetic field direction. e 0 yields: (12) Equation (12) contains only one unknown quantity, cos i The nonlinear equation, where, α Gradient vector T and geomagnetic field vector e The angle between the two sides, cos α The value range of cos is [-1, 1]. α When the value changes, this nonlinear equation has exactly three solutions within the range, corresponding to three different cosine values. i Substituting these values ​​back into equation (11) yields three corresponding direction vectors pointing towards the magnetic sensor array. r 0. Among these, two solutions have no practical significance in physics and are considered pseudo-solutions. They need to be eliminated through appropriate mathematical or physical constraints. Furthermore, the direction vector of the magnetic target is obtained by solving for a single measuring point. By moving the magnetic sensor to another measuring point in space and repeating the above calculation process, another set of direction vectors corresponding to that measuring point is obtained. Then, the following system of equations is constructed: (13) Based on two sets of direction vectors, construct the geometric relationship shown in equation (13), as follows: Figure 1 As shown, the distance between the magnetic target and the sensor array can be calculated. Combining this distance with the corresponding direction vector determines the spatial coordinates of the magnetic target with the magnetic sensor array as the origin. r 1: (14) in, r 1 is the distance from the first measuring point to the magnetic target obtained from equation (13). u 10 Let be the unit direction vector from the magnetic target to the first measuring point of the sensor in equation (11).

[0034] Specifically, this invention obtains a nonlinear equation containing only a single unknown by multiplying the direction vector expression with the unit vector of the geomagnetic field direction. After obtaining three sets of direction vectors, pseudo-solutions without physical meaning are constrained and eliminated. Then, two sets of direction vectors are obtained through dual measurement points, and a set of geometric equations is solved to solve for the distance between the magnetic target and the sensor array. Finally, the spatial coordinates of the magnetic target are determined by combining the distance and the effective direction vector. This can get rid of the requirement that the magnetic moment direction and the geomagnetic field direction must be strictly coincident, effectively solve the problem of non-uniqueness of magnetic detection inversion solutions, and ensure the accuracy and stability of the positioning solution while maintaining a long effective detection distance.

[0035] Furthermore, in S4, to address the issue of spurious solutions in equation (11), a feasible error elimination method is proposed. The flowchart of this method is given below. Figure 2 As shown. In practical applications, this magnetic detection method is mainly aimed at ferromagnetic targets buried underground or submerged underwater, whose true location must be in the space below the flight path of the airborne platform. Therefore, if the direction vector r 0 z A negative axis component indicates that the corresponding spatial point is located in the air above the airborne platform, lacking physical realizability, and can be directly eliminated. If there are pseudo-solutions that cannot be judged by this condition, further screening is required in conjunction with other constraints. For pseudo-solutions that cannot be identified solely by direction, the distance calculation steps need to be repeated multiple times to extend the two-point positioning to a series of discrete point sequences. Since pseudo-solutions do not have a geometrically corresponding actual target, they often exhibit significant instability in distance calculations, with the fluctuation of the calculation results being significantly higher than that of the true solution. By comparing the fluctuation amplitude of the distance calculation, pseudo-solutions without practical significance can be effectively identified and eliminated.

[0036] The specific execution logic of the pseudo-solution filtering mechanism is as follows: First, substitute the three results obtained from equation (12) back into equation (11) to obtain the three unit direction vectors. r 0, and extract the values ​​of each vector. z Coordinate components; at this time, z Number of vectors with coordinates less than 0 N There are only two possible values, namely N =1 or N =2. If N =1, then the unit direction vector is directly determined as a valid solution; if N =2, the two-point positioning method needs to be extended to the trajectory positioning method first, and a distance data set needs to be constructed. A and B Then calculate the standard deviation of the two sets of data respectively. s 1 and s2. Select the unit direction vector corresponding to the dataset with the smaller standard deviation as the correct solution. Finally, based on the selected correct direction vector, combine equations (13) and (14) to complete the final positioning calculation. Among them, data group A , B ={ r 12 , r 23 , r 34 ,…, r ij ; j = i +1}, i Indicates the first i A magnetic sensor array measuring points, j Indicates the first i +1 magnetic sensor array measurement points, r ij Indicates the first i The magnetic sensor array measurement points and the first j The distance to the magnetic target is obtained by joint measurement of the measurement points of the magnetic sensor array.

[0037] Specifically, this invention extracts the unit direction vector obtained from the solution. z Coordinate components that are not physically feasible are directly discarded. z For pseudo-solutions with coordinates less than 0, the two-point positioning method is extended to a trajectory positioning method. Distance data sets are constructed and the standard deviations of the two sets of data are calculated. The unit direction vector corresponding to the dataset with the smaller standard deviation is selected as the correct solution. Finally, the final positioning calculation is completed based on the selected effective direction vectors. This method can stably and efficiently eliminate meaningless pseudo-solutions generated in the positioning calculation, avoid pseudo-solutions from interfering with the positioning results, and improve the accuracy and reliability of magnetic target positioning calculation.

[0038] A computer program product includes a computer program / instructions that, when executed by a processor, implement the aforementioned scalar gradient-based magnetic detection method.

[0039] A storage medium storing a computer program that, when executed by a processor, implements the above-described scalar gradient-based magnetic detection method.

[0040] A computer device includes: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the above-described scalar gradient-based magnetic detection method.

[0041] Specifically, this invention implements the magnetic detection method based on scalar gradients in the form of computer programs, storage media, and computer devices. This enables the entire magnetic detection and positioning process to run automatically via a processor, completing all stages such as signal acquisition, gradient calculation, direction and distance determination, and pseudo-solution elimination without manual intervention. This effectively improves the execution efficiency and stability of the magnetic detection calculation process, while also expanding the applicable scenarios and integration space of the magnetic detection method, allowing it to be easily deployed on different hardware platforms for practical use.

[0042] To verify that this invention significantly improves the positioning accuracy of the scalar method and the detection range of the tensor method, thus overcoming the current limitations of methods in achieving both detection range and positioning accuracy at medium to long distances, the following verification scheme was designed and implemented: The magnetic sensor array uses, for example Figure 3 The array is arranged in a cross shape. It contains six sensors, arranged symmetrically in pairs along three mutually orthogonal lines in space. The distance between two sensors on the same line is a fixed baseline distance. D .

[0043] The geomagnetic field background noise was set to a geomagnetic field amplitude of 55000 nT, a geomagnetic declination of 0°, and a geomagnetic dip of 60°. The magnitude of the induced magnetic moment was then determined. M Unknown magnitude of remanent moment m Baseline distance D Sensor resolution S Standard deviation of Gaussian white noise s The values ​​are shown in Table 1.

[0044]

[0045] Table 1 Magnetic Target Parameters In this invention, positioning error is used. d r As an indicator for measuring the detection accuracy of the system.

[0046] (15) in, x t , y t , z t These are magnetic targets in x , y , z The true value of the coordinates in the direction. x c , y c , z c They arex , y , z Calculated values ​​of the coordinates in the direction.

[0047] The overall scheme employing six magnetic sensors arranged in a spatial cross shape is as follows: Figure 4 As shown. To simulate trajectory coverage of the target area, the flight trajectory of the airborne sensor array was set as a closed square path with a side length of 500 meters, centered on the origin of the spherical model, and data was collected at 50-meter intervals along this trajectory. Simultaneously, the magnetic target to be measured was placed at a radius of... d On the sphere, relevant parameters include detection distance. d spherical model f and oh Values ​​and magnetic target interval step size p The specific values ​​are shown in Table 2. This is to quantify different detection distances. d The positioning accuracy is as follows, for each distance d Calculate the positioning error of the magnetic target at all spatial coordinate points on the spherical model, and take the average value as the positioning error corresponding to that distance.

[0048]

[0049] Table 2 Parameters of the spherical coordinate system This invention successfully verifies that the magnetic detection method based on the scalar gradient method has a significant improvement in positioning accuracy within the effective detection range compared to the magnetic detection method based on the scalar method. Compared to the magnetic detection method based on the tensor method, it still maintains good positioning accuracy at medium and long distances. The positioning errors of the three different detection methods are as follows: Figure 5 As shown.

[0050] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application 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 of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A magnetic detection method based on scalar gradient, characterized in that, Includes the following steps: S1. Use a magnetic sensor array to collect the scalar intensity of the magnetic field at multiple points on the coordinate axis, and use the difference instead of the derivative to obtain the scalar gradient information of the magnetic field. S2. Based on the magnetic field scalar gradient information, the position information of the magnetic target is decomposed into direction information and distance information, and the unit direction vector from the magnetic target to the magnetic sensor array is calculated. S3. Move the magnetic sensor array to another measuring point and repeat S2 to obtain two sets of unit direction vectors. Solve the geometric equations to find the distance between the magnetic target and the sensor array. Combine the unit direction vectors and the distance to determine the spatial coordinates of the magnetic target. S4. After filtering out the false solutions generated by the calculation and obtaining the true and valid solutions, the location is completed.

2. The magnetic detection method based on scalar gradient according to claim 1, characterized in that, In S1, when the detection distance is greater than three times the size of the magnetic target itself, the magnetic target is equivalent to a magnetic dipole. A spatial rectangular coordinate system is established with the magnetic dipole as the origin, and the magnetic induction intensity of the magnetic target is calculated based on the magnetic dipole model. B o : （1） in, B o This represents the magnetic flux density vector generated at the detection point by the magnetic dipole model. μ 0 represents the free permeability, with a value of 4π × 10⁻⁶. -7 H / m, M The magnetic moment vector of the magnetic dipole. r Let be the position vector pointing from the magnetic dipole to the probe point. r The distance from the magnetic dipole to the detection point is denoted as . Taking the modulus of equation (1) yields: （2） in, M magnetic moment vector M The magnitude of the vector and the included angle. φ magnetic moment vector M and position vector r The angle between them.

3. The magnetic detection method based on scalar gradient according to claim 2, characterized in that, In S1, during the detection of magnetic targets under the background of the Earth's magnetic field, the total magnetic field measured by the magnetic sensor array is... B t It is composed of the magnetic field vector of the magnetic dipole. B o With the geomagnetic field vector B e The result of superposition （3） Simultaneously, the modulo values ​​from both sides are obtained as follows: （4） Taylor expansion of equation (4) yields: （5） Among them, the geomagnetic field vector B e Its magnitude is approximately 0.5 to 0.6 Gauss, which is much greater than the magnetic field strength of a magnetic dipole.

4. The magnetic detection method based on scalar gradient according to claim 3, characterized in that, In S1, ignoring the third term in equation (5) and expanding the second term, we get: （6） in, r 0=( r x , r y , r z ) T , m 0=( m x , m y , m z ) T , e 0=( e x , e y , e z ) T These are the unit vectors of the probe position vector, the magnetic dipole moment, and the geomagnetic field, respectively. Approximating the direction of the magnetic moment in equation (6) to the direction of the Earth's magnetic field, it simplifies to: （7） make: （8） in, θ It is the angle between the direction of the magnetic target and the direction of the geomagnetic field.

5. The magnetic detection method based on scalar gradient according to claim 4, characterized in that, In S2, combining equations (7) and (8) and differentiating equation (7), we obtain: （9） （10） in, T The magnetic field gradient representing the spatial location of a magnetic target. The direction vector is obtained by transforming equation (10). r 0: （11）。 6. The magnetic detection method based on scalar gradient according to claim 5, characterized in that, In S3, both sides of equation (11) are multiplied by the unit vector of the geomagnetic field direction. e 0 yields: （12） Equation (12) contains only one unknown quantity, cos θ The nonlinear equation, where, α Gradient vector T and geomagnetic field vector e The angle between the two sides, cos α The value range of cos is [-1, 1]. α When the value changes, this nonlinear equation has exactly three solutions within the range, corresponding to three different cosine values. θ Substituting these values ​​back into equation (11) yields three corresponding direction vectors pointing towards the magnetic sensor array. r 0. Among these, two solutions have no practical significance in physics and are considered pseudo-solutions. They need to be eliminated through appropriate mathematical or physical constraints. Furthermore, the direction vector of the magnetic target is obtained by solving for a single measuring point. By moving the magnetic sensor to another measuring point in space and repeating the above calculation process, another set of direction vectors corresponding to that measuring point is obtained. Then, the following system of equations is constructed: （13） Based on the two sets of direction vectors, construct the geometric relationship shown in equation (13), solve the distance between the magnetic target and the sensor array, and combine the distance with the corresponding direction vector to determine the spatial coordinates of the magnetic target with the magnetic sensor array as the origin. r 1: （14） in, r 1 is the distance from the first measuring point to the magnetic target obtained from equation (13). u 10 Let be the unit direction vector from the magnetic target to the first measuring point of the sensor in equation (11).

7. The magnetic detection method based on scalar gradient according to claim 6, characterized in that, In S4, regarding the problem of pseudo-solutions in equation (11), the pseudo-solution removal mechanism is as follows: First, substitute the three results obtained from equation (12) back into equation (11) to obtain the three unit direction vectors. r 0, and extract the values ​​of each vector. z Coordinate components; at this time, z Number of vectors with coordinates less than 0 N There are only two possible values, namely N =1 or N =2, if N =1, then the unit direction vector is directly determined as a valid solution; if N =2, the two-point positioning method needs to be extended to the trajectory positioning method first, and a distance data set needs to be constructed. A and B Then calculate the standard deviation of the two sets of data respectively. σ 1 and σ 2. Select the unit direction vector corresponding to the dataset with the smaller standard deviation as the correct solution; Finally, based on the correct direction vector obtained through screening, equations (13) and (14) are combined to complete the final positioning calculation. Among them, data group A , B ={ r 12 , r 23 , r 34 ,…, r ij ; j = i +1}, i Indicates the first i A magnetic sensor array measuring points, j Indicates the first i +1 magnetic sensor array measurement points, r ij Indicates the first i The magnetic sensor array measurement points and the first j The distance to the magnetic target is obtained by joint measurement of the measurement points of the magnetic sensor array.

8. A computer program product comprising a computer program / instructions, characterized in that, When the computer program instructions are executed by the processor, they implement the magnetic detection method based on scalar gradient as described in any one of claims 1-7.

9. A storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the magnetic detection method based on scalar gradient as described in any one of claims 1-7.

10. A computer device, characterized in that, include: A memory, a processor, and a computer program stored in the memory and executable on the processor, the processor executing the program to implement the scalar gradient-based magnetic detection method according to any one of claims 1-7.

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