Solution and modeling system for ambiguity of spherical harmonic model of spacecraft magnetic characteristics in zero magnetic chamber

Abstract

The present invention belongs to the field of aerospace, and specifically relates to a solution and modeling system for the ambiguity of the spherical harmonic model of the magnetic characteristics of a spacecraft in a zero magnetic chamber. Acquire sensor data; calculate Fourier coefficients; based on the position information of the sensor and the Fourier coefficients, give a spherical harmonic coefficient calculation matrix; based on the spherical harmonic coefficient calculation matrix, calculate the spherical harmonic coefficients that characterize the spacecraft; calculate the magnetic field distribution of the spacecraft to be tested outside the shielding room by using the calculated spherical harmonic coefficients, and compare with the experimental test values; if an ambiguity problem occurs, the magnetic gradient equation is generated for the spacecraft outside the zero magnetic chamber, that is, the spherical harmonic coefficients that characterize the magnetic characteristics of the spacecraft are unique, and the ambiguity problem is eliminated to complete the modeling of the magnetic characteristics of the spacecraft. If no ambiguity problem occurs, the modeling of the magnetic characteristics of the spacecraft is completed directly. The present invention is used to solve the problem that two spacecraft with different magnetic characteristics may have the same magnetic field distribution in a zero magnetic chamber after the magnetic fields generated by each of them and the magnetic fields generated by their mirror images are superimposed.

Description

Technical Field

[0001] The invention belongs to the field of aerospace, and in particular relates to a solution to the ambiguity of a spherical harmonic model of magnetic characteristics of a spacecraft in a zero-magnetic chamber and a modeling system. 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 exploration and data reliability, it is necessary to conduct magnetic measurement and modeling of the magnetic properties of the spacecraft and to restrict its magnetic field.

[0003] Since the zero magnetic chamber has a highly stable and ultra-clean magnetic field environment, the magnetic measurement of spacecraft in the zero magnetic chamber can eliminate the influence of environmental magnetic interference, thereby improving the accuracy of magnetic property modeling. However, according to the mirror method, the magnetic field distribution of the spacecraft to be measured in the zero magnetic chamber is generated by the original spacecraft and its mirror spacecraft. This may lead to ambiguity, that is, two spacecraft with different magnetic properties may have the same magnetic field distribution in the zero magnetic chamber after the magnetic fields generated by each spacecraft and the magnetic fields generated by their mirror images are superimposed. Summary of the invention

[0004] The present invention provides a solution to the ambiguity of the spherical harmonic model of the magnetic characteristics of a spacecraft in a zero magnetic chamber, so as to solve the problem that two spacecraft with different magnetic characteristics may have the same magnetic field distribution after the magnetic fields generated by each spacecraft and their mirror images are superimposed in the zero magnetic chamber.

[0005] The invention provides a modeling system of a spherical harmonic model of magnetic characteristics of a spacecraft in a zero-magnetic chamber, which is used to solve the ambiguity problem that may occur when the spherical harmonic model of magnetic characteristics of a spacecraft in a zero-magnetic chamber is built.

[0006] The present invention is achieved through the following technical solutions:

[0007] A method for solving the ambiguity of a spherical harmonic model of magnetic characteristics of a spacecraft in a zero magnetic chamber, the method comprising the following steps:

[0008] Step 1: Place the spacecraft to be tested on the non-magnetic turntable, set the distance and placement between the sensor and the non-magnetic turntable inside the zero magnetic chamber, rotate the non-magnetic turntable, and obtain the sensor data;

[0009] Step 2: Calculate the Fourier coefficients based on the data obtained in step 1;

[0010] Step 3: Based on the position information of the sensor in step 1 and the Fourier coefficients in step 2, the matrix is ​​calculated by giving the spherical harmonic coefficients;

[0011] Step 4: Based on the spherical harmonic coefficient calculation matrix in step 3, calculate the spherical harmonic coefficients that characterize the spacecraft;

[0012] Step 5: Calculate the magnetic field distribution of the spacecraft under test outside the shielding room by using the calculated spherical harmonic coefficients, and compare it with the experimental test value to verify whether there is an ambiguity problem; if there is an ambiguity problem, proceed to step 6; if there is no ambiguity problem, proceed to step 7;

[0013] Step 6: Add the magnetic gradient equation generated by the spacecraft in the zero magnetic field room to the spherical harmonic function calculation matrix, and recalculate the spherical harmonic coefficients. That is, the spherical harmonic coefficients that characterize the magnetic characteristics of the spacecraft are unique. After eliminating the ambiguity, proceed directly to step 7;

[0014] Step 7: The spacecraft magnetic properties modeling is completed.

[0015] Furthermore, the step 2 is specifically to calculate the following Fourier coefficients by formula (1):

[0016]

[0017] in, is the Fourier coefficient of the constant component of the n-axis magnetic induction intensity of sensor k; and are the sine and cosine Fourier coefficients of the n-axis magnetic induction intensity of sensor k, The n-axis magnetic induction intensity of sensor k, m is one of the spherical harmonic orders, φ is the azimuth coordinate, and n is the sensor's 3-axis direction.

[0018] Furthermore, the step 3 specifically includes determining the relationship between the spherical harmonic coefficients of the original image spacecraft and the mirror image spacecraft, as shown in the following formula:

[0019]

[0020] in, and are the spherical harmonic coefficients of the original image spacecraft; and are the spherical harmonic coefficients of the mirrored spacecraft along the x-axis; and are the spherical harmonic coefficients of the mirrored spacecraft along the y-axis; and are the spherical harmonic coefficients of the mirrored spacecraft along the z-axis; j and m are the orders of the spherical harmonics.

[0021] Furthermore, the spherical harmonic function expression of the magnetic field generated by the spacecraft in spherical coordinates is as follows:

[0022]

[0023]

[0024]

[0025] Where j and m are the orders of the spherical harmonics, 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.

[0026] Furthermore, the spherical harmonic coefficient a j1 The relationship is expressed as follows:

[0027] Substituting (3)-(5) into formula (1), we get:

[0028]

[0029] Among them, M1 is jointly participated by the spacecraft to be tested and its mirror image;

[0030]

[0031]

[0032]

[0033]

[0034]

[0035] Where k is the sensor number, q is the number of sensors, j is one of the spherical harmonic orders, μ0 is the air magnetic permeability, is the spherical harmonic coefficient calculation matrix of the original image spacecraft; is the spherical harmonic coefficient calculation matrix of the spacecraft mirrored along the x-axis; is the spherical harmonic coefficient calculation matrix of the spacecraft mirrored along the y-axis; is the spherical harmonic coefficient calculation matrix of the spacecraft mirrored along the z-axis, and θ k ′ are the mirror coordinates and pitch angle coordinates of the mirror spacecraft respectively;

[0036] Furthermore, the step 5 is specifically to obtain the spherical harmonic coefficients a by the method of inverting the generalized inverse matrix j1 The least squares solution of ;

[0037] The calculation formula is as follows:

[0038]

[0039] Furthermore, the step 6 is specifically that the spherical harmonic function expression of the magnetic gradient generated by the zero magnetic outdoor spacecraft in spherical coordinates is as follows:

[0040]

[0041]

[0042]

[0043] Substituting the magnetic gradient formulas (13)-(15) above into the equation (1) and adding it to M1, the equation is as follows:

[0044]

[0045] Then, the same method is used to calculate the spherical harmonic coefficients as shown below.

[0046]

[0047] A modeling system for a spherical harmonic model of magnetic characteristics of a spacecraft in a zero-magnetic chamber, the modeling system uses the above-mentioned solution to the ambiguity of the spherical harmonic model of magnetic characteristics of a spacecraft in a zero-magnetic chamber, the modeling system includes

[0048] A calculation module, used for calculating Fourier coefficients of the acquired data;

[0049] Based on the position information of the sensor and the Fourier coefficients, the matrix of spherical harmonic coefficients is calculated;

[0050] Based on the spherical harmonic coefficient calculation matrix, the spherical harmonic coefficients characterizing the spacecraft are calculated;

[0051] The comparison module calculates the magnetic field distribution of the spacecraft under test outside the shielding room through the calculated spherical harmonic coefficients, and compares it with the experimental test values ​​to verify whether there is any ambiguity problem; if there is any ambiguity problem, the ambiguity elimination module is used, and if there is no ambiguity problem, the spacecraft magnetic characteristics modeling is completed;

[0052] The ambiguity elimination module is used to add the magnetic gradient equation generated by the spacecraft in the zero-magnetic field to the spherical harmonic function calculation matrix, and then recalculate the spherical harmonic coefficients. That is, the spherical harmonic coefficients that characterize the magnetic properties of the spacecraft are unique. After eliminating the ambiguity problem, the modeling of the spacecraft magnetic properties is directly completed.

[0053] A computer device comprises a memory, a processor and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the above method is implemented.

[0054] A computer-readable storage medium stores a computer program, and the computer program implements the above method when executed by a processor.

[0055] The beneficial effects of the present invention are:

[0056] The present invention eliminates possible ambiguity problems by adding a magnetic gradient equation, and obtains a deterministic spherical harmonic model of the magnetic characteristics of the spacecraft. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 It is a schematic diagram of the magnetic property test of a spacecraft in a zero-magnetic chamber of the present invention.

[0058] Figure 2 It is a schematic diagram of the spacecraft mirror image in the zero-magnetic room of the present invention.

[0059] Figure 3 It is a schematic diagram of the arrangement of magnetic measurement of spacecraft in the zero-magnetic chamber of the present invention.

[0060] Figure 4 It is a schematic diagram of algorithm verification of the present invention.

[0061] Figure 5 It is a schematic diagram of the arrangement of the zero-magnetic outdoor spacecraft magnetic gradient test of the present invention. DETAILED DESCRIPTION

[0062] In the following description, specific details such as specific system structures, technologies, etc. are provided for the purpose of illustration rather than limitation, so as to provide a thorough understanding of the embodiments of the present application. However, it should be clear to those skilled in the art that the present application may also be implemented in other embodiments without these specific details. In other cases, detailed descriptions of well-known systems, devices, circuits, and methods are omitted to prevent unnecessary details from obstructing the description of the present application.

[0063] It should be understood that when used in this specification and the appended claims, the term "comprising" indicates the presence of described features, integers, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components and / or groups thereof.

[0064] It should also be understood that the terms used in this application specification are only for the purpose of describing specific embodiments and are not intended to limit the application. As used in this application specification and the appended claims, the singular forms "a", "an" and "the" are intended to include plural forms unless the context clearly indicates otherwise.

[0065] The following is attached to this application specification Figure 1-5, the technical solutions in the embodiments of the present application are clearly and completely described. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present application.

[0066] In the following description, many specific details are set forth to facilitate a full understanding of the present application, but the present application may also be implemented in other ways different from those described herein, and those skilled in the art may make similar generalizations without violating the connotation of the present application. Therefore, the present application is not limited to the specific embodiments disclosed below.

[0067] Embodiment 1

[0068] The embodiment of the present invention provides a solution to the ambiguity of the spherical harmonic model of the magnetic characteristics of a spacecraft in a zero magnetic chamber, and the solution includes the following steps:

[0069] Step 1: Place the spacecraft to be tested on the non-magnetic turntable, set the distance and placement position between the fluxgate sensor and the non-magnetic turntable inside the zero magnetic chamber, rotate the non-magnetic turntable, and obtain the data of the fluxgate sensor;

[0070] Step 2: Calculate the Fourier coefficients based on the data obtained in step 1;

[0071] Step 3: Based on the position information of the fluxgate sensor in step 1 and the Fourier coefficients in step 2, a spherical harmonic coefficient calculation matrix is ​​given; here, a calculation matrix considering the magnetic characteristics of the spacecraft and the effect of the zero magnetic chamber needs to be given; Figure 2 A schematic diagram showing the distribution of the mirror image spacecraft when the spacecraft to be tested is placed inside the zero magnetic chamber;

[0072] Step 4: Based on the spherical harmonic coefficient calculation matrix in step 3, calculate the spherical harmonic coefficients that characterize the spacecraft;

[0073] Step 5: Calculate the magnetic field distribution of the spacecraft under test outside the shielding room by using the calculated spherical harmonic coefficients, and compare it with the experimental test value to verify whether there is an ambiguity problem; if there is an ambiguity problem, proceed to step 6; if there is no ambiguity problem, proceed to step 7;

[0074] Step 6: Add the magnetic gradient equation generated by the spacecraft in the zero magnetic field room to the spherical harmonic function calculation matrix, and recalculate the spherical harmonic coefficients. That is, the spherical harmonic coefficients that characterize the magnetic characteristics of the spacecraft are unique. After eliminating the ambiguity, proceed directly to step 7;

[0075] Step 7: The spacecraft magnetic properties modeling is completed.

[0076] Furthermore, the step 2 is specifically to calculate the following Fourier coefficients by formula (1):

[0077]

[0078] in, is the Fourier coefficient of the constant component of the n-axis magnetic induction intensity of sensor k; and are the sine and cosine Fourier coefficients of the n-axis magnetic induction intensity of sensor k, The n-axis magnetic induction intensity of sensor k, m is one of the spherical harmonic orders, φ is the azimuth coordinate, and n is the sensor's 3-axis direction.

[0079] Furthermore, the specific step 3 is that, according to the mirror method, it can be known that, due to the existence of the zero magnetic chamber, the magnetic field distribution of the spacecraft under test in the zero magnetic chamber is actually generated by the spacecraft under test and its mirror image spacecraft. In order to obtain the spherical harmonic coefficient calculation matrix considering the magnetic field generated by the mirror image spacecraft, it is also necessary to know the relationship between the spherical harmonic coefficients of the original image spacecraft and the mirror image spacecraft, as shown in the following formula:

[0080]

[0081] in, and are the spherical harmonic coefficients of the original image spacecraft; and are the spherical harmonic coefficients of the mirrored spacecraft along the x-axis; and are the spherical harmonic coefficients of the mirrored spacecraft along the y-axis; and are the spherical harmonic coefficients of the mirrored spacecraft along the z-axis; j and m are the orders of the spherical harmonics.

[0082] Furthermore, the spherical harmonic function expression of the magnetic field generated by the spacecraft in spherical coordinates is as follows:

[0083]

[0084]

[0085]

[0086] Where j and m are the orders of the spherical harmonics, 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.

[0087] Furthermore, the spherical harmonic coefficient a j1The relationship is expressed as follows:

[0088] Substituting (3)-(5) into formula (1), we get:

[0089]

[0090] Among them, M1 is jointly participated by the spacecraft to be tested and its mirror image;

[0091]

[0092]

[0093]

[0094]

[0095]

[0096] Where k is the sensor number, q is the number of sensors, j is one of the spherical harmonic orders, μ0 is the air magnetic permeability, is the spherical harmonic coefficient calculation matrix of the original image spacecraft; is the spherical harmonic coefficient calculation matrix of the spacecraft mirrored along the x-axis; is the spherical harmonic coefficient calculation matrix of the spacecraft mirrored along the y-axis; is the spherical harmonic coefficient calculation matrix of the spacecraft mirrored along the z-axis, and θ k ′ are the mirror coordinates and pitch angle coordinates of the mirror spacecraft respectively;

[0097] Furthermore, the step 5 is specifically to calculate the spherical harmonic coefficients characterizing the spacecraft, and the spherical harmonic coefficients a can be obtained by the method of inverting the generalized inverse matrix: j1 The least squares solution of ;

[0098] The calculation formula is as follows:

[0099]

[0100] Here only the spherical harmonic coefficients a are given j1 The calculation process of , but other spherical harmonic coefficients can be obtained by the same method.

[0101] Furthermore, the step 6 is specifically that the spherical harmonic function expression of the magnetic gradient generated by the zero magnetic outdoor spacecraft in spherical coordinates is as follows:

[0102]

[0103]

[0104]

[0105] Substituting the magnetic gradient formulas (13)-(15) above into the equation (1) and adding it to M1, the equation is as follows:

[0106]

[0107] Then, the spherical harmonic coefficients are calculated using the same method as above, as shown below.

[0108]

[0109] Specifically, in order to verify the solution to the ambiguity problem in modeling the residual magnetic characteristics of spacecraft in the zero magnetic chamber proposed by the present invention, the magnetic field distribution with a pitch angle of π / 2 and a radius of 0.7m was calculated by the finite element method, the algorithm without adding the gradient equation, and the algorithm adding the gradient equation. The spacecraft to be tested uses a combination of 5 permanent magnets and 3 sensors to measure the magnetic field data when it rotates clockwise once, such as Figure 3 shown.

[0110] The magnetic characteristics of the combination of five permanent magnets are modeled using the measurement data in the zero magnetic chamber, and the model calculates the magnetic field distribution of the permanent magnet combination at a mirror distance of 0.7 m and a pitch angle of π / 2, such as Figure 4 shown.

[0111] The calculation results without adding the gradient algorithm are very different from the finite element results, that is, an ambiguity problem occurs. Therefore, the present invention completes the establishment of the gradient equation and recalculates the spherical harmonic coefficients through the following spacecraft magnetic gradient test layout outside the zero magnetic chamber.

[0112] according to Figure 5 It can be seen that the calculation results of the algorithm model after adding the gradient equation are basically consistent with the finite element calculation results, which can verify that the algorithm proposed in the present invention eliminates ambiguity and obtains a unique definite model, verifying its effectiveness and accuracy.

[0113] A method for modeling the magnetic properties of spacecraft is proposed that combines the magnetic vector inside the zero magnetic chamber with the magnetic gradient outside the zero magnetic chamber; higher-order simulations, more mirror interfaces and magnetic sensor arrangements derived from the above method are within the scope of the rights.

[0114] Embodiment 2

[0115] The present embodiment provides a modeling system for a spherical harmonic model of magnetic characteristics of a spacecraft in a zero-magnetic room. The modeling system uses the solution method for the ambiguity of the spherical harmonic model of magnetic characteristics of a spacecraft in a zero-magnetic room as described in the first embodiment to solve the ambiguity problem in the modeling of the spherical harmonic model of magnetic characteristics of a spacecraft in a zero-magnetic room. The modeling system includes a calculation module, a comparison module and an ambiguity elimination module.

[0116] The calculation module is used to calculate the Fourier coefficients of the acquired data;

[0117] Based on the position information of the fluxgate sensor and the Fourier coefficients, the spherical harmonic coefficient calculation matrix is ​​given; here, the calculation matrix considering the magnetic characteristics of the spacecraft and the effect of the zero magnetic chamber needs to be given; Figure 2 A schematic diagram showing the distribution of the mirror image spacecraft when the spacecraft to be tested is placed inside the zero magnetic chamber;

[0118] Based on the spherical harmonic coefficient calculation matrix, the spherical harmonic coefficients characterizing the spacecraft are calculated;

[0119] The comparison module calculates the magnetic field distribution of the spacecraft under test outside the shielding room through the calculated spherical harmonic coefficients, and compares it with the experimental test values ​​to verify whether there is an ambiguity problem; if there is an ambiguity problem, the ambiguity elimination module is used, and if there is no ambiguity problem, the spacecraft magnetic characteristic modeling is completed;

[0120] The ambiguity elimination module is used to add the magnetic gradient equation generated by the spacecraft in the zero magnetic field outdoor to the spherical harmonic function calculation matrix, and then recalculate the spherical harmonic coefficients, that is, the spherical harmonic coefficients characterizing the magnetic characteristics of the spacecraft are unique. After eliminating the ambiguity problem, the spacecraft magnetic characteristics modeling is directly completed.

[0121] Furthermore, the calculation of the Fourier coefficients in the calculation module is specifically to calculate the following Fourier coefficients by formula (1):

[0122]

[0123] in, is the Fourier coefficient of the constant component of the n-axis magnetic induction intensity of sensor k; and are the sine and cosine Fourier coefficients of the n-axis magnetic induction intensity of sensor k, The n-axis magnetic induction intensity of sensor k, m is one of the spherical harmonic orders, φ is the azimuth coordinate, and n is the sensor's 3-axis direction.

[0124] Furthermore, the given spherical harmonic coefficient calculation matrix of the calculation module is specifically: It can be known from the mirror method that due to the existence of the zero magnetic chamber, the magnetic field distribution of the spacecraft under test in the zero magnetic chamber is actually generated by the spacecraft under test and its mirror image spacecraft. In order to obtain the spherical harmonic coefficient calculation matrix considering the magnetic field generated by the mirror image spacecraft, it is also necessary to know the relationship between the spherical harmonic coefficients of the original image spacecraft and the mirror image spacecraft, as shown in the following formula,

[0125]

[0126] in, and are the spherical harmonic coefficients of the original image spacecraft; and are the spherical harmonic coefficients of the mirrored spacecraft along the x-axis; and are the spherical harmonic coefficients of the mirrored spacecraft along the y-axis; and are the spherical harmonic coefficients of the mirrored spacecraft along the z-axis; j and m are the orders of the spherical harmonics.

[0127] Furthermore, the spherical harmonic function expression of the magnetic field generated by the spacecraft in spherical coordinates is as follows:

[0128]

[0129]

[0130]

[0131] Where j and m are the orders of the spherical harmonics, 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.

[0132] Furthermore, the spherical harmonic coefficient a j1 The relationship is expressed as follows:

[0133] Substituting (3)-(5) into formula (1), we get:

[0134]

[0135] Among them, M1 is jointly participated by the spacecraft to be tested and its mirror image;

[0136]

[0137]

[0138]

[0139]

[0140]

[0141] Where k is the sensor number, q is the number of sensors, j is one of the spherical harmonic orders, μ0 is the air magnetic permeability, is the spherical harmonic coefficient calculation matrix of the original image spacecraft; is the spherical harmonic coefficient calculation matrix of the spacecraft mirrored along the x-axis; is the spherical harmonic coefficient calculation matrix of the spacecraft mirrored along the y-axis; is the spherical harmonic coefficient calculation matrix of the spacecraft mirrored along the z-axis, and θ k ′ are the mirror coordinates and pitch angle coordinates of the mirror spacecraft respectively;

[0142] Furthermore, the calculation module calculates the spherical harmonic coefficients representing the spacecraft specifically as follows: the spherical harmonic coefficients representing the spacecraft can be calculated by the method of inverting the generalized inverse matrix to obtain the spherical harmonic coefficients a j1 The least squares solution of ;

[0143] The calculation formula is as follows:

[0144]

[0145] Here only the spherical harmonic coefficients a are given j1 The calculation process of , but other spherical harmonic coefficients can be obtained by the same method.

[0146] Furthermore, the ambiguity elimination module specifically eliminates the ambiguity problem by expressing the spherical harmonic function of the magnetic gradient generated by the spacecraft in the zero magnetic field outdoor in spherical coordinates as follows:

[0147]

[0148]

[0149]

[0150] Substituting the magnetic gradient formulas (13)-(15) above into the equation (1) and adding it to M1, the equation is as follows:

[0151]

[0152] Then, the spherical harmonic coefficients are calculated using the same method as above, as shown below.

[0153]

[0154] Specifically, this system proposes a spacecraft magnetic properties modeling system that combines a zero-magnetic indoor magnetic vector with a zero-magnetic outdoor magnetic gradient. Higher-order simulations, more mirror interfaces, and magnetic sensor arrangements derived from the above system are all within the scope of the rights.

[0155] Embodiment 3

[0156] An embodiment of the present invention provides an electronic device, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the memory is used to store software programs and modules, and the processor executes various functional applications and data processing by running the software programs and modules stored in the memory. The memory and the processor are connected via a bus. Specifically, the processor implements any step in the first embodiment above by running the computer program stored in the memory.

[0157] It should be understood that in the embodiments of the present invention, the processor referred to may be a central processing unit (CPU), and the processor may also be other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc.

[0158] The memory may include a read-only memory, a flash memory, and a random access memory, and provides instructions and data to the processor. A part or all of the memory may also include a nonvolatile random access memory.

[0159] It should be understood that if the above-mentioned integrated module / unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on such an understanding, the present invention implements all or part of the processes in the above-mentioned embodiment method, and can also be completed by instructing the relevant hardware through a computer program. The above-mentioned computer program can be stored in a computer-readable storage medium, and the computer program can implement the steps of the above-mentioned various method embodiments when executed by the processor. Among them, the above-mentioned computer program includes computer program code, and the above-mentioned computer program code can be in source code form, object code form, executable file or some intermediate form. The above-mentioned computer-readable medium may include: any entity or device capable of carrying the above-mentioned computer program code, recording medium, U disk, mobile hard disk, magnetic disk, optical disk, computer memory, read-only memory (ROM), random access memory (RAM), electric carrier signal, telecommunication signal and software distribution medium. It should be noted that the content contained in the above-mentioned computer-readable storage medium can be appropriately increased or decreased according to the requirements of legislation and patent practice in the jurisdiction.

[0160] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

[0161] Those skilled in the art can clearly understand that, for the convenience and simplicity of description, only the division of the above-mentioned functional units and modules is used as an example for illustration. In practical applications, the above-mentioned function allocation can be completed by different functional units and modules as needed, that is, the internal structure of the above-mentioned device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiment can be integrated in a processing unit, or each unit can exist physically separately, or two or more units can be integrated in one unit. The above-mentioned integrated unit can be implemented in the form of hardware or in the form of software functional units. In addition, the specific names of the functional units and modules are only for the convenience of distinguishing each other, and are not used to limit the scope of protection of the present invention. The specific working process of the units and modules in the above-mentioned system can refer to the corresponding process in the aforementioned method embodiment, which will not be repeated here.

[0162] It should be noted that the methods and detailed examples provided in the above embodiments can be combined with the devices and equipment provided in the embodiments, and references can be made to each other, and no further details will be given.

[0163] Those skilled in the art will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of the present invention.

[0164] In the embodiments provided by the present invention, it should be understood that the disclosed apparatus / terminal equipment and method can be implemented in other ways. For example, the apparatus / equipment embodiments described above are only illustrative, for example, the division of the above modules or units is only a logical function division, and in actual implementation, other division methods can be used, for example, multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed.

[0165] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that the technical solutions described in the above embodiments may still be modified, or some of the technical features may be replaced by equivalents. Such modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention, and should be included in the protection scope of the present invention.

Claims

1. A solution to the ambiguity of the spherical harmonic model of spacecraft magnetic characteristics in a zero-magnetic chamber, characterized in that: The solution includes the following steps: Step 1: Place the spacecraft to be tested on the non-magnetic turntable, set the distance and placement between the sensor and the non-magnetic turntable inside the zero magnetic chamber, rotate the non-magnetic turntable, and obtain the sensor data; Step 2: Calculate the Fourier coefficients based on the data obtained in step 1; Step 3: Based on the position information of the sensor in step 1 and the Fourier coefficients in step 2, the matrix is ​​calculated by giving the spherical harmonic coefficients; Step 4: Based on the spherical harmonic coefficient calculation matrix in step 3, calculate the spherical harmonic coefficients that characterize the spacecraft; Step 5: Calculate the magnetic field distribution of the spacecraft under test outside the shielding room by using the calculated spherical harmonic coefficients, and compare it with the experimental test value to verify whether there is an ambiguity problem; if there is an ambiguity problem, proceed to step 6; if there is no ambiguity problem, proceed to step 7; Step 6: Add the magnetic gradient equation generated by the spacecraft in the zero magnetic field room to the spherical harmonic function calculation matrix, and recalculate the spherical harmonic coefficients. That is, the spherical harmonic coefficients that characterize the magnetic characteristics of the spacecraft are unique. After eliminating the ambiguity, proceed directly to step 7; Step 7: Completed the modeling of the spacecraft magnetic properties; Specifically, step 2 is to calculate the following Fourier coefficients by formula (1): in, is the Fourier coefficient of the constant component of the n-axis magnetic induction intensity of sensor k; and are the sine and cosine Fourier coefficients of the n-axis magnetic induction intensity of sensor k, The n-axis magnetic induction intensity of sensor k, m is one of the spherical harmonic orders, φ is the azimuth coordinate, n is the sensor 3-axis direction, and k is the sensor number; Specifically, step 3 is to determine the relationship between the spherical harmonic coefficients of the original image spacecraft and the mirror image spacecraft, as shown in the following formula: in, and are the spherical harmonic coefficients of the original image spacecraft; and are the spherical harmonic coefficients of the mirrored spacecraft along the x-axis; and are the spherical harmonic coefficients of the mirrored spacecraft along the y-axis; and are the spherical harmonic coefficients of the mirrored spacecraft along the z-axis; j and m are the order and degree of the spherical harmonic function; The spherical harmonic function expression of the magnetic field generated by the spacecraft in spherical coordinates is as follows: Among them, j and m are the order and degree of the spherical harmonics, a jm and b jm are the spherical harmonic coefficients, r, θ and φ are the three coordinates of the sensor in spherical coordinates; is the Schmidt quasi-normalized associated Legendre function, μ0 is the air magnetic permeability.

2. According to claim 1, a method for solving the ambiguity of the spherical harmonic model of the magnetic characteristics of spacecraft in a zero magnetic chamber is characterized in that: Spherical harmonic coefficient a j1 The relationship is expressed as follows: Substituting (3)-(5) into formula (1), we get: Among them, M1 is jointly participated by the spacecraft to be tested and its mirror image; Where k is the sensor number, q is the number of sensors, j is one of the spherical harmonic orders, μ0 is the air magnetic permeability, is the spherical harmonic coefficient calculation matrix of the original image spacecraft; is the spherical harmonic coefficient calculation matrix of the spacecraft mirrored along the x-axis; is the spherical harmonic coefficient calculation matrix of the spacecraft mirrored along the y-axis; is the spherical harmonic coefficient calculation matrix of the spacecraft mirrored along the z-axis, r k ' j+2 and θ k ′ are the mirror coordinates and pitch angle coordinates of the mirror spacecraft respectively.

3. According to claim 1, a method for solving the ambiguity of the spherical harmonic model of the magnetic characteristics of spacecraft in a zero magnetic chamber is characterized in that: Specifically, step 5 is to obtain the spherical harmonic coefficients a by using the generalized inverse matrix inversion method. j1 The least squares solution of ; The calculation formula is as follows:

4. According to claim 3, a method for solving the ambiguity of the spherical harmonic model of the magnetic characteristics of spacecraft in a zero magnetic chamber is characterized in that: Specifically, step 6 is as follows: the spherical harmonic function expression of the magnetic gradient generated by the zero magnetic outdoor spacecraft in spherical coordinates is as follows: Substituting the magnetic gradient formulas (13)-(15) above into the equation (1) and adding it to M1, the equation is as follows: Then, the same method is used to calculate the spherical harmonic coefficients as shown below.

5. A modeling system for a spherical harmonic model of spacecraft magnetic characteristics in a zero-magnetic chamber, characterized in that: The modeling system uses a solution to the ambiguity of the spherical harmonic model of the magnetic characteristics of a spacecraft in a zero magnetic chamber as described in any one of claims 1-4, and the modeling system includes A calculation module, used for calculating Fourier coefficients of the acquired data; Based on the position information of the sensor and the Fourier coefficients, the matrix of spherical harmonic coefficients is calculated; Based on the spherical harmonic coefficient calculation matrix, the spherical harmonic coefficients characterizing the spacecraft are calculated; The comparison module calculates the magnetic field distribution of the spacecraft under test outside the shielding room through the calculated spherical harmonic coefficients, and compares it with the experimental test values ​​to verify whether there is any ambiguity problem; If there is an ambiguity problem, the ambiguity elimination module is used. If there is no ambiguity problem, the spacecraft magnetic characteristics modeling is completed; The ambiguity elimination module is used to add the magnetic gradient equation generated by the spacecraft in the zero magnetic field to the spherical harmonic function calculation matrix, and then recalculate the spherical harmonic coefficients. That is, the spherical harmonic coefficients that characterize the magnetic characteristics of the spacecraft are unique. After eliminating the ambiguity problem, the spacecraft magnetic characteristics modeling is directly completed. The calculation of the Fourier coefficients in the calculation module is specifically to calculate the following Fourier coefficients by formula (1): in, is the Fourier coefficient of the constant component of the n-axis magnetic induction intensity of sensor k; and are the sine and cosine Fourier coefficients of the n-axis magnetic induction intensity of sensor k, The n-axis magnetic induction intensity of sensor k, m is one of the spherical harmonic orders, φ is the azimuth coordinate, n is the sensor 3-axis direction, and k is the sensor number; The given spherical harmonic coefficient calculation matrix of the calculation module is specifically to determine the relationship between the spherical harmonic coefficients of the original image spacecraft and the mirror image spacecraft, as shown in the following formula: in, and are the spherical harmonic coefficients of the original image spacecraft; and are the spherical harmonic coefficients of the mirrored spacecraft along the x-axis; and are the spherical harmonic coefficients of the mirrored spacecraft along the y-axis; and are the spherical harmonic coefficients of the mirrored spacecraft along the z-axis; j and m are the orders of the spherical harmonics; The spherical harmonic function expression of the magnetic field generated by the spacecraft in spherical coordinates is as follows: Where j and m are the orders of the spherical harmonics, 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.

6. A computer device, characterized in that: The method comprises a memory, a processor, and a computer program stored in the memory and running on the processor, wherein when the processor executes the computer program, the method according to any one of claims 1 to 4 is implemented.

7. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the method according to any one of claims 1 to 4 is implemented.

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