A method and system for spatial coordinate positioning of magnetic sensors for spacecraft magnetic property modeling

Abstract

A method and system for spatial coordinate positioning of a magnetic sensor for modeling magnetic characteristics of spacecraft, relating to the field of magnetic field measurement. The method solves the problem that the existing positioning method based on optimization algorithm will increase the complexity of solution, and its results may vary with different initial values, and it is also easy to fall into the local optimization solution. The method includes: constructing the magnetic field distribution generated by the magnetic beacon through spherical harmonic functions, and obtaining the three components of the magnetic beacon in spherical coordinates; expressing the three components of the magnetic sensor in the Cartesian coordinate system through the three components in the spherical coordinate system to obtain the fixed solution equation; calculating the azimuth of the magnetic sensor using Fourier coefficients; calculating the first-order Fourier coefficients of the magnetic sensor, calculating the radial distance of the magnetic sensor according to the first-order Fourier coefficients of the magnetic sensor, and determining the spherical coordinates of the magnetic sensor; converting the spherical coordinates of the magnetic sensor into Cartesian coordinates to complete the three-dimensional coordinate positioning of the magnetic sensor. The present invention is applied to the field of aerospace.

Description

Technical Field

[0001] The invention relates to the field of magnetic field measurement, and in particular to a magnetic sensor space coordinate positioning method for spacecraft magnetic property modeling. Background Art

[0002] Magnetic field measurement is one of the important tasks of deep space exploration. Through magnetic fields, we can remotely sense planetary magnetic field information, study planetary evolution history, and understand the space environment of solar system celestial bodies. Obtaining scientific data through remote sensing and in-situ measurement of highly sensitive miniaturized magnetic sensors is a necessary condition for understanding the above major basic scientific issues. In deep space magnetic exploration missions, magnetic sensors are usually installed on various spacecraft such as orbiters, landers, and rovers. Therefore, in order to ensure the accuracy of magnetic detection and data reliability, it is necessary to conduct magnetic measurement and modeling of the magnetic properties of spacecraft and restrict its magnetic field. The process of modeling the magnetic properties of spacecraft is a typical electromagnetic field inverse problem. It is necessary to obtain the magnetic model of the spacecraft through the positions of magnetic sensors arranged around the spacecraft to be tested and the inversion of their magnetic measurement data. Therefore, the precise positioning method of magnetic sensors is a necessary condition to ensure the accuracy of the spacecraft magnetic model.

[0003] At present, there are patents and literatures that record the positioning method of magnetic sensors based on magnetic sources (magnetic beacons) with known magnetic moments combined with optimization algorithms. However, the positioning method based on the optimization algorithm will increase the complexity of the solution, and its results may vary with different initial values, and it is easy to fall into the local optimization solution, so it is not suitable for practical engineering applications. Summary of the invention

[0004] The present invention aims at the problem that the existing positioning method based on optimization algorithm will increase the complexity of solution, and its result may be different with different initial values, and it is also easy to fall into the local optimization solution. A magnetic sensor spatial coordinate positioning method for spacecraft magnetic property modeling is proposed, and the method includes:

[0005] S1: Construct the magnetic field distribution generated by the magnetic beacon through spherical harmonics and obtain the three components of the magnetic beacon in spherical coordinates;

[0006] S2: The three components of the magnetic sensor in the Cartesian coordinate system are expressed by the three components in the spherical coordinate system to obtain a well-defined equation;

[0007] S3: Calculate the azimuth angle of the magnetic sensor using the Fourier coefficients;

[0008] S4: calculating the first-order Fourier coefficient of the magnetic sensor, calculating the radial distance of the magnetic sensor according to the first-order Fourier coefficient of the magnetic sensor, and determining the spherical coordinates of the magnetic sensor;

[0009] S5: Convert the spherical coordinates of the magnetic sensor into Cartesian coordinates to complete the three-dimensional coordinate positioning of the magnetic sensor.

[0010] Furthermore, a preferred method is proposed, wherein step S1 comprises:

[0011] The three-component expression of the magnetic beacon in spherical coordinates is:

[0012]

[0013] Among them, B r , B θ and B φ are the three components of the magnetic field generated by the magnetic beacon in the spherical coordinate system, r is the radial distance, θ is the polar angle, is the azimuth, j is the order of the spherical harmonics, and m is the degree of the spherical harmonics;

[0014] The relationship between the first-order spherical harmonic coefficient and the three-axis magnetic moment of the magnetic beacon is:

[0015]

[0016] Among them, I x ,I y and I z is the triaxial coil current, S x , S y and S z is the cross-sectional area of ​​the triaxial coil, N x 、N y and N z is the number of turns of the triaxial coil, M x 、M y 、M z They are the three components of the magnetic moment of the magnetic beacon.

[0017] Furthermore, a preferred method is proposed, wherein step S2 comprises:

[0018]

[0019] Among them, B x , B y , B z are the three components of the magnetic field generated by the magnetic beacon in the Cartesian coordinate system.

[0020] Furthermore, a preferred method is proposed, wherein step S3 comprises:

[0021] Place the magnetic beacon on a non-magnetic turntable, and surround the sensor to be tested around the magnetic beacon;

[0022] The origin of the reference coordinate system is set at the center of the magnetic beacon, and the three axes of the reference coordinate system are respectively aligned with the axes of the three-axis coil in the magnetic beacon;

[0023] Rotate the non-magnetic turntable 360 ​​degrees and record the reading of the magnetic sensor every 10 degrees;

[0024] Calculate the zero-order Fourier coefficients of the three-axis readings of the magnetic sensor according to the magnetic measurement data;

[0025] Calculate the azimuth angle φ of the magnetic sensor based on the zero-order Fourier coefficient:

[0026]

[0027] Among them, A y0 is the zero-order Fourier coefficient of the y-axis component of the magnetic sensor, A x0 is the zero-order Fourier coefficient of the x-axis component of the magnetic sensor.

[0028] Furthermore, a preferred method is proposed, wherein the radial distance of the magnetic sensor is calculated according to the first-order Fourier coefficient of the magnetic sensor in step S4, including:

[0029]

[0030] Where μ0 is the magnetic permeability of air, A z1_cos is the first-order cosine Fourier coefficient of the z-axis component of the magnetic sensor.

[0031] Furthermore, a preferred embodiment is proposed, wherein step S5 comprises:

[0032]

[0033] Among them, x, y, and z are the three spatial coordinates of the magnetic sensor.

[0034] Furthermore, a preferred embodiment is proposed, wherein the method further comprises a method for calculating the azimuth angle of the magnetic sensor, comprising:

[0035]

[0036] Based on the same inventive concept, the present invention also proposes a magnetic sensor spatial coordinate positioning system for spacecraft magnetic property modeling, the system comprising:

[0037] A magnetic field distribution construction unit, used to construct the magnetic field distribution generated by the magnetic beacon through spherical harmonic functions, and obtain the three components of the magnetic beacon in spherical coordinates;

[0038] A three-component expression unit, used to express the three components of the magnetic sensor in the Cartesian coordinate system through the three components in the spherical coordinate system to obtain a well-defined equation;

[0039] An azimuth acquisition unit, used for calculating the azimuth of the magnetic sensor using Fourier coefficients;

[0040] The spherical coordinate acquisition unit of the magnetic sensor is used to calculate the first-order Fourier coefficient of the magnetic sensor, calculate the radial distance of the magnetic sensor according to the first-order Fourier coefficient of the magnetic sensor, and determine the spherical coordinate of the magnetic sensor;

[0041] The three-dimensional coordinate positioning unit is used to convert the spherical coordinates of the magnetic sensor into Cartesian coordinates to complete the three-dimensional coordinate positioning of the magnetic sensor.

[0042] Based on the same inventive concept, the present invention also proposes a computer device, including a memory and a processor, wherein the memory stores a computer program. When the processor runs the computer program stored in the memory, the processor executes a magnetic sensor spatial coordinate positioning method for spacecraft magnetic property modeling as described in any one of the above items.

[0043] Based on the same inventive concept, the present invention also proposes a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the steps of a magnetic sensor spatial coordinate positioning method for spacecraft magnetic property modeling as described above are executed.

[0044] The present invention is beneficial in that:

[0045] 1. Compared with the optimization algorithm, the magnetic sensor spatial coordinate positioning method for spacecraft magnetic property modeling proposed in this invention uses spherical harmonics to construct the magnetic field distribution generated by the magnetic beacon, and calculates the azimuth and radial distance through Fourier coefficients. This modeling and positioning method based on the spherical coordinate system can simplify the complexity of the positioning problem and reduce the potential errors introduced by complex algorithms.

[0046] 2. Since the positioning methods in the prior art often use optimization algorithms that are sensitive to initial values, different initial values ​​may lead to different final results, or even fall into a local optimal solution. The present invention proposes a magnetic sensor spatial coordinate positioning method for modeling the magnetic characteristics of spacecraft, which is based on the method of spherical harmonics and Fourier coefficients, and performs positioning in a more mathematically stable manner, reducing the dependence on initial values, thereby improving the consistency and accuracy of the positioning results. The positioning method using a spherical coordinate system can better adapt to the complex magnetic field conditions and working environment changes that spacecraft may face in a deep space environment, and improve the stability and reliability of the positioning results.

[0047] 3. Compared with the optimization algorithm, the magnetic sensor spatial coordinate positioning method for spacecraft magnetic property modeling proposed in the present invention obtains an explicit calculation formula for the magnetic sensor spatial coordinate by introducing Fourier coefficients, which no longer depends on the optimization algorithm, and the calculation result is more accurate and the calculation speed is faster;

[0048] 4. Compared with the optimization algorithm, the magnetic sensor spatial coordinate positioning method for spacecraft magnetic property modeling proposed in the present invention can simultaneously locate the positions of multiple magnetic sensors through the magnetic measurement data of one rotation, without quantity limitation;

[0049] 5. Compared with the optimization algorithm, the magnetic sensor spatial coordinate positioning method for spacecraft magnetic property modeling proposed in the present invention can realize the spatial positioning of short-range magnetic sensors by increasing the order of spherical harmonic functions. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 A flow chart of a method for spatial coordinate positioning of a magnetic sensor for modeling magnetic characteristics of a spacecraft according to implementation mode 1;

[0051] Figure 2 A schematic diagram of the test arrangement of the magnetic sensor position according to the fourth embodiment;

[0052] Figure 3 This is a schematic diagram of a finite element model according to the eleventh embodiment;

[0053] Figure 4 This is a schematic diagram of the magnetic field calculation data at target point 1 described in Implementation Example 11. DETAILED DESCRIPTION

[0054] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments.

[0055] Implementation method 1, see Figure 1 The present embodiment is described as follows: a method for spatial coordinate positioning of a magnetic sensor for modeling magnetic characteristics of a spacecraft, the method comprising:

[0056] S1: Construct the magnetic field distribution generated by the magnetic beacon through spherical harmonics and obtain the three components of the magnetic beacon in spherical coordinates;

[0057] S2: The three components of the magnetic sensor in the Cartesian coordinate system are expressed by the three components in the spherical coordinate system to obtain a well-defined equation;

[0058] S3: Calculate the azimuth angle of the magnetic sensor using the Fourier coefficients;

[0059] S4: calculating the first-order Fourier coefficient of the magnetic sensor, calculating the radial distance of the magnetic sensor according to the first-order Fourier coefficient of the magnetic sensor, and determining the spherical coordinates of the magnetic sensor;

[0060] S5: Convert the spherical coordinates of the magnetic sensor into Cartesian coordinates to complete the three-dimensional coordinate positioning of the magnetic sensor.

[0061] Compared with the optimization algorithm, the magnetic sensor spatial coordinate positioning method for spacecraft magnetic property modeling proposed in this embodiment uses spherical harmonic functions to construct the magnetic field distribution generated by the magnetic beacon, and calculates the azimuth and radial distance through Fourier coefficients. This modeling and positioning method based on the spherical coordinate system can simplify the complexity of the positioning problem and reduce potential errors introduced by complex algorithms.

[0062] Since the positioning methods in the prior art often use optimization algorithms that are sensitive to initial values, different initial values ​​may lead to different final results, or even fall into a local optimal solution. The present embodiment proposes a magnetic sensor spatial coordinate positioning method for modeling the magnetic characteristics of a spacecraft, which is based on the method of spherical harmonics and Fourier coefficients, and performs positioning in a more mathematically stable manner, reducing the dependence on initial values, thereby improving the consistency and accuracy of the positioning results. The positioning method using a spherical coordinate system can better adapt to the complex magnetic field conditions and working environment changes that a spacecraft may face in a deep space environment, and improve the stability and reliability of the positioning results.

[0063] The present embodiment proposes a method for spatial coordinate positioning of magnetic sensors for modeling the magnetic characteristics of spacecraft. Through the precise calculation of spherical harmonic functions and Fourier coefficients, the azimuth and radial distance of the magnetic sensor can be more accurately obtained, thereby improving the positioning accuracy and meeting the requirements of deep space exploration for precise scientific data. This method based on spherical coordinates can not only be applied to the spatial positioning of magnetic sensors, but can also be extended to other application fields that require precise positioning, such as applications in positioning and navigation systems, and has good versatility and applicability.

[0064] Embodiment 2: This embodiment further defines the method for spatial coordinate positioning of a magnetic sensor for modeling magnetic characteristics of a spacecraft described in Embodiment 1. Step S1 includes:

[0065] The three-component expression of the magnetic beacon in spherical coordinates is:

[0066]

[0067] Among them, B r , B θ and B φ are the three components of the magnetic field generated by the magnetic beacon in the spherical coordinate system, r is the radial distance, θ is the polar angle, is the azimuth, j is the order of the spherical harmonics, and m is the degree of the spherical harmonics;

[0068] The relationship between the first-order spherical harmonic coefficient and the three-axis magnetic moment of the magnetic beacon is:

[0069]

[0070] Among them, I x ,I y and I z is the triaxial coil current, S x , S y and S z is the cross-sectional area of ​​the triaxial coil, N x 、N y and N z is the number of turns of the triaxial coil, M x 、M y 、M z They are the three components of the magnetic moment of the magnetic beacon.

[0071] In this embodiment, the spherical coordinate system is used to more effectively describe the position and direction of the magnetic beacon in space. The three-component expression in the spherical coordinate system makes it possible to obtain the position information of the magnetic beacon (radial distance r, polar angle θ and azimuth angle) ) is more intuitive and accurate. Through the order j and degree m of the spherical harmonic function, the magnetic field characteristics of the magnetic beacon can be accurately modeled, providing a good mathematical basis for subsequent positioning.

[0072] In the second formula, the relationship between the first-order spherical harmonic coefficient and the three-axis magnetic moment of the magnetic beacon is explained. By measuring the three-axis coil currents Ix, Iy, Iz and the cross-sectional areas Sx, Sy, Sz and the number of turns Nx, Ny, Nz of the coil, the magnetic field information of the magnetic beacon can be calculated. The establishment of this relationship enables the magnetic field characteristics of the magnetic beacon to be measured and subsequent positioning and analysis can be performed. By integrating the spherical coordinate system description and spherical harmonic function analysis, this method can provide more accurate and reliable spatial coordinate positioning of the magnetic sensor. By measuring and calculating the magnetic field information, the position and attitude of the spacecraft relative to the magnetic beacon can be accurately determined, providing important real-time information support for the control and navigation of the spacecraft.

[0073] Implementation method 3: This implementation method further limits the method for spatial coordinate positioning of magnetic sensors for modeling magnetic properties of spacecraft described in implementation method 1. Step S2 includes:

[0074]

[0075] Among them, B x , B y , B z are the three components of the magnetic field generated by the magnetic beacon in the Cartesian coordinate system.

[0076] Implementation method 4: See Figure 2This embodiment further defines the method for spatial coordinate positioning of magnetic sensors for modeling magnetic properties of spacecraft described in Embodiment 1, and the step S3 includes:

[0077] Place the magnetic beacon on a non-magnetic turntable, and surround the sensor to be tested around the magnetic beacon;

[0078] The origin of the reference coordinate system is set at the center of the magnetic beacon, and the three axes of the reference coordinate system are respectively aligned with the axes of the three-axis coil in the magnetic beacon;

[0079] Rotate the non-magnetic turntable 360 ​​degrees and record the reading of the magnetic sensor every 10 degrees;

[0080] Calculate the zero-order Fourier coefficients of the three-axis readings of the magnetic sensor according to the magnetic measurement data;

[0081] Calculate the azimuth angle φ of the magnetic sensor based on the zero-order Fourier coefficient:

[0082]

[0083] Among them, A y0 is the zero-order Fourier coefficient of the y-axis component of the magnetic sensor, A x0 is the zero-order Fourier coefficient of the x-axis component of the magnetic sensor.

[0084] This embodiment can obtain 360-degree magnetic field data by placing the magnetic beacon on a non-magnetic turntable, rotating the sensor to be tested around it and recording the readings. Recording a reading every 10 degrees can provide sufficiently dense data points, so that the subsequent calculation of the azimuth angle is more accurate. Setting the origin of the reference coordinate system at the center of the magnetic beacon and ensuring that the three axes of the reference coordinate system are aligned with the axes of the three-axis coil in the magnetic beacon helps to ensure the accuracy and consistency of the measurement. This setting can eliminate the influence of sensor posture changes on the measurement results and improve the accuracy of positioning.

[0085] Furthermore, the zero-order Fourier coefficients of the three-axis readings of the magnetic sensor are calculated based on the magnetic measurement data, and then the azimuth of the sensor is calculated using these coefficients. Fourier analysis can effectively process periodic signals. By calculating the Fourier coefficients, azimuth information can be extracted from complex magnetic field data, which is critical for spatial positioning and navigation. The method covers a 360-degree measurement range, which means that the sensor measures in all directions. This omnidirectional data acquisition ensures a comprehensive understanding of the magnetic field characteristics, making the positioning results more comprehensive and accurate.

[0086] This method is not only suitable for modeling the magnetic properties of spacecraft, but can also be applied to other scenarios that require precise spatial positioning, such as robot navigation, drone trajectory control, etc. Therefore, it has wide applicability and scalability and can be used in a variety of engineering and scientific applications.

[0087] Implementation mode 5: This implementation mode further limits the method for spatial coordinate positioning of a magnetic sensor for modeling magnetic characteristics of a spacecraft described in implementation mode 1. In step S4, the radial distance of the magnetic sensor is calculated according to the first-order Fourier coefficient of the magnetic sensor, including:

[0088]

[0089] Where μ0 is the magnetic permeability of air, A z1_cos is the first-order cosine Fourier coefficient of the z-axis component of the magnetic sensor.

[0090] Embodiment 6: This embodiment further limits the method for spatial coordinate positioning of a magnetic sensor for modeling magnetic characteristics of a spacecraft described in Embodiment 1, and step S5 includes:

[0091]

[0092] Among them, x, y, and z are the three spatial coordinates of the magnetic sensor.

[0093] Embodiment 7: This embodiment further limits the method for spatial coordinate positioning of a magnetic sensor for modeling magnetic characteristics of a spacecraft described in embodiment 1. The method also includes a method for calculating the azimuth angle of the magnetic sensor, including:

[0094]

[0095] Embodiment 8: A magnetic sensor spatial coordinate positioning system for spacecraft magnetic property modeling described in this embodiment, the system includes:

[0096] A magnetic field distribution construction unit, used to construct the magnetic field distribution generated by the magnetic beacon through spherical harmonic functions, and obtain the three components of the magnetic beacon in spherical coordinates;

[0097] A three-component expression unit, used to express the three components of the magnetic sensor in the Cartesian coordinate system through the three components in the spherical coordinate system to obtain a well-defined equation;

[0098] An azimuth acquisition unit, used for calculating the azimuth of the magnetic sensor using Fourier coefficients;

[0099] The spherical coordinate acquisition unit of the magnetic sensor is used to calculate the first-order Fourier coefficient of the magnetic sensor, calculate the radial distance of the magnetic sensor according to the first-order Fourier coefficient of the magnetic sensor, and determine the spherical coordinate of the magnetic sensor;

[0100] The three-dimensional coordinate positioning unit is used to convert the spherical coordinates of the magnetic sensor into Cartesian coordinates to complete the three-dimensional coordinate positioning of the magnetic sensor.

[0101] Embodiment 9. A computer device described in this embodiment includes a memory and a processor, wherein a computer program is stored in the memory. When the processor runs the computer program stored in the memory, the processor executes a magnetic sensor spatial coordinate positioning method for spacecraft magnetic property modeling described in any one of embodiments 1 to 7.

[0102] Embodiment 10. A computer-readable storage medium described in this embodiment stores a computer program, and when the computer program is executed by a processor, the steps of a magnetic sensor spatial coordinate positioning method for spacecraft magnetic property modeling as described in any one of embodiments 1 to 7 are executed.

[0103] Implementation eleven: This implementation provides a specific example of a magnetic sensor spatial coordinate positioning method for spacecraft magnetic property modeling described in Implementation one, and is also used to explain Implementations two to seven. Specifically:

[0104] Step 1: First, the magnetic field distribution generated by the magnetic beacon is expressed by spherical harmonics. The three-component expression of the magnetic beacon in spherical coordinates is as follows:

[0105]

[0106] In the formula, j is the order of the spherical harmonic function, m is the degree of the spherical harmonic function, and a jm and b jm are the spherical harmonic coefficients, r, θ and are the three coordinates of the sensor in spherical coordinates, is the Schmidt quasi-normalized associated Legendre function.

[0107] Here, the magnetic beacon uses 3-axis orthogonal coils. According to the principle of magnetic dipole, when the distance between the magnetic sensor and the magnetic beacon is more than 3 times the size of the magnetic beacon, the magnetic beacon can be used as a magnetic dipole. Therefore, the three orthogonal coils correspond exactly to the 3-axis orthogonal magnetic moment vector M x , M y and M z .

[0108] In equations (1)-(3), if the spherical harmonic order j is set to 1, the magnetic field expression generated by the magnetic dipole in space can be obtained as follows:

[0109]

[0110] According to the multi-level expansion law of spherical harmonics, the relationship between the first-order spherical harmonic coefficient and the three-axis magnetic moment of the magnetic beacon is as follows:

[0111]

[0112] In the formula, I x ,I y and I z is the triaxial coil current, S x , S y and S z is the cross-sectional area of ​​the triaxial coil, N x 、N y and N z is the number of turns of the three-axis coil. Therefore, as long as the electromagnetic parameters and input current of the magnetic beacon are known, its magnetic field at any position in space can be calculated by equations (4)-(7).

[0113] Step 2: Express the three components of the magnetic sensor in the Cartesian coordinate system through the three components in the spherical coordinate system as follows:

[0114]

[0115] Substituting equations (4)-(6) into (8), we can obtain the following expression:

[0116]

[0117] It can be seen from equation (9) that there are three well-defined equations. Since the system of equations is relatively complex, it can only be calculated by optimization algorithm, and the expression of each coordinate cannot be given. However, the optimization algorithm will increase the complexity of the solution, and its result may vary with different initial points, and it is easy to fall into the local optimization solution, so it is not suitable for practical engineering applications.

[0118] Step 3: To solve the above problem, this embodiment introduces an intermediate quantity, Fourier coefficient, to solve the spatial coordinates of each sensor. Figure 2 As shown. The magnetic beacon is placed on a non-magnetic turntable, and the sensor to be tested is surrounded by the magnetic beacon. The origin of the reference coordinate system is set at the center of the magnetic beacon, and the three axes of the coordinate system are aligned with the axes of the three-axis coil in the magnetic beacon. Only 10 sensors are shown in the figure, but this method has no restrictions on the number of sensors and their specific placement, and can simultaneously complete the spatial positioning of any number of sensors.

[0119] Rotate the non-magnetic turntable 360 ​​degrees and record the readings of the magnetic sensor every 10 degrees (the step angle can be adjusted as needed); calculate the zero-order Fourier coefficients of the three-axis readings of the magnetic sensor based on the magnetic measurement data, as shown below:

[0120]

[0121] During the rotation process, only the magnetic beacon rotates while the positions of the sensors remain unchanged. Therefore, equation (9) can be written as follows:

[0122]

[0123] Substituting formula (11) into (10), we can get the following form:

[0124]

[0125] According to the above formula, the azimuth angle of the magnetic sensor can be calculated first.

[0126]

[0127] Step 4: After calculating the azimuth of the magnetic sensor, the first-order Fourier coefficients of the magnetic sensor are calculated as follows:

[0128]

[0129] For A y1_sin The expression is expanded as follows:

[0130]

[0131] Divide the above formula by A z0 , we can get the following expression:

[0132]

[0133] From the above formula, we can see that only the pitch angle of the magnetic sensor is unknown, and the other variables are known. The above formula is simplified as follows to obtain the calculation expression of the pitch angle.

[0134]

[0135] c=2aba 10 +ab 11 sinφ (19)

[0136] d=2ab 11 sinφ+aba 10 (20)

[0137] f=aa 11 cosφ (21)

[0138]

[0139] For A in formula (14), z1_cosThe expression is expanded as follows:

[0140]

[0141] Substituting the calculated pitch angle into (23), the radial distance of the magnetic sensor can be calculated as follows:

[0142]

[0143] Step 5: Convert the spherical coordinates of the magnetic sensor to Cartesian coordinates.

[0144]

[0145] Step 6: The inverse tangent function and the inverse sine function are used in formulas (13) and (14) respectively. Therefore, there is an ambiguity problem. Therefore, the following improvements are made to formulas (13) and (14):

[0146]

[0147] At this point, the three-dimensional coordinate calculation of the magnetic sensor is completed.

[0148] In order to verify the magnetic sensor spatial positioning method proposed in the present invention, the finite element method is used for verification. The finite element model is as follows: Figure 3 Magnetic beacons and target points are annotated by red and blue markers, respectively.

[0149] When the magnetic beacon rotates one circle, the calculated value of the magnetic field at target point 1 is as follows: Figure 4 shown.

[0150] pass Figure 4 The magnetic field data recorded at target point 1 is substituted into the calculation formula derived above to obtain the positioning coordinates. In the same way, the coordinates of the other 7 target points are predicted, and the actual values ​​are compared with the predicted values, as shown in Table 1. It can be seen that the actual values ​​are basically consistent with the predicted values, which can verify the accuracy and effectiveness of the positioning method proposed in this patent.

[0151] Table 1 Positioning results of different target points

[0152]

[0153] Although preferred embodiments of the present disclosure have been described, those skilled in the art may make additional changes and modifications to these embodiments once they are aware of the basic creative concepts. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present disclosure. Obviously, those skilled in the art may make various changes and modifications to the present disclosure without departing from the spirit and scope of the present disclosure. Thus, if these modifications and variations of the present disclosure fall within the scope of the claims of the present disclosure and their equivalents, the present disclosure is also intended to include these modifications and variations.

[0154] Those skilled in the art will appreciate that the embodiments of the present disclosure may be provided as methods, systems or computer program products. Therefore, the present disclosure may take the form of a complete hardware embodiment, a complete software embodiment or an embodiment combining software and hardware. Moreover, the present disclosure may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0155] The present disclosure is described with reference to flowcharts and / or block diagrams of methods, devices (systems) and computer program products according to embodiments of the present disclosure. It should be understood that each process and / or block in the flowchart and / or block diagram and the combination of processes and / or blocks in the flowchart and / or block diagram can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 These computer program instructions can also be stored in a computer-readable memory that can guide a computer or other programmable data processing device to work in a specific way, so that the instructions stored in the computer-readable memory produce a product including an instruction device, which implements the functions specified in the process. Figure 1 A process or multiple processes and / or boxes Figure 1 These computer program instructions can also be loaded onto a computer or other programmable data processing device, so that a series of operation steps are executed on the computer or other programmable device to produce a computer-implemented process, so that the instructions executed on the computer or other programmable device provide for implementing the process in the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0156] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present disclosure rather than to limit its protection scope. Although the present disclosure has been described in detail with reference to the above embodiments, ordinary technicians in the relevant field should understand that after reading the present disclosure, those skilled in the art can still make various changes, modifications or equivalent substitutions to the specific implementation methods of the invention, but these changes, modifications or equivalent substitutions are all within the protection scope of the disclosed claims to be approved.

Claims

1. A method for spatial coordinate positioning of a magnetic sensor for modeling magnetic properties of a spacecraft, characterized in that: The method comprises: S1: Construct the magnetic field distribution generated by the magnetic beacon through spherical harmonics and obtain the three components of the magnetic beacon in spherical coordinates; S2: The three components of the magnetic sensor in the Cartesian coordinate system are expressed by the three components in the spherical coordinate system to obtain a well-defined equation; S3: Calculate the azimuth angle of the magnetic sensor using the Fourier coefficients; S4: calculating the first-order Fourier coefficient of the magnetic sensor, calculating the radial distance of the magnetic sensor according to the first-order Fourier coefficient of the magnetic sensor, and determining the spherical coordinates of the magnetic sensor; S5: converting the spherical coordinates of the magnetic sensor into Cartesian coordinates to complete the three-dimensional coordinate positioning of the magnetic sensor; The step S1 comprises: The three-component expression of the magnetic beacon in spherical coordinates is: in, , and They are the three components of the magnetic field generated by the magnetic beacon in the spherical coordinate system, r is the radial distance, θ is the polar angle, φ is the azimuth; The relationship between the first-order spherical harmonic coefficient and the three-axis magnetic moment of the magnetic beacon is: in, I x , I y and I z is the three-axis coil current, S x , S y and S z is the cross-sectional area of ​​the triaxial coil, N x , N y and N z is the number of turns of the triaxial coil, , , They are the three components of magnetic moment of the magnetic beacon; The step S2 comprises: in, , , They are the three components of the magnetic field of the magnetic beacon in the Cartesian coordinate system, , , They are the three components of the magnetic moment of the magnetic beacon.

2. A method for spatial coordinate positioning of a magnetic sensor for modeling magnetic properties of a spacecraft according to claim 1, characterized in that: The step S3 comprises: Place the magnetic beacon on a non-magnetic turntable, and surround the sensor to be tested around the magnetic beacon; The origin of the reference coordinate system is set at the center of the magnetic beacon, and the three axes of the reference coordinate system are respectively aligned with the axes of the three-axis coil in the magnetic beacon; Rotate the non-magnetic turntable 360 ​​degrees and record the reading of the magnetic sensor every 10 degrees; Calculate the zero-order Fourier coefficients of the three-axis readings of the magnetic sensor according to the magnetic measurement data; Calculate the azimuth of the magnetic sensor based on the zero-order Fourier coefficient : in, For magnetic sensor y The zero-order Fourier coefficient of the axis component, For magnetic sensor x The zero-order Fourier coefficient of the axis component.

3. The method for spatial coordinate positioning of a magnetic sensor for modeling magnetic properties of a spacecraft according to claim 1, characterized in that: The step S4 calculates the radial distance of the magnetic sensor according to the first-order Fourier coefficient of the magnetic sensor, including: in, is the magnetic permeability of air, For magnetic sensor z First-order cosine Fourier coefficients of the axis components.

4. The method for spatial coordinate positioning of a magnetic sensor for modeling magnetic properties of a spacecraft according to claim 1, characterized in that: The step S5 comprises: in, x , y , z They are the three spatial coordinates of the magnetic sensor.

5. The method for spatial coordinate positioning of a magnetic sensor for modeling magnetic properties of a spacecraft according to claim 1, characterized in that: The method also includes a calculation method for optimizing the azimuth angle of the magnetic sensor, comprising: 。 6. A magnetic sensor spatial coordinate positioning system for spacecraft magnetic property modeling, characterized in that: The system comprises: A magnetic field distribution construction unit is used to construct the magnetic field distribution generated by the magnetic beacon through spherical harmonic functions, and obtain the three components of the magnetic beacon in spherical coordinates; including: The three-component expression of the magnetic beacon in spherical coordinates is: in, , and They are the three components of the magnetic field generated by the magnetic beacon in the spherical coordinate system, r is the radial distance, θ is the polar angle, φ is the azimuth; The relationship between the first-order spherical harmonic coefficient and the three-axis magnetic moment of the magnetic beacon is: in, I x , I y and I z is the three-axis coil current, S x , S y and S z is the cross-sectional area of ​​the triaxial coil, N x , N y and N z is the number of turns of the triaxial coil, , , They are the three components of magnetic moment of the magnetic beacon; The three-component expression unit is used to express the three components of the magnetic sensor in the Cartesian coordinate system through the three components in the spherical coordinate system to obtain a well-defined equation; including: in, , , They are the three components of the magnetic field generated by the magnetic beacon in the Cartesian coordinate system, , , They are the three components of magnetic moment of the magnetic beacon; An azimuth acquisition unit, used for calculating the azimuth of the magnetic sensor using Fourier coefficients; The spherical coordinate acquisition unit of the magnetic sensor is used to calculate the first-order Fourier coefficient of the magnetic sensor, calculate the radial distance of the magnetic sensor according to the first-order Fourier coefficient of the magnetic sensor, and determine the spherical coordinate of the magnetic sensor; The three-dimensional coordinate positioning unit is used to convert the spherical coordinates of the magnetic sensor into Cartesian coordinates to complete the three-dimensional coordinate positioning of the magnetic sensor.

7. A computer device, characterized in that: It includes a memory and a processor, wherein a computer program is stored in the memory. When the processor runs the computer program stored in the memory, the processor executes a magnetic sensor spatial coordinate positioning method for spacecraft magnetic property modeling according to any one of claims 1 to 5.

8. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, which, when executed by a processor, executes the steps of a method for spatial coordinate positioning of a magnetic sensor for modeling magnetic properties of a spacecraft as described in any one of claims 1-5.

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