A scalar in-situ calibration method for a three-axis magnetic field reference source in a magnetic shielded environment

Abstract

The application relates to a scalar in-situ calibration method for a three-axis magnetic field reference source in a magnetic shielding environment, and relates to the fields of weak magnetic measurement and quantum precision measurement. In order to solve the problem that the prior art cannot execute in-situ calibration in a closed environment without complex alignment, the application takes the magnetic field modulus data obtained by a scalar magnetometer as the only input, constructs a global error model, and quantifies the mapping relationship between the coil input current and the actual output magnetic field; taking the minimum residual error between the scalar field measurement value and the model calculation value as the optimization target, the LM algorithm is used to inversely solve the coil actual response matrix and the environmental background magnetic field, and the global compensation of the system error is completed; meanwhile, the magnetic coupling distortion effect of the magnetic shielding boundary is calculated by using the mirror method, the coil geometric size is optimized, the magnetic field uniformity and the boundary magnetization effect suppression are balanced from the design source, and finally the accurate mapping model of the input current and the actual output magnetic field is established. The application calibrates the three-axis coil with high precision.

Description

Technical Field

[0001] This invention belongs to the field of weak magnetic field measurement and quantum precision measurement technology, specifically relating to a scalar in-situ calibration method for a triaxial magnetic field reference source under magnetic shielding environment, which is used to perform high-precision calibration of a triaxial coil in a closed magnetic shielding space. Background Technology

[0002] In cutting-edge scientific fields such as quantum precision measurement, fundamental physics experiments, and biomagnetic detection (e.g., magnetoencephalography, magnetocardiography), constructing a highly accurate magnetic field reference source is a prerequisite for experimental success. Because the Earth's magnetic field and electromagnetic noise in urban environments can significantly interfere with high-sensitivity magnetic sensors, these precision experiments typically need to be conducted within high-performance magnetic shielding systems (such as permalloy shielding cylinders or multi-layered magnetic shielding chambers). However, in practical applications, constructing a highly accurate magnetic field environment within a confined shielded space presents an increasingly severe technical challenge.

[0003] First, the "boundary effect" introduced by the magnetic shield is the primary factor limiting the accuracy of the magnetic field. When the excitation coil is placed in a shielded environment with high permeability, the magnetic lines of force generated by the coil will be strongly magnetically coupled to the shield. According to the principle of the method of images, the shield will induce a complex magnetic field. This nonlinear superposition caused by the shield will severely distort the original magnetic field distribution, resulting in a drastic reduction in the accuracy of coils traditionally designed in open spaces (such as standard Helmholtz coils or Maxwell coils), which cannot meet the requirements of precision experiments for precise magnetic fields.

[0004] Secondly, changes in the coil's physical structure are a core concern affecting system reliability. Long-term engineering practice has revealed that during winding, assembly, and actual operation, the coil's geometry inevitably deforms due to machining tolerances, thermal expansion and contraction caused by environmental temperature fluctuations, and installation stress. This microscopic shift in physical structure directly degrades the axial orthogonality of the coil system. For a triaxial magnetic field reference source, non-orthogonality introduces severe inter-axial cross-coupling interference, significantly reducing the directional accuracy of the synthesized magnetic field. Simultaneously, structural changes cause the coil coefficients (i.e., the magnetic field strength generated per unit current) to deviate from the theoretical design value. This drift renders the magnetic field reference source meaningless, directly interfering with sensor sensitivity calibration and the accurate observation of weak magnetic phenomena.

[0005] To address the aforementioned bottlenecks, simply improving manufacturing precision or physical alignment is insufficient to fundamentally eliminate systematic errors. Therefore, researching a modeling and construction method based on scalar-based backfit calibration is crucial.

[0006] In particular, the high permeability shielding body and the excitation coil generate strong magnetic coupling under magnetic shielding environment. The induced magnetic field caused by the boundary effect will nonlinearly superimpose and distort the original magnetic field distribution of the coil. This leads to the technical defect that the magnetic field accuracy of the standard coil designed in traditional open space is greatly reduced in the shielded space and cannot meet the requirements of precision magnetic field output.

[0007] In addition, the magnetic field coil is affected by factors such as winding processing tolerance, thermal expansion and contraction due to environmental temperature changes, and installation stress, resulting in geometric deformation. This leads to deterioration of coil orthogonality, cross-coupling interference between shafts, and deviation of coil coefficients from theoretical values. Simply improving the precision of mechanical manufacturing and physical alignment cannot fundamentally eliminate the bottleneck of systematic errors in the industry.

[0008] Furthermore, there is the industry challenge of achieving in-situ, efficient, and high-precision calibration of high-accuracy magnetic field reference sources within a sealed magnetically shielded space, particularly in cutting-edge fields such as quantum precision measurement, biomagnetic detection, and fundamental physics experiments.

[0009] In summary, existing technologies neglect the boundary coupling effect of the magnetic shield and cannot compensate for the non-orthogonality and coefficient drift caused by coil structural deformation, resulting in a significant decrease in the magnetic field accuracy of traditional coils within the shielded space. Furthermore, they lack in-situ calibration methods that can be performed in a closed environment without complex alignment. Summary of the Invention

[0010] The purpose of this invention is to address the problem that existing technologies cannot provide in-situ calibration methods that can be performed in a closed environment without complex alignment. Therefore, this invention provides a scalar in-situ calibration method for a triaxial magnetic field reference source under magnetic shielding conditions.

[0011] The technical solution of this invention is: a scalar in-situ calibration method for a triaxial magnetic field reference source under magnetic shielding environment, comprising the following steps:

[0012] Step 1: Hardware setup and initialization of the calibration system;

[0013] A triaxial excitation coil system is fixedly installed in situ inside the magnetic shielding cavity device, and a scalar magnetometer is placed at the center of its uniform magnetic field region, so that the sensitive center of the scalar magnetometer coincides with the geometric center of the coil system, thus completing the hardware construction and initialization of the calibration system; Step 2: Construct a global coil system error model;

[0014] Step 21: Construct a reference model of the ideal coil magnetic field:

[0015] Suppose that a triaxial coil system generates magnetic fields along the X, Y, and Z directions under ideal conditions. , , The corresponding input current is Theoretically, the output magnetic field vector With input current The relationship between them is:

[0016]

[0017] in, This is the coil response matrix under ideal conditions. Under ideal orthogonal error-free conditions, it is a diagonal matrix, and the diagonal elements are the theoretical coil coefficients of the triaxial coil.

[0018] Step 22: Constructing an actual coil error model:

[0019] Because the actual output magnetic field of the coil has an inherent deviation from the theoretical value, and considering the background magnetic field of the magnetic shielding environment and measurement noise, the actual output magnetic field of the coil... With input current The model between them is:

[0020]

[0021] in, The coil response matrix to be estimated is used to quantify the inherent system errors of coil coefficient drift, triaxial nonorthogonality, and interaxial cross-coupling.

[0022] The vector of the background residual magnetic field within the magnetically shielded environment of the coil;

[0023] This refers to the random noise term during the measurement process.

[0024] Step 3: Based on the measurement characteristics of the scalar magnetometer, construct a solvable reverse calibration optimization objective and solve it using the LM algorithm; Step 4: To address the magnetic field distribution distortion caused by the magnetization effect of the magnetic shielding boundary, the boundary effect is quantitatively calculated using the image method, and the coil geometry is optimized based on the magnetic field uniformity index, thereby reducing the impact of boundary distortion from the design source. Step 5: Precise generation and closed-loop compensation of the magnetic field; Step 6: Using the optimal parameter model obtained from calibration, calculate the required input current command in reverse according to the desired target magnetic field, and reconstruct a high-accuracy vector magnetic field reference in the magnetically shielded confined space through closed-loop compensation.

[0025] Furthermore, the calibration system hardware setup and initialization described in step 1 are carried out entirely in situ within the target magnetic shielding device.

[0026] Preferably, step 1 specifically includes:

[0027] Step 11: Complete the fixed installation of the triaxial excitation coil system inside the target magnetic shielding cavity device. After the coil is installed, its geometric center coincides with the central axis of the magnetic shielding cavity to ensure that the working uniform area of ​​the coil is in the low distortion area of ​​the shielding cavity.

[0028] Step 12: Set up a scalar magnetometer at the center of the uniform magnetic field region of the triaxial excitation coil system. The scalar magnetometer should be selected with a measurement accuracy that is more than one order of magnitude better than the design accuracy of the target magnetic field reference source, to ensure that the sensitive center of the scalar magnetometer is completely coincident with the geometric center of the coil system.

[0029] Step 13: Complete the communication connection between the triaxial excitation coil system and the high-precision constant current drive source, the scalar magnetometer and the host computer data acquisition module, complete the system power-on initialization, drive current linearity verification, and magnetic field measurement noise baseline test, and ensure that the output current error of the drive system is not greater than 0.01%, the data acquisition system has no abnormal jumps, and the overall operation is stable.

[0030] Furthermore, step 3 specifically includes the following steps:

[0031] Step 31: Description of the reference characteristics for scalar measurement;

[0032] During the calibration process, a scalar magnetometer is used as the magnetic field reference standard. Only the total field modulus of the magnetic field needs to be measured. There is no need for high-precision vector measurement and complex multi-degree-of-freedom attitude alignment operations, which is suitable for in-situ calibration requirements in magnetically shielded confined spaces. At the same time, the triaxial excitation coil system has linear characteristics within the working range. Even if calibration is completed under a micro-Tesla level magnetic field, the calibration model can be reliably applied to the accurate calculation and output of nano-Tesla level weak magnetic fields.

[0033] Step 32: Optimize the objective function construction;

[0034] The measured value of the magnetic field modulus obtained by the scalar magnetometer is expressed as:

[0035] ;

[0036] Based on the least squares criterion, an optimization objective function is constructed, and the coil response matrix to be estimated is solved in reverse by using multiple sets of measurement data. and background residual magnetic field vector :

[0037]

[0038] in, For the first Group input current, To address the measured magnetic field magnitude, the optimization problem is solved using the LM algorithm.

[0039] Furthermore, step 4 includes the following steps:

[0040] Step 41: Balance and maximize the relationship between the size of the triaxial excitation coil and the suppression of boundary magnetization effects;

[0041] The mirror method is used to calculate the distortion effect of the boundary on the original magnetic field by superimposing the magnetic fields of virtual mirror coils, thus simplifying the solution for magnetic field distribution under complex boundaries, as follows:

[0042]

[0043] in, For mirror current, This is the actual current. The magnetic permeability in air. The permeability of the magnetic shielding material is due to Therefore, the following equation is considered to be true:

[0044]

[0045] Image current Substituting this into the Biot-Savart law, we get:

[0046]

[0047] in,

[0048]

[0049] Represents the order of the coil array. Represents the image current density , , Order, The position vector of the coil array, The position vector of the observation point. and It is the direction factor that determines the direction of the coil current density;

[0050] Step 42: Define magnetic field homogeneity as the ratio of the maximum deviation of the magnetic field magnitude within the central volume region to the magnetic field magnitude at the central point:

[0051]

[0052] in, The central region is represented by the magnetic field magnitude values ​​of each sampling point within a cube with sides of 10cm. The modulus at the center point of the coil;

[0053] By establishing a model of the coil and the magnetically shielded chamber, and combining the method of images and the Biot-Savart law, different coil side lengths were set, while keeping the coil center fixed. The magnetic field distribution within the central cubic region was calculated, and the magnetic field uniformity was plotted. The curve showing the relationship between the coil size and the coil dimensions; The smaller the value, the better the uniformity of the coil's magnetic field, which can then be used to determine the size of the coil.

[0054] Furthermore, in step 5, when the user needs to generate a specific vector magnetic field within the shielded space... At that time, the triaxial excitation coil system utilizes a calibrated mapping model. The required compensated input current command is calculated in reverse. ;

[0055] Through the above closed-loop calculation process, the triaxial excitation coil system can automatically offset the nonlinear deviation caused by coil deformation and the magnetization effect of the shield boundary.

[0056] The final output is a highly accurate reference magnetic field, providing a reliable reference for the subsequent calibration of the weak magnetic sensor.

[0057] Furthermore, step 6 specifically includes the following steps:

[0058] Step 61: Complete the fixed construction of the triaxial Helmholtz coil system in the magnetically shielded room, ensuring that the sensitive center of the high-precision scalar magnetometer, the geometric center of the coil system, and the preset measurement point are completely coaxially aligned.

[0059] Step 62: Pass no less than n sets of excitation current combinations into the triaxial excitation coil system, n≥12, the total modulus of the synthetic magnetic field corresponding to each set of current combinations is consistent, and the vector direction of the synthetic magnetic field uniformly covers the eight quadrants of space centered on the measurement point, providing full space constraints for solving the calibration parameters;

[0060] Step 63: Complete magnetic field sampling using a scalar magnetometer positioned at the center, and simultaneously record the total magnetic field modulus data corresponding to each set of excitation current combinations, providing sufficient effective samples for subsequent backfit calibration;

[0061] The actual effective geometric parameters and non-orthogonality factor of the coil are obtained by running the LM algorithm for nonlinear iterative solution.

[0062] Step 64: Use the calibrated model to correct the current control command in real time, compensate for the errors caused by physical deformation and shielding coupling, and thus reconstruct a high-precision vector magnetic field reference in a confined space.

[0063] Furthermore, the combination of excitation currents in step 62 is as follows:

[0064] Coil response matrix It is a 3×3 matrix with 9 unknowns;

[0065] Environmental background magnetic field It is a three-dimensional space vector There are 3 unknowns;

[0066] Therefore, the entire triaxial excitation coil system has 12 independent unknown parameters to be solved, and at least 12 sets of current combinations are required to construct the overdetermined equations.

[0067] Preferably, in step 62, a current combination of at least five times the number of independent unknown parameters to be solved is introduced.

[0068] Compared with the prior art, the present invention has the following advantages:

[0069] 1. This invention uses magnetic field modulus data obtained from a high-precision scalar magnetometer as the sole input to construct a global error model covering the inherent error of the coil system and the environmental background magnetic field, quantifying the mapping relationship between the coil input current and the actual output magnetic field. With minimizing the residual between the scalar field measurement value and the model calculation value as the optimization objective, the Levenberg-Marquardt (LM) algorithm is used to solve the actual coil response matrix and the environmental background magnetic field in reverse, completing the global compensation of system errors. Simultaneously, the image method is combined to equivalently calculate the magnetic coupling distortion effect at the magnetic shielding boundary. The coil geometry is optimized through a magnetic field uniformity quantification index, balancing magnetic field uniformity and boundary magnetization suppression from the design source. Finally, an accurate mapping model between the input current and the actual output magnetic field is established, enabling in-situ calibration of a high-precision magnetic field reference source within a magnetically shielded confined space. This provides a highly stable and reliable magnetic field reference for the vector calibration of triaxial magnetic sensors under weak magnetic fields.

[0070] 2. This invention incorporates an innovative in-situ reverse calibration method for magnetically shielded environments based on scalar measurements.

[0071] This invention pioneers a scalar in-situ reverse calibration method adapted to magnetically shielded / zero-magnetic confined spaces. Using only the total magnetic field modulus obtained from a high-precision scalar magnetometer as the sole measurement input, it enables the entire calibration process of a magnetic field reference source without disassembling the coil system or leaving the target magnetically shielded environment. This method significantly reduces the implementation threshold and equipment cost of precision magnetic field source calibration, completely solving the industry engineering problem of traditional calibration schemes being difficult to implement in-situ within confined magnetic shielding devices. It provides a completely new technical path for constructing high-precision magnetic field benchmarks in confined spaces.

[0072] 3. This invention adopts an innovative integrated synchronous compensation model for system-wide, global errors.

[0073] This invention constructs a global response model covering the entire system error of the coil. It integrates inherent errors in manufacturing and installation processes, such as coil winding tolerances, installation deviations, triaxial non-orthogonality, and inter-axis cross-coupling, with environmental interference terms like the background residual magnetic field and measurement noise within the magnetically shielded environment, into a unified parameter system for estimation. This achieves an integrated quantitative characterization of all system errors. Based on this, a nonlinear optimization objective function is constructed using the least squares criterion. The globally optimal solution is obtained through reverse engineering using the fast-converging and robust LM algorithm. This allows for simultaneous compensation of all system errors with a single calibration, overcoming the limitations of traditional methods that can only correct individual errors step-by-step. Furthermore, leveraging the wide-range linear operating characteristics of the coil system, it achieves reliable adaptation of micro-Tesla-level calibration results to nano-Tesla-level weak magnetic scenarios, significantly expanding the applicable range and application scenarios of the magnetic field reference source.

[0074] 4. This invention innovates in the source suppression of magnetic coupling distortion at the magnetic shielding boundary and in the optimized design of the coil.

[0075] To address the core bottleneck of coil magnetic field distribution distortion caused by the magnetization effect of ferromagnetic boundaries in magnetically shielded environments, this invention introduces the mirror method to accurately quantify and characterize the magnetic coupling effect of the shielding boundary. By superimposing the magnetic field of a virtual mirror coil, the magnetic field distribution under complex boundaries is calculated equivalently, filling the technical gap in traditional open-space coil designs that do not fully consider the coupling effect of the shielding boundary. Simultaneously, this invention defines a quantitative evaluation index for the magnetic field uniformity in the coil's central region and, combined with the Biot-Savart law, performs simulation calculations of the magnetic field distribution under different coil sizes. This balances the core contradiction between improving coil magnetic field uniformity and suppressing boundary magnetization effects, reducing the negative impact of the shielding boundary on magnetic field accuracy from the design stage, and further ensuring the output uniformity and accuracy of the magnetic field reference source.

[0076] 5. Innovation of a highly robust precision magnetic field reference full-process technology system

[0077] This invention establishes a complete technical system encompassing coil forward optimization design, in-situ data acquisition, reverse model parameter solving, and precise output of target magnetic field compensation. The solution boasts ultra-high calibration accuracy, strong environmental adaptability, and engineering feasibility. The calibration process is repeatable, and periodic in-situ calibration can correct parameter drift caused by environmental temperature changes and material stress release during long-term operation, significantly improving the long-term robustness of the magnetic field reference source. It can provide a highly stable, reliable, and wide-range precision magnetic field reference for cutting-edge fields such as quantum precision measurement, biomagnetic detection, vector calibration of weak magnetic sensors, and fundamental physics experiments. Attached Figure Description

[0078] Figure 1 This is a schematic diagram of the mirror current model inside the magnetic shielding device;

[0079] Figure 2 This is a schematic diagram of a magnetic sensor placed in a triaxial Helmholtz coil inside a magnetically shielded room;

[0080] Figure 3 This is a comparison diagram of the coil magnetic field before and after calibration. As can be seen from the diagram, there is a significant difference between the uncalibrated magnetic field and the calibrated magnetic field, which indicates that calibration is necessary.

[0081] Figure 4 This is a graph showing the deviation between the calibrated coil magnetic field modulus and the output magnetic field of the optical pump magnetometer under a magnetic field of 32 μT.

[0082] Figure 5 This is a flowchart of the present invention. Detailed Implementation

[0083] Specific implementation method one: Combining Figures 1 to 5 This embodiment describes a scalar in-situ calibration method for a triaxial magnetic field reference source under magnetic shielding conditions, comprising the following steps:

[0084] Step 1: Hardware setup and initialization of the calibration system;

[0085] A triaxial excitation coil system is fixedly installed in situ inside the magnetic shielding cavity device, and a scalar magnetometer is arranged in the center of its uniform magnetic field region so that the sensitive center of the scalar magnetometer coincides with the geometric center of the coil system, thus completing the hardware construction and initialization of the calibration system. Step 2: Construct a global coil system error model;

[0086] Step 21: Construct a reference model of the ideal coil magnetic field:

[0087] Suppose that a triaxial coil system generates magnetic fields along the X, Y, and Z directions under ideal conditions. , , The corresponding input current is Theoretically, the output magnetic field vector With input current The relationship between them is:

[0088]

[0089] in, This is the coil response matrix under ideal conditions. Under ideal orthogonal error-free conditions, it is a diagonal matrix, and the diagonal elements are the theoretical coil coefficients of the triaxial coil.

[0090] Step 22: Constructing an actual coil error model:

[0091] Because the actual output magnetic field of the coil has an inherent deviation from the theoretical value, and considering the background magnetic field of the magnetic shielding environment and measurement noise, the actual output magnetic field of the coil... With input current The model between them is:

[0092]

[0093] in, The coil response matrix to be estimated is used to quantify the inherent system errors of coil coefficient drift, triaxial nonorthogonality, and interaxial cross-coupling.

[0094] The vector of the background residual magnetic field within the magnetically shielded environment of the coil;

[0095] This refers to the random noise term during the measurement process.

[0096] Step 3: Based on the measurement characteristics of the scalar magnetometer, construct a solvable reverse calibration optimization objective and solve it using the LM algorithm; Step 4: To address the magnetic field distribution distortion caused by the magnetization effect of the magnetic shielding boundary, the boundary effect is quantitatively calculated using the image method, and the coil geometry is optimized based on the magnetic field uniformity index, thereby reducing the impact of boundary distortion from the design source. Step 5: Precise generation and closed-loop compensation of the magnetic field; Step 6: Using the optimal parameter model obtained from calibration, calculate the required input current command in reverse according to the desired target magnetic field, and reconstruct a high-accuracy vector magnetic field reference in the magnetically shielded confined space through closed-loop compensation.

[0097] To provide a high-precision calibration benchmark under weak magnetic fields, this embodiment proposes a coil reverse calibration method based on a high-precision scalar magnetometer. By using the magnetic field magnitude data measured by the scalar magnetometer, the parameters of the coil system are reversed to establish an accurate mapping model between the input current and the actual output magnetic field, thereby providing a reliable magnetic field benchmark for subsequent vector calibration of triaxial sensors under weak magnetic fields.

[0098] To address the technical shortcomings of traditional open-space standard coils where magnetic field accuracy significantly decreases within shielded spaces, failing to meet the requirements for precise magnetic field output, this invention quantifies the magnetic coupling influence factor of the shield by using scalar field global measurement and inverse fitting modeling. This eliminates magnetic field distribution distortion caused by shielding boundary effects, enabling accurate restoration and controllable output of the target magnetic field within a magnetically shielded confined space.

[0099] Addressing the industry bottleneck that relying solely on improving mechanical manufacturing precision and physical alignment cannot fundamentally eliminate systematic errors due to coil orthogonality degradation, inter-axis cross-coupling interference, and coil coefficient deviation from theoretical values, this invention uses a nonlinear optimization algorithm to backfit the actual effective geometric parameters of the coil, simultaneously compensating for coil non-orthogonality deviation, inter-axis coupling interference, and coil coefficient drift. This eliminates the magnetic field amplitude and direction errors introduced by coil structural deformation at the root, significantly improving the calibration accuracy and long-term operational robustness of the magnetic field reference source.

[0100] To address the industry challenge of achieving high-accuracy, in-situ, efficient, and high-precision calibration of magnetic field reference sources within a confined, magnetically shielded space, this invention provides a scalar inverse calibration method that can be performed in-situ within a shielded, confined space without complex vector measurements. This method integrates shielding coupling interference and coil structural errors into a scalar field distribution model for precise reconstruction, providing a highly stable and accurate magnetic field reference for ultra-sensitive weak magnetic field detection and sensor calibration, and ensuring the reliable conduct of precision magnetic measurement experiments.

[0101] Specific Implementation Method Two: Combining Figure 5 This embodiment describes the calibration system hardware setup and initialization described in step 1, which is carried out entirely within the target magnetic shielding device.

[0102] This implementation method establishes the hardware foundation for in-situ calibration. By fixing the coil system and scalar magnetometer inside the magnetic shielding device, it ensures that the sensitive center and the geometric center coincide, providing a physical platform for all subsequent calibration steps.

[0103] Specific implementation method three: Combining Figure 5 This embodiment describes step 1, which specifically includes:

[0104] Step 11: Complete the fixed installation of the triaxial excitation coil system inside the target magnetic shielding cavity device. After the coil is installed, its geometric center coincides with the central axis of the magnetic shielding cavity to ensure that the working uniform area of ​​the coil is in the low distortion area of ​​the shielding cavity.

[0105] Step 12: Set up a scalar magnetometer at the center of the uniform magnetic field region of the triaxial excitation coil system. The scalar magnetometer should be selected with a measurement accuracy that is more than one order of magnitude better than the design accuracy of the target magnetic field reference source, to ensure that the sensitive center of the scalar magnetometer is completely coincident with the geometric center of the coil system.

[0106] Step 13: Complete the communication connection between the triaxial excitation coil system and the high-precision constant current drive source, the scalar magnetometer and the host computer data acquisition module, complete the system power-on initialization, drive current linearity verification, and magnetic field measurement noise baseline test, and ensure that the output current error of the drive system is not greater than 0.01%, the data acquisition system has no abnormal jumps, and the overall operation is stable.

[0107] The overall purpose of this implementation method is to build an in-situ calibration hardware platform with precise positioning, high device accuracy, and stable operation, providing a reliable physical basis for subsequent error modeling and parameter solving.

[0108] Specific implementation method four: Combination Figure 1 This embodiment describes step 3, which specifically includes the following steps:

[0109] Step 31: Description of the reference characteristics for scalar measurement;

[0110] During the calibration process, a scalar magnetometer is used as the magnetic field reference standard. Only the total field modulus of the magnetic field needs to be measured. There is no need for high-precision vector measurement and complex multi-degree-of-freedom attitude alignment operations, which is suitable for in-situ calibration requirements in magnetically shielded confined spaces. At the same time, the triaxial excitation coil system has linear characteristics within the working range. Even if calibration is completed under a micro-Tesla level magnetic field, the calibration model can be reliably applied to the accurate calculation and output of nano-Tesla level weak magnetic fields.

[0111] Step 32: Optimize the objective function construction;

[0112] The measured value of the magnetic field modulus obtained by the scalar magnetometer is expressed as:

[0113] ;

[0114] Based on the least squares criterion, an optimization objective function is constructed, and the coil response matrix to be estimated is solved in reverse by using multiple sets of measurement data. and background residual magnetic field vector :

[0115]

[0116] in, For the first Group input current, To address the measured magnetic field magnitude, the optimization problem is solved using the LM algorithm.

[0117] This implementation method is based on an optimization solution framework for scalar measurement. It utilizes the total field modulus data obtained by a scalar magnetometer and aims to minimize the residual between the measured value and the calculated value of the model. The LM algorithm is used to solve the coil response matrix and the parameter values ​​of the background magnetic field in reverse, thus completing the mathematical inversion from the original measurement data to the error parameters.

[0118] Specific Implementation Method Five: Combining Figure 1 This embodiment describes step 4, which includes the following steps:

[0119] Step 41: Balance and maximize the relationship between the size of the triaxial excitation coil and the suppression of boundary magnetization effects;

[0120] The mirror method is used to calculate the distortion effect of the boundary on the original magnetic field by superimposing the magnetic fields of virtual mirror coils, thus simplifying the solution for magnetic field distribution under complex boundaries, as follows:

[0121]

[0122] in, For mirror current, This is the actual current. The magnetic permeability in air. The permeability of the magnetic shielding material is due to Therefore, the following equation is considered to be true:

[0123]

[0124] Image current Substituting this into the Biot-Savart law, we get:

[0125]

[0126] in,

[0127]

[0128] Represents the order of the coil array. Represents the image current density , , Order, The position vector of the coil array, The position vector of the observation point. and It is the direction factor that determines the direction of the coil current density;

[0129] Step 42: Define magnetic field homogeneity as the ratio of the maximum deviation of the magnetic field magnitude within the central volume region to the magnetic field magnitude at the central point:

[0130]

[0131] in, The central region is represented by the magnetic field magnitude values ​​of each sampling point within a cube with sides of 10cm. The modulus at the center point of the coil;

[0132] By establishing a model of the coil and the magnetically shielded chamber, and combining the method of images and the Biot-Savart law, different coil side lengths were set, while keeping the coil center fixed. The magnetic field distribution within the central cubic region was calculated, and the magnetic field uniformity was plotted. The curve showing the relationship between the coil size and the coil dimensions; The smaller the value, the better the uniformity of the coil's magnetic field, which can then be used to determine the size of the coil.

[0133] This implementation method suppresses the interference of the magnetic shielding boundary on magnetic field uniformity from the design stage. It quantifies the magnetic coupling distortion effect of the shielding body using the image method, defines a uniformity index, and establishes the relationship between coil size and magnetic field uniformity. This optimizes the coil geometry, achieving a balance between maximizing the uniform region and suppressing boundary effects, laying the foundation for subsequent high-precision magnetic field output.

[0134] Specific Implementation Method Six: Combination Figure 5 This embodiment describes step 5, where the user needs to generate a specific vector magnetic field within the shielded space. At that time, the triaxial excitation coil system utilizes a calibrated mapping model. The required compensated input current command is calculated in reverse. ;

[0135] Through the above closed-loop calculation process, the triaxial excitation coil system can automatically offset the nonlinear deviation caused by coil deformation and the magnetization effect of the shield boundary.

[0136] The final output is a highly accurate reference magnetic field, providing a reliable reference for the subsequent calibration of the weak magnetic sensor.

[0137] This implementation method utilizes a calibrated model to achieve precise generation of the magnetic field. By reverse-calculating the input current command and performing closed-loop compensation, errors caused by coil deformation and shield coupling are automatically offset, resulting in a highly accurate reference magnetic field output, providing a reliable basis for subsequent calibration of the weak magnetic sensor.

[0138] Specific implementation method seven: Combining Figure 5 This embodiment describes step 6, which specifically includes the following steps:

[0139] Step 61: Complete the fixed construction of the triaxial Helmholtz coil system in the magnetically shielded room, ensuring that the sensitive center of the high-precision scalar magnetometer, the geometric center of the coil system, and the preset measurement point are completely coaxially aligned.

[0140] Step 62: Pass no less than n sets of excitation current combinations into the triaxial excitation coil system, n≥12, the total modulus of the synthetic magnetic field corresponding to each set of current combinations is consistent, and the vector direction of the synthetic magnetic field uniformly covers the eight quadrants of space centered on the measurement point, providing full space constraints for solving the calibration parameters;

[0141] Step 63: Complete magnetic field sampling using a scalar magnetometer positioned at the center, and simultaneously record the total magnetic field modulus data corresponding to each set of excitation current combinations, providing sufficient effective samples for subsequent backfit calibration;

[0142] The actual effective geometric parameters and non-orthogonality factor of the coil are obtained by running the LM algorithm for nonlinear iterative solution.

[0143] Step 64: Use the calibrated model to correct the current control command in real time, compensate for the errors caused by physical deformation and shielding coupling, and thus reconstruct a high-precision vector magnetic field reference in a confined space.

[0144] This implementation method completes the final calibration and application of the magnetic field reference source through full-space sampling and LM algorithm inversion. By introducing multiple sets of excitation currents uniformly covering the eight quadrants, sufficient total field magnitude data is collected. The actual error parameters of the coil are obtained using the LM algorithm inversion, and the current command is corrected in real time. Finally, a high-precision vector magnetic field reference is reconstructed within the shielded space.

[0145] Specific implementation method eight: Combination Figure 5 This embodiment describes the following: the combination of excitation currents in step 62 of this embodiment is as follows:

[0146] Coil response matrix It is a 3×3 matrix with 9 unknowns;

[0147] Environmental background magnetic field It is a three-dimensional space vector There are 3 unknowns;

[0148] Therefore, the entire triaxial excitation coil system has 12 independent unknown parameters to be solved, and at least 12 sets of current combinations are required to construct the overdetermined equations.

[0149] This implementation clearly defines the number of parameters to be solved and determines the minimum number of excitation current combinations required accordingly. By explaining that there are 12 independent unknown parameters in the coil response matrix (9 parameters) and the ambient background magnetic field (3 parameters), it is pointed out that at least 12 current combinations are required to construct the overdetermined equations, providing a theoretical basis for subsequent data acquisition and ensuring the sufficiency of the solution.

[0150] Specific Implementation Method Nine: Combining Figure 5 To illustrate this embodiment, in step 62 of this embodiment, a current combination of at least 5 times the number of independent unknown parameters to be solved is introduced.

[0151] This implementation improves the accuracy and robustness of parameter solving by using sufficient redundant data. At least 60 current combinations are required for the 12 unknown parameters, effectively suppressing measurement noise and random errors, ensuring that the obtained coil response matrix and background magnetic field parameters are more accurate and reliable.

[0152] While the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the invention. Those skilled in the art can make other changes within the spirit of the invention and apply it to fields not mentioned in the invention. Of course, all such changes made in accordance with the spirit of the invention should be included within the scope of protection claimed by the invention.

Claims

1. A scalar in-situ calibration method for a triaxial magnetic field reference source under magnetic shielding conditions, characterized in that: Includes the following steps: Step 1: Hardware setup and initialization of the calibration system; A triaxial excitation coil system is fixedly installed in situ inside the magnetic shielding cavity device, and a scalar magnetometer is arranged in the center of its uniform magnetic field region so that the sensitive center of the scalar magnetometer coincides with the geometric center of the coil system, thus completing the hardware construction and initialization of the calibration system. Step 2: Construct a global coil system error model; Step 21: Construct a reference model of the ideal coil magnetic field: Suppose that a triaxial coil system generates magnetic fields along the X, Y, and Z directions under ideal conditions. , , The corresponding input current is Theoretically, the output magnetic field vector With input current The relationship between them is: in, This is the coil response matrix under ideal conditions. Under ideal orthogonal error-free conditions, it is a diagonal matrix, and the diagonal elements are the theoretical coil coefficients of the triaxial coil. Step 22: Constructing an actual coil error model: Because the actual output magnetic field of the coil has an inherent deviation from the theoretical value, and considering the background magnetic field of the magnetic shielding environment and measurement noise, the actual output magnetic field of the coil... With input current The model between them is: in, The coil response matrix to be estimated is used to quantify the inherent system errors of coil coefficient drift, triaxial nonorthogonality, and interaxial cross-coupling. The vector of the background residual magnetic field within the magnetically shielded environment of the coil; This refers to the random noise term during the measurement process. Step 3: Based on the measurement characteristics of the scalar magnetometer, construct a solvable reverse calibration optimization objective and solve it using the LM algorithm; Step 4: To address the magnetic field distribution distortion caused by the magnetization effect of the magnetic shielding boundary, the boundary effect is quantitatively calculated using the image method, and the coil geometry is optimized based on the magnetic field uniformity index, thereby reducing the impact of boundary distortion from the design source. Step 5: Precise generation and closed-loop compensation of the magnetic field; Step 6: Using the optimal parameter model obtained from calibration, calculate the required input current command in reverse according to the desired target magnetic field, and reconstruct a high-accuracy vector magnetic field reference in the magnetically shielded confined space through closed-loop compensation.

2. The scalar in-situ calibration method for a triaxial magnetic field reference source under magnetic shielding environment according to claim 1, characterized in that: The hardware setup and initialization of the calibration system described in step 1 are carried out entirely in situ within the target magnetic shielding device.

3. The scalar in-situ calibration method for a triaxial magnetic field reference source under magnetic shielding environment according to claim 1, characterized in that: Step 1 specifically includes: Step 11: Complete the fixed installation of the triaxial excitation coil system inside the target magnetic shielding cavity device. After the coil is installed, its geometric center coincides with the central axis of the magnetic shielding cavity to ensure that the working uniform area of ​​the coil is in the low distortion area of ​​the shielding cavity. Step 12: Set up a scalar magnetometer at the center of the uniform magnetic field region of the triaxial excitation coil system. The scalar magnetometer should be selected with a measurement accuracy that is more than one order of magnitude better than the design accuracy of the target magnetic field reference source, to ensure that the sensitive center of the scalar magnetometer is completely coincident with the geometric center of the coil system. Step 13: Complete the communication connection between the triaxial excitation coil system and the high-precision constant current drive source, the scalar magnetometer and the host computer data acquisition module, complete the system power-on initialization, drive current linearity verification, and magnetic field measurement noise baseline test, and ensure that the output current error of the drive system is not greater than 0.01%, the data acquisition system has no abnormal jumps, and the overall operation is stable.

4. The scalar in-situ calibration method for a triaxial magnetic field reference source under magnetic shielding environment according to claim 3, characterized in that: Step 3 specifically includes the following steps: Step 31: Description of the reference characteristics for scalar measurement; During the calibration process, a scalar magnetometer is used as the magnetic field reference standard. Only the total field modulus of the magnetic field needs to be measured. There is no need for high-precision vector measurement and complex multi-degree-of-freedom attitude alignment operations, which is suitable for in-situ calibration requirements in magnetically shielded confined spaces. At the same time, the triaxial excitation coil system has linear characteristics within the working range. Even if calibration is completed under a micro-Tesla level magnetic field, the calibration model can be reliably applied to the accurate calculation and output of nano-Tesla level weak magnetic fields. Step 32: Optimize the objective function construction; The measured value of the magnetic field modulus obtained by the scalar magnetometer is expressed as: ； Based on the least squares criterion, an optimization objective function is constructed, and the coil response matrix to be estimated is solved in reverse by using multiple sets of measurement data. and background residual magnetic field vector : in, For the first Group input current, To address the measured magnetic field magnitude, the optimization problem is solved using the LM algorithm.

5. The scalar in-situ calibration method for a triaxial magnetic field reference source under magnetic shielding environment according to claim 1, characterized in that: Step 4 includes the following steps: Step 41: Balance and maximize the relationship between the size of the triaxial excitation coil and the suppression of boundary magnetization effects; The mirror method is used to calculate the distortion effect of the boundary on the original magnetic field by superimposing the magnetic fields of virtual mirror coils, thus simplifying the solution for magnetic field distribution under complex boundaries, as follows: in, For mirror current, This is the actual current. The magnetic permeability in air. The permeability of the magnetic shielding material is due to Therefore, the following equation is considered to be true: Image current Substituting this into the Biot-Savart law, we get: in, Represents the order of the coil array. Represents the image current density , , Order, The position vector of the coil array, The position vector of the observation point. and It is the direction factor that determines the direction of the coil current density; Step 42: Define magnetic field homogeneity as the ratio of the maximum deviation of the magnetic field magnitude within the central volume region to the magnetic field magnitude at the central point: in, The central region is represented by the magnetic field magnitude values ​​of each sampling point within a cube with sides of 10cm. The modulus at the center point of the coil; By establishing a model of the coil and the magnetically shielded chamber, and combining the method of images and the Biot-Savart law, different coil side lengths were set, while keeping the coil center fixed. The magnetic field distribution within the central cubic region was calculated, and the magnetic field uniformity was plotted. The curve showing the relationship between the coil size and the coil dimensions; The smaller the value, the better the uniformity of the coil's magnetic field, which can then be used to determine the size of the coil.

6. The scalar in-situ calibration method for a triaxial magnetic field reference source under magnetic shielding environment according to claim 1, characterized in that: In step 5, when the user needs to generate a specific vector magnetic field within the shielded space... At that time, the triaxial excitation coil system utilizes a calibrated mapping model. The required compensated input current command is calculated in reverse. ; Through the above closed-loop calculation process, the triaxial excitation coil system can automatically offset the nonlinear deviation caused by coil deformation and the magnetization effect of the shield boundary. The final output is a highly accurate reference magnetic field, providing a reliable reference for the subsequent calibration of the weak magnetic sensor.

7. The scalar in-situ calibration method for a triaxial magnetic field reference source under magnetic shielding environment according to claim 1, characterized in that: Step 6 specifically includes the following steps: Step 61: Complete the fixed construction of the triaxial Helmholtz coil system in the magnetically shielded room, ensuring that the sensitive center of the high-precision scalar magnetometer, the geometric center of the coil system, and the preset measurement point are completely coaxially aligned. Step 62: Pass no less than n sets of excitation current combinations into the triaxial excitation coil system, n≥12, the total modulus of the synthetic magnetic field corresponding to each set of current combinations is consistent, and the vector direction of the synthetic magnetic field uniformly covers the eight quadrants of space centered on the measurement point, providing full space constraints for solving the calibration parameters; Step 63: Complete magnetic field sampling using a scalar magnetometer positioned at the center, and simultaneously record the total magnetic field modulus data corresponding to each set of excitation current combinations, providing sufficient effective samples for subsequent backfit calibration; The actual effective geometric parameters and non-orthogonality factor of the coil are obtained by running the LM algorithm for nonlinear iterative solution. Step 64: Use the calibrated model to correct the current control command in real time, compensate for the errors caused by physical deformation and shielding coupling, and thus reconstruct a high-precision vector magnetic field reference in a confined space.

8. A scalar in-situ calibration method for a triaxial magnetic field reference source under magnetic shielding environment according to claim 7, characterized in that: The excitation current combination in step 62 is as follows: Coil response matrix It is a 3×3 matrix with 9 unknowns; Environmental background magnetic field It is a three-dimensional space vector There are 3 unknowns; Therefore, the entire triaxial excitation coil system has 12 independent unknown parameters to be solved, and at least 12 sets of current combinations are required to construct the overdetermined equations.

9. A scalar in-situ calibration method for a triaxial magnetic field reference source under magnetic shielding environment according to claim 7, characterized in that: In step 62, a current combination of at least 5 times the number of independent unknown parameters to be solved is applied.

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