Two-step target positioning method under low signal-to-noise ratio based on magnetic gradient tensor

Abstract

This invention discloses a two-step target localization method based on magnetic gradient tensor under low signal-to-noise ratio conditions, specifically implemented according to the following steps: Step 1, construct a magnetic gradient tensor measurement system, establish a magnetic target localization model, and obtain magnetic anomaly signals and magnetic gradient anomaly component signals; Step 2, perform orthogonal basis decomposition target detection on the magnetic anomaly signals to obtain the corresponding orthogonal basis coefficient signals and the closest distance between the actual target and the magnetic gradient tensor measurement system; Step 3, perform full gradient tensor signal orthogonal basis decomposition detection on the magnetic gradient anomaly component signals to obtain the corresponding orthogonal basis coefficient signals; Step 4, using the orthogonal basis coefficient signals obtained in Steps 2 and 3, employ the two-step magnetic target position localization method to obtain the target position. This invention solves the problems of existing magnetic target localization methods, such as sensitivity to noise and degradation of positioning accuracy.

Description

Technical Field

[0001] This invention belongs to the field of magnetic target localization technology, specifically relating to a two-step target localization method based on magnetic gradient tensor under low signal-to-noise ratio conditions. Background Technology

[0002] Magnetic target positioning technology has a wide range of applications due to its non-contact, all-weather, high-efficiency, and adaptability to complex environments. It is used not only in geological exploration and mineral resource development to detect underground metal ore bodies and in archaeology to discover buried artifacts, but also in marine engineering to locate shipwrecks, pipelines, and lost equipment. Furthermore, in public safety and defense, this technology can be used for the detection of unexploded ordnance and the clearance of hazardous materials, effectively reducing risks.

[0003] However, existing magnetic target localization methods, whether based on total quantity, components, or magnetic gradient tensor invariants, essentially establish one or more sets of relationships between the target's magnetic field amplitude information in the observation point space and the target's position or magnetic moment. The accuracy of target localization is highly dependent on the accuracy of the measured target magnetic field data. However, in practical applications, magnetic anomaly signals decay rapidly with distance, while environmental noise and carrier interference remain relatively constant or even amplify. This causes measurement errors to dominate the signal, making the inversion model ill-conditioned, the solution unstable, and the localization results prone to divergence or significant deviations. In this situation, only conventional magnetic anomaly detection methods can barely maintain an early warning of the target's existence and approximate distance, but they are powerless to provide the spatial orientation information needed for precise strikes or evasion, severely restricting the engineering applicability of magnetic gradient tensor systems. Summary of the Invention

[0004] The purpose of this invention is to provide a two-step target localization method based on magnetic gradient tensor under low signal-to-noise ratio, which solves the problems of existing magnetic target localization methods, such as sensitivity to noise and degradation of localization accuracy.

[0005] The technical solution adopted in this invention is a two-step target localization method based on magnetic gradient tensor under low signal-to-noise ratio, which is implemented according to the following steps: Step 1: Build a magnetic gradient tensor measurement system, establish a magnetic target localization model, and obtain magnetic anomaly signals and magnetic gradient anomaly component signals; Step 2: Perform orthogonal basis decomposition target detection on the magnetic anomaly signal from Step 1 to obtain the corresponding orthogonal basis coefficient signal and the closest distance between the actual target and the magnetic gradient tensor measurement system. Step 3: Perform full gradient tensor signal orthogonal basis decomposition detection on the magnetic gradient anomaly component signal in Step 1 to obtain the corresponding orthogonal basis coefficient signal; Step 4: Using the orthogonal basis coefficient signals obtained in Steps 2 and 3, the target position is obtained by employing a two-step magnetic target position positioning method.

[0006] The invention is further characterized in that, Step 1 specifically involves: Step 1.1: Construct a magnetic gradient tensor measurement system. For detection distances much larger than the size of the magnetic target itself, model the magnetic target as a magnetic dipole for method derivation. The magnetic field distribution at a location 2.5 times larger than the target's size is equated to the magnetic field generated by the magnetic dipole, establishing a magnetic target localization model. The stationary magnetic dipole is located in the actual detection coordinate system. The origin, the magnetic moment vector is The direction of the magnetic moment is denoted as: ; Step 1.2, when the magnetic gradient tensor measurement system moves at a constant speed from one side of the target. On the other side, the trajectory of movement is In the plane, and parallel to Axis, where, plane and The included angle between the planes is The closest distance between the magnetic gradient tensor measurement system and the magnetic target is denoted as . The target magnetic anomaly and magnetic gradient tensors obtained respectively are: (1) in, For the target magnetic anomaly, B ij For magnetic gradient tensor, magnetic gradient tensor : In terms of geomagnetic direction, It is the magnetic moment modulus. For the Kronecker function, The permeability of free space, The position vector pointing from the magnetic target to the measuring point. This indicates the distance between the magnetic target source and the measuring point; Step 1.3: Project the target magnetic anomaly obtained in Step 1.2 onto the geomagnetic direction using the total differential signal of the magnetic anomaly. The square of the magnetic gradient anomaly signal in the geomagnetic direction is: (2) in, They are respectively The position vector increments in three directions, and the square of the magnetic gradient anomaly signal. It has rotational invariance; (3).

[0007] Step 2 specifically involves: Step 2.1, in the magnetic anomaly detection coordinate system The direction of the target magnetic moment vector is; (4) The target position vector is; (5) in, For dimensionless variables, For search time, and These are the coordinate systems for magnetic anomaly detection. x direction and z The unit vector of direction; target position vector Introducing the target magnetic anomaly middle; (6) in, As a group only with The relevant orthogonal basis, To be orthogonal base The corresponding orthogonal basis function coefficients, This is the closest distance between the detection system and the target; (7) orthogonal basis Corresponding orthogonal basis function coefficients for; (8) in, This is an intermediate parameter, and its expression is: (9) in, It is the geomagnetic tilt angle. Deflection angle, orthogonal basis function coefficients Given the magnetic moment vector and the nearest detection distance, based on the inherent properties of the standard orthogonal basis, the coefficients of the corresponding orthogonal basis function are obtained by integrating the magnetic anomaly signal with the corresponding orthogonal basis. (10) in, For the integral element; Step 2.2: In actual magnetic anomaly detection, the acquired magnetic gradient anomaly component signals are essentially discrete, and the orthogonal basis functions are approximately zero outside the finite spatial region. A length of... The sliding window segments the measured invariant signal; Step 2.3: Multiply the truncated signal by the corresponding orthogonal basis sample values ​​and sum them to approximate the integral, thus obtaining the expanded coefficient signal: (11) in , Dimensionless variable Discrete form, expressed as: , The signal sampling period; Step 2.4: Squaring and summing the expanded coefficient signals from Step 2.3 to obtain the energy signal; (12) in, For indexing; Step 2.5, preset threshold, and By comparing the energy values ​​at different times, it can be determined whether there is a magnetic anomaly target. Step 2.6, through multiple sets of different Multi-channel detection is used to estimate the closest distance between the actual target and the magnetic gradient tensor measurement system. .

[0008] Step 3 specifically involves: Step 3.1, in the actual detection coordinate system The target magnetic moment vector is: (13) Step 3.2, in the actual detection coordinate system middle The magnetic moment deflection angle and tilt angle are respectively, and both are dimensionless. Using the same set of standard orthogonal bases The linear combination of these components is expressed as the magnetic gradient anomaly component, which is composed of the magnetic gradient tensor components. Signal, with For example; (14) Among them, orthogonal basis The corresponding coefficient is ; Step 3.3, the orthogonal basis functions are; (15) Among them, orthogonal basis The corresponding coefficient value is only related to It is related to the direction of the target magnetic moment; similarly, in time detection, it is related to the magnetic gradient anomaly component signal. Obtain the orthogonal basis coefficient signal, in order to For example, the orthogonal basis coefficient signal is obtained as follows; (16).

[0009] Step 4 specifically involves converting the sliding window integration process described by equations (11) and (16) into a cross-correlation operation between the magnetic anomaly signal and the orthogonal basis functions, in order to expand the coefficient signal. For example, expand equations (11) and (16) as follows: (17) in, Orthogonal basis functions autocorrelation, and They are respectively and orthogonal basis and The cross-correlation function; When step 2 obtains the CPA distance Afterwards, the aforementioned correlation and cross-correlation functions are all known; the expanded coefficient signal It is composed of orthogonal bases It is composed of linear combinations of auto / cross-correlation signals, and the corresponding coefficients are It is only related to the direction of the target magnetic moment.

[0010] Step 4 specifically involves: Step 4.1, in the magnetic anomaly detection coordinate system In this process, an estimation model for the direction of the target magnetic moment is obtained; Step 4.2: Establish the objective function, obtain the objective parameters, and obtain the objective position.

[0011] The estimation model for the target magnetic moment direction is as follows: (18) in, The actual acquired coefficient signal, This is the theoretical value. and These are the starting and ending sample points for the estimation, respectively. All the signals mentioned above use normalized values, therefore they are unaffected by the unknown magnetic moment modulus. The impact.

[0012] After obtaining the direction of the target magnetic moment, in the actual detection coordinate system middle, The acquired orthogonal basis coefficient signals are only related to the target position vector. shaft and Projection of the axis , Related, due to CPA distance It has been obtained during the testing process. , The angle between the two coordinate systems This means that the target location problem is transformed into a parameter... The estimation problem, using The obtained orthogonal basis coefficient signals are used to establish the objective function; (19) Get By simultaneously minimizing these six objective functions, the objective parameters are estimated. ,in Using the estimate from the first step Multiply by The relevant rotation matrix is ​​obtained, and the target position is then estimated as follows: (20).

[0013] The beneficial effects of this invention are: the two-step target localization method based on magnetic gradient tensor under low signal-to-noise ratio can improve the accuracy of target detection, significantly enhance feasibility and localization effect, and realize the effective detection of magnetic target signals. It achieves high-precision target localization at long distances and low signal-to-noise ratio, and has extremely high theoretical value and urgent engineering significance. Attached Figure Description

[0014] Figure 1 This is a schematic diagram of the magnetic target positioning model established by the present invention; Figure 2 This is a schematic diagram of the magnetic gradient tensor array structure in Embodiment 6 of the present invention; Figure 3 This is the target function parameter scan diagram in Embodiment 6 of the present invention; Figure 4 The scanning parameters corresponding to the minimum value of the objective function in Embodiment 6 of the present invention are This is a parameter scan at 30°. Figure 5 The scanning parameters corresponding to the minimum value of the objective function in Embodiment 6 of the present invention are This is a parametric scan at 120°. Figure 6 The scanning parameters corresponding to the minimum value of the objective function in Embodiment 6 of the present invention are This is a parametric scan at 210°. Figure 7 The scanning parameters corresponding to the minimum value of the objective function in Embodiment 6 of the present invention are This is a parameter scan diagram at 300°. Detailed Implementation

[0015] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0016] Example 1 This invention presents a two-step target localization method based on magnetic gradient tensor under low signal-to-noise ratio conditions, which is implemented according to the following steps: Step 1: Build a magnetic gradient tensor measurement system, establish a magnetic target localization model, and obtain magnetic anomaly signals and magnetic gradient anomaly component signals; Step 2: Perform orthogonal basis decomposition target detection on the magnetic anomaly signal from Step 1 to obtain its corresponding orthogonal basis coefficient signal and the closest distance between the actual target and the magnetic gradient tensor measurement system. Step 3: Perform full gradient tensor signal orthogonal basis decomposition detection on the magnetic gradient anomaly component signal in Step 1 to obtain the corresponding orthogonal basis coefficient signal; Step 4: Using the orthogonal basis coefficient signals obtained in Steps 2 and 3, the target position is obtained by employing a two-step magnetic target position positioning method.

[0017] Example 2 This invention presents a two-step target localization method based on magnetic gradient tensor under low signal-to-noise ratio conditions, which is implemented according to the following steps: Step 1: Build a magnetic gradient tensor measurement system, establish a magnetic target localization model, and obtain magnetic anomaly signals and magnetic gradient anomaly component signals; Step 1.1: Construct a magnetic gradient tensor measurement system. For detection distances much larger than the size of the magnetic target itself, model the magnetic target as a magnetic dipole for method derivation. The magnetic field distribution at a location 2.5 times larger than the target's size is equated to the magnetic field generated by the magnetic dipole, establishing a magnetic target localization model, such as... Figure 1 As shown, the stationary magnetic dipole is located in the actual detection coordinate system. The origin, the magnetic moment vector is The direction of the magnetic moment is denoted as: ; Step 1.2, when the magnetic gradient tensor measurement system moves at a constant speed from one side of the target. On the other side, the trajectory of movement is In the plane, and parallel to Axis, where, plane and The included angle between the planes is The closest distance between the magnetic gradient tensor measurement system and the magnetic target is denoted as . The target magnetic anomaly and magnetic gradient tensors obtained respectively are: (1) in, For the target magnetic anomaly, B ij For magnetic gradient tensor, magnetic gradient tensor : In terms of geomagnetic direction, It is the magnetic moment modulus. For the Kronecker function, The permeability of free space, The position vector pointing from the magnetic target to the measuring point. This indicates the distance between the magnetic target source and the measuring point.

[0018] Step 1.3: Project the target magnetic anomaly obtained in Step 1.2 onto the geomagnetic direction using the total differential signal of the magnetic anomaly. The square of the magnetic gradient anomaly signal in the geomagnetic direction is: (2) in, They are respectively The position vector increments in three directions, and the square of the magnetic gradient anomaly signal. It has rotational invariance; (3).

[0019] Step 2: Perform orthogonal basis decomposition target detection on the magnetic anomaly signal from Step 1 to obtain its corresponding orthogonal basis coefficient signal and the closest distance between the actual target and the magnetic gradient tensor measurement system. Step 3: Perform full gradient tensor signal orthogonal basis decomposition detection on the magnetic gradient anomaly component signal in Step 1 to obtain the corresponding orthogonal basis coefficient signal; Step 4: Using the orthogonal basis coefficient signals obtained in Steps 2 and 3, the target position is obtained by employing a two-step magnetic target position positioning method.

[0020] Example 3 This invention presents a two-step target localization method based on magnetic gradient tensor under low signal-to-noise ratio conditions, which is implemented according to the following steps: Step 1: Build a magnetic gradient tensor measurement system, establish a magnetic target localization model, and obtain magnetic anomaly signals and magnetic gradient anomaly component signals; Step 1.1: Construct a magnetic gradient tensor measurement system. For detection distances much larger than the size of the magnetic target itself, model the magnetic target as a magnetic dipole for method derivation. The magnetic field distribution at a location 2.5 times larger than the target's size is equated to the magnetic field generated by the magnetic dipole, establishing a magnetic target localization model. The stationary magnetic dipole is located in the actual detection coordinate system. The origin, the magnetic moment vector is The direction of the magnetic moment is denoted as: ; Step 1.2, when the magnetic gradient tensor measurement system moves at a constant speed from one side of the target. On the other side, the trajectory of movement is In the plane, and parallel to Axis, where, plane and The included angle between the planes is The closest distance between the magnetic gradient tensor measurement system and the magnetic target is denoted as . The target magnetic anomaly and magnetic gradient tensors obtained respectively are: (1) in, For the target magnetic anomaly, B ij For magnetic gradient tensor, magnetic gradient tensor : In terms of geomagnetic direction, It is the magnetic moment modulus. For the Kronecker function, The permeability of free space, The position vector pointing from the magnetic target to the measuring point. This indicates the distance between the magnetic target source and the measuring point.

[0021] Step 1.3: Project the target magnetic anomaly obtained in Step 1.2 onto the geomagnetic direction using the total differential signal of the magnetic anomaly. The square of the magnetic gradient anomaly signal in the geomagnetic direction is: (2) in, They are respectively The position vector increments in three directions, and the square of the magnetic gradient anomaly signal. It has rotational invariance; (3).

[0022] Step 2: Perform orthogonal basis decomposition target detection on the magnetic anomaly signal from Step 1 to obtain its corresponding orthogonal basis coefficient signal and the closest distance between the actual target and the magnetic gradient tensor measurement system. Step 2.1, in the magnetic anomaly detection coordinate system The direction of the target magnetic moment vector is; (4) The target position vector is; (5) in, For dimensionless variables, For search time, and These are the coordinate systems for magnetic anomaly detection. x direction and z The unit vector of direction; target position vector Introducing the target magnetic anomaly middle; (6) in, As a group only with The relevant orthogonal basis, To be orthogonal base The corresponding orthogonal basis function coefficients, This is the closest distance between the detection system and the target; (7) orthogonal basis Corresponding orthogonal basis function coefficients for; (8) in, This is an intermediate parameter, and its expression is: (9) in, It is the geomagnetic tilt angle. Deflection angle, orthogonal basis function coefficients Given the magnetic moment vector and the nearest detection distance, based on the inherent properties of the standard orthogonal basis, the coefficients of the corresponding orthogonal basis function are obtained by integrating the magnetic anomaly signal with the corresponding orthogonal basis. (10) in, is an integral element.

[0023] Step 2.2: In actual magnetic anomaly detection, the acquired magnetic gradient anomaly component signals are essentially discrete, and the orthogonal basis functions are approximately zero outside the finite spatial region. A length of... The sliding window segments the measured invariant signal; Step 2.3: Multiply the truncated signal by the corresponding orthogonal basis sample values ​​and sum them to approximate the integral, thus obtaining the expanded coefficient signal: (11) in , Dimensionless variable Discrete form, expressed as: , The period is the signal sampling period.

[0024] Step 2.4: Squaring and summing the expanded coefficient signals from Step 2.3 to obtain the energy signal; (12) in For indexing.

[0025] Step 2.5, preset threshold, and By comparing the energy values ​​at different times, it can be determined whether there is a magnetic anomaly target. Step 2.6, through multiple sets of different Multi-channel detection is used to estimate the closest distance between the actual target and the magnetic gradient tensor measurement system. .

[0026] Step 3: Perform full gradient tensor signal orthogonal basis decomposition detection on the magnetic gradient anomaly component signal in Step 1 to obtain the corresponding orthogonal basis coefficient signal; Step 4: Using the orthogonal basis coefficient signals obtained in Steps 2 and 3, the target position is obtained by employing a two-step magnetic target position positioning method.

[0027] Example 4 This invention presents a two-step target localization method based on magnetic gradient tensor under low signal-to-noise ratio conditions, which is implemented according to the following steps: Step 1: Build a magnetic gradient tensor measurement system, establish a magnetic target localization model, and obtain magnetic anomaly signals and magnetic gradient anomaly component signals; Step 1.1: Construct a magnetic gradient tensor measurement system. For detection distances much larger than the size of the magnetic target itself, model the magnetic target as a magnetic dipole for method derivation. The magnetic field distribution at a location 2.5 times larger than the target's size is equated to the magnetic field generated by the magnetic dipole, establishing a magnetic target localization model. The stationary magnetic dipole is located in the actual detection coordinate system. The origin, the magnetic moment vector is The direction of the magnetic moment is denoted as: ; Step 1.2, when the magnetic gradient tensor measurement system moves at a constant speed from one side of the target. On the other side, the trajectory of movement is In the plane, and parallel to Axis, where, plane and The included angle between the planes is The closest distance between the magnetic gradient tensor measurement system and the magnetic target is denoted as . The target magnetic anomaly and magnetic gradient tensors obtained respectively are: (1) in, For the target magnetic anomaly, B ij For magnetic gradient tensor, magnetic gradient tensor : In terms of geomagnetic direction, It is the magnetic moment modulus. For the Kronecker function, The permeability of free space, The position vector pointing from the magnetic target to the measuring point. This indicates the distance between the magnetic target source and the measuring point.

[0028] Step 1.3: Project the target magnetic anomaly obtained in Step 1.2 onto the geomagnetic direction using the total differential signal of the magnetic anomaly. The square of the magnetic gradient anomaly signal in the geomagnetic direction is: (2) in, They are respectively The position vector increments in three directions, and the square of the magnetic gradient anomaly signal. It has rotational invariance; (3).

[0029] Step 2: Perform orthogonal basis decomposition target detection on the magnetic anomaly signal from Step 1 to obtain its corresponding orthogonal basis coefficient signal and the closest distance between the actual target and the magnetic gradient tensor measurement system. Step 2.1, in the magnetic anomaly detection coordinate system The direction of the target magnetic moment vector is; (4) The target position vector is; (5) in, For dimensionless variables, For search time, and These are the coordinate systems for magnetic anomaly detection. x direction and z The unit vector of direction; target position vector Introducing the target magnetic anomaly middle; (6) in, As a group only with The relevant orthogonal basis, To be orthogonal base The corresponding orthogonal basis function coefficients, This is the closest distance between the detection system and the target; (7) orthogonal basis Corresponding orthogonal basis function coefficients for; (8) in, This is an intermediate parameter, and its expression is: (9) in, It is the geomagnetic tilt angle. Deflection angle, orthogonal basis function coefficients Given the magnetic moment vector and the nearest detection distance, based on the inherent properties of the standard orthogonal basis, the coefficients of the corresponding orthogonal basis function are obtained by integrating the magnetic anomaly signal with the corresponding orthogonal basis. (10) in, is an integral element.

[0030] Step 2.2: In actual magnetic anomaly detection, the acquired magnetic gradient anomaly component signals are essentially discrete, and the orthogonal basis functions are approximately zero outside the finite spatial region. A length of... The sliding window segments the measured invariant signal; Step 2.3: Multiply the truncated signal by the corresponding orthogonal basis sample values ​​and sum them to approximate the integral, thus obtaining the expanded coefficient signal: (11) in , Dimensionless variable Discrete form, expressed as: , The period is the signal sampling period.

[0031] Step 2.4: Squaring and summing the expanded coefficient signals from Step 2.3 to obtain the energy signal; (12) in For indexing.

[0032] Step 2.5, preset threshold, and By comparing the energy values ​​at different times, it can be determined whether there is a magnetic anomaly target. Step 2.6, through multiple sets of different Multi-channel detection is used to estimate the closest distance between the actual target and the magnetic gradient tensor measurement system. .

[0033] Step 3: Perform full gradient tensor signal orthogonal basis decomposition detection on the magnetic gradient anomaly component signal in Step 1 to obtain the corresponding orthogonal basis coefficient signal; Step 3.1, in the actual detection coordinate system The target magnetic moment vector is: (13) Step 3.2, in the actual detection coordinate system middle The magnetic moment deflection angle and tilt angle are respectively, and both are dimensionless. Using the same set of standard orthogonal bases The linear combination of these components is expressed as the magnetic gradient anomaly component, which is composed of the magnetic gradient tensor components. Signal, with For example; (14) Among them, orthogonal basis The corresponding coefficient is ; Step 3.3, the orthogonal basis functions are; (15) Among them, orthogonal basis The corresponding coefficient value is only related to It is related to the direction of the target magnetic moment; similarly, in time detection, it is related to the magnetic gradient anomaly component signal. Obtain the orthogonal basis coefficient signal, in order to For example, the orthogonal basis coefficient signal is obtained as follows; (16).

[0034] Step 4: Using the orthogonal basis coefficient signals obtained in Steps 2 and 3, the target position is obtained by employing a two-step magnetic target position positioning method.

[0035] Example 5 This invention presents a two-step target localization method based on magnetic gradient tensor under low signal-to-noise ratio conditions, the process of which is as follows: Figure 1 As shown, the specific implementation steps are as follows: Step 1: Build a magnetic gradient tensor measurement system, establish a magnetic target localization model, and obtain magnetic anomaly signals and magnetic gradient anomaly component signals; Step 1.1: Construct a magnetic gradient tensor measurement system. For detection distances much larger than the size of the magnetic target itself, model the magnetic target as a magnetic dipole for method derivation. The magnetic field distribution at a location 2.5 times larger than the target's size is equated to the magnetic field generated by the magnetic dipole, establishing a magnetic target localization model. The stationary magnetic dipole is located in the actual detection coordinate system. The origin, the magnetic moment vector is The direction of the magnetic moment is denoted as: ; Step 1.2, when the magnetic gradient tensor measurement system moves at a constant speed from one side of the target. On the other side, the trajectory of movement is In the plane, and parallel to Axis, where, plane and The included angle between the planes is The closest distance between the magnetic gradient tensor measurement system and the magnetic target is denoted as . The target magnetic anomaly and magnetic gradient tensors obtained respectively are: (1) in, For the target magnetic anomaly, B ij For magnetic gradient tensor, magnetic gradient tensor : In terms of geomagnetic direction, It is the magnetic moment modulus. For the Kronecker function, The permeability of free space, The position vector pointing from the magnetic target to the measuring point. This indicates the distance between the magnetic target source and the measuring point.

[0036] Step 1.3: Project the target magnetic anomaly obtained in Step 1.2 onto the geomagnetic direction using the total differential signal of the magnetic anomaly. The square of the magnetic gradient anomaly signal in the geomagnetic direction is: (2) in, They are respectively The position vector increments in three directions, and the square of the magnetic gradient anomaly signal. It has rotational invariance; (3).

[0037] Step 2: Perform orthogonal basis decomposition target detection on the magnetic anomaly signal from Step 1 to obtain its corresponding orthogonal basis coefficient signal and the closest distance between the actual target and the magnetic gradient tensor measurement system. Step 2.1, in the magnetic anomaly detection coordinate system The direction of the target magnetic moment vector is; (4) The target position vector is; (5) in, For dimensionless variables, For search time, and These are the coordinate systems for magnetic anomaly detection. x direction and z The unit vector of direction; target position vector Introducing the target magnetic anomaly middle; (6) in, As a group only with The relevant orthogonal basis, To be orthogonal base The corresponding orthogonal basis function coefficients, This is the closest distance between the detection system and the target; (7) orthogonal basis Corresponding orthogonal basis function coefficients for; (8) in, This is an intermediate parameter, and its expression is: (9) in, It is the geomagnetic tilt angle. Deflection angle, orthogonal basis function coefficients Given the magnetic moment vector and the nearest detection distance, based on the inherent properties of the standard orthogonal basis, the coefficients of the corresponding orthogonal basis function are obtained by integrating the magnetic anomaly signal with the corresponding orthogonal basis. (10) in, is an integral element.

[0038] Step 2.2: In actual magnetic anomaly detection, the acquired magnetic gradient anomaly component signals are essentially discrete, and the orthogonal basis functions are approximately zero outside the finite spatial region. A length of... The sliding window segments the measured invariant signal; Step 2.3: Multiply the truncated signal by the corresponding orthogonal basis sample values ​​and sum them to approximate the integral, thus obtaining the expanded coefficient signal: (11) in , Dimensionless variable Discrete form, expressed as: , The period is the signal sampling period.

[0039] Step 2.4: Squaring and summing the expanded coefficient signals from Step 2.3 to obtain the energy signal; (12) in For indexing.

[0040] Step 2.5, preset threshold, and By comparing the energy values ​​at different times, it can be determined whether there is a magnetic anomaly target. Step 2.6, through multiple sets of different Multi-channel detection is used to estimate the closest distance between the actual target and the magnetic gradient tensor measurement system. .

[0041] Step 3: Perform full gradient tensor signal orthogonal basis decomposition detection on the magnetic gradient anomaly component signal in Step 1 to obtain the corresponding orthogonal basis coefficient signal; Step 3.1, in the actual detection coordinate system The target magnetic moment vector is: (13) Step 3.2, in the actual detection coordinate system middle The magnetic moment deflection angle and tilt angle are respectively, and both are dimensionless. Using the same set of standard orthogonal bases The linear combination of these components is expressed as the magnetic gradient anomaly component, which is composed of the magnetic gradient tensor components. Signal, with For example; (14) Among them, orthogonal basis The corresponding coefficient is ; Step 3.3, the orthogonal basis functions are; (15) Among them, orthogonal basis The corresponding coefficient value is only related to It is related to the direction of the target magnetic moment; similarly, in time detection, it is related to the magnetic gradient anomaly component signal. Obtain the orthogonal basis coefficient signal, in order to For example, the orthogonal basis coefficient signal is obtained as follows; (16).

[0042] Step 4: Derive and prove that the orthogonal basis coefficient signal obtained by discrete detection is actually a linear combination of the cross-correlation and autocorrelation of orthogonal basis functions. Using the orthogonal basis coefficient signals obtained in Step 2 and Step 3, the target position is obtained by adopting the two-step magnetic target position positioning method.

[0043] Step 4 specifically involves: the sliding window integration process described by equations (11) and (16) is equivalent to the cross-correlation operation between the magnetic anomaly signal and the orthogonal basis functions, in order to expand the coefficient signal. For example, expand equations (11) and (16) as follows: (17) in, Orthogonal basis functions autocorrelation, and They are respectively and orthogonal basis and The cross-correlation function; When step 2 obtains the CPA distance Afterwards, the aforementioned correlation and cross-correlation functions are all known; the expanded coefficient signal It is composed of orthogonal bases It is composed of linear combinations of auto / cross-correlation signals, and the corresponding coefficients are It is only related to the direction of the target magnetic moment.

[0044] Step 4.1, in the magnetic anomaly detection coordinate system In this process, an estimation model for the target magnetic moment direction is obtained: (18) in, The actual acquired coefficient signal, This is the theoretical value. and These are the starting and ending sample points for the estimation, respectively. All the signals mentioned above use normalized values, therefore they are unaffected by the unknown magnetic moment modulus. The impact.

[0045] Step 4.2: Establish the objective function, obtain the objective parameters, and obtain the objective position.

[0046] After obtaining the direction of the target magnetic moment, in the actual detection coordinate system middle, The acquired orthogonal basis coefficient signals are only related to the target position vector. shaft and Projection of the axis , Related, due to CPA distance It has been obtained during the testing process. , The angle between the two coordinate systems This means that the target location problem is transformed into a parameter... The estimation problem, using The obtained orthogonal basis coefficient signals are used to establish the objective function; (19) Get By simultaneously minimizing these six objective functions, the objective parameters are estimated. ,in Using the estimate from the first step Multiply by The relevant rotation matrix is ​​obtained, and the target position is then estimated as follows: (20).

[0047] Example 6 This invention presents a two-step target localization method based on magnetic gradient tensor under low signal-to-noise ratio conditions. A target localization scenario is simulated, with the magnetic target being a magnetic dipole source and its magnetic moment modulus set to 1000. The direction of the target magnetic moment is The unit vector of the magnetic moment direction is The magnetic gradient tensor array adopts a rectangular tetrahedral configuration, such as... Figure 2 As shown, the CPA distance between the magnetic gradient tensor measurement system and the target. The sampling period of the magnetic measurement system is 0.01s. Considering the random noise present in actual magnetic anomaly detection, the mean value of the magnetic field component noise is set to 0. The variance is The local geomagnetic field direction is set as follows: Target azimuth parameters Set them to: .

[0048] The target magnetic anomaly signal is obtained by projecting the signal measured by the vector magnetometer at the center point of the magnetic gradient tensor array onto the geomagnetic direction. The first step of the target localization model is to estimate the direction of the target magnetic moment using the angle scanning method according to equation (21), where... The parameter search ranges are respectively and The scan interval is set to The objective function can be obtained. Parameter scan graph, such as Figure 3 As shown, the objective function The parameter corresponding to the minimum value is This corresponds exactly to the preset theoretical value.

[0049] After estimating the target magnetic moment direction, the magnetic gradient tensor components are obtained using a tetrahedral measurement system. Considering the existence of actual noise, and since magnetic field gradient measurement can suppress most common-mode noise, a value of 0.3 is added, with a mean of 0 and a variance of 0.3. to Simulate actual measurement data and calculate Signal, based on parameters The estimation model underwent four simulation experiments. The parameter scan diagram also uses the parameter scan method. The search scope is The four simulation experiments were set up respectively. The theoretical values ​​are 30°, 120°, 210°, and 300°. The parameter scan results show that the objective function of the four simulation experiments... Scan parameters corresponding to the minimum value For the preset theoretical value, such as Figures 4-7 As shown, this invention can accurately obtain the target's orientation relative to the measurement trajectory, combined with the CPA distance obtained during detection. According to equation (20), the target location information can be accurately obtained, which is of great significance for target localization at long distances with low signal-to-noise ratio.

[0050] The same parameter scanning method is used. The search scope is As can be seen from the parameter scan graph, the objective function The parameter corresponding to the minimum value The preset value allows for accurate acquisition of the target's orientation relative to the measurement trajectory using this invention. Combined with the CPA distance acquired during detection, the target's location information can be accurately obtained, which is of great significance for target localization at long distances with low signal-to-noise ratios.

[0051] A target location estimation method based on magnetic gradient tensor invariants is adopted, labeled as Method 1. This method utilizes the magnetic gradient tensor of the observation point and the three components of the magnetic field of the target to quickly invert the target's location information. The location formula is as follows: (twenty one) in, For the magnetic gradient tensor, the closest point of the detection system to the target is used as the observation point in the simulation, i.e., using... The target position is obtained by solving the magnetic field information at the location. After obtaining the target magnetic moment information, the target magnetic moment vector is obtained, and its expression is: (twenty two) The positioning results obtained using the method and method 1 of this invention are shown in Table 1: Table 1 shows a comparison of the positioning results.

[0052] As shown in Table 1, the method proposed in this invention accurately estimates the parameters in the four sets of detection experiments. Based on the accurate target location information obtained from the CPA distance estimation, in contrast, the target position vector obtained using Method 1 in the four detection experiments deviated completely from the set theoretical value, causing the target magnetic moment direction estimated based on this location information to also deviate from the set theoretical value. Although the simulation experiment only compared with the classical method, most existing magnetic positioning methods, consistent with Method 1, are basically based on the magnetic field magnitude information of the observation point to invert the target information. Therefore, they are inevitably affected by noise, leading to a decrease in inversion accuracy.

[0053] This invention presents a two-step target localization method based on magnetic gradient tensor under low signal-to-noise ratio conditions. This method achieves accurate target location estimation at long distances under low signal-to-noise ratio conditions. It not only improves the stability and reliability of magnetic localization in complex environments but also provides a new technical approach for high-precision detection and identification of long-distance weak magnetic targets. It has significant practical value in engineering applications and can provide effective theoretical support for underwater target detection, unmanned platform target localization, and other weak magnetic anomaly target detection tasks, thus solving the problem of inaccurate localization in existing methods.

Claims

1. A two-step target positioning method based on magnetic gradient tensor under low signal-to-noise ratio, characterized in that, The specific steps are as follows: Step 1: Build a magnetic gradient tensor measurement system, establish a magnetic target localization model, and obtain magnetic anomaly signals and magnetic gradient anomaly component signals; Step 2: Perform orthogonal basis decomposition on the magnetic anomaly signal to detect the target, and obtain the corresponding orthogonal basis coefficient signal and the closest distance between the actual target and the magnetic gradient tensor measurement system; Step 3: Perform full gradient tensor signal orthogonal basis decomposition detection on the magnetic gradient anomaly component signal to obtain the corresponding orthogonal basis coefficient signal; Step 4: Using the orthogonal basis coefficient signals obtained in Steps 2 and 3, the target position is obtained by employing a two-step magnetic target position positioning method.

2. The two-step target positioning method based on magnetic gradient tensor with low signal-to-noise ratio according to claim 1, characterized in that, Step 1 specifically involves: Step 1.1, build a magnetic gradient tensor measurement system, for the detection distance is much larger than the size of the magnetic target itself, the magnetic target is modeled as a magnetic dipole to derive the method; the position greater than 2.5 times the size of the magnetic target itself, the magnetic field distribution law generated is equivalent to the magnetic field generated by the magnetic dipole, and a magnetic target positioning model is established. The static magnetic dipole is located at the origin of the actual detection coordinate system, the magnetic moment vector is , and the magnetic moment direction is denoted as . ; Step 1.2, when the magnetic gradient tensor measurement system moves at a constant speed from one side of the target. On the other side, the trajectory of movement is In the plane, and parallel to Axis, where, plane and The included angle between the planes is The closest distance between the magnetic gradient tensor measurement system and the magnetic target is denoted as . The target magnetic anomaly and magnetic gradient tensors obtained respectively are: （1） wherein, is the target magnetic anomaly, B ij is the magnetic gradient tensor, the magnetic gradient tensor : is the geomagnetic direction, is the magnetic moment modulus, is the Kronecker function, is the vacuum permeability, is the position vector from the magnetic target to the measurement point, denotes the distance from the magnetic target source to the measurement point; Step 1.3: Project the target magnetic anomaly obtained in Step 1.2 onto the geomagnetic direction using the total differential signal of the magnetic anomaly. The square of the magnetic gradient anomaly signal in the geomagnetic direction is: （2） wherein respectively three directional position vector increments, square of the magnetic gradient anomaly signal have a rotational invariance; (3).

3. The two-step target locating method based on magnetic gradient tensor with low signal-to-noise ratio according to claim 2, characterized in that, Step 2 specifically involves: Step 2.1, the target magnetic moment vector direction in the magnetic anomaly detection coordinate system is; （4） The target position vector is; （5） wherein, is a dimensionless variable, is a search time, and are unit vectors in the magnetic anomaly detection coordinate system x direction and z direction, respectively. The target position vector The target magnetic anomaly medium; （6） in, As a group only with The relevant orthogonal basis, To be orthogonal base The corresponding orthogonal basis function coefficients, This is the closest distance between the detection system and the target; （7） orthogonal basis Corresponding orthogonal basis function coefficients for; （8） in, This is an intermediate parameter, and its expression is: （9） in, It is the geomagnetic tilt angle. Deflection angle, orthogonal basis function coefficients Given the magnetic moment vector and the nearest detection distance, based on the inherent properties of the standard orthogonal basis, the coefficients of the corresponding orthogonal basis function are obtained by integrating the magnetic anomaly signal with the corresponding orthogonal basis. （10） in, For the integral element; Step 2.2: In actual magnetic anomaly detection, the acquired magnetic gradient anomaly component signals are essentially discrete, and the orthogonal basis functions are approximately zero outside the finite spatial region. A length of... The sliding window segments the measured invariant signal; Step 2.3: Multiply the truncated signal by the corresponding orthogonal basis sample values ​​and sum them to approximate the integral, thus obtaining the expanded coefficient signal: （11） in , Dimensionless variable Discrete form, expressed as: , The signal sampling period; Step 2.4: Squaring and summing the expanded coefficient signals from Step 2.3 to obtain the energy signal; （12） in, For indexing; Step 2.5, preset threshold, and By comparing the energy values ​​at different times, it can be determined whether there is a magnetic anomaly target. Step 2.6, through multiple sets of different Multi-channel detection is used to estimate the closest distance between the actual target and the magnetic gradient tensor measurement system. .

4. The two-step target localization method based on magnetic gradient tensor with low signal-to-noise ratio according to claim 3, characterized in that, Step 3 specifically involves: Step 3.1, in the actual detection coordinate system The target magnetic moment vector is: （13） Step 3.2, in the actual detection coordinate system middle The magnetic moment deflection angle and tilt angle are respectively, and both are dimensionless. Using the same set of standard orthogonal bases The linear combination of these components is expressed as the magnetic gradient anomaly component, which is composed of the magnetic gradient tensor components. Signal, with For example; （14） Among them, orthogonal basis The corresponding coefficient is ; Step 3.3, the orthogonal basis functions are; （15） Among them, orthogonal basis The corresponding coefficient value is only related to It is related to the direction of the target magnetic moment; similarly, in time detection, it is related to the magnetic gradient anomaly component signal. Obtain the orthogonal basis coefficient signal, in order to For example, the orthogonal basis coefficient signal is obtained as follows; （16）。 5. The two-step target localization method based on magnetic gradient tensor with low signal-to-noise ratio according to claim 4, characterized in that, Step 4 specifically involves converting the sliding window integration process described by equations (11) and (16) into a cross-correlation operation between the magnetic anomaly signal and the orthogonal basis functions, in order to expand the coefficient signal. For example, expand equations (11) and (16) as follows: （17） in, Orthogonal basis functions autocorrelation, and They are respectively and orthogonal basis and The cross-correlation function; When step 2 obtains the CPA distance Afterwards, the aforementioned correlation and cross-correlation functions are all known; the expanded coefficient signal It is composed of orthogonal bases It is composed of linear combinations of auto / cross-correlation signals, and the corresponding coefficients are It is only related to the direction of the target magnetic moment.

6. The two-step target localization method based on magnetic gradient tensor with low signal-to-noise ratio according to claim 4, characterized in that, Step 4 specifically involves: Step 4.1, in the magnetic anomaly detection coordinate system In this process, an estimation model for the direction of the target magnetic moment is obtained; Step 4.2: Establish the objective function, obtain the objective parameters, and obtain the objective position.

7. The two-step target localization method based on magnetic gradient tensor with low signal-to-noise ratio according to claim 6, characterized in that, The estimation model for the target magnetic moment direction is as follows: （18） in, The actual acquired coefficient signal, This is the theoretical value. and These are the starting and ending sample points for the estimation, respectively. All the signals mentioned above use normalized values, therefore they are unaffected by the unknown magnetic moment modulus. The impact.

8. The two-step target localization method based on magnetic gradient tensor with low signal-to-noise ratio according to claim 7, characterized in that, After obtaining the direction of the target magnetic moment, in the actual detection coordinate system middle, The acquired orthogonal basis coefficient signals are only related to the target position vector. shaft and Projection of the axis , Related, due to CPA distance It has been obtained during the testing process. , The angle between the two coordinate systems This means that the target location problem is transformed into a parameter... The estimation problem, using The obtained orthogonal basis coefficient signals are used to establish the objective function; （19） Get By simultaneously minimizing these six objective functions, the objective parameters are estimated. ,in Using the estimate from the first step Multiply by The relevant rotation matrix is ​​obtained, and the target position is then estimated as follows: （20）。

Images