A three-dimensional positioning and magnetic moment direction evaluation method based on magnetic anomaly vector

Abstract

The present invention belongs to the field of magnetic exploration and is a three-dimensional positioning and magnetic moment direction evaluation method based on magnetic anomaly vectors. The method comprises the following steps: obtaining uniformly distributed two-dimensional magnetic vector data; performing convolution on the two-dimensional magnetic vector data using a two-dimensional orthogonal basis function of magnetic vectors with a preset height and truncated by a window to obtain all orthogonal basis coefficients of the two-dimensional orthogonal basis of the magnetic vectors; calculating the sum of all orthogonal basis coefficients of the two-dimensional orthogonal basis of the magnetic vectors and the sum of the squares of all orthogonal basis coefficients to obtain energy data of pseudo-l1 norms and pseudo-l2 norms of each magnetic anomaly component; fusing the energy data to obtain inversion energy and total energy; performing two-dimensional constant false alarm rate detection on the total energy to obtain the number of targets and the horizontal position of each target; performing parameter inversion of the vertical position and magnetic moment direction; and after evaluating the vertical position and magnetic moment direction of all targets, avoiding the situation where targets with small energy peak values ​​are missed due to large differences between energy peaks.

Description

Technical Field

[0001] The present invention belongs to the field of magnetic exploration, and specifically relates to a three-dimensional positioning and magnetic moment direction evaluation method based on magnetic anomaly vectors. Background Art

[0002] Magnetic anomalies refer to changes in the spatial distribution of the Earth's magnetic field caused by ferromagnetic targets. Magnetic anomaly detection (MAD) has become an attractive technique for passively detecting and locating ferromagnetic sources in pipelines, mines, and unexploded ordnance (UXO), due to its concealment, immunity to environmental conditions, and non-contact measurement. While scalar sensors offer low noise levels, they are not only expensive but also affected by the inclination and declination of the Earth's magnetic field when used for magnetic anomaly location, and they cannot fully utilize the magnetic anomaly information. Vector sensors, such as fluxgates, can fully utilize magnetic anomaly information and are inexpensive. Magnetic anomaly location and magnetic moment assessment provide valuable technical support for scientific research, resource development, and security monitoring in various fields, and their applications are widespread and of great value. Accurate magnetic target location and magnetic moment direction estimation are crucial for the successful removal of unexploded ordnance and precise vehicle navigation.

[0003] Currently, the location of magnetic anomalies and the assessment of magnetic moment direction primarily rely on dual sensors or even sensor arrays. However, increasing the number of sensors not only exponentially increases the cost of the magnetometer, but also increases operational difficulty and noise interference. The few existing methods for assessing target position and magnetic moment parameters based on a single magnetic sensor primarily rely on solving linear and nonlinear equations. For linear equation methods, linearizing nonlinear equations introduces method errors. For nonlinear equation methods, these methods currently primarily transform them into optimization problems and utilize intelligent algorithms for parameter search. However, these methods are highly sensitive to the number of parameters and noise, especially in multi-target situations, and also require prior information such as the number of targets. Summary of the Invention

[0004] The present invention provides a three-dimensional positioning and magnetic moment direction evaluation method based on magnetic anomaly vector, which solves the problems of high sensitivity to the number of parameters and noise and dependence on the number of targets in multi-target situations.

[0005] The present invention is achieved in this way:

[0006] A three-dimensional positioning and magnetic moment direction evaluation method based on magnetic anomaly vectors, the method comprising:

[0007] The one-dimensional survey line magnetic anomaly data obtained by the three-component magnetometer is pre-processed and then interpolated and gridded to obtain uniformly distributed two-dimensional magnetic vector data;

[0008] The two-dimensional magnetic vector data is convolved with a two-dimensional orthogonal basis function of a magnetic vector with a preset height and truncated by a window to obtain all orthogonal basis coefficients of the two-dimensional orthogonal basis of the magnetic vector;

[0009] Calculate the sum of all orthogonal basis coefficients and the sum of squares of all orthogonal basis coefficients of the two-dimensional orthogonal basis of the magnetic vector to obtain the pseudo-l1 norm and pseudo-l2 norm energy data of each magnetic anomaly component;

[0010] The energy data of the pseudo-l1 norm and pseudo-l2 norm of each magnetic anomaly component are fused to obtain the inversion energy and total energy;

[0011] Perform two-dimensional constant false alarm rate detection on the total energy to obtain the number of targets and the horizontal position of each target;

[0012] According to the horizontal position of the target, the inversion model composed of the inversion energy is used to invert the parameters of the vertical position and magnetic moment direction;

[0013] After evaluating the vertical position and magnetic moment direction of all targets, determine whether the evaluation of all targets is completed. If not, continue to repeat the parameter inversion of the vertical position and magnetic moment direction until the parameter inversion of all targets is completed.

[0014] Furthermore, all coefficients of the two-dimensional orthogonal basis of the magnetic vector are obtained, including:

[0015] The two-dimensional orthogonal basis function of the magnetic vector is expressed as follows,

[0016]

[0017] where f Bkl , k = x, y, z, l = 1, 2, 3 represents the orthogonal basis function of the preset height; x, y are horizontal coordinates; the prior information z is the preset height, and the two-dimensional orthogonal basis function of each magnetic vector meets the following orthogonality and standardization requirements:

[0018]

[0019] A window of preset size is used to intercept all two-dimensional orthogonal basis functions of magnetic vectors, so that each magnetic anomaly component is convolved with each two-dimensional orthogonal basis function of each magnetic vector to obtain the corresponding orthogonal basis coefficient a. Bkl (m,n);

[0020] The convolution operation is:

[0021]

[0022] Where m0 is the modulus of the magnetic moment vector; μ0 is the vacuum permeability; B kis the two-dimensional magnetic anomaly vector data; I and J represent the sliding window size, which is used to control the boundary of discrete numerical integration; Δx and Δy are the discrete integration intervals along the x-axis and y-axis respectively; m and n represent the horizontal and vertical coordinates of the orthogonal basis coefficients; x m:i ,y n:j The horizontal and vertical coordinates represent the magnetic anomaly components; x i ,y j Represents the horizontal and vertical coordinates of the two-dimensional orthogonal basis function of the magnetic vector.

[0023] Furthermore, the inversion energy is: E Inv =∑ k<x,y,z E k1 , E Inv Represents the inversion energy, the total energy is: E tot =∑ k<x,y,z E k2 , E tot represents the total energy;

[0024] E k1 Indicates magnetic anomaly B k The pseudo-l1 norm energy of the component, E k2 Indicates magnetic anomaly B k Pseudo-l2-norm energy of the component.

[0025] Further, k is the category of magnetic anomaly component, a Bkl with a Bkl (m,n) have the same meaning.

[0026] Furthermore, a two-dimensional constant false alarm rate detection is performed on the total energy to obtain the number of targets and the horizontal position of each target. The calculation process includes:

[0027] N R =N TR +N GR

[0028] N C =N TC +N GC

[0029] N=(2N R +1)(2N C +1)-(2N GR +1)(2N GC +1)

[0030]

[0031]

[0032] if E tot >T(x m ,yn )→X s ,Y s =argmax E tot

[0033] Among them, N TR and N TC are the number of rows and columns of training units respectively; N GR and N GC are the number of rows and columns of protection units respectively; N is the number of training units; P FA is the probability of false alarm; E(x m:i ,y n:j ) indicates the coordinate is x m:i ,y n:j energy, T is the dynamic threshold; θ is the threshold factor; N R is the sum of the number of rows of training units and protection units; N C is the sum of the number of columns of training units and protection units; x m ,y n The horizontal and vertical coordinates represent the dynamic threshold; X s ,Y s is the horizontal position of the target obtained, and the subscript s is the serial number of the evaluation target.

[0034] Furthermore, according to the horizontal position of the target, the inversion model composed of the inversion energy is used to perform parameter inversion of the vertical position and magnetic moment direction, specifically including:

[0035] The inversion model of the inversion energy composition is:

[0036]

[0037] Z s ,I s ,D s =argmin LS s

[0038] Among them, LS s is the loss function value, Z s is the vertical position of the inversion, I s is the inverted magnetic moment inclination, D s is the inverted magnetic moment deflection, and the subscript s is the serial number of the evaluation target; is the estimated inversion energy; P and Q are used to control the size of the matching window, p and q are index subscripts, x s:p ,y s:q are the coordinates of the inverted energy and the estimated inverted energy;

[0039] The horizontal position of the target is substituted into the inversion model composed of inversion energy to perform parameter inversion of the vertical position and magnetic moment direction.

[0040] Compared with the prior art, the present invention has the following beneficial effects:

[0041] Compared to fixed thresholds, the method of the present invention utilizes two-dimensional constant false alarm rate detection, eliminating the need to set any thresholds. This largely avoids the situation where targets with smaller energy peaks are missed due to large differences between energy peaks. The pseudo-L2 norm of the orthogonal basis coefficients is used to construct the total energy, enhancing noise suppression and improving horizontal positioning accuracy. The pseudo-L1 norm of the orthogonal basis coefficients is used to construct the inverted energy, avoiding the spatial symmetry of the total energy, eliminating the multi-solution problem of the optimized inversion, and improving the inversion accuracy. Compared to existing methods that directly utilize magnetic anomalies to construct optimization functions and perform parameter optimization inversion, the method of the present invention not only requires no prior information on the number of magnetic targets, but also eliminates the need for iterative confirmation of the number of magnetic targets, reduces the number of optimization parameters, reduces sensitivity to noise, and improves the accuracy and efficiency of the inversion. Compared to existing methods of using two-dimensional orthogonal basis methods for the total magnetic field, the method of the present invention is insensitive to magnetic moment direction, produces rich inversion results, and has high inversion accuracy and a low false alarm rate. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 A flowchart of a method provided by an embodiment of the present invention;

[0043] Figure 2 The two-dimensional orthogonal basis surface of magnetic vectors and its contour map provided by the embodiment of the present invention, (a) f1 = f Bx1 , (b)f2=f By1 , (c)f3=f Bx2 =f By2 ,(d)f4=f Bz2 =f By3 , (e)f5=f Bx3 =f Bz3 ,(f)f6=f Bz1 ;

[0044] Figure 3 Two-dimensional magnetic anomaly (a)B generated by simulation according to an embodiment of the present invention x Component, (b)B y Component and (c)B z Quantity;

[0045] Figure 4 (a) Energy B of the three components of magnetic anomaly in the simulation experiment provided by the embodiment of the present invention x2 (b) Energy B y2 and (c) energy B z2 ;

[0046] Figure 5 The total energy surface of magnetic anomaly and its contour lines of the simulation experiment provided by the embodiment of the present invention;

[0047] Figure 6 A diagram showing the results of a two-dimensional constant false alarm rate detection of the total energy of magnetic anomalies in a simulation experiment provided by an embodiment of the present invention;

[0048] Figure 7 Two-dimensional magnetic anomaly of field data provided by the embodiment of the present invention (a) B x Component, (b)B y Component and (c)B z Quantity;

[0049] Figure 8 The energy B of the three components of magnetic anomaly in field data provided by the embodiment of the present invention is (a) x2 (b) Energy B y2 ) and (c) energy B z2 ;

[0050] Figure 9 The magnetic anomaly total energy surface and its contour lines of field data provided by the embodiment of the present invention;

[0051] Figure 10 An embodiment of the present invention provides a two-dimensional constant false alarm rate detection result diagram of the total energy of magnetic anomalies using field data. DETAILED DESCRIPTION

[0052] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the 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.

[0053] See also Figure 1 As shown, a three-dimensional positioning and magnetic moment direction evaluation method based on magnetic anomaly vector includes:

[0054] The one-dimensional survey line magnetic anomaly data obtained by the three-component magnetometer is pre-processed and then interpolated and gridded to obtain uniformly distributed two-dimensional magnetic vector data;

[0055] The two-dimensional magnetic vector data is convolved with a two-dimensional orthogonal basis function of a magnetic vector with a preset height and truncated by a window to obtain all orthogonal basis coefficients of the two-dimensional orthogonal basis of the magnetic vector;

[0056] Calculate the sum of all orthogonal basis coefficients and the sum of squares of all orthogonal basis coefficients of the two-dimensional orthogonal basis of the magnetic vector to obtain the pseudo-l1 norm and pseudo-l2 norm energy data of each magnetic anomaly component;

[0057] Fusing the energy of each magnetic anomaly component to obtain inversion energy and total energy;

[0058] Perform two-dimensional constant false alarm rate detection on the total energy to obtain the number of targets and the horizontal position of each target;

[0059] According to the horizontal position of the target, the inversion model composed of the inversion energy is used to invert the parameters of the vertical position and magnetic moment direction;

[0060] After evaluating the vertical position and magnetic moment direction of all targets, determine whether the evaluation of all targets is completed. If not, continue to repeat the parameter inversion of the vertical position and magnetic moment direction until the parameter inversion of all targets is completed.

[0061] Among them, in the embodiment of the present invention, a strapdown MAD device composed of a fluxgate sensor and an inertial navigation system is used to acquire one-dimensional survey line magnetic anomaly data, attitude data, and coordinate data. Specifically, after determining the survey area, the device is moved along several parallel survey lines for continuous measurement. The strapdown MAD device collects magnetic anomaly vectors, attitude data, and coordinate data in a continuous sampling manner (the sampling frequency is set to 10Hz). Then, the obtained one-dimensional survey line magnetic anomaly data is subjected to sensor error correction, misalignment error correction, attitude restoration, and detrending operations. The interpolation method selects the linear interpolation method; after interpolation and gridding, the intervals of the data in both directions along the survey line and perpendicular to the survey line are 0.1m. Two-dimensional magnetic vector data that does not contain the geomagnetic field in the geographic coordinate system is obtained.

[0062] The two-dimensional magnetic vector data is convolved with a two-dimensional orthogonal basis function of a preset height and truncated by a window to obtain all the orthogonal basis coefficients of the two-dimensional orthogonal basis of the magnetic vector. Including:

[0063] The two-dimensional orthogonal basis function of the magnetic vector is expressed as follows,

[0064]

[0065] where f Bkl , k = x, y, z, l = 1, 2, 3 represents the orthogonal basis function of the preset height; x, y are horizontal coordinates; the prior information z is the preset height, and the two-dimensional orthogonal basis function of each magnetic vector meets the following orthogonality and standardization requirements:

[0066]

[0067] A window of preset size is used to intercept all two-dimensional orthogonal basis functions of magnetic vectors, so that each magnetic anomaly component is convolved with each two-dimensional orthogonal basis function of each magnetic vector to obtain the corresponding orthogonal basis coefficient a. Bkl (m,n);

[0068] In this embodiment, the truncation window is set to a square with a side length of 5m, that is, the side length of the sliding window is set to 5m (2I=2J=5m), and the window is used to truncate all two-dimensional orthogonal basis functions of the magnetic vector.

[0069] The convolution operation is:

[0070]

[0071] Where m0 is the modulus of the magnetic moment vector; μ0 is the vacuum permeability; B k is the two-dimensional magnetic anomaly vector data; I and J represent the sliding window size, which is used to control the boundary of discrete numerical integration; Δx and Δy are the discrete integration intervals along the x-axis and y-axis respectively; m and n represent the horizontal and vertical coordinates of the orthogonal basis coefficients; x m:i ,y n:j The horizontal and vertical coordinates represent the magnetic anomaly components; x i ,y j Represents the horizontal and vertical coordinates of the two-dimensional orthogonal basis function of the magnetic vector.

[0072] In this embodiment, the preset height z=1m, and the surface and contour map of the two-dimensional orthogonal basis function (OBF) of the magnetic vector with the x (west-east direction) and y (north-south direction) range of 10m are calculated, as shown in FIG. Figure 2 shown. Figure 2 The OBF f1 in (a) is the basis function f Bx1 The surface diagram of Figure 2 (b) OBF f2 is the basis function f By1 The surface diagram of Figure 2 The OBF f3 in (c) is the two-dimensional orthogonal basis function f of the magnetic vector Bx2 and f By2 The surface diagram of Figure 2 The OBF f4 in (d) is the two-dimensional orthogonal basis function f of the magnetic vector Bz2 and f By3 The surface diagram of Figure 2 (e)OBF f5 is the two-dimensional orthogonal basis function f of the magnetic vector Bx3 and f Bz3 The surface diagram of Figure 2 The OBF f6 of (f) is the two-dimensional orthogonal basis function of the magnetic vector f Bz1 Surface plot of . Figure 2 (a) and Figure 2 (b) in the figure shows that the rotation of x and y conforms to the law of the two-dimensional orthogonal basis function of the magnetic vector. Figure 2 (d) and Figure 2 (e) in the figure also shows the rotation of x and y, which conforms to the law of the two-dimensional orthogonal basis function of the magnetic vector.

[0073] The sum of all orthogonal basis coefficients and the sum of squares of all orthogonal basis coefficients of the two-dimensional orthogonal basis of the magnetic vector are calculated to obtain the pseudo-l1 norm and pseudo-l2 norm energy data of each magnetic anomaly component. The energy data includes: k is the category of magnetic anomaly component, Ek1 Indicates magnetic anomaly B k The pseudo-l1 norm energy of the component, E k2 Indicates magnetic anomaly B k Pseudo-l2-norm energy of the component.

[0074] The energy of each magnetic anomaly component is integrated to obtain the inversion energy and the total energy. In essence, the sum of all orthogonal basis coefficients (pseudo-l1 norm) and the sum of the squares of all orthogonal basis coefficients (pseudo-l2 norm) are calculated to obtain the inversion energy E. Inv and total energy E tot , and finally, energy normalization is performed separately. Normalization of total energy facilitates comparative analysis during multi-target inversion; normalization of inversion energy can eliminate a magnetic moment modulus parameter, thus significantly improving inversion accuracy.

[0075] E Inv =∑ k<x,y,z E k1

[0076]

[0077] Perform two-dimensional constant false alarm rate detection on the total energy to obtain the number of targets and the horizontal position of each target. The calculation process includes:

[0078] N R =N TR +N GR

[0079] N C =N TC +N GC

[0080] N=(2N R +1)(2N C +1)-(2N GR +1)(2N GC +1)

[0081]

[0082] if E tot >T(x m ,y n )→X s ,Y s =argmax E tot

[0083] Among them, N TR and N TC are the number of rows and columns of training units respectively; N GR and N GC are the number of rows and columns of protection units respectively; N is the number of training units; PFA is the probability of false alarm; E(x m:i ,y n:j ) indicates the coordinate is x m:i ,y n:j energy, T is the dynamic threshold; θ is the threshold factor; N R is the sum of the number of rows of training units and protection units; N C is the sum of the number of columns of training units and protection units; x m ,y n The horizontal and vertical coordinates represent the dynamic threshold; X s ,Y s is the horizontal position of the target obtained, and the subscript s is the evaluation target number.

[0084] By performing a two-dimensional constant false alarm rate test on the normalized total energy, the dynamic threshold of the entire measurement area is obtained. Then, the total energy and the dynamic threshold are compared. The areas with total energy higher than the dynamic threshold are considered to contain targets, and the number of these areas is used as the evaluation value of the target number. The horizontal coordinate of the energy maximum in each area is used as the evaluation value of the horizontal position of the corresponding target.

[0085] The number of rows in the training unit N TR and the number of columns N TC Set to 40 (4m) points; the number of rows of protection units N GR and the number of columns N GC Set to 10 (1m) points; N is the number of training units; set the probability of false alarm P FA is 0.01; E(x m:i ,y n:j ) indicates the coordinate is x m:i ,y n:j Energy, T represents the dynamic threshold; X s ,Y s is the obtained target horizontal position, and the subscript s is the sequence number of the evaluation target.

[0086] According to the horizontal position of the target, the inversion model composed of the inversion energy is used to invert the parameters of the vertical position and magnetic moment direction, including:

[0087] The inversion model of the inversion energy composition is:

[0088]

[0089] Z s ,I s ,D s =argmin LS s

[0090] Among them, LS s is the loss function value, Z sis the vertical position of the inversion, I s is the inverted magnetic moment inclination, D s is the inverted magnetic moment deflection, and the subscript s is the serial number of the evaluation target; is the estimated inversion energy; P and Q are used to control the size of the matching window, p and q are index subscripts, x s:p ,y s:q are the coordinates of the inverted energy and the estimated inverted energy;

[0091] The horizontal position of the target is substituted into the inversion model composed of inversion energy to perform parameter inversion of the vertical position and magnetic moment direction.

[0092] In order to improve the inversion accuracy and computational efficiency, it is necessary to select a matching window of appropriate size when performing energy matching. The selection principle aims to maximize the inclusion of energy information of a specific target while minimizing interference from other targets. In this embodiment, a square window with a side length of 3m (2P=2Q=3m) is selected as the matching window, and the horizontal position of the target is used as the center position of the matching window. In a multi-target scenario, the horizontal position of each target is also used as the center position of the matching window. When the estimated inversion energy is closest to the actual inversion energy, that is, when the loss function value is minimized, the inversion results of the vertical position and magnetic moment direction parameters are obtained.

[0093] In order to verify the effectiveness and practicality of the present invention, multi-objective multi-parameter inversion simulation and field experiments were carried out as a demonstration.

[0094] Simulation experiment:

[0095] The measurement line spacing is set to 0.5m, and the length is 30m, with a total of 41 measurement lines, forming a measurement area of ​​20×30m 2 ; The noise level is Gaussian white noise with a standard deviation of 20nT; the detection plane is 1m above the ground. Taking the southwest corner of the survey area as the coordinate origin, 6 magnetic dipole targets are randomly generated in the survey area. The preset parameters (X, Y, Z, I, D) of targets 1 to 6 are (4m, 4m, 0.3m, -30°, -170°), (10m, 14m, 0.5m, 58°, 86°), (12m, 6m, 0.5m, 70°, 176°), (14m, 5m, 0.6m, 60°, 0°), (20m, 14m, 0.4m, 30°, -3°) and (24m, 8m, 0.2m, 0°, 45°). In order to verify that the method of the present invention is not affected by the magnetic moment modulus and to ensure that the generated magnetic anomaly data has almost the same signal-to-noise ratio, the magnetic moment modulus of the calculation end is set to 1A〃m 2 The estimated end moment modulus range is set to [1-100A"m 2 ].

[0096] According to the above conditions, after linear interpolation and gridding, the grid size of the data is 0.1m, and the three components of the calculated magnetic anomaly (Bx, By, Bz) are generated as follows: Figure 3 As shown, x (west-east) and y (north-south), can be obtained from Figure 3 (a) Figure 3 (b) It is found that the magnetic anomaly signal is almost drowned by the noise. Figure 3 A weak magnetic anomaly signal can be observed in the Bz component in (c), but its shape is also severely distorted by noise.

[0097] The sliding window side length is set to 5m, and the corresponding magnetic anomaly component is used to perform a two-dimensional convolution operation with the corresponding component's magnetic vector two-dimensional orthogonal basis function to obtain the corresponding orthogonal basis coefficients. Then, the pseudo-l1 norm and pseudo-l2 norm of the orthogonal basis coefficients of each magnetic vector two-dimensional orthogonal basis are calculated to obtain the energy data of the corresponding component. The pseudo-l2 norm energy data of the three components of the magnetic anomaly are as follows: Figure 4 As shown in the figure, it can be seen that compared with the magnetic anomaly component, the signal-to-noise ratio in the energy domain is significantly improved, and the magnetic target is very easy to detect. Figure 4 (a) and Figure 4 (b) Energy E x2 and energy E y2 The size of the energy E y2 The two targets with smaller energy in the middle target have energy E x2 In contrast, the Figure 4 (c) Energy E z2 The energy peak values ​​of each target are slightly different. The peak values ​​of these three components are used to locate the horizontal position, and it is found that the energy E z2 Higher-precision positioning can also be achieved. However, this paper only illustrates the highest-precision positioning method, which uses the fusion energy of these three components to determine horizontal position. The pseudo-l1-norm energy maps of the three components of the magnetic anomaly are similar to the pseudo-l2-norm energy maps and are not shown here.

[0098] Next, energy fusion is performed to calculate the three pseudo-l1 norm component energies (E x1 、E y1 and E z1 ) and obtain the inversion energy E Inv , calculate the three pseudo l2 norm component energies (E x2 、E y2 and E z2 ) and obtain the total energy E tot After normalization, the total energy surface and its contour lines are as follows Figure 5 As shown, it can be seen that energy fusion reduces the difference between the energy maxima of the magnetic dipoles and improves the regularity of their energy shapes, thereby reducing the false alarm rate and improving the accuracy of horizontal positioning. Figure 5Six energy peaks can be easily identified, including two adjacent peaks.

[0099] Then the total energy is tested with a two-dimensional constant false alarm rate. The test results are as follows: Figure 6 As shown in the figure, six energy peaks exceeding the dynamic threshold are detected, indicating that six targets are detected. The horizontal coordinates of these six regional energy peaks are then obtained, indicating that the six targets are horizontally located. The horizontal positioning results (X, Y) for these six targets are (4.00m, 4.00m), (10.10m, 14.00m), (12.10m, 6.00m), (13.90m, 5.10m), (20.00m, 14.00m), and (24.10m, 8.00m).

[0100] The horizontal position results of the aforementioned targets were sequentially substituted into the inversion model constructed from the inversion energy. A 3-meter square window was selected as the matching window. Then, an intelligent algorithm was used to perform parameter inversion, repeated six times for the number of targets. The inversion results for the three-dimensional parameters (Z / m, I / °, D / °) of the six targets were obtained: (0.32 m, -39.71°, -191.88°), (0.32 m, 63.76°, 98.21°), (0.65 m, 59.22°, 195.26°), (0.68 m, 49.10°, -26.04°), (0.43 m, 35.40°, -7.59°), and (0.22 m, -0.82°, 41.55°). In this 5D parameter inversion simulation, the maximum inversion errors for the five parameters (X / m, Y / m, Z / m, I / °, and D / °) were (0.10 m, 0.10 m, 0.18 m, 10.9°, and 26.04°), respectively. The fourth target had the largest errors in magnetic dip and declination, at 10.9° and 26.04°, respectively. Considering the proximity of the target, the high noise level, and the lack of any filtering, the inversion accuracy is still satisfactory.

[0101] Field experiment:

[0102] The survey line in the field experiment was east-west, 20m long, with a line spacing of 0.5m, and the survey area was 20×20m. 2 The detection plane is 1.1m above the ground. Taking the ground at the southwest corner of the survey area as the coordinate origin, three iron pipes of the same size and material are randomly placed in the survey area. The outer diameter of the iron pipes is 10cm, the thickness is 3mm, and the length is 30cm. Their three-dimensional coordinates are (7.80m, 9.62m, 0.05m), (13.76m, 12.96m, -0.05m), and (13.95m, 5.95m, 0.05m).

[0103] First, a strapdown MAD system consisting of a fluxgate sensor and an inertial navigation system (INS) is used to acquire one-dimensional line magnetic anomaly data, attitude data, and position data. The magnetic anomaly vector data is then corrected for sensor errors, misalignment errors, attitude restoration, and detrending using Euler angle data from the INS. This yields one-dimensional line magnetic anomaly data in a geographic coordinate system that excludes the geomagnetic field. This one-dimensional line magnetic anomaly data is then linearly interpolated and gridded to obtain two-dimensional magnetic vector data, or three-component two-dimensional magnetic anomaly data.

[0104] After the above processing, the two-dimensional magnetic vector data surface map and contour map with a grid size of 0.1m are obtained as shown in the figure. Figure 7 As shown. It can be seen that the noise is large. Figure 7 (a) Figure 7 The three components of the magnetic anomaly in (b) are almost drowned by the noise, only Figure 7 (c)E z The component can distinguish weak magnetic anomaly signals.

[0105] The sliding window side length is set to 5m, and a two-dimensional convolution operation is performed on each magnetic anomaly component and the two-dimensional orthogonal basis function of the magnetic vector in each group to obtain the corresponding orthogonal basis coefficients. Then, the pseudo-l1 norm and pseudo-l2 norm of the orthogonal basis coefficients of the two-dimensional orthogonal basis of each magnetic vector are calculated to obtain the energy data of the corresponding component. The pseudo-l2 norm energy of the three components of the magnetic anomaly is as follows: Figure 8 As shown, Figure 8 (a) Figure 8 (b) and Figure 8 In (c), we can see that the signal-to-noise ratio of the signal in the energy domain is high, and the signal is easy to be detected.

[0106] Then energy fusion is performed to calculate the three pseudo l1 norm component energies (E x1 、E y1 and E z1 ) and obtain the inversion energy E Inv , calculate the three pseudo l2 norm component energies (E x2 、E y2 and E z2 ) and obtain the total energy E tot After normalization, the total energy surface and its contour map are as follows: Figure 9 As shown, it can be seen that the signal-to-noise ratio of the total energy is higher, and the magnetic target is more easily detected.

[0107] Then the total energy is tested with a two-dimensional constant false alarm rate. The test results are as follows: Figure 10As shown, there are three energy peaks exceeding the dynamic threshold, indicating that three targets are detected. The coordinates of these three peaks are then obtained, indicating the horizontal positioning of the three targets. The horizontal positioning (X, Y) results for the three targets are (7.70m, 9.25m), (13.45m, 13.05m), and (14.00m, 5.85m), respectively.

[0108] The above horizontal positioning results are substituted into the inversion model in turn, a square window with a side length of 3m is selected as the matching window, and then three independent parameter optimization inversions are performed using the ocean predator algorithm. The inversion results of the three-dimensional parameters (Z / m, I / °, D / °) of the three targets obtained are (0.14m, 47.57°, -68.54°), (-0.24m, 43.50°, -147.95°) and (-0.12m, 28.39°, 68.26°). The inversion errors of the three-dimensional positions of the three targets in this field experiment are (0.10m, 0.37m, 0.09m), (0.31m, 0.09m, 0.19m) and (0.05m, 0.10m, 0.17m) respectively. Considering such large colored noise conditions, these results are acceptable, which verifies the effectiveness of the method of the present invention and its powerful noise suppression ability.

[0109] 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 in the scope of protection of the present invention.

Claims

1. A three-dimensional positioning and magnetic moment direction evaluation method based on magnetic anomaly vector, characterized in that: The method includes: The one-dimensional survey line magnetic anomaly data obtained by the three-component magnetometer is pre-processed and then interpolated and gridded to obtain uniformly distributed two-dimensional magnetic vector data; The two-dimensional magnetic vector data is convolved with a two-dimensional orthogonal basis function of a magnetic vector with a preset height and truncated by a window to obtain all orthogonal basis coefficients of the two-dimensional orthogonal basis of the magnetic vector; Calculate the sum of all orthogonal basis coefficients and the sum of squares of all orthogonal basis coefficients of the two-dimensional orthogonal basis of the magnetic vector to obtain the pseudo-magnetic anomaly components. Norm and Pseudo Energy data of norm; Pseudo-analysis of each magnetic anomaly component Norm and Pseudo The fusion of norm energy data to obtain inversion energy and total energy; Perform two-dimensional constant false alarm rate detection on the total energy to obtain the number of targets and the horizontal position of each target; According to the horizontal position of the target, the inversion model composed of the inversion energy is used to invert the parameters of the vertical position and magnetic moment direction; After evaluating the vertical position and magnetic moment direction of all targets, determine whether the evaluation of all targets is completed. If not, continue to repeat the parameter inversion of the vertical position and magnetic moment direction until the parameter inversion of all targets is completed.

2. The method for three-dimensional positioning and magnetic moment direction evaluation based on magnetic anomaly vector according to claim 1, characterized in that: Obtain all coefficients of the two-dimensional orthogonal basis of magnetic vectors, including: The two-dimensional orthogonal basis function of the magnetic vector is expressed as follows, ， in , , Expressed as orthogonal basis functions of preset height; is the horizontal coordinate; prior information To preset the height, the two-dimensional orthogonal basis functions of each magnetic vector meet the following orthogonality and standardization requirements: ， Use a preset size window to intercept all the two-dimensional orthogonal basis functions of the magnetic vector, so that each magnetic anomaly component is convolved with each of the two-dimensional orthogonal basis functions of the magnetic vector to obtain the corresponding orthogonal basis coefficients. ; The convolution operation is: ， in, is the modulus of the magnetic moment vector; is the vacuum permeability; It is two-dimensional magnetic anomaly vector data; and Indicates the sliding window size, which is used to control the boundary of discrete numerical integration; and Along Axis and Discrete integration intervals for the axis; The horizontal and vertical coordinates represent the orthogonal basis coefficients; The horizontal and vertical coordinates represent the magnetic anomaly components; Represents the horizontal and vertical coordinates of the two-dimensional orthogonal basis function of the magnetic vector.

3. The method for three-dimensional positioning and magnetic moment direction evaluation based on magnetic anomaly vector according to claim 2, characterized in that: Perform two-dimensional constant false alarm rate detection on the total energy to obtain the number of targets and the horizontal position of each target. The calculation process includes: ， ， ， ， ， in, and are the number of rows and columns of training units respectively; and are the number of rows and columns of protection units respectively; is the number of training units; is the probability of false alarm; The coordinates are energy, is the dynamic threshold; is the threshold factor; is the sum of the number of rows of training units and protection units; is the sum of the number of columns of training units and protection units; The horizontal and vertical coordinates represent the dynamic threshold; is the horizontal position of the target, subscript s is the serial number of the target to be evaluated, Represents the total energy.

4. The method for three-dimensional positioning and magnetic moment direction evaluation based on magnetic anomaly vector according to claim 3, characterized in that: According to the horizontal position of the target, the inversion model composed of the inversion energy is used to invert the parameters of the vertical position and magnetic moment direction, including: The inversion model of the inversion energy composition is: ， ， in, is the loss function value, is the vertical position of the inversion, is the inverted magnetic moment inclination, is the inverted magnetic moment deflection, and the subscript s is the serial number of the evaluation target; is the estimated inversion energy; P and Q are used to control the size of the matching window, p and q are index subscripts, are the coordinates of the inverted energy and the estimated inverted energy; The horizontal position of the target is substituted into the inversion model composed of inversion energy to perform parameter inversion of the vertical position and magnetic moment direction.

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