A method for calculating and tracking the response of a moving magnetic target based on induced electromotive force

Abstract

This invention provides a method for calculating and tracking the response of moving magnetic targets based on induced electromotive force (EMF). The method constructs a sensor array consisting of at least three three-component magnetic induction coils. Utilizing the induced EMF in the sensors caused by the motion of the magnetic target, the method first obtains the position vector of the moving magnetic target by solving a least-squares problem. Then, based on the obtained position vector, a stable velocity vector is obtained through polynomial fitting. Finally, the magnetic moment vector is calculated using the position and velocity vectors. The data used in this invention is the induced EMF of the three-component magnetic induction coils. The amplitude of this data is proportional to the velocity of the moving magnetic target. Compared to traditional magnetic induction intensity data, it inherently carries the velocity information of the moving target, making it more advantageous for obtaining accurate velocity and position information. This invention provides a new approach for the detection and tracking of moving targets, and this method is more sensitive to velocity.

Description

Technical Field

[0001] This invention belongs to the field of magnetic exploration technology, specifically relating to a method for calculating and tracking the response of a moving magnetic target based on induced electromotive force. Background Technology

[0002] Moving targets such as land vehicles and ships are typically composed of ferromagnetic materials. The remanence and magnetization of these ferromagnetic materials themselves create a magnetic source, generating a static magnetic field. This static magnetic field is a crucial characteristic signal of a moving target, serving as fundamental information for magnetic target localization. The localization method for moving targets essentially utilizes the target's static electromagnetic field to perform real-time position inversion at a specific moment. This method uses data such as the target's magnetic flux density or gradient value at that specific instant, employing magnetometers that measure the absolute value of the underwater target's static magnetic field, such as fluxgate magnetometers and SQUIDs. However, these sensors, which measure absolute field values, are typically expensive and have a narrow detection sensitivity range, thus limiting their application. Furthermore, this localization method does not consider the target's velocity, meaning the localization accuracy is independent of the target's speed.

[0003] Magnetic induction coils are magnetic field sensors based on electromagnetic induction. Their detection sensitivity range is wider than other sensors, making them ideal for capturing weak magnetic fields. When a magnetic induction coil is placed at a predetermined location, the movement of a magnetic target causes a change in the magnetic flux at the coil's location, inducing an electromotive force (EMF). The greater the target's speed, the stronger the response. Therefore, the target's speed itself is valuable information. Consequently, the response of the magnetic induction coil is directly proportional to the target's speed, giving it a natural advantage in tracking moving targets. However, publicly available reports rarely mention algorithms for target localization using the speed information of magnetic targets. Summary of the Invention

[0004] The purpose of this invention is to provide a method for calculating and tracking the response of a moving magnetic target based on induced electromotive force. This method uses induced electromotive force data carrying velocity information and can be applied to achieve long-range detection and tracking of moving magnetic targets.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] A method for calculating and tracking the response of a moving magnetic target based on induced electromotive force, specifically including:

[0007] S1. Read the induced electromotive force data of the sensor array participating in the inversion, set the inversion execution parameters and design the initial inversion model;

[0008] S2. Construct the objective function for tracking moving magnetic targets. and has the following forms

[0009]

[0010] in, These are model parameters, including the position vector of the magnetic target. velocity vector and magnetic moment vector [ ], For the forward modeling operator of induced electromotive force. Let be the standard deviation of the i-th data point. For observation data vectors, The number of observations;

[0011] S3. Obtain the position vector of the magnetic moving target by solving the least squares problem;

[0012] S4. Calculate the target's velocity vector based on the obtained position information;

[0013] S5. Calculate the magnetic moment vector of the magnetic target based on the obtained position and velocity information.

[0014] The sensor array described in S1 consists of at least three three-component magnetic induction coil sensors.

[0015] The calculation method for the forward modeling of the induced electromotive force described in S2 is as follows:

[0016]

[0017] in, To induce electromotive force. The relative permeability of the core material of the induction coil. The vertical cross-sectional area of ​​the induction coil, The magnetic flux density is parallel to the induction coil, and t is time. Let be the partial derivative of the magnetic flux density at the sensor location with respect to time caused by the motion of the magnetic target. The components in the three orthogonal directions can be expressed as:

[0018]

[0019] in, These represent the velocities of the magnetic target in three orthogonal directions. The coefficient matrix has the following form for each element.

[0020]

[0021] in, , ,as well as For the coefficient, specifically:

[0022]

[0023]

[0024]

[0025]

[0026] In the above formula, The position vector between the target and the sensor. Position vector The model, [ ] represents the magnetic moment vector of the moving magnetic target.

[0027] The velocity vector of the target, as described in S4, is calculated based on the obtained position information. A polynomial is used to fit the velocity vector at different times to reduce velocity anomalies caused by sudden changes in position at different times.

[0028] The method for calculating the magnetic moment vector of a magnetic target based on the obtained position and velocity information, as described in S5, is as follows:

[0029]

[0030] in, Let be the partial derivative of the magnetic flux density at the sensor location with respect to time caused by the motion of the magnetic target. Let be a coefficient matrix, and have and

[0031]

[0032] Compared with the prior art, the beneficial effects of the method provided in some embodiments of the present invention are as follows:

[0033] This invention addresses the problem of long-range detection and tracking of moving magnetic targets, proposing a method for calculating and tracking the response of moving magnetic targets based on induced electromotive force. This method constructs a sensor array consisting of at least three three-component magnetic induction coils, utilizing the induced electromotive force generated in the sensors due to the motion of the magnetic target. The position vector of the moving magnetic target is obtained by solving a least-squares problem. Based on the obtained position vector, a stable velocity vector is obtained through polynomial fitting. Finally, the magnetic moment vector is calculated using the position and velocity vectors.

[0034] This invention utilizes the induced electromotive force of a three-component magnetic induction coil. The amplitude of this data is proportional to the velocity of the magnetic target. Compared to traditional magnetic induction intensity data, it inherently carries the velocity information of the moving target, making it more advantageous for obtaining accurate velocity and position information of the moving magnetic target. This invention provides a new approach to the detection and tracking of moving targets. This method is more sensitive to velocity and more effective in obtaining accurate velocity information, possessing practical application value. Attached Figure Description

[0035] To more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0036] Figure 1 This is a flowchart of the method of the present invention;

[0037] Figure 2 A schematic diagram of the motion state of a magnetic induction coil array and a magnetic target;

[0038] Figure 3 A comparison diagram of the estimated trajectory of the magnetic target and the actual trajectory;

[0039] Figure 4 A graph showing the absolute error between the estimated velocity of the magnetic target and its actual velocity;

[0040] Figure 5 This is a graph showing the absolute error between the estimated target magnetic moment and the actual magnetic moment. Detailed Implementation

[0041] To make the technical problems to be solved, the technical solutions, and the beneficial effects of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0042] This invention provides a method for calculating and tracking the response of a moving magnetic target based on induced electromotive force. See the flowchart for the detailed calculation process. Figure 1 Specifically, this includes:

[0043] S1. Read the induced electromotive force data of the sensor array participating in the inversion. Since the inversion model has 9 parameters, and one sensor can only provide 3 data points at a time, the sensor array must consist of at least 3 three-component magnetic induction coil sensors to ensure that the amount of data is greater than the number of position parameters. Set the inversion execution parameters and design the initial inversion model. The execution parameters include the maximum number of inversion iterations, iteration step size, convergence error accuracy, etc.

[0044] S2. Construct the objective function for tracking moving magnetic targets. and has the following forms

[0045]

[0046] in, These are model parameters, including the position vector of the magnetic target. velocity vector and magnetic moment vector [ ], For the forward modeling operator of induced electromotive force. Let be the standard deviation of the i-th data point. For observation data vectors, The number of observations.

[0047] Induced electromotive force forward modeling operator The purpose is to calculate the induced electromotive force of the current inversion model, and the calculation method is as follows:

[0048]

[0049] in, To induce electromotive force. The relative permeability of the core material of the induction coil. The vertical cross-sectional area of ​​the induction coil, The magnetic flux density is parallel to the induction coil, and t is time. Let be the partial derivative of the magnetic flux density at the sensor location with respect to time caused by the motion of the magnetic target. The components in the three orthogonal directions can be expressed as:

[0050]

[0051] in, These represent the velocities of the magnetic target in three orthogonal directions. The coefficient matrix has the following form for each element.

[0052]

[0053] in, , ,as well as For the coefficient, specifically:

[0054]

[0055]

[0056]

[0057]

[0058] In the above formula, The position vector between the target and the sensor. Position vector The model, [ ] represents the magnetic moment vector of the moving magnetic target.

[0059] S3. Solve the least squares problem using Newton's method. When the inversion reaches the maximum number of iterations or the convergence error accuracy is reached, exit the inversion and output the position vector of the magnetic moving target.

[0060] S4. Since the velocity and magnetic moment in the inversion results are coupled, the velocity vector and magnetic moment vector need to be calculated separately. Using the obtained position, the target's velocity vector can be calculated by subtracting the vectors of adjacent positions and dividing by the time interval. Based on this, a polynomial is used to fit the velocity vectors at different times to reduce velocity anomalies caused by abrupt changes in position at different times.

[0061] S5. Calculate the magnetic moment vector of the magnetic target based on the obtained position and velocity information. The calculation method is as follows:

[0062]

[0063] in, Let be the partial derivative of the magnetic flux density at the sensor location with respect to time caused by the motion of the magnetic target. Let be a coefficient matrix, and have and

[0064]

[0065] See Figure 2 A sensor array consisting of three three-component magnetic induction coils is constructed, located at (0,0,0)m, (0,10,0)m, and (0,20,0)m respectively. The magnetic moment vector of the magnetic target is (0,10,0)Am. 2The target moves from point A(0,0,3) to point B(10,20,3) at a speed of (1,2,0) m / s. The data sampling frequency of the sensor is set to 2Hz. When the magnetic target starts moving from point A, the sensor array starts recording measurement data. After 10s, the target moves from point A to point B.

[0066] Read the sensor measurement data involved in the inversion, i.e., the induced electromotive force of the electromagnetic sensor array, set the inversion execution parameters and design the initial inversion model; construct the moving magnetic target tracking objective function as shown in formula (1), and obtain the magnetic target position vector at different times by solving the objective function at different times. The positioning results are as follows: Figure 3 As shown. By Figure 3 It can be seen that the trajectory of the magnetic target from A(0,0,3) to B(10,20,3) is a straight line, and the estimated trajectory almost coincides with the actual trajectory.

[0067] Based on the obtained position information, and using polynomial fitting to calculate the velocity vector at different times, the results are compared with the true velocity and the absolute error is calculated. Figure 4 As shown in the figure, the maximum absolute error between the estimated velocity and the actual velocity is less than 0.015 m / s, and the result is very close to the actual result.

[0068] Based on the obtained position and velocity vectors, the magnetic moment vector of the magnetic target is calculated using formulas (5) and (6). After comparing it with the actual velocity and calculating its absolute error, the results are as follows: Figure 5 As shown in the figure, the maximum absolute error between the estimated magnetic moment and the true magnetic moment is less than 0.05 Am. 2 The results were very close to the actual results.

[0069] This demonstrates that the algorithm proposed in this invention can obtain a relatively accurate position, velocity, and magnetic moment vector of a moving magnetic target.

[0070] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for calculating and tracking the response of a moving magnetic target based on induced electromotive force, characterized in that, Specifically, it includes: S1. Read the induced electromotive force data of the sensor array participating in the inversion, set the inversion execution parameters and design the initial inversion model; S2. Construct the objective function for tracking moving magnetic targets. and has the following forms ;in, These are model parameters, including the position vector of the magnetic target. velocity vector and magnetic moment vector [ ], For the forward modeling operator of induced electromotive force. Let be the standard deviation of the i-th data point. For observation data vectors, S3, obtain the position vector of the magnetic moving target by solving the least squares problem; S4, calculate the velocity vector of the target based on the obtained position information; S5, calculate the magnetic moment vector of the magnetic target based on the obtained position and velocity information; the calculation method of induced electromotive force forward modeling is as follows: ;in, To induce electromotive force. The relative permeability of the core material of the induction coil. The vertical cross-sectional area of ​​the induction coil, The magnetic flux density is parallel to the induction coil, and t is time. Let be the partial derivative of the magnetic flux density at the sensor location with respect to time caused by the motion of the magnetic target. The components in the three orthogonal directions are represented as ;in, These represent the velocities of the magnetic target in three orthogonal directions. The coefficient matrix has the following form: ; in, , ,as well as For the coefficient, specifically In the above formula, The position vector between the target and the sensor. Position vector The model, [ ] represents the magnetic moment vector of the moving magnetic target.

2. The method for calculating and tracking the response of a moving magnetic target based on induced electromotive force as described in claim 1, characterized in that, The sensor array described in S1 consists of at least three three-component magnetic induction coil sensors.

3. The method for calculating and tracking the response of a moving magnetic target based on induced electromotive force as described in claim 1, characterized in that, The velocity vector of the target, as described in S4, is calculated based on the obtained position information. A polynomial is used to fit the velocity vector at different times to reduce velocity anomalies caused by sudden changes in position at different times.

4. The method for calculating and tracking the response of a moving magnetic target based on induced electromotive force as described in claim 1, characterized in that, The method for calculating the magnetic moment vector of a magnetic target based on the obtained position and velocity information, as described in S5, is as follows: ;in, Let be the partial derivative of the magnetic flux density at the sensor location with respect to time caused by the motion of the magnetic target. Let be a coefficient matrix, and have and .

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