Method for positioning a moving alternating magnetic body

Abstract

The application provides a moving alternating magnet positioning method, which adopts a product objective function based on a Dubin-Watson statistic to realize positioning of a magnetic target. The product objective function has the characteristics that different data weights do not need to be manually selected, and the weights of different types of data are adaptively adjusted according to the fitting condition of the data in the inversion process. The Dubin-Watson statistic can reduce the autocorrelation of the residual between the measured data and the inversion model response, thereby avoiding the condition that the inversion model response deviates from the measured data while the fitting difference is small, and to a certain extent, avoiding the data overfitting phenomenon. Through the trial calculation of the noise-added synthetic data, the results show that the method can obtain more accurate magnetic body position, speed and magnetic moment information. The application provides a new technical scheme for the detection and tracking of the moving magnetic target. Compared with the traditional additive objective function positioning method, the application can obtain more robust positioning results, and has practical application value.

Description

Technical Field

[0001] This invention belongs to the field of magnetic exploration technology, specifically relating to a method for locating a moving alternating magnetic body. Background Technology

[0002] Moving targets such as land vehicles and naval vessels are typically composed of ferromagnetic materials. The remanence and magnetization of these ferromagnetic materials themselves constitute a magnetic source, generating a static magnetic field. Electromagnetic fuses, as the most widely used non-trigger fuses, radiate alternating magnetic field signals of a certain frequency through a transmitting coil. The static and alternating magnetic field responses are important characteristic signals of moving targets, providing fundamental information for magnetic target localization. The static magnetic field characterizes the magnitude of the magnetic field strength at the sensor location, while the alternating magnetic field response also contains information about the rate of change of the magnetic field over time, including the velocity of the magnetic target. The induction coil response can be used to analyze both the static and alternating magnetic field responses; however, their characteristics differ. How to combine these two responses for inversion localization of magnetic targets and fully reflect their respective characteristics is an ongoing research task.

[0003] Traditional multi-type data joint inversion methods employ an additive objective function, requiring manual selection of weighting factors to assign weights to different data types. However, the electrical structure obtained through this joint inversion largely depends on the selection method of the data weighting factors and the initial conditions. Furthermore, the signal from magnetic targets is weak; when the signal-to-noise ratio of the target signal received by the sensor is low, it may enhance the ambiguity of the positioning results, ultimately leading to inaccurate positioning results. Summary of the Invention

[0004] The purpose of this invention is to provide a method for locating moving alternating magnetic objects. This method proposes to locate moving magnetic objects based on a product objective function of the Durbin-Watson statistic, achieves adaptive weight selection for different data types, and reduces the autocorrelation of the residuals between the measurement data and the inversion model response based on the Durbin-Watson statistic. This avoids situations where the inversion model response deviates from the measurement data due to a small fitting difference, and to a certain extent avoids the phenomenon of data overfitting. As a result, a more robust location result can be obtained than that of the traditional additive objective function inversion.

[0005] To achieve the above objectives, the present invention provides the following technical solution: a method for positioning a moving alternating magnetic body, comprising the following steps:

[0006] S1. Obtain the magnetic dipole induction coil data and magnetic dipole magnetic field strength data of the alternating magnetic material;

[0007] S2. Construct an objective function for the positioning product of a moving alternating magnetic body based on the Durbin-Watson statistic.

[0008] Φ(m)=φ A (m)×φ B (m)×φ DW (m)

[0009] In the formula, Φ(m) is the objective function of the inversion algorithm; m is the model inversion parameter vector, which includes the position, velocity, and magnetic moment of the magnetic body; φ A (m)=||(d A -F A (m))|| 2 φ represents the fitting difference of the magnetic dipole induction coil data. B (m)=||(d B -F B (m))|| 2 The fitting difference is the difference between the magnetic field strength data of the magnetic dipole. Let be the regularization function of the Durbin-Watson statistic, where e i =d i -F(m) i Let m be the residual of the i-th data point, and m be the number of corresponding data points. Let e ​​be the mean of the residual vector e;

[0010] S3. Establish and screen the initial inversion model;

[0011] S4. Solve the problem of finding the minimum value of the objective function;

[0012] S5. Calculate the update step size using the parabolic fitting method;

[0013] S6. Has the inversion iteration reached the maximum number of updates or the accuracy requirement? If not, return to S4 and continue the inversion iteration. If yes, output the position vector, velocity vector and magnetic moment vector obtained by inversion.

[0014] S7. Update the velocity vector based on the position vector;

[0015] S8. Update the magnetic moment vector based on analytical magnetic dipole magnetic field strength data;

[0016] S9. Output the positioning result.

[0017] The specific steps for establishing and screening the initial inversion model as described in S3 include:

[0018] S31. Using the midpoint of the receiving system as the center, divide the xoy plane into grids at certain intervals, and use the locations of all grid nodes as the initial model set.

[0019] S32. Calculate the objective function values ​​of the models in the initial model set;

[0020] S33. Select the model with the minimum objective function value as the final initial model.

[0021] The specific steps for calculating the update step size using the parabolic fitting method described in S5 include:

[0022] S51. Given a step size α0 = 0, calculate Ф(α0) = Ф(m) i +α0p i ), where i is the current iteration number, p i This refers to the model update amount;

[0023] S52, Set step size in (k = 1, ..., n) represents the gradient of the objective function, n is the number of data points, and γ is a small positive constant 10. -4 ;

[0024] S53. Calculate the objective function value Ф(α1)=Ф(m i +α1p i ) and its partial derivative Ф'(α1);

[0025] S54. If Ф(α1)>Ф(α0) or Ф'(α1)>0 is not true, then go to S3; if it is true, then go to S6.

[0026] S55. Let α2 = 2α1, calculate the objective function value Ф(α2) = Ф(m i +a2p i ) and its partial derivative Ф'(a2);

[0027] S56. If Ф(a2)≤Ф(a1) or Ф'(α2)<0 is not true, then go to S5; if it is true, then go to S7.

[0028] S57. Determine the parabola Ф(α)=aα using three points (α0,Ф(α0)), (α1,Ф(α1)) and (α2,Ф(α2)). 2 +bα+c, the step size factor is α. i = -b / (2a).

[0029] The position vector-based velocity vector update method described in S7 uses polynomial fitting of velocity vectors at different times to reduce velocity anomalies caused by sudden changes in position at different times.

[0030] The method for updating the magnetic moment vector based on analytical magnetic dipole magnetic field strength data, as described in S8, is as follows:

[0031]

[0032] in, It is the magnetic moment vector. For the analytical magnetic dipole magnetic field strength data, Let be the coefficient matrix, and have

[0033]

[0034] a yx =a xy ;

[0035] a zx =a xz ;a zy =a yz ;

[0036] In the above formula, (x,y,z) is the position vector of the inversion output, R is the magnitude of the position vector (x,y,z), and μ0 is the permeability in vacuum.

[0037] Compared with the prior art, the beneficial effects of the method provided in some embodiments of the present invention are as follows:

[0038] This invention addresses the problems of manually selecting weights for data and the ambiguity of positioning results in additive objective functions, proposing a method for locating moving alternating magnetic objects. This method proposes a product objective function based on the Durbin-Watson statistic to locate moving magnetic targets. Instead of manually selecting weights for different data types, this method adaptively adjusts the weights of different data types during the inversion process based on the data fit. Furthermore, the Durbin-Watson statistic can reduce the autocorrelation of the residuals between the measured data and the inversion model response, thus avoiding situations where the inversion model response deviates from the measured data due to a small fit difference, and mitigating overfitting to some extent. This invention provides a new technical solution for the detection and tracking of moving magnetic targets. Compared to traditional additive objective function positioning methods, the proposed method yields more robust positioning results and has practical application value. Attached Figure Description

[0039] 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.

[0040] Figure 1 This is a flowchart of the method of the present invention;

[0041] Figure 2 A schematic diagram showing the motion state of the sensor array and the alternating magnetic body;

[0042] Figure 3A comparison diagram of the inverted magnetic target's trajectory and velocity with the actual trajectory and velocity;

[0043] Figure 4 A comparison diagram of the total velocity of the inverted magnetic target motion and its actual velocity;

[0044] Figure 5 This shows a comparison between the inverted target magnetic moment and the actual magnetic moment. Detailed Implementation

[0045] 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.

[0046] This invention provides a method for locating a moving alternating magnetic body; see the detailed calculation flowchart below. Figure 1 .

[0047] S1. First, acquire the magnetic dipole induction coil data d from different sensors. A magnetic dipole magnetic field strength data d B And the magnetic dipole induction coil data d A magnetic dipole magnetic field strength data d B As observational data for inversion.

[0048] S2. Construct an objective function for the positioning product of a moving alternating magnetic body based on the Durbin-Watson statistic.

[0049] Φ(m)=φ A (m)×φ B (m)×φ DW (m)

[0050] In the formula, Φ(m) is the objective function of the inversion algorithm; m is the model inversion parameter vector, which includes the position, velocity, and magnetic moment of the magnetic body; φ A (m)=||(d A -F A (m))|| 2 φ represents the fitting difference of the magnetic dipole induction coil data. B (m)=||(d B -F B (m))|| 2 The fitting difference is the difference between the magnetic field strength data of the magnetic dipole. Let be the regularization function of the Durbin-Watson statistic, where e i =d i -F(m) i Let m be the residual of the i-th data point, and m be the number of corresponding data points. Let e ​​be the mean of the residual vector.

[0051] S3. Establish and screen the initial inversion model. Specific steps include:

[0052] S31. Using the midpoint of the receiving system as the center, divide the xoy plane into grids at certain intervals, and use the locations of all grid nodes as the initial model set.

[0053] S32. Calculate the objective function values ​​of the models in the initial model set;

[0054] S33. Select the model with the minimum objective function value as the final initial model for inversion.

[0055] S4. Solve the problem of minimizing the objective function by finding the gradient g of the objective function. i The sum is the Hessian matrix H i Finally, the update amount of the transformation parameters in the current iteration is obtained. Where i represents the i-th inversion iteration.

[0056] S5. Calculate the update step size using the parabolic fitting method. Specific steps include:

[0057] S51. Given a step size α0 = 0, calculate Ф(α0) = Ф(m) i +α0p i ), where i is the current iteration number, p i This refers to the model update amount;

[0058] S52, Set step size in (k = 1, ..., n) represents the gradient of the objective function, n is the number of data points, and γ is a small positive constant 10. -4 ;

[0059] S53. Calculate the objective function value Ф(α1)=Ф(m i +α1p i ) and its partial derivative Ф'(α1);

[0060] S54. If Ф(α1)>Ф(α0) or Ф'(α1)>0 is not true, then go to S3; if it is true, then go to S6.

[0061] S55. Let α2 = 2α1, calculate the objective function value Ф(α2) = Ф(m i +α2p i ) and its partial derivative Ф'(α2);

[0062] S56. If Ф(α2)≤Ф(α1) or Ф'(α2)<0 is not true, then go to S5-5; if it is true, then go to S5-7.

[0063] S57. Determine the parabola Ф(α)=aα using three points (α0,Ф(α0)), (α1,Ф(α1)) and (α2,Ф(α2)). 2 +bα+c, the step size factor is α. i = -b / (2a).

[0064] S6. Check if the inversion iteration has reached the maximum number of updates or the accuracy requirement. If not, return to S4 and continue the inversion iteration. If yes, output the position vector, velocity vector and magnetic moment vector obtained by inversion.

[0065] S7. Considering that there will be no abrupt changes or flying points in the velocity in the real model, a polynomial is used to fit the velocity vector at different times, and the fitted velocity is used to update the original velocity vector to reduce the velocity anomaly caused by abrupt changes in position at different times.

[0066] S8. Update the magnetic moment vector based on analytical magnetic dipole magnetic field strength data, using the following method:

[0067]

[0068] in, It is the magnetic moment vector. For the analytical magnetic dipole magnetic field strength data, Let be the coefficient matrix, and have

[0069]

[0070] a yx =a xy ;

[0071] a zx =a xz ;a zy =a yz ;

[0072] In the above formula, (x,y,z) is the position vector of the inversion output, R is the magnitude of the position vector (x,y,z), and μ0 is the permeability in vacuum.

[0073] S9. Output the positioning result.

[0074] See Figure 2 A sensor array consisting of three quadruped magnetic induction coils is constructed. The four sensors are located at (0,0,3), (0,10,3), (0,20,3), and (10,10,3), respectively. The magnetic moment vector of the magnetic target is (5,10,5)Am. 2The magnetic target moves from the starting point (0,0,0) to the ending point (40,80,0) at a speed of (1,2,0) m / s. The sensor's data sampling frequency is set to 100Hz. When the magnetic target starts moving from the starting point, the sensor array begins recording measurement data for 40 seconds. The data obtained from the sensor array, with a 2% error added, is used as the observation data for subsequent inversion.

[0075] See Figure 3 In order to follow Figure 1 The flowchart shown illustrates the processing and inversion of measurement data, resulting in a comparison between the inverted magnetic target trajectory and velocity and the actual trajectory and velocity. In the diagram, dark gray circles and arrows represent the actual position and velocity vectors of the magnetic object, while light gray circles and arrows represent the inverted position and velocity vectors. Figure 3 It can be seen that the inverted magnetic trajectory is very accurate at close range. As the distance increases, the positioning error gradually increases. This is because the magnetic target is farther away from the sensor array and the field value is smaller. However, overall, the inverted trajectory is almost a straight line from (0,0,0) to (40,80,0), and the velocity vector is very close to the actual result.

[0076] See Figure 4 The figure shows a comparison between the total velocity of the inverted magnetic target motion and the actual velocity. As can be seen from the figure, the result after polynomial fitting is relatively stable. Although the velocity obtained by inversion has slightly larger errors at the starting and ending points, there are no abnormal velocity abrupt changes throughout the process.

[0077] See Figure 5 This shows the comparison between the inverted target magnetic moment and the actual magnetic moment. Since a set of magnetic moments of the magnetic body is obtained at each moment during the inversion process, but the target magnetic moment remains constant during motion, we average the inverted magnetic moment results. Figure 5 It can be seen that the maximum absolute error between the inverted magnetic moment vector and modulus and the true magnetic moment is less than 0.23 Am. 2 The results are very close to the actual results. The numerical examples demonstrate the correctness and effectiveness of this method.

[0078] 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 of positioning a moving alternating magnetic body, characterized by, The method comprises the following steps: S1, acquiring magnetic dipole induction coil data and magnetic dipole magnetic field intensity data of the moving magnetized body; S2, constructing a motion magnetized body positioning product objective function based on a Dubin-Watson statistical quantity, Φ(m) = φ A (m) x φ B (m) x φ DW (m) where Φ(m) is the objective function of the inversion algorithm; m is the model inversion parameter vector, which contains the position, velocity and magnetic moment of the magnetic body, φ A (m) = ||d A -F A (m))| 2 is the fitting error of the magnetic dipole induction coil data, φ B (m) = ||d B -F B (m))| 2 is the fitting error of the magnetic dipole magnetic field intensity data, is the Dubin-Watson statistic regular function, where e i = d i -F(m) i is the residual error of the i-th data, m is the corresponding data number, is the mean of the residual error vector e; S3, establishing and screening an inversion initial model; S4, solving a minimum value problem of the objective function; S5, calculating an updating step length by using a parabolic fitting method; S6, determining whether the inversion iteration reaches a maximum updating number or a precision requirement, if not, returning to S4 to continue the inversion iteration, if yes, outputting a position vector, a velocity vector and a magnetic moment vector obtained by inversion; S7, updating the velocity vector based on the position vector; S8, updating the magnetic moment vector based on the analytical magnetic dipole magnetic field intensity data; S9, outputting a positioning result.

2. The method of claim 1, wherein the motion- alternating magnetizable body is positioned such that the magnetic field is applied to the motion- alternating magnetizable body in a direction that is substantially perpendicular to the direction of motion of the motion- alternating magnetizable body. The specific steps of establishing and screening the inversion initial model in S3 comprise: S31, taking a midpoint of a receiving system as a center, dividing a grid in an xoy plane at a certain interval, and taking positions of all grid nodes as an initial model set; S32, calculating an objective function value of a model in the initial model set; S33, selecting a model with a minimum objective function value as a final initial model.

3. The method of claim 1, wherein the motion- alternating magnetizable body is positioned in a magnetic field of a magnetic resonance imaging system. The specific steps of calculating the updating step length by using the parabolic fitting method in S5 comprise: S51, set step size a0=0, calculate F(a0)=F(m i + a0p i ), where i is the current iteration number, p i is the model update amount; S52, set step length wherein is the gradient of the objective function, n is the number of data, and γ is a small positive number -4 ; S53, calculate the objective function value F(a1) = F(m i + a1p i ) and its partial derivative F'(a1); S54, if Ф(α1)>Ф(α0) or Ф'(α1)>0 is not established, turning to S3, if established, turning to S6; S55, set a2 = 2a1, calculate the objective function value F(a2) = F(m i + a2p i ) and its partial derivative F'(a2); S56, if Ф(α2)≤Ф(α1) or Ф'(α2)<0 is not established, turning to S5, if established, turning to S7; S57, the parabola Φ(α) = aα is determined by three points (α0, Φ(α0)), (α1, Φ(α1)) and (α2, Φ(α2)) 2 + bα + c, and the step factor is α = -b / (2a). i + bα + c, and the step factor is α = -b / (2a).

4. The method of claim 1, wherein the motion- alternating magnetizable body is positioned in a magnetic field. The method for updating the velocity vector based on the position vector in S7 adopts a polynomial fitting method to fit velocity vectors at different times to reduce velocity abnormalities caused by position mutations at different times.

5. The method of claim 1, wherein the motion- alternating magnetizable body is positioned in a magnetic field. The method for updating the magnetic moment vector based on the analytical magnetic dipole magnetic field intensity data in S8 is: wherein is the magnetic moment vector, is the analytical magnetic dipole field strength data, is the coefficient matrix, and has a yx = a xy ; a zx = a xz ; a zy = a yz ; In the formula, (x, y, z) is a position vector output by inversion, R is a module of the position vector (x, y, z), and μ0 is a magnetic permeability in vacuum.

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