Planetary magnetic field model coefficient determination method and apparatus, and electronic device

Abstract

The present disclosure provides a planetary magnetic field model coefficient determination method and apparatus, and an electronic device, applied to a planetary magnetic field model based on spherical harmonic function fitting. The method comprises: acquiring a magnetic field observation vector of a target planet, and constructing linear equations between the magnetic field observation vector and a model coefficient corresponding to a planetary magnetic field model; determining a linear coefficient matrix corresponding to the linear equations, dividing the linear coefficient matrix into a plurality of coefficient matrix blocks according to a preset number of rows, and dividing the magnetic field observation vector into a plurality of vector blocks; for each coefficient matrix block and a corresponding vector block, substituting the matrix block and the corresponding vector block into the linear equations to calculate a corresponding block intermediate solution; and summing all block intermediate solutions to determine a target planetary magnetic field model coefficient. The present disclosure has low complexity and reduces the memory required for solving the linear equations, so that the process can be implemented on a personal computer, thereby facilitating scientific experiments.

Description

Method and device for determining coefficients of a planetary magnetic field model, and electronic device

[0001] Cross-reference to Related Applications

[0002] The present application claims priority to the Chinese patent application No. 202410424488.4, filed on April 10, 2024, and entitled "Method and device for determining coefficients of a planetary magnetic field model, and electronic device", the entire content of which is incorporated herein by reference. TECHNICAL FIELD

[0003] The present disclosure relates to the technical field of magnetic field analysis, in particular to a method and device for determining coefficients of a planetary magnetic field model, and an electronic device. BACKGROUND

[0004] At present, in the process of solving the coefficients of a planetary magnetic field model based on spherical harmonic function fitting, a large linear equation set needs to be solved. Generally, the linear equation set is converted into a weighted least square problem with a regularization term introduced, and an optimal solution is obtained through iteration.

[0005] However, taking the Earth's magnetic field as an example, the spherical harmonic coefficients required to describe the Earth's magnetic field have a high order, and the number of coefficients usually exceeds 10,000. Meanwhile, the number of observation values is huge, generally reaching the order of magnitude of millions. Since matrix multiplication operations are involved in solving a large linear equation set, the huge number of observation values corresponds to the number of rows of the influence matrix. The calculation process is relatively complex and needs to be performed in a distributed parallel computing cluster with a large memory, which cannot be implemented on a personal computer and is inconvenient for scientific experiments.

[0006] SUMMARY

[0007] The embodiments of the present disclosure at least provide a method and device for determining coefficients of a planetary magnetic field model, and an electronic device, which have a low complexity and reduce the memory required for solving a linear equation set, so that the process can be implemented on a personal computer and is convenient for scientific experiments.

[0008] The embodiments of the present disclosure provide a method for determining coefficients of a planetary magnetic field model, which is applied to a planetary magnetic field model based on spherical harmonic function fitting. The method comprises the following steps:

[0009] Obtaining a magnetic field observation value vector of a target planet, and constructing a linear equation set between the magnetic field observation value vector and the model coefficients corresponding to the planetary magnetic field model;

[0010] Determining a linear coefficient matrix corresponding to the linear equation set, dividing the linear coefficient matrix into a plurality of coefficient matrix blocks according to a preset row number, and dividing the magnetic field observation value vector into a plurality of vector blocks;

[0011] calculating a corresponding block intermediate solution for each of the coefficient matrix blocks and the corresponding vector blocks;

[0012] adding up all the block intermediate solutions and bringing into the linear equation set to calculate target planetary magnetic field model coefficients.

[0013] In an alternative embodiment, after determining the linear coefficient matrix corresponding to the linear equation set, dividing the linear coefficient matrix into a plurality of matrix blocks according to a preset row number, and dividing the magnetic field observation value vector into a plurality of vector blocks, the method further comprises:

[0014] configuring a corresponding weight for each magnetic field observation value in the magnetic field observation value vector to generate a weight matrix, wherein the weight matrix is a diagonal matrix;

[0015] dividing the weight matrix into a plurality of weight matrix blocks according to the preset row number.

[0016] In an alternative embodiment, the calculation of the corresponding block intermediate solution specifically comprises:

[0017] respectively multiplying each of the coefficient matrix blocks with the weight matrix block to determine a first intermediate matrix;

[0018] respectively multiplying each of the vector blocks with the weight matrix block to determine a first intermediate vector;

[0019] multiplying the first intermediate matrix with a transposed matrix corresponding to the first intermediate matrix to determine a first target matrix;

[0020] multiplying the transposed matrix corresponding to the first intermediate matrix with the first intermediate vector to determine a second target matrix;

[0021] determining the first target matrix and the second target matrix as the block intermediate solution.

[0022] In an alternative embodiment, the step of calculating target planetary magnetic field model coefficients specifically comprises:

[0023] adding up all the first target matrices;

[0024] adding up all the second target matrices;

[0025] calculating the product between the inverse matrix corresponding to the added-up first target matrices and the added-up second target matrices as the target planetary magnetic field model coefficients.

[0026] In an alternative embodiment, after dividing the weight matrix into a plurality of weight matrix blocks according to the preset row number, the method further comprises:

[0027] The out-point removal processing is performed on the magnetic field observation value of the target planet to generate a corresponding out-point suppression matrix, wherein the out-point suppression matrix is a diagonal matrix;

[0028] The square root operation is performed on the diagonal elements of the out-point suppression matrix to generate a second intermediate matrix;

[0029] The second intermediate matrix is divided into a plurality of out-point suppression matrix blocks according to the preset row number.

[0030] In an optional implementation, the calculation of the corresponding block intermediate solution specifically includes:

[0031] For each out-point suppression matrix block, the out-point suppression matrix block and the first intermediate matrix are multiplied respectively to determine a third intermediate matrix;

[0032] The out-point suppression matrix block and the first intermediate vector are multiplied respectively to determine a second intermediate vector;

[0033] The third intermediate matrix and the transpose matrix corresponding to the third intermediate matrix are multiplied to determine a third target matrix;

[0034] The transpose matrix corresponding to the third intermediate matrix and the second intermediate vector are multiplied to determine a fourth target matrix;

[0035] The third target matrix and the fourth target matrix are determined as the block intermediate solution.

[0036] In an optional implementation, the step of calculating the target planet magnetic field model coefficient specifically includes:

[0037] All the third target matrices are accumulated and summed;

[0038] All the fourth target matrices are accumulated and summed;

[0039] The product between the inverse matrix corresponding to the accumulated and summed third target matrix and the accumulated and summed fourth target matrix is the target planet magnetic field model coefficient.

[0040] In an optional implementation, the calculation of the target planet magnetic field model coefficient by bringing all the block intermediate solutions into the linear equation set after accumulation and summation includes: x = (D T D) -1 D T b

[0041] Wherein, x represents the target planet magnetic field model coefficient, D j = W j Aj ; b j = W j d j ; A j represents the jth coefficient matrix block; d j represents the jth vector block; W j represents the jth weight matrix block.

[0042] The magnetic field observation value vector of the target planet is obtained, comprising:

[0043] The magnetic field of the target planet is observed, the planet surface is divided into a plurality of observation grids according to the latitude and longitude of the target planet, the magnetic field of the observation points in the grid is observed, and the magnetic field observation value vector including all observation values is determined.

[0044] In an optional implementation, the linear equation set between the magnetic field observation value vector and the model coefficient corresponding to the planet magnetic field model comprises: Ax = d

[0045] Wherein, A represents a linear coefficient matrix composed of linear relationship coefficients between model coefficients and magnetic field observation values; x represents the model coefficient corresponding to the planet magnetic field model; d represents the magnetic field observation value vector.

[0046] In an optional implementation, the linear coefficient matrix is divided into a plurality of coefficient matrix blocks according to the preset number of rows, and the magnetic field observation value vector is divided into a plurality of vector blocks, comprising:

[0047] According to the preset number of rows, the linear coefficient matrix is divided into a plurality of coefficient matrix blocks horizontally without changing the number of linear coefficient matrices corresponding to the linear equation set; wherein the number of rows of each coefficient matrix block is equal to the preset number of rows;

[0048] According to the preset number of rows, the magnetic field observation value vector is divided into a plurality of vector blocks, and each vector block includes a number of magnetic field observation values equal to the preset number of rows.

[0049] In an optional implementation, the corresponding block intermediate solution is calculated for each coefficient matrix block and corresponding vector block, comprising:

[0050] In an optional implementation, the corresponding block intermediate solution is calculated for each coefficient matrix block and corresponding vector block, comprising:

[0051] The embodiment of the present disclosure further provides a device for determining coefficients of a planetary magnetic field model, applied to a planetary magnetic field model based on spherical harmonic function fitting, and the device comprises:

[0052] a linear equation set construction module configured to acquire a magnetic field observation value vector of a target planet, and construct a linear equation set between the magnetic field observation value vector and model coefficients corresponding to the planetary magnetic field model;

[0053] a block division module configured to determine a linear coefficient matrix corresponding to the linear equation set, divide the linear coefficient matrix into a plurality of coefficient matrix blocks according to a preset row number, and divide the magnetic field observation value vector into a plurality of vector blocks;

[0054] a block solution module configured to calculate a corresponding block intermediate solution for each of the coefficient matrix blocks and the corresponding vector blocks;

[0055] a model coefficient calculation module configured to calculate target planetary magnetic field model coefficients by bringing a summation of all the block intermediate solutions into the linear equation set.

[0056] The embodiment of the present disclosure further provides an electronic device, comprising a processor, a memory and a bus, the memory stores machine readable instructions executable by the processor, when the electronic device is running, the processor and the memory communicate through the bus, and the machine readable instructions are executed by the processor to perform the above-mentioned method for determining coefficients of a planetary magnetic field model, or steps in any possible implementation manner of the above-mentioned method for determining coefficients of a planetary magnetic field model.

[0057] The embodiment of the present disclosure further provides a computer readable storage medium, which stores a computer program, and the computer program is executed by a processor to perform the above-mentioned method for determining coefficients of a planetary magnetic field model, or steps in any possible implementation manner of the above-mentioned method for determining coefficients of a planetary magnetic field model.

[0058] The embodiment of the present disclosure further provides a computer program product, comprising a computer program / instruction, which is executed by a processor to implement the above-mentioned method for determining coefficients of a planetary magnetic field model, or steps in any possible implementation manner of the above-mentioned method for determining coefficients of a planetary magnetic field model.

[0059] The method for determining a planetary magnetic field model coefficient provided by the embodiments of the present disclosure, the device and the electronic equipment, applied to a planetary magnetic field model based on spherical harmonic function fitting, a magnetic field observation value vector of a target planet is obtained, a linear equation set between the magnetic field observation value vector and the model coefficient corresponding to the planetary magnetic field model is constructed; a linear coefficient matrix corresponding to the linear equation set is determined, the linear coefficient matrix is divided into a plurality of coefficient matrix blocks according to a preset row number, and the magnetic field observation value vector is divided into a plurality of vector blocks; for each coefficient matrix block and the corresponding vector block, the matrix block and the corresponding vector block are substituted into the linear equation set respectively, and the corresponding block intermediate solution is calculated; all the block intermediate solutions are accumulated and summed to determine the target planetary magnetic field model coefficient. The complexity can be low, the memory required for solving the linear equation set is reduced, the process can be realized on a personal computer, and scientific experiments are facilitated.

[0060] In order to make the above-mentioned purpose, features and advantages of the present disclosure more obvious and easy to understand, the following preferred embodiments are specifically described below, and the accompanying drawings are described in detail as follows. BRIEF DESCRIPTION OF DRAWINGS

[0061] In order to more clearly illustrate the technical solutions of the embodiments of the present disclosure, the following will briefly introduce the drawings needed to be used in the embodiments. The drawings are incorporated into the specification and form a part of the specification, which show the embodiments consistent with the present disclosure, and are used to illustrate the technical solutions of the present disclosure together with the specification. It should be understood that the following drawings only show some embodiments of the present disclosure, and therefore should not be regarded as a limitation on the scope, and for those skilled in the art, other related drawings can also be obtained without creative labor.

[0062] FIG. 1 shows a flowchart of a method for determining a planetary magnetic field model coefficient provided by the embodiments of the present disclosure;

[0063] FIG. 2 shows a flowchart of a method for calculating a block intermediate solution provided by the embodiments of the present disclosure;

[0064] FIG. 3 shows a flowchart of another method for calculating a block intermediate solution provided by the embodiments of the present disclosure;

[0065] FIG. 4 shows a schematic diagram of a device for determining a planetary magnetic field model coefficient provided by the embodiments of the present disclosure;

[0066] FIG. 5 shows a schematic diagram of an electronic equipment provided by the embodiments of the present disclosure. DETAILED DESCRIPTION

[0067] To make the purposes, technical solutions, and advantages of the embodiments of the present disclosure clearer, the technical solutions in the embodiments of the present disclosure will be described clearly and completely below with reference to the drawings in the embodiments of the present disclosure. Obviously, the described embodiments are only a part of the embodiments of the present disclosure, but not all the embodiments. The components of the embodiments of the present disclosure generally described and shown in the drawings herein can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present disclosure provided in the drawings is not intended to limit the scope of the claimed present disclosure, but only represents selected embodiments of the present disclosure. Based on the embodiments of the present disclosure, all other embodiments obtained by those skilled in the art without creative work fall within the scope of protection of the present disclosure.

[0068] It should be noted that similar reference numbers and letters represent similar items in the following drawings, and therefore, once an item is defined in one drawing, it does not need to be further defined and explained in subsequent drawings.

[0069] The term "and / or" herein only describes an association relationship, which means that there can be three relationships, for example, A and / or B can mean that A exists alone, A and B exist together, and B exists alone. In addition, the term "at least one" herein means any one of a plurality or any combination of at least two of a plurality, for example, including at least one of A, B, and C can mean including any one or more elements selected from the set consisting of A, B, and C.

[0070] It is found through research that, at present, in the process of solving the coefficients of a planetary magnetic field model based on spherical harmonic function fitting, a large linear equation set needs to be solved, and the linear equation set is generally converted into a weighted least square problem with a regularization term introduced, and an optimal solution is obtained through iteration. However, taking the Earth's magnetic field as an example, the spherical harmonic coefficients required to describe the Earth's magnetic field have a high order, the number of coefficients usually exceeds 10,000, and the number of observation values is huge, generally reaching the order of magnitude of millions. Since matrix multiplication operations are involved in the process of solving a large linear equation set, the huge number of observation values correspond to the number of rows of the influence matrix, the calculation process is relatively complex, needs to be carried out in a distributed parallel computing cluster with large memory, and cannot be implemented on a personal computer, which is inconvenient for scientific experiments.

[0071] Based on the above research, the present disclosure provides a method and device for determining the coefficients of a planetary magnetic field model, and an electronic device. The method is applied to a planetary magnetic field model based on spherical harmonic function fitting. A magnetic field observation value vector of a target planet is obtained, and a linear equation set between the magnetic field observation value vector and the corresponding model coefficients of the planetary magnetic field model is constructed. A linear coefficient matrix corresponding to the linear equation set is determined, and the linear coefficient matrix is divided into multiple coefficient matrix blocks according to a preset row number. The magnetic field observation value vector is divided into multiple vector blocks. For each coefficient matrix block and the corresponding vector block, the matrix block and the corresponding vector block are substituted into the linear equation set, respectively, and a corresponding block intermediate solution is calculated. All the block intermediate solutions are accumulated and summed to determine the target planetary magnetic field model coefficients. The method can have a lower complexity, reduce the required memory for solving the linear equation set, and can be implemented on a personal computer, which is convenient for scientific experiments.

[0072] To facilitate the understanding of the present embodiment, first, a method for determining the coefficients of a planetary magnetic field model is described in detail. The execution subject of the method for determining the coefficients of a planetary magnetic field model provided by the present embodiment is generally a computer device with certain computing power, which may, for example, include a terminal device or a server or other processing device. The terminal device may, for example, be a user equipment (UE), a mobile device, a user terminal, a terminal, a cellular phone, a cordless phone, a personal digital assistant (PDA), a handheld device, a computing device, a vehicle-mounted device, a wearable device, etc. In some possible implementation manners, the method for determining the coefficients of a planetary magnetic field model can be implemented by a processor calling computer-readable instructions stored in a memory.

[0073] Referring to FIG. 1, a flowchart of a method for determining the coefficients of a planetary magnetic field model is provided. The method includes steps S101-S104.

[0074] S101, a magnetic field observation value vector of a target planet is obtained, and a linear equation set between the magnetic field observation value vector and the corresponding model coefficients of the planetary magnetic field model is constructed.

[0075] In a specific implementation, the magnetic field of a target planet is observed, the surface of the planet is divided into multiple observation grids according to the latitude and longitude of the target planet, the magnetic field of the observation points in the grids is observed, and a magnetic field observation value vector including all observation values is determined.

[0076] Here, the magnetic field observation value vector is a column vector with a row number equal to the number of magnetic field observation values.

[0077] Further, a linear equation set between the magnetic field observation value vector and the model coefficients corresponding to the planetary magnetic field model is constructed, as shown in the following formula: Ax=d

[0078] Wherein, A represents a linear coefficient matrix composed of linear relationship coefficients between the model coefficients and the magnetic field observation value; x represents the model coefficients corresponding to the planetary magnetic field model; d represents the magnetic field observation value vector.

[0079] S102, determine the linear coefficient matrix corresponding to the linear equation set, and divide the linear coefficient matrix into multiple coefficient matrix blocks according to a preset row number, and divide the magnetic field observation value vector into multiple vector blocks.

[0080] In a specific implementation, according to the preset row number, the linear coefficient matrix is divided into multiple coefficient matrix blocks horizontally without changing the column number of the linear coefficient matrix corresponding to the linear equation set, and the row number of each coefficient matrix block is equal to the preset row number.

[0081] Here, the column number of the linear coefficient matrix is equal to the element number of the model coefficient, and the element number of the model coefficient is related to the order of the spherical harmonic coefficients required to describe the planetary magnetic field.

[0082] Further, the magnetic field observation value vector is also divided into multiple vector blocks according to the preset row number, and each vector block includes a number of magnetic field observation values equal to the preset row number.

[0083] It should be noted that the preset row number can be set according to actual needs, which is not limited here.

[0084] S103, for each coefficient matrix block and corresponding vector block, calculate the corresponding block intermediate solution.

[0085] In a specific implementation, the model coefficient can be expressed by using the linear coefficient matrix and the magnetic field observation value vector in an inversion manner, and each coefficient matrix block and the corresponding vector block are substituted to calculate the corresponding block intermediate solution.

[0086] Specifically, the block intermediate solution can be calculated based on the following steps 1-3:

[0087] Step 1, for each coefficient matrix block, calculate the first matrix product between the coefficient matrix block and the corresponding transpose matrix.

[0088] Step 2, for each vector block, calculate the second matrix product between the vector block and the transpose matrix corresponding to each coefficient matrix block.

[0089] Step 3, determine the first matrix product and the second matrix product as the block intermediate solution.

[0090] For example, for the coefficient matrix block Aj The corresponding first matrix product is For the vector block d j The corresponding second matrix product is

[0091] S104, accumulate and sum all the partial intermediate solutions to determine the target planetary magnetic field model coefficient.

[0092] In a specific implementation, after accumulating and summing all the first matrix products and all the second matrix products respectively, the product between the inverse matrix corresponding to the accumulated and summed first matrix product and the accumulated and summed second matrix product is the target planetary magnetic field model coefficient.

[0093] For example, for the first matrix product The second matrix product The corresponding target planetary magnetic field model coefficient can be calculated based on the following formula: x = (D T D) -1 D T b

[0094] Where x represents the model coefficient corresponding to the planetary magnetic field model; D j = A j ; b j = d j ; A j represents the jth coefficient matrix block; d j represents the jth vector block.

[0095] As a possible implementation, after the division of the coefficient matrix block and the vector block, a corresponding weight can also be configured for each magnetic field observation value in the magnetic field observation value vector to generate a weight matrix, where the weight matrix is a diagonal matrix, and the elements on the diagonal are the weight values of the corresponding magnetic field observation values; the weight matrix is divided into multiple weight matrix blocks according to a preset row number, and the row number and the column number of the weight matrix block are equal to the preset row number.

[0096] Optionally, the weight value of the magnetic field observation value can adopt the inverse of the standard deviation corresponding to each magnetic field observation value in the observation grid, which can be set according to actual needs, without specific limitation here.

[0097] In a specific implementation, referring to the flowchart of a method for calculating a partial intermediate solution provided by an embodiment of the disclosure shown in FIG. 2, the method comprises steps S201-S205, wherein:

[0098] S201, for each weight matrix block, multiply the weight matrix block with each coefficient matrix block respectively to determine a first intermediate matrix.

[0099] S202, respectively multiplying the weight matrix block with each of the vector blocks to determine a first intermediate vector.

[0100] S203, multiplying the first intermediate matrix with a transposed matrix corresponding to the first intermediate matrix to determine a first target matrix.

[0101] S204, multiplying the transposed matrix corresponding to the first intermediate matrix with the first intermediate vector to determine a second target matrix.

[0102] S205, determining that the first target matrix and the second target matrix are the block intermediate solution.

[0103] In a specific implementation, for the coefficient matrix block A j , the vector block d j , and the weight matrix block W j , the first intermediate matrix is D j =W j A j , and the first target matrix is Wherein D j =W j A j ; the second target matrix is Wherein b j =W j d j .

[0104] Further, in the process of calculating the target planetary magnetic field model coefficient, all the first target matrices are accumulated and summed; all the second target matrices are accumulated and summed; the product between the inverse matrix corresponding to the accumulated and summed first target matrix and the accumulated and summed second target matrix is the target planetary magnetic field model coefficient.

[0105] Illustratively, the target planetary magnetic field model coefficient can also be calculated using the formula in step S104, and can be calculated based on the following formula: x=(D T D) -1 D T b

[0106] Wherein, x represents the planetary magnetic field model corresponding model coefficient; D j =W j A j ; b j =W j d j ; A j represents the jth coefficient matrix block; d j represents the jth vector block; W j represents the jth weight matrix block.

[0107] As another possible implementation, after the division process of the weight matrix block, an outlier removal process can also be performed on the magnetic field observation values of the target planet to generate a corresponding outlier suppression matrix, wherein the outlier suppression matrix is a diagonal matrix; the diagonal elements of the outlier suppression matrix are subjected to square root operation to generate a second intermediate matrix; and the second intermediate matrix is divided into a plurality of outlier suppression matrix blocks according to a preset row number.

[0108] Here, the outlier removal process can adopt existing outlier removal techniques to remove data points that are not needed in the magnetic field model coefficient process.

[0109] In a specific implementation, referring to FIG. 3, a flowchart of another method for calculating a block intermediate solution provided by an embodiment of the present disclosure is shown, and the method includes steps S301-S305, wherein:

[0110] S301, for each of the outlier suppression matrix blocks, the outlier suppression matrix block is multiplied with the first intermediate matrix respectively to determine a third intermediate matrix.

[0111] S302, the outlier suppression matrix block is multiplied with the first intermediate vector respectively to determine a second intermediate vector.

[0112] S303, the third intermediate matrix is multiplied with a transpose matrix corresponding to the third intermediate matrix to determine a third target matrix.

[0113] S304, the transpose matrix corresponding to the third intermediate matrix is multiplied with the second intermediate vector to determine a fourth target matrix.

[0114] S305, the third target matrix and the fourth target matrix are determined as the block intermediate solution.

[0115] In a specific implementation, for the coefficient matrix block A j , the vector block d j , the weight matrix block W j , and the outlier suppression matrix block M j , first, each diagonal element in the outlier suppression matrix block M j in the form of a diagonal matrix is subjected to square root operation to obtain a second intermediate matrix The third intermediate matrix is The fourth target matrix is wherein The fourth target matrix is wherein

[0116] Further, in the process of calculating the target planetary magnetic field model coefficient, for each outer point suppression matrix block, the outer point suppression matrix block is multiplied with the first intermediate matrix respectively to determine a third intermediate matrix; the outer point suppression matrix block is multiplied with the first intermediate vector respectively to determine a second intermediate vector; the third intermediate matrix is multiplied with a transpose matrix corresponding to the third intermediate matrix to determine a third target matrix; a transpose matrix corresponding to the third intermediate matrix is multiplied with the second intermediate vector to determine a fourth target matrix; the third target matrix and the fourth target matrix are determined as the block intermediate solution.

[0117] For example, the target planetary magnetic field model coefficient can also be calculated by the formula in step S104, based on the following formula: x = (D T D) -1 D T b

[0118] Wherein, x represents the planetary magnetic field model corresponding model coefficient; A j represents the jth coefficient matrix block; d j represents the jth vector block; W j represents the jth weight matrix block; represents the jth second intermediate matrix.

[0119] The method for determining a planetary magnetic field model coefficient provided by the embodiments of the present disclosure is applied to a planetary magnetic field model based on spherical harmonic function fitting. By obtaining a magnetic field observation value vector of a target planet, a linear equation set between the magnetic field observation value vector and the planetary magnetic field model corresponding model coefficient is constructed. A linear coefficient matrix corresponding to the linear equation set is determined, the linear coefficient matrix is divided into multiple coefficient matrix blocks according to a preset row number, and the magnetic field observation value vector is divided into multiple vector blocks. For each coefficient matrix block and the corresponding vector block, the matrix block and the corresponding vector block are substituted into the linear equation set respectively, and a corresponding block intermediate solution is calculated. The target planetary magnetic field model coefficient is determined by accumulating and summing all the block intermediate solutions. The method can have a lower complexity, reduce the required memory for solving the linear equation set, and can be implemented on a personal computer, which is convenient for scientific experiments.

[0120] Those skilled in the art can understand that the sequence of writing each step in the above method of the specific embodiment does not mean a strict execution sequence and does not constitute any limitation on the implementation process. The specific execution sequence of each step should be determined by its function and possible internal logic.

[0121] Based on the same inventive concept, the disclosure embodiments also provide a device for determining planetary magnetic field model coefficients corresponding to the method for determining planetary magnetic field model coefficients. Since the principle of the device in the disclosure embodiments solves the problem similarly to the above-mentioned method for determining planetary magnetic field model coefficients in the disclosure embodiments, the implementation of the device can be referred to the implementation of the method, and the repeated parts will not be described here.

[0122] Please refer to FIG. 4, which is a schematic diagram of a device for determining planetary magnetic field model coefficients provided by the disclosure embodiments. As shown in FIG. 4, the device 400 for determining planetary magnetic field model coefficients provided by the disclosure embodiments applied to the planetary magnetic field model based on spherical harmonic function fitting includes:

[0123] The linear equation set construction module 410 is configured to obtain the magnetic field observation value vector of the target planet, and construct a linear equation set between the magnetic field observation value vector and the model coefficients corresponding to the planetary magnetic field model.

[0124] The block division module 420 is configured to determine the linear coefficient matrix corresponding to the linear equation set, divide the linear coefficient matrix into a plurality of coefficient matrix blocks according to a preset row number, and divide the magnetic field observation value vector into a plurality of vector blocks.

[0125] The block solution module 430 is configured to calculate a corresponding block intermediate solution for each of the coefficient matrix blocks and the corresponding vector blocks.

[0126] The model coefficient calculation module 440 is configured to calculate the target planetary magnetic field model coefficients by adding and summing all the block intermediate solutions and bringing them into the linear equation set.

[0127] The description of the processing flow of each module in the device and the interaction flow between the modules can be referred to the related description in the above-mentioned method embodiments, which will not be described in detail here.

[0128] The device for determining planetary magnetic field model coefficients provided by the disclosure embodiments is applied to the planetary magnetic field model based on spherical harmonic function fitting. By obtaining the magnetic field observation value vector of the target planet, a linear equation set between the magnetic field observation value vector and the model coefficients corresponding to the planetary magnetic field model is constructed. The linear coefficient matrix corresponding to the linear equation set is determined, the linear coefficient matrix is divided into a plurality of coefficient matrix blocks according to a preset row number, and the magnetic field observation value vector is divided into a plurality of vector blocks. For each of the coefficient matrix blocks and the corresponding vector blocks, the matrix block and the corresponding vector block are respectively substituted into the linear equation set, and the corresponding block intermediate solution is calculated. All the block intermediate solutions are added and summed to determine the target planetary magnetic field model coefficients. It can have a lower complexity, and reduce the required memory for solving the linear equation set, so that the process can be implemented on a personal computer, which is convenient for scientific experiments.

[0129] Corresponding to the method for determining the planetary magnetic field model coefficients in FIG. 1, the embodiment of the present disclosure further provides an electronic device 500, as shown in FIG. 5, which is a structural schematic diagram of the electronic device 500 provided by the embodiment of the present disclosure, and includes:

[0130] The processor 51, the memory 52, and the bus 53; the memory 52 is configured to store execution instructions, including the internal memory 521 and the external memory 522; the internal memory 521 is also called the internal storage, which is configured to temporarily store operation data in the processor 51 and exchange data with the external memory 522 such as a hard disk, and the processor 51 exchanges data with the external memory 522 through the internal memory 521; when the electronic device 500 is running, the processor 51 and the memory 52 communicate through the bus 53, so that the processor 51 executes the steps of the method for determining the planetary magnetic field model coefficients in FIG. 1.

[0131] The embodiment of the present disclosure further provides a computer readable storage medium, which stores a computer program, and the computer program is run by a processor to execute the steps of the method for determining the planetary magnetic field model coefficients described in the above method embodiment. Wherein, the storage medium can be a volatile or non-volatile computer readable storage medium.

[0132] The embodiment of the present disclosure further provides a computer program product, which includes computer instructions, and the computer instructions are executed by a processor to execute the steps of the method for determining the planetary magnetic field model coefficients described in the above method embodiment. For details, please refer to the above method embodiment, which will not be described here.

[0133] Wherein, the above computer program product can be specifically implemented by hardware, software or a combination thereof. In one optional embodiment, the computer program product is specifically embodied as a computer storage medium, and in another optional embodiment, the computer program product is specifically embodied as a software product, such as a software development kit (Software Development Kit, SDK) and the like.

[0134] Those skilled in the art can clearly understand that, for the convenience and brevity of the description, the specific working process of the apparatus described above can refer to the corresponding process in the foregoing method embodiment, and will not be repeated here. In several embodiments provided in the present disclosure, it should be understood that the disclosed apparatus and method can be implemented in other ways. The apparatus embodiments described above are only schematic. For example, the division of the units is only a logical function division, and another division can be made in actual implementation. For example, a plurality of units or components can be combined or integrated into another system, or some features can be ignored or not executed. In addition, the coupling or direct coupling or communication connection between the units shown or discussed can be indirect coupling or communication connection through some communication interface, and can be electrical, mechanical or other forms.

[0135] The units described as separate components can or can not be physically separate, and the components shown as units can or can not be physical units, i.e. can be located in one place or distributed on a plurality of network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the embodiment.

[0136] In addition, the functional units in each embodiment of the present disclosure can be integrated in one processing unit, or each unit can be physically present separately, or two or more units can be integrated in one unit.

[0137] If the functions are realized in the form of software function units and sold or used as independent products, they can be stored in a non-volatile computer readable storage medium executable by a processor. Based on this understanding, the technical solutions of the present disclosure essentially or the part that contributes to the prior art or part of the technical solutions can be embodied in the form of a software product. The computer software product is stored in a storage medium, and includes a plurality of instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the method described in the various embodiments of the present disclosure. The foregoing storage medium includes: a U disk, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk, and various program code storage media.

[0138] Finally, it should be noted that the above-described embodiments are merely specific implementations of the present disclosure, which are used to illustrate the technical solutions of the present disclosure, but not to limit the same. The protection scope of the present disclosure is not limited thereto. Although the present disclosure has been described in detail with reference to the foregoing embodiments, it should be understood by those skilled in the art that any modification or easy-to-think change or equivalent replacement of some technical features of the technical solutions recorded in the foregoing embodiments can be made within the technical range disclosed by the present disclosure. The modification, change or replacement do not make the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present disclosure, and should be covered within the protection scope of the present disclosure. Therefore, the protection scope of the present disclosure should be subject to the protection scope of the claims. Industrial applicability

[0139] The present disclosure constructs a linear equation set between the magnetic field observation value vector of the target planet and the corresponding model coefficients of the planet magnetic field model by acquiring the magnetic field observation value vector of the target planet; determines a linear coefficient matrix corresponding to the linear equation set, divides the linear coefficient matrix into multiple coefficient matrix blocks according to a preset row number, divides the magnetic field observation value vector into multiple vector blocks; for each coefficient matrix block and the corresponding vector block, respectively, substitutes the matrix block and the corresponding vector block into the linear equation set, calculates the corresponding block intermediate solution; accumulates and sums all the block intermediate solutions to determine the target planet magnetic field model coefficient. It can have lower complexity, reduce the required memory for solving the linear equation set, and make the process be implemented on a personal computer, which is convenient for scientific experiments and has better practicability.

Claims

1. A method for determining the coefficients of a planetary magnetic field model, characterized in that: Applied to a planetary magnetic field model based on spherical harmonic function fitting, the method includes: Obtaining a magnetic field observation value vector of a target planet, and constructing a linear equation system between the magnetic field observation value vector and corresponding model coefficients of the planetary magnetic field model; Determining a linear coefficient matrix corresponding to the linear equation system, dividing the linear coefficient matrix into a plurality of coefficient matrix blocks according to a preset number of rows, and dividing the magnetic field observation value vector into a plurality of vector blocks; For each coefficient matrix block and the corresponding vector block, calculating a corresponding block intermediate solution; All the intermediate solutions of the blocks are accumulated and summed up and then brought into the linear equation group to calculate the magnetic field model coefficients of the target planet.

2. The method according to claim 1, characterized in that After determining a linear coefficient matrix corresponding to the linear equation system, dividing the linear coefficient matrix into a plurality of coefficient matrix blocks according to a preset number of rows, and dividing the magnetic field observation value vector into a plurality of vector blocks, the method further includes: Configuring a corresponding weight for each magnetic field observation value in the magnetic field observation value vector to generate a weight matrix, wherein the weight matrix is ​​a diagonal matrix; The weight matrix is ​​divided into a plurality of weight matrix blocks according to the preset number of rows.

3. The method according to claim 2, characterized in that Calculate the intermediate solution of the block, including: For each of the weight matrix blocks, multiply the weight matrix block by each of the coefficient matrix blocks to determine a first intermediate matrix; Multiplying the weight matrix block by each of the vector blocks respectively to determine a first intermediate vector; multiplying the first intermediate matrix by a transposed matrix corresponding to the first intermediate matrix to determine a first target matrix; multiplying the transposed matrix corresponding to the first intermediate matrix by the first intermediate vector to determine a second target matrix; The first target matrix and the second target matrix are determined to be the block intermediate solution.

4. The method according to claim 3, characterized in that The steps for calculating the target planet magnetic field model coefficients include: Accumulate and sum all the first target matrices; Accumulate and sum all the second target matrices; The inverse matrix corresponding to the first target matrix after cumulative summation is calculated, and the product of the inverse matrix and the second target matrix after cumulative summation is the target planet magnetic field model coefficient.

5. The method according to claim 3, characterized in that After dividing the weight matrix into a plurality of weight matrix blocks according to the preset number of rows, the method further includes: Performing outlier removal processing on the magnetic field observation values ​​of the target planet to generate a corresponding outlier suppression matrix, wherein the outlier suppression matrix is ​​a diagonal matrix; Performing a square root operation on the diagonal elements of the exterior point suppression matrix to generate a second intermediate matrix; The second intermediate matrix is ​​divided into a plurality of outlier suppression matrix blocks according to the preset number of rows.

6. The method according to claim 5, characterized in that The calculation of the block intermediate solution specifically includes: For each of the outlier suppression matrix blocks, multiply the outlier suppression matrix block by the first intermediate matrix to determine a third intermediate matrix; multiplying the outlier suppression matrix block by the first intermediate vector respectively to determine a second intermediate vector; multiplying the third intermediate matrix by a transposed matrix corresponding to the third intermediate matrix to determine a third target matrix; multiplying the transposed matrix corresponding to the third intermediate matrix by the second intermediate vector to determine a fourth target matrix; The third target matrix and the fourth target matrix are determined as the block intermediate solutions.

7. The method according to claim 6, characterized in that The steps for calculating the target planet magnetic field model coefficients include: Accumulate and sum all the third target matrices; Accumulate and sum all the fourth target matrices; The inverse matrix corresponding to the third target matrix after cumulative summation is calculated, and the product of the inverse matrix and the fourth target matrix after cumulative summation is the target planet magnetic field model coefficient.

8. The method according to any one of claims 2 to 7, characterized in that: The cumulative sum of all the intermediate solutions of the blocks is brought into the linear equation group to calculate the target planet magnetic field model coefficients, including: x = (D T D) -1 D T b Wherein, x represents the magnetic field model coefficient of the target planet, D j =W j A j ; b j =W j d j ; A j represents the jth coefficient matrix block; d j represents the jth vector block; W j represents the jth weight matrix block.

9. The method according to any one of claims 1 to 8, characterized in that The step of obtaining the magnetic field observation value vector of the target planet includes: The magnetic field of the target planet is observed, the planet surface is divided into a plurality of observation grids according to the latitude and longitude of the target planet, magnetic field observations are performed at observation points within the grids, and the magnetic field observation value vector including all observation values ​​is determined.

10. The method according to any one of claims 1 to 8, characterized in that The linear equations between the magnetic field observation vector and the model coefficients corresponding to the planetary magnetic field model are constructed, including: Ax = d Wherein, A represents the linear coefficient matrix composed of the linear relationship coefficients of spherical harmonic function fitting between the model coefficients and the magnetic field observation values; x represents the model coefficients corresponding to the planetary magnetic field model; and d represents the magnetic field observation value vector.

11. The method according to claim 10, characterized in that The step of dividing the linear coefficient matrix into a plurality of coefficient matrix blocks according to a preset number of rows and dividing the magnetic field observation value vector into a plurality of vector blocks includes: According to the preset number of rows, the linear coefficient matrix is ​​horizontally divided into a plurality of coefficient matrix blocks while the number of columns of the linear coefficient matrix corresponding to the linear equation system remains unchanged; wherein the number of rows of each coefficient matrix block is equal to the preset number of rows; The magnetic field observation value vector is divided into a plurality of vector blocks according to the preset number of rows, and each vector block includes magnetic field observation values ​​whose number is equal to the preset number of rows.

12. The method according to claim 10, characterized in that The step of calculating a corresponding block intermediate solution for each coefficient matrix block and the corresponding vector block includes: The inversion method is adopted to express the model coefficients corresponding to the planetary magnetic field model using the linear coefficient matrix and the magnetic field observation value vector, and each coefficient matrix block and the corresponding vector block are substituted to calculate the corresponding block intermediate solution.

13. A device for determining the coefficients of a planetary magnetic field model, characterized in that: Applied to a planetary magnetic field model based on spherical harmonic function fitting, the device comprises: a linear equations construction module configured to obtain a magnetic field observation value vector of a target planet and construct a linear equations system between the magnetic field observation value vector and corresponding model coefficients of the planetary magnetic field model; a block division module configured to determine a linear coefficient matrix corresponding to the linear equation system, divide the linear coefficient matrix into a plurality of coefficient matrix blocks according to a preset number of rows, and divide the magnetic field observation value vector into a plurality of vector blocks; A block solving module configured to calculate a corresponding block intermediate solution for each coefficient matrix block and the corresponding vector block; The model coefficient calculation module is configured to add up all the intermediate solutions of the blocks and then bring them into the linear equation group to calculate the magnetic field model coefficients of the target planet.

14. An electronic device, characterized in that: include: A processor, a memory, and a bus, wherein the memory stores machine-readable instructions executable by the processor. When the electronic device is running, the processor and the memory communicate via the bus. When the machine-readable instructions are executed by the processor, the steps of the method for determining the planetary magnetic field model coefficients according to any one of claims 1 to 12 are performed.

15. 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 the method for determining the planetary magnetic field model coefficients according to any one of claims 1 to 12.

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