Magnetic anomaly detection method based on tensor invariants and improved orthogonal basis function decomposition

Abstract

The invention discloses a magnetic anomaly detection method based on tensor invariants and improved orthogonal basis function decomposition. According to the method, a detection platform composed of four fluxgate sensors which are arranged in a cross shape is used, 12 component signals of magnetic signals are collected, a magnetic induction intensity change matrix is obtained according to differential signals among the sensors, five independent magnetic gradient tensor elements are obtained based on passivity and non-rotation of a magnetic field, wavelet packet decomposition and reconstruction are carried out on the five elements, and the magnetic gradient tensor elements are obtained. Band-pass filtering is achieved to remove noise and trend terms, and then magnetic gradient tensor invariants are obtained through combination. Variational modal extraction is carried out on the tensor elements to obtain an expected modal of the tensor elements, the change of the magnetic induction intensity is projected to the geomagnetic direction, and six composition components are obtained according to tensor invariants; variational mode extraction is carried out on seven primary functions in the full magnetic gradient orthogonal basis decomposition method, then Schmidt orthogonalization and standardization processing are carried out, and seven improved orthogonal primary functions are obtained. The method comprises the following steps: firstly, projecting six components to a geomagnetic direction, then decomposing the six components projected to the geomagnetic direction by using an improved orthogonal basis function to obtain six energy coefficients, calculating the sum of squares of the energy coefficients, multiplying the sum of squares of the energy coefficients by the square of a tensor invariant to serve as a comprehensive anomaly evaluation index, and finally judging whether magnetic anomaly exists in a signal to be detected according to the comprehensive anomaly evaluation index. According to the method, magnetic anomaly detection can still be realized in an environment with an extremely low signal-to-noise ratio.

Description

Technical Field

[0001] The invention relates to signal processing technologies such as variational mode extraction and orthogonal basis function decomposition, and belongs to the field of magnetic anomaly signal detection. In particular, the invention relates to a magnetic anomaly detection method based on tensor invariants and improved orthogonal basis function decomposition. Background Art

[0002] The Earth's magnetic field changes slowly in spatial distribution. The magnetic field of ferromagnetic objects will change the spatial distribution of the Earth's magnetic field, thus producing magnetic anomalies. Magnetic sensors can be used to capture magnetic anomaly signals and detect, locate and identify magnetic targets. Since the change of the magnetic field is not affected by non-ferromagnetic media such as soil and smoke, magnetic anomaly detection is widely used in geological exploration, unexploded bomb detection, underwater detection, regional intrusion detection and other fields.

[0003] At present, the method widely used in magnetic anomaly detection is the orthogonal basis function decomposition method based on the magnetic anomaly waveform characteristics, such as the full magnetic gradient orthogonal basis function detection method. When the signal-to-noise ratio of the signal to be detected is low, the signal needs to be filtered and denoised first. The denoising process may change the waveform characteristics of the original abnormal signal. When the theoretical orthogonal basis function is directly used for decomposition, the incomplete matching of the basis function and the magnetic anomaly waveform may make the signal-to-noise ratio of the detection output signal low, resulting in detection failure.

[0004] In view of this problem, the present invention discloses a magnetic anomaly detection method based on tensor invariant and improved orthogonal basis function decomposition, which uses wavelet packet filtering and variational mode extraction (VME) algorithm to pre-process the detection signal, and then uses the VME algorithm with the same parameters to improve the 7 basis functions in the full magnetic gradient decomposition method, and then comprehensively utilizes the tensor invariant characteristics of the magnetic gradient signal to effectively improve the signal-to-noise ratio of the detection output signal. This method can still determine whether there is a magnetic anomaly in the signal to be detected in an environment with a low signal-to-noise ratio of the magnetic signal. Summary of the invention

[0005] The purpose of the present invention is to provide a magnetic anomaly detection method based on tensor invariants and improved orthogonal basis function decomposition, so as to improve the signal-to-noise ratio of the detection output signal and realize the detection of weak magnetic anomaly signals.

[0006] To achieve the above object, the present invention provides a magnetic anomaly detection method based on tensor invariants and improved orthogonal basis function decomposition, comprising the following steps:

[0007] Step 1: Use four three-axis fluxgate sensors to form a cross-shaped detection platform with equal spacing, synchronously collect 12 component signals of the four sensors in the x, y, and z directions, calculate the differential signal between the four sensors, and obtain five independent magnetic gradient signals G xx , G xy , Gxz , G yy , G yz , and its calculation formula is:

[0008]

[0009] Where d is the distance between the center points of two sensors on the same axis, g is S1x represents the magnetic signal component of the S1 sensor in the x direction, g S2y It represents the magnetic signal component of the S2 sensor in the y direction, and the other symbols are similar;

[0010] Step 2: The five magnetic gradient signals G obtained in step 1 xx , G xy , G xz , G yy , G yz Perform wavelet packet decomposition, retain the sub-band containing magnetic anomaly information, clear other sub-bands, and then reconstruct to obtain the magnetic gradient signal G' with noise and trend terms removed. xx , G' xy , G' xz , G' yy , G' yz ;

[0011] Step 3: Use the five de-noised magnetic gradient signals obtained in step 2 to calculate the tensor invariant I. The calculation formula is:

[0012] I=G' xx G' xy +G' yy G' zz +G' xx G' zz -G' xy 2 -G' xz 2 -G' yz 2

[0013] Step 4: Calculate the five de-noised magnetic gradient signals G' obtained in step 2 xx , G' xy , G' xz , G' yy , G' yz Variational mode extraction (VME) is performed to obtain five desired modes B xx , B xy , B xz , B yy , B yz ;

[0014] Step 5: Transpose the five desired modes obtained in step 4 and project them to the geomagnetic direction according to the magnetic angle relationship to obtain six projection elements S Gxx , S Gxy , S Gxz , S Gyy , S Gyz , S Gzz , and its calculation formula is:

[0015]

[0016] In the formula, o, p, and q are the unit vectors of the geomagnetic field vector projected on the x, y, and z axes respectively. The calculation formula is:

[0017] o=cos(I)cos(D)

[0018] p=cos(I)sin(D)

[0019] q=sin(I)

[0020] Where I and D are the geomagnetic field inclination and declination of the detection point respectively;

[0021] Step 6: Use VME to improve the full magnetic gradient orthogonal basis function decomposition method. The method is: use the VME parameters in step 4 to improve the 7 orthogonal basis functions h in the full magnetic gradient orthogonal basis function decomposition method. j (j=1-7) to perform VME, and obtain the corresponding 7 expected modes. Then, the 7 expected modes are subjected to Schmidt orthogonal and normalized processing to obtain 7 improved standard orthogonal basis functions f j (j=1-7);

[0022] Step 7: Use the 7 improved orthogonal basis functions f obtained in step 6 j (j=1-7), respectively for the six projection elements S obtained in step 5 Gxx , S Gxy , S Gxz , S Gyy , S Gyz , S Gzz Perform orthogonal basis decomposition to obtain 6 decomposition energy coefficients k i (i=xx,xy,xz,yy,yz,zz), where the formula for orthogonal basis decomposition is:

[0023]

[0024] In the formula Where n is the number of sampling points, n = 1, 2, ..., N, v is the speed of the magnetic target, f s is the sampling frequency, CPA is the shortest distance from the sensor to the moving trajectory of the magnetic target;

[0025] Step 8: Calculate the 6 energy coefficients k obtained in step 7 i The sum of the squares of (i=xx,xy,xz,yy,yz,zz) is calculated and multiplied by the square of the tensor invariant I obtained in step 3 to obtain a magnetic anomaly evaluation index E, which is calculated as follows:

[0026]

[0027] Step 9: A dynamic threshold is set according to the constant false alarm detection principle. When the magnetic anomaly evaluation index E is greater than the threshold, it is determined that there is a magnetic anomaly in the signal to be detected; otherwise, it is determined that there is no magnetic anomaly in the signal to be detected.

[0028] In the above steps, the specific steps of obtaining the desired mode using the variational mode extraction (VME) method described in step 4 and step 5 are:

[0029] Step 4-1: Let the signal to be extracted be f o (t) is given by the expected mode f d (t) and the residual signal f r (t) composition, that is: f o (t) = f d (t)+f r (t)

[0030] Step 4-2: Establish a combination of quadratic penalty terms and Lagrange multipliers, and the calculation formula is:

[0031]

[0032] Where λ is the Lagrange multiplier, ω is the frequency, α represents the balance parameter of the two penalty functions, and ω d represents the center frequency of the desired mode, represents f d The Fourier transform of (t), and the other symbols are similar, where The frequency response function of the filter is:

[0033]

[0034] Step 4-3: Set the initial expected mode Initial expected center frequency Penalty parameter α, convergence accuracy ε, maximum number of iterations N, update parameter τ of λ, and initialize the number of iterations n to 1;

[0035] Step 4-4: Update the expected mode. The update formula is:

[0036]

[0037] In the formula, represents the updated desired mode, is the expected mode before updating;

[0038] Step 4-5: Update the desired mode according to step 4-4 Center frequency Update, the update formula is:

[0039]

[0040] Step 4-6: Use the dual ascent method to solve the Lagrange multiplier in step 4-2 Update and increase the number of iterations n by 1. The update formula is:

[0041]

[0042] Where τ is the update parameter set in step 4-3;

[0043] Step 4-7: Determine whether the expected mode meets the accuracy requirements. If the accuracy requirements are met or the specified maximum number of iterations N is reached, proceed to step 4-8; otherwise, return to step 4-4 and repeat the iterations of steps 4-4 to 4-7; the criteria for determining whether the expected mode meets the accuracy requirements are:

[0044]

[0045] Where ε is the convergence accuracy set in step 4-3;

[0046] Step 4-8: Expected mode obtained in step 4-4 As the desired mode f obtained by VME d .

[0047] In the above steps, the steps of using VME to improve the full magnetic gradient orthogonal basis function described in step 6 are:

[0048] Step 6-1: Decompose the seven basis functions h in the full magnetic gradient decomposition method j (j=1~7) perform VME to obtain 7 expected modes h' corresponding to 7 basis functions j (j=1-7), wherein the parameters used in performing VME are the same as the VME parameters used in step 4;

[0049] Step 6-2: For the 7 expected modes h' obtained in step 6-1 j (j=1~7) is subjected to Schmidt orthogonalization, and the orthogonalized basis function is f j '(j=1~7), the formula of Schmidt orthogonalization is:

[0050]

[0051] Step 6-3: Standardize the basis function orthogonalized in step 6-2 to obtain the improved full magnetic gradient standard orthogonal basis function f j (j=1~7), the standardization formula is:

[0052] BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 The present invention is a flow chart of a magnetic anomaly detection method based on tensor invariants and improved orthogonal basis function decomposition.

[0054] Figure 2 It is a schematic diagram of the structure of a cross-shaped magnetic gradient tensor detection platform.

[0055] Figure 3 It is a schematic diagram of the relationship between the detection platform and the motion trajectory of the magnetic target during the detection process.

[0056] Figure 4 This is a waveform diagram of one of the independent gradient signals, where the dotted box indicates the moment when the magnetic anomaly signal appears.

[0057] Figure 5 It is the waveform diagram of the tensor invariant I obtained by combining the gradient tensors.

[0058] Figure 6 It is the waveform diagram of seven improved orthogonal basis functions obtained after variational mode extraction.

[0059] Figure 7 It is the waveform diagram of the comprehensive abnormal index E. DETAILED DESCRIPTION

[0060] In order to make the purpose, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below in conjunction with specific examples and with reference to the accompanying drawings. It should be noted that in the drawings or descriptions, similar or identical parts use the same figure numbers. The implementation methods not drawn or described in the drawings are forms known to ordinary technicians in the relevant technical field. In addition, although demonstrations of parameters containing specific values ​​may be provided herein, it should be understood that the parameters do not need to be exactly equal to the corresponding values, but are approximated to the corresponding values ​​within an acceptable error tolerance or design constraint. Therefore, the terms used are used to illustrate the content of the invention and are not used to limit the scope of protection of the present invention.

[0061] The present invention discloses a magnetic anomaly detection method based on tensor invariants and improved orthogonal basis function decomposition. Figure 1 , the method comprises the following steps:

[0062] Step 1: Collect magnetic anomaly gradient tensor signals. Figure 2 The detection platform shown in the figure consists of four fluxgate sensors placed in a cross shape with equal spacing, and 12 component signals of the four sensors in the x, y, and z directions are collected synchronously. The detection platform is stationary, and the ferromagnetic object moves in a straight line. The position relationship between the two is as follows: Figure 3 As shown; calculate the differential signal between the four sensors to obtain five independent gradient signals G xx , G xy , G xz , G yy , G yz , Figure 4 This is a waveform diagram of one of the independent gradient signals. The dotted box indicates the location of the magnetic anomaly signal. The calculation formula for the five independent gradient signals is:

[0063]

[0064] Where d is the distance between the center points of two sensors on the same axis, g is S1x represents the magnetic signal component of the S1 sensor in the x direction, g S2y It represents the magnetic signal component of the S2 sensor in the y direction, and the other symbols are similar;

[0065] Step 2: Magnetic gradient tensor signal G xx , G xy , G xz , G yy , G yz Preprocessing is performed. Wavelet packet decomposition is used to decompose the tensor signal into 10 layers to obtain 1024 layers of sub-bands. After frequency rearrangement, the sub-bands from the 3rd to the 32nd layers are selected for reconstruction to obtain the magnetic gradient signal G' without trend terms and high-frequency background noise. xx , G' xy , G' xz , G' yy , G' yz ;

[0066] Step 3: Use the five de-noised magnetic gradient signals obtained in step 2 to calculate the tensor invariant I. The calculation formula is:

[0067] I=G' xx G' xy +G' yy G' zz +G' xx G' zz -G' xy 2 -G' xz 2 -G' yz2

[0068] Step 4: Calculate the five de-noised magnetic gradient signals G' obtained in step 2 xx , G' xy , G' xz , G' yy , G' yz Variational mode extraction (VME) is performed to obtain five desired modes B xx , B xy , B xz , B yy , B yz , the specific steps are:

[0069] Step 4-1: Assume the magnetic gradient signal to be extracted is f o (t), from the expected mode f d (t) and the residual signal f r (t)

[0070] Composition, namely:

[0071] f o (t) = f d (t)+f r (t)

[0072] Step 4-2: Establish a combination of quadratic penalty terms and Lagrange multipliers, and the calculation formula is:

[0073]

[0074] Where λ is the Lagrange multiplier, ω is the frequency, α represents the balance parameter of the two penalty functions, and ω d represents the center frequency of the desired mode, represents f d The Fourier transform of (t), and the other symbols are similar, where is the frequency response function of the filter, that is:

[0075]

[0076] Step 4-3: Set the initial expected mode is 0, the initial expected center frequency is 0, the penalty parameter α is 700000, the convergence accuracy ε is 1.0E-5, the maximum number of iterations N is 1000, the update parameter τ of λ is 1.0E-6, and the number of iterations n is initialized to 1;

[0077] Step 4-4: Update the expected mode. The update formula is:

[0078]

[0079] In the formula, represents the updated desired mode, is the expected mode before updating;

[0080] Step 4-5: Based on the updated expected mode obtained in step 4-4 Center frequency Update, the update formula is:

[0081]

[0082] Step 4-6: Use the dual ascent method to solve the Lagrange multiplier in step 4-2 Update and increase the number of iterations n by 1. The update formula is:

[0083]

[0084] Where τ is the update parameter set in step 4-3;

[0085] Step 4-7: Determine whether the expected mode meets the accuracy requirements. If the accuracy requirements are met or the specified maximum number of iterations N is reached, proceed to step 4-8; otherwise, return to step 4-4 and repeat the iterations of steps 4-4 to 4-7; the criteria for determining whether the expected mode meets the accuracy requirements are:

[0086]

[0087] Where ε is the convergence accuracy set in step 4-3;

[0088] Step 4-8: Expected mode obtained in step 4-4 As the desired mode f obtained by VME d . With G' xx For example, when the number of iterations n is 222, the accuracy requirement is met. As the final desired mode B xx .

[0089] Step 5: Transpose the five desired modes obtained in step 4 and project them to the geomagnetic direction according to the magnetic angle relationship to obtain six projection elements S Gxx , S Gxy , S Gxz , S Gyy , S Gyz , S Gzz , and its calculation formula is:

[0090]

[0091] In the formula, o, p, and q are the unit vectors of the geomagnetic field vector projected on the x, y, and z axes respectively. The calculation formula is:

[0092] o=cos(I)cos(D)

[0093] p=cos(I)sin(D)

[0094] q=sin(I)

[0095] Where I and D are the geomagnetic field inclination and declination of the detection point respectively;

[0096] Step 6: Use VME to improve the full magnetic gradient orthogonal basis function and obtain 7 improved standard orthogonal basis functions f j (j=1-7), the specific steps of the improved method are:

[0097] Step 6-1: Use the VME parameters in step 4 to decompose the 7 basis functions h in the full magnetic gradient decomposition method. j (j=1~7) VME processing is performed to obtain the expected mode h' of the basis function j (j=1~7), where 7 basis functions h j The formula for (j=1-7) is:

[0098]

[0099] In the formula Where n is the number of sampling points, n = 1, 2, ..., N, v is the speed of the magnetic target, f s is the sampling frequency, CPA is the shortest distance from the sensor to the moving trajectory of the magnetic target;

[0100] Step 6-2: Perform Schmidt orthogonalization on the 7 desired modes obtained in step 6-1, and the orthogonalized basis function is f j '(j=1~7), the formula of Schmidt orthogonalization is:

[0101]

[0102] Step 6-3: Standardize the basis function orthogonalized in step 6-2 to obtain the improved full magnetic gradient standard orthogonal basis function f j (j=1~7), the standardization formula is:

[0103]

[0104] Finally, the improved orthogonal basis function is obtained, such as Figure 6 shown.

[0105] Step 7: Use the 7 improved orthogonal basis functions f obtained in step 6j (j=1-7), respectively for the six projection elements S obtained in step 5 Gxx , S Gxy , S Gxz , S Gyy , S Gyz , S Gzz Perform orthogonal basis decomposition to obtain 6 decomposition energy coefficients k i (i=xx,xy,xz,yy,yz,zz), the formula for orthogonal basis decomposition is:

[0106]

[0107] Step 8: Calculate the 6 energy coefficients k obtained in step 7 i The sum of the squares of (i=xx,xy,xz,yy,yz,zz) is multiplied by the square of the tensor invariant I obtained in step 3 to obtain a magnetic anomaly evaluation index E, such as Figure 7 As shown, the calculation formula is:

[0108]

[0109] Step 9: A dynamic threshold is set according to the constant false alarm detection principle. When the magnetic anomaly evaluation index E is greater than the threshold, it is determined that there is a magnetic anomaly in the signal to be detected; otherwise, it is determined that there is no magnetic anomaly in the signal to be detected.

[0110] Obviously, the above embodiments of the present invention are merely examples for clearly explaining the present invention, and are not intended to limit the implementation methods of the present invention. For those skilled in the art, other different forms of changes or modifications can be made based on the above description, and it is impossible to list all the implementation methods here. Any modification, equivalent substitution and improvement made within the technical ideas and principles of the present invention shall be included in the protection scope of the claims of the present invention.

Claims

1. A magnetic anomaly detection method based on tensor invariant and improved orthogonal basis function decomposition, characterized in that: The following steps are involved: Step 1: Use four three-axis fluxgate sensors to form a cross-shaped detection platform with equal spacing, synchronously collect 12 component signals of the four sensors in the x, y, and z directions, calculate the differential signal between the four sensors, and obtain five independent magnetic gradient signals G xx , G xy , G xz , G yy , G yz , and its calculation formula is: Where d is the distance between the center points of two sensors on the same axis, g is S1x represents the magnetic signal component of the S1 sensor in the x direction, g S2y It represents the magnetic signal component of the S2 sensor in the y direction, and the other symbols are similar; Step 2: The five magnetic gradient signals G obtained in step 1 xx , G xy , G xz , G yy , G yz Perform wavelet packet decomposition, retain the sub-band containing magnetic anomaly information, clear other sub-bands, and then reconstruct to obtain the magnetic gradient signal G' with noise and trend terms removed. xx , G' xy , G' xz , G' yy , G' yz ; Step 3: Use the five de-noised magnetic gradient signals obtained in step 2 to calculate the tensor invariant I. The calculation formula is: I=G' xx G' xy +G' yy G' zz +G' xx G' zz -G' xy 2 -G' xz 2 -G' yz 2 Step 4: Calculate the five de-noised magnetic gradient signals G' obtained in step 2 xx , G' xy , G' xz , G' yy , G' yz Variational mode extraction (VME) is performed to obtain five desired modes B xx , B xy , B xz , B yy , B yz ; Step 5: Transpose the five desired modes obtained in step 4 and project them to the geomagnetic direction according to the magnetic angle relationship to obtain six projection elements S Gxx , S Gxy , S Gxz , S Gyy , S Gyz , S Gzz , and its calculation formula is: In the formula, o, p, and q are the unit vectors of the geomagnetic field vector projected on the x, y, and z axes respectively. The calculation formula is: o=cos(I)cos(D) p=cos(I)sin(D) q=sin(I) Where I and D are the geomagnetic field inclination and declination of the detection point respectively; Step 6: Use VME to improve the full magnetic gradient orthogonal basis function decomposition method. The method is: use the VME parameters in step 4 to improve the 7 orthogonal basis functions h in the full magnetic gradient orthogonal basis function decomposition method. j (j=1-7) to perform VME, and obtain the corresponding 7 expected modes. Then, the 7 expected modes are subjected to Schmidt orthogonal and normalized processing to obtain 7 improved standard orthogonal basis functions f j (j=1-7); Step 7: Use the 7 improved orthogonal basis functions f obtained in step 6 j (j=1-7), respectively for the six projection elements S obtained in step 5 Gxx , S Gxy , S Gxz , S Gyy , S Gyz , S Gzz Perform orthogonal basis decomposition to obtain 6 decomposition energy coefficients k i (i=xx,xy,xz,yy,yz,zz), where the formula for orthogonal basis decomposition is: In the formula Where n is the number of sampling points, n = 1, 2, ..., N, v is the speed of the magnetic target, f s is the sampling frequency, CPA is the shortest distance from the sensor to the moving trajectory of the magnetic target; Step 8: Calculate the 6 energy coefficients k obtained in step 7 i The sum of the squares of (i=xx,xy,xz,yy,yz,zz) is calculated and multiplied by the square of the tensor invariant I obtained in step 3 to obtain a magnetic anomaly evaluation index E, which is calculated as follows: Step 9: A dynamic threshold is set according to the constant false alarm detection principle. When the magnetic anomaly evaluation index E is greater than the threshold, it is determined that there is a magnetic anomaly in the signal to be detected; otherwise, it is determined that there is no magnetic anomaly in the signal to be detected.

2. A magnetic anomaly detection method based on tensor invariants and improved orthogonal basis function decomposition according to claim 1, characterized in that: The steps for obtaining the desired modes using the variational mode extraction (VME) method described in steps 4 and 5 are: Step 4-1: Let the signal to be extracted be f o (t) is given by the expected mode f d (t) and the residual signal f r (t) composition, that is: f o (t) = f d (t)+f r (t) Step 4-2: Establish a combination of quadratic penalty terms and Lagrange multipliers, and the calculation formula is: Where λ is the Lagrange multiplier, ω is the frequency, α represents the balance parameter of the two penalty functions, and ω d represents the center frequency of the desired mode, represents f d The Fourier transform of (t), and the other symbols are similar, where The frequency response function of the filter is: Step 4-3: Set the initial expected mode Initial expected center frequency Penalty parameter α, convergence accuracy ε, maximum number of iterations N, update parameter τ of λ, and initialize the number of iterations n to 1; Step 4-4: Update the expected mode. The update formula is: In the formula, represents the updated desired mode, is the expected mode before updating; Step 4-5: Update the desired mode according to step 4-4 Center frequency Update, the update formula is: Step 4-6: Use the dual ascent method to solve the Lagrange multiplier in step 4-2 Update and increase the number of iterations n by 1. The update formula is: Where τ is the update parameter set in step 4-3; Step 4-7: Determine whether the expected mode meets the accuracy requirements. If the accuracy requirements are met or the specified maximum number of iterations N is reached, proceed to step 4-8; otherwise, return to step 4-4 and repeat the iterations of steps 4-4 to 4-7; the criteria for determining whether the expected mode meets the accuracy requirements are: Where ε is the convergence accuracy set in step 4-3; Step 4-8: Expected mode obtained in step 4-4 As the desired mode f obtained by VME d .

3. A magnetic anomaly detection method based on tensor invariant and improved orthogonal basis function decomposition according to claim 1, characterized in that: The steps of using VME to improve the full magnetic gradient orthogonal basis function described in step 6 are: Step 6-1: Decompose the seven basis functions h in the full magnetic gradient decomposition method j (j=1~7) perform VME to obtain 7 expected modes h' corresponding to 7 basis functions j (j=1-7), wherein the parameters used in performing VME are the same as the VME parameters used in step 4; Step 6-2: For the 7 expected modes h' obtained in step 6-1 j (j=1-7) is subjected to Schmidt orthogonalization, and the orthogonalized basis function is f j '(j=1~7), the formula of Schmidt orthogonalization is: Step 6-3: Standardize the basis function orthogonalized in step 6-2 to obtain the improved full magnetic gradient standard orthogonal basis function f j (j=1~7), the standardization formula is:

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