Satellite magnetic measurement data downward continuation method, device, equipment and medium

Abstract

The invention provides a satellite magnetic measurement data downward continuation method, device and equipment and a medium, and the method comprises the steps: inputting observation data, and converting the observation data obtained during satellite in-orbit measurement from a spherical coordinate system to a rectangular coordinate system; determining a model calculation domain, and generating a series of configuration points in the model calculation domain; normalizing observation data position coordinates, configuration point position coordinates and magnetic field three-component data under the rectangular coordinate system to serve as training data; inputting observation data position coordinates and configuration point position coordinates under the rectangular coordinate system into a neural network model, constructing a loss function based on observation data fitting errors and Laplacian equation physical constraints, and training the neural network model; and according to application requirements, generating a target position coordinate on a target continuation plane or space, inputting the target position coordinate into the trained neural network model, obtaining magnetic field three-component data at the target position coordinate, and realizing high-precision downward continuation.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of geophysical exploration, and in particular to a satellite magnetic survey data downward continuation method, device, equipment and medium. BACKGROUND

[0002] Satellite magnetic survey data is an important means of obtaining global geomagnetic field data, and its observation data is of great significance to geophysical research, resource exploration and space environment monitoring. However, the observation data is difficult to directly or accurately reflect the fine structure and local anomaly characteristics of the ground and near-space magnetic field due to the attenuation effect of the space distance and the interference of external field sources, as the satellite orbit is usually located at an altitude of hundreds of kilometers from the ground. Therefore, the downward continuation technology of converting high-altitude satellite observation data to low-altitude or ground has become a core step to improve the data resolution and application value.

[0003] Traditional spherical coordinate system continuation methods, such as Landweber iteration method, Tikhonov regularization method and other methods based on integral equation, will cause significant boundary oscillation phenomenon when the data coverage area is incomplete (such as polar region data missing); the direct solution of Poisson equation needs to construct and invert a large kernel matrix, which consumes a lot of memory and is difficult to meet the global scale data processing demand; at the same time, high-frequency observation noise will be amplified exponentially in the continuation process, and the existing methods are difficult to achieve optimal balance between noise suppression and signal fidelity.

[0004] Therefore, it is of great theoretical research value and practical application significance to develop a spherical coordinate system satellite magnetic survey data downward continuation technology suitable for global scale, with high computational efficiency and numerical stability. SUMMARY

[0005] In view of the low precision and low computational efficiency of the traditional spherical coordinate system downward continuation technology, the present application provides a satellite magnetic survey data downward continuation method, device, equipment and medium, which can realize the downward continuation of satellite magnetic survey data in global or large-scale regions.

[0006] To achieve the above-mentioned purpose, the technical scheme adopted by the present application is as follows: On the one hand, the present application provides a satellite magnetic survey data downward continuation method, comprising: inputting observation data, including observation data position coordinates and corresponding magnetic field three-component data obtained by satellite in-orbit measurement; performing coordinate conversion on the observation data position coordinates and corresponding magnetic field three-component data obtained by satellite in-orbit measurement, from spherical coordinate system to rectangular coordinate system; The radius of the outer sphere is determined based on the satellite orbit radius with the Earth's center as the center during satellite on-orbit measurements. The three-dimensional spherical shell space determined between the outer sphere radius and the Earth's radius is used as the model calculation domain, and a series of configuration points are generated within the model calculation domain. The observation data location coordinates, the configuration point location coordinates, and the magnetic field three-component data corresponding to the observation data location coordinates in the rectangular coordinate system are normalized and used as training data. The position coordinates of the observation data in the rectangular coordinate system and the position coordinates of the configuration point are input into the neural network model. The neural network model is used to learn the mapping relationship between the position coordinates and the three components of the magnetic field data, and outputs the predicted three components of the magnetic field data. A loss function is constructed based on the fitting error of the observation data and the physical constraints of the Laplace equation to train the neural network model. Based on application requirements, the target position coordinates on the target extension plane or space are generated. The target position coordinates are then input into a trained neural network model to obtain the three-component magnetic field data at the target position coordinates, thereby achieving high-precision downward extension.

[0007] Furthermore, the target position coordinates in the Cartesian coordinate system and the predicted three components of the magnetic field can be converted back to the spherical coordinate system.

[0008] On the other hand, the present invention provides a satellite magnetic measurement data downward extrapolation device, comprising: The first module is used to input observation data, including the position coordinates of the observation data obtained during satellite on-orbit measurements and the corresponding three-component magnetic field data. The second module is used to perform coordinate transformation on the position coordinates of the observation data and the corresponding three-component magnetic field data obtained during satellite on-orbit measurement, transforming them from spherical coordinates to rectangular coordinates. The third module is used to determine the radius of the outer sphere based on the satellite orbit radius with the Earth's center as the center during satellite on-orbit measurement, and to generate a series of configuration points within the model calculation domain based on the three-dimensional spherical shell space determined between the outer sphere radius and the Earth's radius. The fourth module is used to normalize the position coordinates of the observation data in the rectangular coordinate system, the position coordinates of the placement point, and the three components of the magnetic field corresponding to the position coordinates of the observation data in the rectangular coordinate system, and then use them as training data. The fifth module is used to input the position coordinates of the observation data in the rectangular coordinate system and the position coordinates of the configuration point into the neural network model. The neural network model learns the mapping relationship between the position coordinates and the three components of the magnetic field data, outputs the predicted three components of the magnetic field data, constructs a loss function based on the fitting error of the observation data and the physical constraints of the Laplace equation, and trains the neural network model. The sixth module is used to generate the target position coordinates on the target extension plane or in space according to application requirements. The target position coordinates are input into the trained neural network model to obtain the three-component magnetic field data at the target position coordinates, thereby achieving high-precision downward extension.

[0009] On the other hand, the present invention provides a computer device including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of the above-described method for downward extension of satellite magnetic measurement data.

[0010] On the other hand, the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the above-described method for downward extension of satellite magnetic measurement data.

[0011] On the other hand, the present invention provides a computer program product stored on a computer-readable storage medium and including computer instructions that, when executed by a processor, cause a computer device to implement the steps of the above-described method for downward extension of satellite magnetic measurement data.

[0012] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention constructs a physics-driven deep learning framework by embedding the Laplace equation as a physical constraint term into the neural network loss function. This eliminates the need for discretization of the magnetic field, significantly improving the model's stability with noisy data. Furthermore, it overcomes the traditional method's reliance on boundary integrity, maintaining stable extension accuracy even in areas with incomplete data coverage. This invention directly receives spatial coordinates and outputs the corresponding magnetic field components, and has universal adaptability to data distribution. This method can simultaneously process regular grid data, non-uniform orbit data and sparse observation data, and significantly reduces the workload of data preprocessing compared with traditional gridding methods.

[0013] This invention employs a multi-task learning architecture to synchronously output the three components of the magnetic field by sharing hidden layer features, strictly satisfying the fundamental constraints of potential field theory. This design eliminates the theoretical inconsistency caused by processing each component separately in traditional methods, ensuring physical consistency among the components. Attached Figure Description

[0014] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.

[0015] Figure 1This is a flowchart of a method for downward extrapolation of satellite magnetic measurement data provided in one embodiment; Figure 2 This is a schematic diagram of the orbit of the Zhangheng-1 satellite, which is the source of satellite data used in one embodiment. Figure 3 Here are the calculated values ​​of the three components of the magnetic field in one embodiment, where Figure 3 (a) represents the three components of the magnetic field. Component calculation value, Figure 3 (b) represents the three components of the magnetic field. Component calculation value, Figure 3 (c) represents the three components of the magnetic field. Component calculation value; Figure 4 Here are the reference values ​​for the three components of the magnetic field in one embodiment, where Figure 4 (a) represents the three components of the magnetic field. Component reference value, Figure 4 (b) represents the three components of the magnetic field. Component reference value, Figure 4 (c) represents the three components of the magnetic field. Component reference values. Detailed Implementation

[0016] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0017] Reference Figure 1 One embodiment provides a method for downward extrapolation of satellite magnetic measurement data, comprising: Input observation data, including the position coordinates of the observation data obtained during satellite on-orbit measurements and the corresponding three-component magnetic field data; The position coordinates of the observation data and the corresponding three-component magnetic field data obtained during satellite in-orbit measurement are transformed from spherical coordinates to rectangular coordinates. The radius of the outer sphere is determined based on the satellite orbit radius with the Earth's center as the center during satellite on-orbit measurements. The three-dimensional spherical shell space determined between the outer sphere radius and the Earth's radius is used as the model calculation domain, and a series of configuration points are generated within the model calculation domain. The observation data location coordinates, the configuration point location coordinates, and the magnetic field three-component data corresponding to the observation data location coordinates in the rectangular coordinate system are normalized and used as training data. The position coordinates of the observation data in the rectangular coordinate system and the position coordinates of the configuration point are input into the neural network model. The neural network model is used to learn the mapping relationship between the position coordinates and the three components of the magnetic field data, and outputs the predicted three components of the magnetic field data. A loss function is constructed based on the fitting error of the observation data and the physical constraints of the Laplace equation to train the neural network model. Based on application requirements, the target position coordinates on the target extension plane or space are generated. The target position coordinates are then input into a trained neural network model to obtain the three-component magnetic field data at the target position coordinates, thereby achieving high-precision downward extension.

[0018] The above embodiments, by constructing a fully connected network with spatial spherical coordinates as input and magnetic field tri-components as output, introducing the Laplace equation as a physical constraint, and employing an adaptive dynamic weight adjustment strategy, minimize data loss and physical loss. This invention achieves a balance between computational accuracy and efficiency in the downward extension of global or large-scale regional satellite magnetic measurement data, and significantly improves the stability of the downward extension process.

[0019] The observation data in this invention comes from satellite magnetic measurement data. In one embodiment, the dataset of position coordinates obtained during satellite in-orbit measurements is acquired. Transform from spherical coordinate system to rectangular coordinate system , ,in, Represents the total number of observed data, the first... i spherical coordinates of each observation point ,in These represent radial distance (the straight-line distance from the satellite to the Earth's center of mass), polar angle, and azimuth angle, respectively. Let x, y, and z represent the x-axis coordinates, y-axis coordinates, and z-axis coordinates of the i-th observation point in the rectangular coordinate system, respectively.

[0020] The three components of the magnetic field data obtained during satellite in-orbit measurements Transform from spherical coordinate system to rectangular coordinate system , ,in, Represents the total number of observed data, the first... i Three-component magnetic field data obtained from observation points ,in These represent the radial component, polar component, and azimuth component of the magnetic field, respectively. They represent the first i The three components of the magnetic field measured at each observation point are the x-axis, y-axis, and z-axis components in a rectangular coordinate system.

[0021] Merging observation data coordinates

[0022]

[0023]

[0024] Merging the three components of the magnetic field in the observation data

[0025]

[0026]

[0027] The radius of the outer sphere is determined based on the satellite's orbital radius centered on the Earth during on-orbit measurements. The radius of the outer sphere is taken as the maximum orbital radius of the satellite. Simultaneously, the radius of an inner sphere is defined. inner sphere radius That is, the Earth's radius. The three-dimensional spherical shell space defined by the distance between the outer sphere's radius and the Earth's radius is used as the model's computational domain. Within this domain, a random sampling technique is employed to generate a set of placement points, each with coordinates in a Cartesian coordinate system. , ,in, Indicates the number of configuration points.

[0028] Merge configuration point coordinates:

[0029]

[0030]

[0031] Combine the coordinates of the observation data and the coordinates of the placement points as training data:

[0032]

[0033]

[0034] Next, the location coordinates of the observation data and the location coordinates of the placement points in the rectangular coordinate system are normalized, including: Calculate the position coordinates of the observed data in all rectangular coordinate systems. , Location coordinates of the configuration point global minimum value and global maximum value : ,

[0035] in , , , , , , , , , , This represents the total number of observed data. , Indicates the number of configuration points; Calculate coordinate normalization parameters and :

[0036]

[0037] The same set of normalization parameters is used to normalize the position coordinates of the observation data and the position coordinates of the placement points in the rectangular coordinate system:

[0038]

[0039]

[0040]

[0041]

[0042]

[0043] The three components of the magnetic field data corresponding to the position coordinates of the observation data in the angular coordinate system are normalized, including: Calculate the three components of the magnetic field corresponding to the position coordinates of the observed data in a rectangular coordinate system. global minimum value and global maximum value :

[0044]

[0045] in , This represents the total number of observed data. They represent the first i The x-axis, y-axis, and z-axis components of the magnetic field of each observation data point; , , ; Calculate the normalized parameters of the three components of the magnetic field and :

[0046]

[0047] Using the normalized parameters of the three components of the magnetic field and Normalize the three components of the magnetic field data:

[0048]

[0049]

[0050] In one embodiment, a fully connected neural network model is defined, and the number of network inputs is set. Output the number Number of hidden layers Number of nodes per layer .

[0051] The Swish function was chosen as the activation function for the hidden layer.

[0052] Determine the input-output relationship of the neural network model:

[0053] in, For network input, representing spatial coordinates; Indicates network parameters; For network output, it represents the three components of the output magnetic field.

[0054] In another embodiment, a loss function is constructed based on the fitting error of the observed data and the physical constraints of the Laplace equation, including: The magnetic field three-component loss function of the observation data is constructed based on the fitting error between the magnetic field three-component data corresponding to the position coordinates of the observation data in the rectangular coordinate system predicted by the neural network model and the actual magnetic field three-component data corresponding to the position coordinates of the observation data in the rectangular coordinate system. The physical constraint loss function of the Laplace equation is constructed based on the three-component magnetic field data corresponding to the configuration point predicted by the neural network model. Dynamic weights are set based on the magnetic field three-component loss function of the observed data. And Laplace equation physical constraint loss function The final loss function is obtained. ,in, For dynamic weights.

[0055] During the training of a neural network model, the Adam optimizer is selected, and the loss function is adjusted. To optimize, the initial learning rate can be set to... The exponential decay coefficient is 0.8, and the network parameters are initialized using Xavier.

[0056] The loss function for the three components of the observed magnetic field data is as follows:

[0057] in , Represents the total number of observed data, the normalized i-th i The three components of the magnetic field corresponding to the location coordinates of each observation data point , They represent the normalized i-th The x-axis, y-axis, and z-axis components of the magnetic field corresponding to the location coordinates of each observation data point. This represents the first Cartesian coordinate system predicted by the neural network model. The magnetic field data corresponding to the location coordinates of each observation point, including the x-axis component. y-axis components z-axis component ; The physical constraint loss function of the Plas equation is as follows:

[0058] in Represents the Laplace operator. This represents the three components of the magnetic field at the k-th placement point predicted by the neural network, including the x-axis component. y-axis components z-axis component , This indicates the number of configuration points.

[0059] Preset dynamic weights initial value For the dynamic weights in the nth iteration of training Calculated using the following formula:

[0060]

[0061] in This indicates that the loss function is calculated by taking the gradient with respect to the current neural network parameters. , These represent the loss functions of the three components of the magnetic field in the observed data, respectively. And Laplace equation physical constraint loss function Calculate the gradient of the current neural network parameters; This indicates taking the maximum value. This indicates taking the average value. and They represent the first Second and third Dynamic weights during each iteration of training This represents an intermediate variable used in the dynamic weight calculation.

[0062] Set the number of network training sessions. Set the initial learning rate to The decay coefficient is 0.8, and an exponential decay learning rate scheduling strategy is adopted.

[0063] The network weights are initialized using Xavier, and iterative training begins. Once the training reaches convergence, the model parameters are saved. .

[0064] Generate a set of coordinate points on the target extension plane or space according to application requirements. , ,in, This indicates the number of coordinates for the downward extension position.

[0065] The target location coordinates are input into a saved and trained neural network model to calculate the three components of the magnetic field at the target location, achieving high-precision downward extension.

[0066]

[0067] Furthermore, the target position coordinates in the Cartesian coordinate system and the predicted three components of the magnetic field can be converted back to the spherical coordinate system.

[0068] This invention realizes a novel method for downward extrapolation of satellite magnetic measurement data in spherical coordinates based on a physical information neural network. This method overcomes the inherent ill-posedness, high-frequency noise amplification effect, and strong dependence on model assumptions and data distribution of traditional spherical coordinate extrapolation techniques, significantly improving the accuracy and reliability of downward extrapolation of global or large-scale regional satellite magnetic measurement data.

[0069] The accuracy of the downward extension method for satellite magnetic measurement data in spherical coordinates provided by this invention will be verified below.

[0070] The actual observation data from one week of operation of the Zhang Heng-1 satellite was selected as the test dataset, and its trajectory is as follows. Figure 2 As shown in the figure, this dataset contains 471,510 observation points. The satellite operates at an altitude between 6,878 km and 6,887 km. During the data processing phase, the position coordinates and magnetic field components in the original spherical coordinate system were first transformed to a rectangular coordinate system to construct a standardized observation dataset.

[0071] A spherical computational domain was established, with the Earth's average radius of 6371 km as the inner boundary and the satellite's highest operating altitude of 6887 km as the outer boundary. Within this computational domain, 543,570 placement points were generated using random sampling techniques, which, together with measured observation data, constituted the training dataset for the neural network.

[0072] The training dataset is input into the neural network for training to obtain a predictive model with downward extension capability.

[0073] Based on the Earth's average radius of 6371 km, 64261 uniformly distributed extension point coordinates were constructed within the range of longitude 89°E to 89°W (1° interval) and latitude 179°N to 179°S (1° interval). Finally, these extension point coordinates were input into the trained prediction model to obtain the predicted values ​​of the three components of the geomagnetic field for each point.

[0074] The reference values ​​of the three components of the geomagnetic field at the extension point were calculated using the IGRF14 calculator and compared with the predicted values ​​of the three components of the geomagnetic field obtained using the method of this invention. Figure 3 Here are the calculated values ​​of the three components of the magnetic field in one embodiment. Figure 4 In one embodiment, the reference values ​​for the three components of the magnetic field are identical in shape. Figure 3 (a) represents the three components of the magnetic field. Component calculation value, Figure 3 (b) represents the three components of the magnetic field. Component calculation value, Figure 3 (c) represents the three components of the magnetic field. Component calculation value; Figure 4 (a) represents the three components of the magnetic field. Component reference value, Figure 4 (b) represents the three components of the magnetic field. Component reference value, Figure 4 (c) represents the three components of the magnetic field. Component reference values. The relative error is obtained by subtracting the calculated value from the reference value, dividing the absolute value of the difference by the reference value, and then statistically analyzing the relative error. The results are shown in Table 1. It can be seen that the method has high accuracy.

[0075] Table 1. Statistics on the relative errors of reference and calculated values ​​of the three components of the magnetic field.

[0076] In another embodiment, a satellite magnetic measurement data downward extrapolation device is provided, comprising: The first module is used to input observation data, including the position coordinates of the observation data obtained during satellite on-orbit measurements and the corresponding three-component magnetic field data. The second module is used to perform coordinate transformation on the position coordinates of the observation data and the corresponding three-component magnetic field data obtained during satellite on-orbit measurement, transforming them from spherical coordinates to rectangular coordinates. The third module is used to determine the radius of the outer sphere based on the satellite orbit radius with the Earth's center as the center during satellite on-orbit measurement, and to generate a series of configuration points within the model calculation domain based on the three-dimensional spherical shell space determined between the outer sphere radius and the Earth's radius. The fourth module is used to normalize the position coordinates of the observation data in the rectangular coordinate system, the position coordinates of the placement point, and the three components of the magnetic field corresponding to the position coordinates of the observation data in the rectangular coordinate system, and then use them as training data. The fifth module is used to input the position coordinates of the observation data in the rectangular coordinate system and the position coordinates of the configuration point into the neural network model. The neural network model learns the mapping relationship between the position coordinates and the three components of the magnetic field data, outputs the predicted three components of the magnetic field data, constructs a loss function based on the fitting error of the observation data and the physical constraints of the Laplace equation, and trains the neural network model. The sixth module is used to generate the target position coordinates on the target extension plane or in space according to application requirements. The target position coordinates are input into the trained neural network model to obtain the three-component magnetic field data at the target position coordinates, thereby achieving high-precision downward extension.

[0077] The implementation methods of the above modules are the same as those provided in the corresponding embodiments above, and will not be repeated here.

[0078] On the other hand, the present invention provides a computer device including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps of the satellite magnetic measurement data downward extrapolation method provided in any of the above embodiments. The computer device may be a server. The computer device includes a processor, a memory, a network interface, and a database connected via a system bus. The processor of the computer device provides computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores an operating system, a computer program, and a database. The internal memory provides an environment for the operation of the operating system and computer program in the non-volatile storage medium. The database of the computer device stores sample data. The network interface of the computer device is used for communication with external terminals via a network connection.

[0079] On the other hand, the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, it implements the steps of the satellite magnetic measurement data downward extension method provided in any of the above embodiments.

[0080] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in a variety of forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), RAMbus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0081] Matters not covered in this invention are common knowledge.

[0082] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0083] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these modifications and improvements all fall within the protection scope of this application.

[0084] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for downward extrapolation of satellite magnetic measurement data, characterized in that, include: Input observation data, including the position coordinates of the observation data obtained during satellite on-orbit measurements and the corresponding three-component magnetic field data; The position coordinates of the observation data and the corresponding three-component magnetic field data obtained during satellite in-orbit measurement are transformed from spherical coordinates to rectangular coordinates. The radius of the outer sphere is determined based on the satellite orbit radius with the Earth's center as the center during satellite on-orbit measurements. The three-dimensional spherical shell space determined between the outer sphere radius and the Earth's radius is used as the model calculation domain, and a series of configuration points are generated within the model calculation domain. The observation data location coordinates, the configuration point location coordinates, and the magnetic field three-component data corresponding to the observation data location coordinates in the rectangular coordinate system are normalized and used as training data. The position coordinates of the observation data in the rectangular coordinate system and the position coordinates of the configuration point are input into the neural network model. The neural network model is used to learn the mapping relationship between the position coordinates and the three components of the magnetic field data, and outputs the predicted three components of the magnetic field data. A loss function is constructed based on the fitting error of the observation data and the physical constraints of the Laplace equation to train the neural network model. Based on application requirements, the target position coordinates on the target extension plane or space are generated. The target position coordinates are then input into a trained neural network model to obtain the three-component magnetic field data at the target position coordinates, thereby achieving high-precision downward extension.

2. The method for downward extrapolation of satellite magnetic measurement data according to claim 1, characterized in that, A series of configuration points are randomly generated within the model computation domain.

3. The method for downward extrapolation of satellite magnetic measurement data according to claim 1 or 2, characterized in that, Normalize the location coordinates of the observation data and the location coordinates of the placement points in the rectangular coordinate system, including: Calculate the position coordinates of the observed data in all rectangular coordinate systems. , Location coordinates of the configuration point global minimum value and global maximum value ， in , , , , , , , , , , This represents the total number of observed data. , Indicates the number of configuration points; Calculate coordinate normalization parameters and : The same set of normalization parameters is used to normalize the position coordinates of the observation data and the position coordinates of the placement points in the rectangular coordinate system: 。 4. The method for downward extrapolation of satellite magnetic measurement data according to claim 3, characterized in that, The three components of the magnetic field data corresponding to the position coordinates of the observation data in the angular coordinate system are normalized, including: Calculate the three components of the magnetic field corresponding to the position coordinates of the observed data in a rectangular coordinate system. global minimum value and global maximum value : in , This represents the total number of observed data. They represent the first i The x-axis, y-axis, and z-axis components of the magnetic field of each observation data point; , , ; Calculate the normalized parameters of the three components of the magnetic field and : Using the normalized parameters of the three components of the magnetic field and Normalize the three components of the magnetic field data: 。 5. The method for downward extrapolation of satellite magnetic measurement data according to claim 1, 2, or 4, characterized in that, A loss function is constructed based on the fitting error of the observed data and the physical constraints of the Laplace equation, including: The magnetic field three-component loss function of the observation data is constructed based on the fitting error between the magnetic field three-component data corresponding to the position coordinates of the observation data in the rectangular coordinate system predicted by the neural network model and the actual magnetic field three-component data corresponding to the position coordinates of the observation data in the rectangular coordinate system. The physical constraint loss function of the Laplace equation is constructed based on the three-component magnetic field data corresponding to the configuration point predicted by the neural network model. Dynamic weights are set based on the magnetic field three-component loss function of the observed data. And Laplace equation physical constraint loss function The final loss function is obtained. ,in, For dynamic weights.

6. The method for downward extrapolation of satellite magnetic measurement data according to claim 5, characterized in that, The loss function for the three components of the magnetic field in the observed data is as follows: in , Represents the total number of observed data, the normalized i-th i The three components of the magnetic field corresponding to the location coordinates of each observation data point , They represent the normalized i-th i The x-axis, y-axis, and z-axis components of the magnetic field corresponding to the location coordinates of each observation data point. This represents the first Cartesian coordinate system predicted by the neural network model. i The magnetic field data corresponding to the location coordinates of each observation point, including the x-axis component. y-axis components z-axis component ; The physical constraint loss function of the Plas equation is as follows: in Represents the Laplace operator. This represents the three components of the magnetic field at the k-th placement point predicted by the neural network, including the x-axis component. y-axis components z-axis component , This indicates the number of configuration points.

7. The method for downward extrapolation of satellite magnetic measurement data according to claim 5, characterized in that, Preset dynamic weights initial value For the dynamic weights in the nth iteration of training Calculated using the following formula: in This indicates that the loss function is calculated by taking the gradient with respect to the current neural network parameters. , These represent the loss functions of the three components of the magnetic field in the observed data, respectively. And Laplace equation physical constraint loss function Calculate the gradient of the current neural network parameters; This indicates taking the maximum value. This indicates taking the average value. and They represent the first Second and third Dynamic weights during each iteration of training This represents an intermediate variable used in the dynamic weight calculation.

8. A satellite magnetic measurement data downward extrapolation device, characterized in that, include: The first module is used to input observation data, including the position coordinates of the observation data obtained during satellite on-orbit measurements and the corresponding three-component magnetic field data. The second module is used to perform coordinate transformation on the position coordinates of the observation data and the corresponding three-component magnetic field data obtained during satellite on-orbit measurement, transforming them from spherical coordinates to rectangular coordinates. The third module is used to determine the radius of the outer sphere based on the satellite orbit radius with the Earth's center as the center during satellite on-orbit measurement, and to generate a series of configuration points within the model calculation domain based on the three-dimensional spherical shell space determined between the outer sphere radius and the Earth's radius. The fourth module is used to normalize the position coordinates of the observation data in the rectangular coordinate system, the position coordinates of the placement point, and the three components of the magnetic field corresponding to the position coordinates of the observation data in the rectangular coordinate system, and then use them as training data. The fifth module is used to input the position coordinates of the observation data in the rectangular coordinate system and the position coordinates of the configuration point into the neural network model. The neural network model learns the mapping relationship between the position coordinates and the three components of the magnetic field data, outputs the predicted three components of the magnetic field data, constructs a loss function based on the fitting error of the observation data and the physical constraints of the Laplace equation, and trains the neural network model. The sixth module is used to generate the target position coordinates on the target extension plane or in space according to application requirements. The target position coordinates are input into the trained neural network model to obtain the three-component magnetic field data at the target position coordinates, thereby achieving high-precision downward extension.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the satellite magnetic measurement data downward extension method as described in claim 1.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the satellite magnetic measurement data downward extension method as described in claim 1.

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