A method for predicting external gravitational acceleration of small celestial bodies based on interpolation neural network

Abstract

The present invention relates to the technical field of orbit calculation of small celestial body detectors, and specifically discloses a method for predicting the external gravitational acceleration of a small celestial body based on an interpolation neural network, the method comprising: taking the coordinate increments corresponding to the sample points outside the target small celestial body as inputs and the gravitational acceleration measurement values ​​of the sample points as labels, iteratively training the interpolation neural network used to predict the gravitational acceleration of the points outside the small celestial body to obtain a target interpolation neural network; wherein the coordinate increment corresponding to any sample point outside the target small celestial body is the coordinate increment between the rectangular coordinates of the sample point and the rectangular coordinates of the remaining known sample points around it; the coordinate increment of the to-be-measured point outside the target small celestial body is input into the target interpolation neural network to obtain the predicted value of the gravitational acceleration of the to-be-measured point. The present invention can realize the rapid and accurate calculation of the gravitational acceleration of the to-be-measured point outside the small celestial body, and can reduce the modeling time of the gravity field.

Description

Background Art

[0002] Small celestial bodies are the early remnants of the formation of the solar system, and they preserve the early information of the formation of the solar system. The exploration of small celestial bodies can help us better understand the characteristics and evolutionary history of small celestial bodies themselves, as well as the formation and evolution process of the solar system. In-depth research on small celestial bodies is of great significance to future space exploration and development.

[0003] In the exploration of small celestial bodies, the dynamic environment of the spacecraft is very complex. The gravity field of a small celestial body is one of the important prior information that needs to be obtained in the exploration mission. It affects the orbit design, flight control and landing sampling of the probe. At present, the traditional methods for constructing the gravity field of a small celestial body include spherical harmonic function method, mass tumor method (Mascons), polyhedron method and interpolation method. Spherical harmonic function represents the gravity field of a small celestial body through a set of spherical harmonic coefficients and is often used in gravity field inversion. The Mascons method fills the small celestial body with a set of mass elements of equal density, and the sum of the masses of all mass elements is equal to the total mass of the small celestial body. The polyhedron method uses Gauss's formula and Green's formula to finally transform the volume integral in the gravitational potential into the line integral of the edges of the polyhedron. Unlike large celestial bodies, the external gravity field of small celestial bodies is generally weak. Some studies have used the method of interpolating the estimated points by connecting the estimated points with the surrounding known points to calculate the external acceleration of small celestial bodies.

[0004] The spherical harmonics method is a series approximation modeling method for the gravity field. This method has the problem of non-convergence in the Brillouin sphere, which greatly limits its application in missions such as probe approach detection, sampling and landing. The Mascons method is a discretized gravity field calculation method. Its accuracy is affected by the filling rate and model approximation. In addition, the summation of Mascon points in the gravity field construction process will cause the accumulation of error terms. The polyhedron method needs to adopt a uniform density assumption. Since the polyhedron method needs to integrate all the faces and edges of the three-dimensional model once to calculate each point, the computational cost of the polyhedron model increases sharply with the increase of the number of model edges and faces; and for small celestial bodies with complex shapes, the number of model faces is required to be high, so the computational efficiency is low. The interpolation method usually smoothes the data to obtain a more continuous curve, so it may smooth out the local gravitational characteristics of the small celestial body, resulting in inaccurate estimation of the acceleration of the small celestial body. If you want to improve the interpolation accuracy, you can introduce a shape model or adopt a small range interpolation method.

[0005] Therefore, in view of the calculation limitations of the traditional interpolation method of gravitational acceleration of small celestial bodies, it is urgent to provide a technical solution to solve the above problems. Summary of the invention

[0006] In order to solve the above technical problems, the present invention provides a method for predicting the external gravitational acceleration of small celestial bodies based on an interpolation neural network.

[0007] In a first aspect, the present invention provides a method for predicting the external gravitational acceleration of a small celestial body based on an interpolation neural network. The technical solution of the method is as follows:

[0008] Taking the coordinate increments corresponding to the sample points outside the target small celestial body as input and the gravitational acceleration measurement values ​​of the sample points as labels, the interpolation neural network used to predict the gravitational acceleration of the points outside the small celestial body is iteratively trained to obtain the target interpolation neural network; wherein the coordinate increment corresponding to any sample point outside the target small celestial body is the coordinate increment between the rectangular coordinates of the sample point and the rectangular coordinates of the other surrounding known sample points;

[0009] The coordinate increment of the to-be-measured point outside the target small celestial body is input into the target interpolation neural network to obtain the predicted value of the gravitational acceleration of the to-be-measured point.

[0010] The beneficial effects of the method for predicting external gravitational acceleration of a small celestial body based on an interpolation neural network of the present invention are as follows:

[0011] The method of the present invention can realize the rapid and accurate calculation of the gravitational acceleration of the point to be measured outside the small celestial body, and can reduce the modeling time of the gravity field.

[0012] On the basis of the above scheme, the method for predicting the external gravitational acceleration of a small celestial body based on an interpolation neural network of the present invention can also be improved as follows.

[0013] In an optional manner, the steps of iteratively training an interpolation neural network for predicting the gravitational acceleration of points outside a target small celestial body with coordinate increments corresponding to sample points outside the target small celestial body as input and gravitational acceleration measurements of the sample points as labels to obtain a target interpolation neural network include:

[0014] Inputting the coordinate increment corresponding to any sample point outside the target small celestial body into the interpolation neural network to obtain the predicted value of gravity acceleration of any sample point, and determining the loss value of any sample point according to the predicted value of gravity acceleration and the measured value of gravity acceleration of any sample point, until the loss value of each sample point outside the target small celestial body is determined;

[0015] Based on all the loss values, the interpolation neural network is parameter optimized to obtain an optimized interpolation neural network, and the optimized interpolation neural network is used as the interpolation neural network and returns to execute the step of inputting the coordinate increment corresponding to any sample point outside the target small celestial body into the interpolation neural network, until the optimized interpolation neural network meets the iterative training conditions, and the optimized interpolation neural network is determined as the target interpolation neural network.

[0016] In an optional manner, the interpolation neural network includes: a generalized distance module and a hidden layer module; the step of inputting the coordinate increment corresponding to any sample point outside the target small celestial body into the interpolation neural network to obtain the predicted value of gravity acceleration of any sample point includes:

[0017] Input the coordinate increment corresponding to any sample point outside the target small celestial body into the generalized distance module, obtain the generalized spatial distance value of any sample point and input it into the hidden layer module to obtain the spatial weight value of any sample point;

[0018] The predicted value of gravity acceleration of any sample point is obtained according to the spatial weight value of any sample point, the coefficients corresponding to the other known sample points around the any sample point and the external gravity acceleration measurement value.

[0019] In an optional manner, the step of obtaining the gravity acceleration measurement value of each sample point includes:

[0020] Using the polyhedron method, the gravitational acceleration measurement value of each sample point is calculated separately.

[0021] In an optional manner, the step of determining a sample point outside the target small celestial body includes:

[0022] Using a ball sampling method, a plurality of external points within a preset range around the target small celestial body are acquired;

[0023] The spherical coordinate value of each external point is converted into a rectangular coordinate value, and the external point whose rectangular coordinate value is outside the target small celestial body is determined as a sample point.

[0024] In a second aspect, the present invention provides a small celestial body external gravity acceleration prediction system based on an interpolation neural network, and the technical solution of the system is as follows:

[0025] Includes: training module and prediction module;

[0026] The training module is used to: use the coordinate increments corresponding to the sample points outside the target small celestial body as inputs and the gravitational acceleration measurements of the sample points as labels, and iteratively train the interpolation neural network used to predict the gravitational acceleration of the points outside the small celestial body to obtain the target interpolation neural network; wherein the coordinate increment corresponding to any sample point outside the target small celestial body is the coordinate increment between the rectangular coordinates of the sample point and the rectangular coordinates of the other surrounding known sample points;

[0027] The prediction module is used to input the coordinate increment of the to-be-measured point outside the target small celestial body into the target interpolation neural network to obtain the predicted value of the gravity acceleration of the to-be-measured point.

[0028] The beneficial effects of the small celestial body external gravity acceleration prediction system based on interpolation neural network of the present invention are as follows:

[0029] The system of the present invention can realize rapid and accurate calculation of the gravitational acceleration of the point to be measured outside the small celestial body, and can reduce the modeling time of the gravity field.

[0030] On the basis of the above scheme, the small celestial body external gravity acceleration prediction system based on interpolation neural network of the present invention can also be improved as follows.

[0031] In an optional manner, the training module includes: a first training module and a second training module;

[0032] The first training module is used to: input the coordinate increment corresponding to any sample point outside the target small celestial body into the interpolation neural network to obtain the predicted value of gravity acceleration of any sample point, and determine the loss value of any sample point according to the predicted value of gravity acceleration and the measured value of gravity acceleration of any sample point, until the loss value of each sample point outside the target small celestial body is determined;

[0033] The second training module is used to: optimize the parameters of the interpolation neural network based on all loss values ​​to obtain an optimized interpolation neural network, and use the optimized interpolation neural network as the interpolation neural network and return to call the first training module until the optimized interpolation neural network meets the iterative training conditions, and determine the optimized interpolation neural network as the target interpolation neural network.

[0034] In an optional manner, the interpolation neural network includes: a generalized distance module and a hidden layer module; the step of inputting the coordinate increment corresponding to any sample point outside the target small celestial body into the interpolation neural network in the first training module to obtain the predicted value of gravity acceleration of any sample point includes:

[0035] Input the coordinate increment corresponding to any sample point outside the target small celestial body into the generalized distance module, obtain the generalized spatial distance value of any sample point and input it into the hidden layer module to obtain the spatial weight value of any sample point;

[0036] The predicted value of gravity acceleration of any sample point is obtained according to the spatial weight value of any sample point, the coefficients corresponding to other known sample points around any sample point and the external gravity acceleration measurement value.

[0037] In a third aspect, a technical solution of an electronic device of the present invention is as follows:

[0038] The invention comprises a memory, a processor and a program stored in the memory and running on the processor. When the processor executes the program, the steps of the method for predicting the external gravity acceleration of a small celestial body based on an interpolation neural network of the present invention are implemented.

[0039] In a fourth aspect, the present invention provides a computer-readable storage medium having the following technical solution:

[0040] Instructions are stored in the computer-readable storage medium. When the computer-readable storage medium reads the instructions, the computer-readable storage medium executes the steps of the method for predicting the external gravity acceleration of a small celestial body based on an interpolation neural network of the present invention.

[0041] The above description is only an overview of the technical solution of the present invention. In order to more clearly understand the technical means of the present invention, it can be implemented according to the contents of the specification. In order to make the above and other purposes, features and advantages of the present invention more obvious and easy to understand, the specific implementation methods of the present invention are listed below. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] The accompanying drawings are only used to illustrate the embodiments and are not to be considered as limiting the present invention. In addition, the same reference symbols are used to represent the same components throughout the accompanying drawings. In the accompanying drawings:

[0043] Figure 1 It is a schematic flow chart of an embodiment of a method for predicting external gravitational acceleration of a small celestial body based on an interpolation neural network of the present invention;

[0044] Figure 2 It is a schematic diagram of the structure of the interpolation neural network;

[0045] Figure 3 It is a schematic diagram of the structure of the generalized distance module;

[0046] Figure 4 is a schematic diagram of external point acceleration;

[0047] Figure 5 It is a schematic diagram of the relative error of acceleration of external points;

[0048] Figure 6 It is a structural schematic diagram of an embodiment of a small celestial body external gravity acceleration prediction system based on an interpolation neural network of the present invention;

[0049] Figure 7 The figure is a schematic structural diagram of an embodiment of an electronic device of the present invention. DETAILED DESCRIPTION

[0050] Exemplary embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. Although exemplary embodiments of the present invention are shown in the drawings, it should be understood that the present invention can be implemented in various forms and should not be limited to the embodiments set forth herein.

[0051] Figure 1 The present invention provides a flow chart of an embodiment of a method for predicting the external gravitational acceleration of a small celestial body based on an interpolation neural network. Figure 1 As shown, the following steps are included:

[0052] S1. Taking the coordinate increments corresponding to the sample points outside the target small celestial body as input and the gravitational acceleration measurements of the sample points as labels, the interpolation neural network used to predict the gravitational acceleration of the external points of the small celestial body is iteratively trained to obtain the target interpolation neural network.

[0053] Among them, the target small celestial body is the small celestial body that needs to calculate the external gravitational acceleration in this embodiment. The sample point is the external point outside the target small celestial body used for interpolation neural network training. The number of sample points must meet a certain threshold, and the threshold can be set according to the actual required accuracy, and there is no restriction here. The coordinate increment corresponding to any sample point outside the target small celestial body is the coordinate increment between the rectangular coordinates of the sample point and the rectangular coordinates of the remaining known sample points around it. The target interpolation neural network is a trained interpolation neural network for predicting the gravitational acceleration of the external points of small celestial bodies.

[0054] It should be noted that the surrounding known external points corresponding to each sample point are the same. Since the three-dimensional rectangular coordinate value of each sample point is different, the coordinate increment corresponding to each sample point is different.

[0055] S2. Inputting the coordinate increment of the point to be measured outside the target small celestial body into the target interpolation neural network to obtain the predicted value of the gravitational acceleration of the point to be measured.

[0056] The point to be measured is an external point outside the target small celestial body where the gravitational acceleration needs to be predicted.

[0057] In an optional manner, S2 includes:

[0058] S21. Input the coordinate increment corresponding to any sample point outside the target small celestial body into the interpolation neural network to obtain the predicted value of gravity acceleration of any sample point, and determine the loss value of any sample point based on the predicted value of gravity acceleration and the measured value of gravity acceleration of any sample point, until the loss value of each sample point outside the target small celestial body is determined.

[0059] Among them, the coordinate increment corresponding to any sample point is X ij =(P i -Pj )=(x i -x j ,y i -y j ,z i -z j )=(dx ij ,dy ij ,dz ij );X ij is the coordinate increment between the i-th sample point and the j-th surrounding known sample point, i = 0, 1, 2...n, j = 0, 1, 2...n, n is a positive integer, P i (x i ,y i ,z i ) is the i-th sample point, P j (x j ,y j ,z j ) is the jth known sample point around, dx ij is the coordinate increment of the ith sample point and the jth surrounding known sample point in the x-axis direction in the three-dimensional rectangular coordinate system, dy ij is the coordinate increment of the ith sample point and the jth surrounding known sample point in the y-axis direction in the three-dimensional rectangular coordinate system, dz ij is the coordinate increment of the i-th sample point and the j-th surrounding known sample point in the z-axis direction in the three-dimensional rectangular coordinate system.

[0060] It should be noted that the interpolation neural network has a loss function, which determines the loss value according to the preset functional relationship between the predicted value of gravity acceleration and the measured value of gravity acceleration. In addition, the process of determining the loss value of each sample point outside the target small celestial body is the same, which will not be repeated here.

[0061] S22. Based on all the loss values, the interpolation neural network is parameter optimized to obtain an optimized interpolation neural network, and the optimized interpolation neural network is used as the interpolation neural network and returns to execute the step of inputting the coordinate increment corresponding to any sample point outside the target small celestial body into the interpolation neural network, until the optimized interpolation neural network meets the iterative training conditions, and the optimized interpolation neural network is determined as the target interpolation neural network.

[0062] The default iterative training condition is to reach the maximum number of iterative training times or the loss converges. It can also be set according to actual needs and there is no limit here.

[0063] In an alternative approach, Figure 2 As shown, the interpolation neural network includes: a generalized distance module and a hidden layer module.

[0064] The step of inputting the coordinate increment corresponding to any sample point outside the target small celestial body into the interpolation neural network to obtain the predicted value of gravity acceleration of any sample point includes:

[0065] The coordinate increment corresponding to any sample point outside the target small celestial body is input into the generalized distance module to obtain the generalized spatial distance value of any sample point and input into the hidden layer module to obtain the spatial weight value of any sample point.

[0066] Among them, the generalized distance module consists of three neural network layers Composition. First layer Contains 3 neurons, the second layer Contains 10 neurons, the third layer Contains 3 neurons. Hidden layer module It consists of three neural network layers. The first layer Contains 512 neurons, the second layer Contains 256 neurons, the third layer Contains 4500 neurons. In the network training process, this embodiment uses only 90% of the training samples (the total number of training samples is 5000), that is, the number of known sample points is 4500, and each known sample point corresponds to an output weight, so the number of neurons in the third layer of the hidden layer module is 4500.

[0067] It should be noted that the core of spatial interpolation is to establish a distance-based mapping relationship between the sampling area and the non-sampling area. Traditional two-dimensional spatial interpolation methods usually use Euclidean space distance to represent spatial correlation, but in three-dimensional and high-dimensional space, the change trend and speed of elements may change along different axis directions, and there are local variations. The Euclidean distance interpolation method is an isotropic solution that loses a lot of relative position information between points, limiting the accuracy of multidimensional linear space interpolation. In order to better capture the nonlinear effects of element change trends in three-dimensional space, a generalized spatial distance module based on the distance components of each axis that considers anisotropy is adopted in this embodiment. Figure 3 The schematic diagram of the generalized distance module is shown, and its expression is: d ij =Net d (Δ x ,Δ y ,Δ z ). After obtaining the generalized spatial distance value of the sample point, the hidden layer module is used to further obtain the spatial weight value, which is expressed as: ρ i =(ρ i1 ,ρ i2 ,…ρ in )=Net(d i1 ,di2 ,…d in )=

[0068] Net(Net d (dx i1 ,dy i1 ,dz i1 ),…Net d (dx in ,dy in ,dz in )); i is the spatial weight value of the i-th sample point.

[0069] The predicted value of gravity acceleration of any sample point is obtained according to the spatial weight value of any sample point, the coefficients corresponding to other known sample points around any sample point and the external gravity acceleration measurement value.

[0070] Among them, after outputting the spatial weight value of the sample point, the spatial weight value needs to be multiplied by a coefficient k. This is because the spatial weight value output by the network contains its own weight value. In order to prevent overfitting, the weight value should be 0. The expression is: w ij represents the weight of the jth surrounding known sample point to the ith sample point, and further resets the point's own weight: w ij =ρ ij ×k ij , k ij is the coefficient of the jth surrounding known sample point to the ith sample point, and the complete weight expression is: The predicted value of gravity acceleration at the sample point is:

[0071] In an optional manner, the step of obtaining the gravity acceleration measurement value of each sample point includes:

[0072] Using the polyhedron method, the gravitational acceleration measurement value of each sample point is calculated separately.

[0073] Specifically, the process of calculating the gravitational acceleration measurement value of the sample point using the polyhedron method is:

[0074] 1) The relationship between gravitational acceleration and gravitational potential is:

[0075] 2) In the process of obtaining the gravitational acceleration measurement value g of the sample point, the target small celestial body is divided into several volume elements, S is a volume element with a mass of dm inside the target small celestial body, and r is the distance from S to the sample point P. The gravitational potential energy at the sample point is defined by the triple integral: M is the total mass of the target small celestial body, and Ω is the total volume of the target small celestial body.

[0076] 3) Applying Gauss's formula and Green's formula, the gravitational acceleration g is derived as: G is the gravitational constant, σ is the density of the target small celestial body, r e Extending from the external point to any point on each face and edge, E e and F f is a tensor corresponding to each edge and face, L e is the logarithmic term representing the line potential, ω f is the solid angle corresponding to the surface when viewed from an external point, dimensionless a and b are the distances from the selected external points to the common edge vertices, e is the length of the edge, E e With F f for: is the normal vector of each face, is the normal vector from edge i to edge j on face B. r i For r i Module length, r i 、r j 、r k are continuous vectors from external points to the vertices of the triangle faces.

[0077] In an optional manner, the step of determining a sample point outside the target small celestial body includes:

[0078] A spherical sampling method is used to obtain multiple external points within a preset range around the target small celestial body.

[0079] Among them, the preset range around the target small celestial body is a space of 1*1*1.

[0080] The spherical coordinate value of each external point is converted into a rectangular coordinate value, and the external point whose rectangular coordinate value is outside the target small celestial body is determined as a sample point.

[0081] Among them, the coordinates of the external point ball obtained by the ball sampling method are θ is the spherical longitude, Latitude and r spherical radius. The formula for converting spherical coordinates to three-dimensional rectangular coordinates is:

[0082]

[0083] It should be noted that after obtaining the rectangular coordinates, the polyhedron model file is used for judgment. The principle is used to determine whether the external point is outside the target small celestial body.

[0084] In order to better illustrate the technical solution of this embodiment, the following example is used for illustration: Based on 1000 check points in the Eros reference radius [r, 3r] interval, acceleration interpolation is performed to calculate the gravity acceleration g, the simulation parameters are shown in Table 1, and the simulation results are shown in Tables 2 and 3.

[0085] Table 1 Simulation parameters

[0086] Number of sample points 5000 Number of test points 1000 <![CDATA[Density of small celestial body (kg / m 3 )]]> 2670 Reference radius(m) 16000

[0087] Table 2 Modeling time and accuracy

[0088] Mean relative error Polyhedron method calculation time Interpolation network calculation time 3.28％ 12s 1.2s

[0089] Table 3 Average relative error statistics (R = r ~ 3r)

[0090] Error range 0～4％ 4～8％ 8～12％ 12％～ Number of sample points 632 338 30 0

[0091] From Table 2-Table 3 and Figure 4-Figure 5 It can be seen that the interpolation method of gravitational acceleration of small celestial bodies based on interpolation neural network can realize the fast and accurate solution of gravitational acceleration of test points near small celestial bodies, especially in operation time compared with traditional methods. This efficient gravitational acceleration calculation method can greatly reduce the modeling time of gravity field and help shorten the design cycle of small celestial body exploration missions. It can also be seen that the error distribution has no strong correlation with the shape model and the distance from the surface.

[0092] The technical solution of this embodiment can realize the rapid and accurate calculation of the gravitational acceleration of the point to be measured outside the small celestial body, which can reduce the modeling time of the gravity field.

[0093] Figure 6 FIG. 2 is a schematic diagram of an embodiment of a small celestial body external gravity acceleration prediction system 200 based on an interpolation neural network provided by the present invention. Figure 6 As shown, the system 200 includes: a training module 210 and a prediction module 220;

[0094] The training module 210 is used to: use the coordinate increments corresponding to the sample points outside the target small celestial body as inputs and the gravitational acceleration measurements of the sample points as labels, and iteratively train the interpolation neural network used to predict the gravitational acceleration of the points outside the small celestial body to obtain the target interpolation neural network; wherein the coordinate increment corresponding to any sample point outside the target small celestial body is the coordinate increment between the rectangular coordinates of the sample point and the rectangular coordinates of the other surrounding known sample points;

[0095] The prediction module 220 is used to input the coordinate increment of the to-be-measured point outside the target small celestial body into the target interpolation neural network to obtain the predicted value of the gravitational acceleration of the to-be-measured point.

[0096] In an optional manner, the training module 210 includes: a first training module and a second training module;

[0097] The first training module is used to: input the coordinate increment corresponding to any sample point outside the target small celestial body into the interpolation neural network to obtain the predicted value of gravity acceleration of any sample point, and determine the loss value of any sample point according to the predicted value of gravity acceleration and the measured value of gravity acceleration of any sample point, until the loss value of each sample point outside the target small celestial body is determined;

[0098] The second training module is used to: optimize the parameters of the interpolation neural network based on all loss values ​​to obtain an optimized interpolation neural network, and use the optimized interpolation neural network as the interpolation neural network and return to call the first training module until the optimized interpolation neural network meets the iterative training conditions, and determine the optimized interpolation neural network as the target interpolation neural network.

[0099] In an optional manner, the interpolation neural network includes: a generalized distance module and a hidden layer module; the step of inputting the coordinate increment corresponding to any sample point outside the target small celestial body into the interpolation neural network in the first training module to obtain the predicted value of gravity acceleration of any sample point includes:

[0100] Input the coordinate increment corresponding to any sample point outside the target small celestial body into the generalized distance module, obtain the generalized spatial distance value of any sample point and input it into the hidden layer module to obtain the spatial weight value of any sample point;

[0101] The predicted value of gravity acceleration of any sample point is obtained according to the spatial weight value of any sample point, the coefficients corresponding to other known sample points around any sample point and the external gravity acceleration measurement value.

[0102] In an optional manner, the method further includes: a measurement module; the measurement module is used to:

[0103] Using the polyhedron method, the gravitational acceleration measurement value of each sample point is calculated separately.

[0104] In an optional manner, the method further includes: a determination module; the determination module is used to:

[0105] Using a ball sampling method, a plurality of external points within a preset range around the target small celestial body are acquired;

[0106] The spherical coordinate value of each external point is converted into a rectangular coordinate value, and the external point whose rectangular coordinate value is outside the target small celestial body is determined as a sample point.

[0107] The technical solution of this embodiment can realize the rapid and accurate calculation of the gravitational acceleration of the point to be measured outside the small celestial body, which can reduce the modeling time of the gravity field.

[0108] The above-mentioned parameters and steps for each module to implement corresponding functions in the small celestial body external gravity acceleration prediction system 200 based on interpolation neural network in this embodiment can refer to the parameters and steps in the embodiment of the small celestial body external gravity acceleration prediction method based on interpolation neural network above, and will not be repeated here.

[0109] like Figure 7 As shown, an electronic device 300 of an embodiment of the present invention includes a processor 320, the processor 320 is coupled to a memory 310, and the memory 310 stores at least one computer program 330, and the at least one computer program 330 is loaded and executed by the processor 320, so that the electronic device 300 implements any of the above-mentioned methods for predicting external gravity acceleration of small celestial bodies based on interpolation neural networks, specifically:

[0110] The electronic device 300 may have relatively large differences due to different configurations or performances, and may include one or more processors 320 (Central Processing Units, CPU) and one or more memories 310, wherein the one or more memories 310 store at least one computer program 330, and the at least one computer program 330 is loaded and executed by the one or more processors 320, so that the electronic device 300 implements any of the small celestial body external gravity acceleration prediction methods based on interpolation neural networks provided in the above embodiments. Of course, the electronic device 300 may also have components such as a wired or wireless network interface, a keyboard, and an input and output interface for input and output, and the electronic device 300 may also include other components for implementing device functions, which will not be repeated here.

[0111] A computer-readable storage medium according to an embodiment of the present invention stores at least one computer program, and the at least one computer program is loaded and executed by a processor so that the computer implements any of the above-mentioned methods for predicting the external gravitational acceleration of small celestial bodies based on interpolation neural networks.

[0112] Optionally, the computer-readable storage medium may be a read-only memory (ROM), a random access memory (RAM), a compact disc (CD-ROM), a magnetic tape, a floppy disk, an optical data storage device, and the like.

[0113] In an exemplary embodiment, a computer program product or a computer program is also provided, the computer program product or the computer program including computer instructions, the computer instructions being stored in a computer-readable storage medium. A processor of an electronic device reads the computer instructions from the computer-readable storage medium, and the processor executes the computer instructions, so that the electronic device executes any of the above-mentioned methods for predicting external gravity acceleration of a small celestial body based on an interpolation neural network.

[0114] It should be noted that the terms "first", "second", etc. in the specification and claims of the present application are used to distinguish similar objects and represent the definition of a specific order or sequence. The order of use of similar objects can be interchanged where appropriate, so that the embodiments of the present application described herein can be implemented in an order other than the order shown or described.

[0115] Those skilled in the art know that the present invention can be implemented as a system, method or computer program product. Therefore, the present disclosure can be specifically implemented in the following forms, namely: it can be complete hardware, it can be complete software (including firmware, resident software, microcode, etc.), or it can be a combination of hardware and software, which is generally referred to as "circuit", "module" or "system" herein. In addition, in some embodiments, the present invention can also be implemented in the form of a computer program product in one or more computer-readable media, and the computer-readable medium contains computer-readable program code.

[0116] Any combination of one or more computer-readable media can be used. Computer-readable media can be computer-readable signal media or computer-readable storage media. Computer-readable storage media can be, for example, but not limited to, electrical, magnetic, optical, electromagnetic, infrared, or semiconductor systems, devices or devices, or any combination of the above. More specific examples of computer-readable storage media (a non-exhaustive list) include: an electrical connection with one or more wires, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above. In the present application, a computer-readable storage medium can be any tangible medium containing or storing a program, which can be used by an instruction execution system, device or device or used in combination with it.

[0117] Although the embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and are not to be construed as limitations of the present invention. A person skilled in the art may change, modify, replace and vary the above embodiments within the scope of the present invention.

Claims

1. A method for predicting external gravitational acceleration of small celestial bodies based on interpolation neural network, characterized in that: include: Taking the coordinate increments corresponding to the sample points outside the target small celestial body as input and the gravitational acceleration measurement values ​​of the sample points as labels, the interpolation neural network used to predict the gravitational acceleration of the points outside the small celestial body is iteratively trained to obtain the target interpolation neural network; wherein the coordinate increment corresponding to any sample point outside the target small celestial body is the coordinate increment between the rectangular coordinates of the sample point and the rectangular coordinates of the other surrounding known sample points; Inputting the coordinate increment of the to-be-measured point outside the target small celestial body into the target interpolation neural network to obtain the predicted value of the gravitational acceleration of the to-be-measured point; The steps of iteratively training the interpolation neural network for predicting the gravitational acceleration of the external points of the small celestial body with the coordinate increments corresponding to the sample points outside the target small celestial body as input and the gravitational acceleration measurement values ​​of the sample points as labels to obtain the target interpolation neural network include: Inputting the coordinate increment corresponding to any sample point outside the target small celestial body into the interpolation neural network to obtain the predicted value of gravity acceleration of any sample point, and determining the loss value of any sample point according to the predicted value of gravity acceleration and the measured value of gravity acceleration of any sample point, until the loss value of each sample point outside the target small celestial body is determined; Based on all the loss values, the interpolation neural network is parameter optimized to obtain an optimized interpolation neural network, and the optimized interpolation neural network is used as the interpolation neural network and the step of inputting the coordinate increment corresponding to any sample point outside the target small celestial body into the interpolation neural network is returned to execute, until the optimized interpolation neural network meets the iterative training conditions, the optimized interpolation neural network is determined as the target interpolation neural network; The interpolation neural network includes: a generalized distance module and a hidden layer module; the step of inputting the coordinate increment corresponding to any sample point outside the target small celestial body into the interpolation neural network to obtain the predicted value of gravity acceleration of any sample point includes: Input the coordinate increment corresponding to any sample point outside the target small celestial body into the generalized distance module, obtain the generalized spatial distance value of any sample point and input it into the hidden layer module to obtain the spatial weight value of any sample point; The predicted value of gravity acceleration of any sample point is obtained according to the spatial weight value of any sample point, the coefficients corresponding to other known sample points around any sample point and the external gravity acceleration measurement value.

2. The method for predicting external gravitational acceleration of a small celestial body based on an interpolation neural network according to claim 1 is characterized in that: The steps to obtain the gravitational acceleration measurement value of each sample point include: Using the polyhedron method, the gravitational acceleration measurement value of each sample point is calculated separately.

3. The method for predicting external gravitational acceleration of small celestial bodies based on interpolation neural network according to claim 1 is characterized in that: The step of determining a sample point outside the target small celestial body comprises: Using a spherical sampling method, a plurality of sample points within a preset range around the target small celestial body are obtained; The spherical coordinate value of each external point is converted into a rectangular coordinate value, and the external point whose rectangular coordinate value is outside the target small celestial body is determined as a sample point.

4. A small celestial body external gravity acceleration prediction system based on interpolation neural network, characterized in that: include: Training module and prediction module; The training module is used to: use the coordinate increments corresponding to the sample points outside the target small celestial body as inputs and the gravitational acceleration measurements of the sample points as labels, and iteratively train the interpolation neural network used to predict the gravitational acceleration of the points outside the small celestial body to obtain the target interpolation neural network; wherein the coordinate increment corresponding to any sample point outside the target small celestial body is the coordinate increment between the rectangular coordinates of the sample point and the rectangular coordinates of the other surrounding known sample points; The prediction module is used to: input the coordinate increment of the to-be-measured point outside the target small celestial body into the target interpolation neural network to obtain the predicted value of the gravity acceleration of the to-be-measured point; The training module includes: a first training module and a second training module; The first training module is used to: input the coordinate increment corresponding to any sample point outside the target small celestial body into the interpolation neural network to obtain the predicted value of gravity acceleration of any sample point, and determine the loss value of any sample point according to the predicted value of gravity acceleration and the measured value of gravity acceleration of any sample point, until the loss value of each sample point outside the target small celestial body is determined; The second training module is used to: optimize the parameters of the interpolation neural network based on all loss values ​​to obtain an optimized interpolation neural network, and use the optimized interpolation neural network as the interpolation neural network and return to call the first training module until the optimized interpolation neural network meets the iterative training conditions, and the optimized interpolation neural network is determined as the target interpolation neural network; The interpolation neural network includes: a generalized distance module and a hidden layer module; the step of inputting the coordinate increment corresponding to any sample point outside the target small celestial body into the interpolation neural network in the first training module to obtain the predicted value of gravity acceleration of any sample point includes: Input the coordinate increment corresponding to any sample point outside the target small celestial body into the generalized distance module, obtain the generalized spatial distance value of any sample point and input it into the hidden layer module to obtain the spatial weight value of any sample point; The predicted value of gravity acceleration of any sample point is obtained according to the spatial weight value of any sample point, the coefficients corresponding to other known sample points around any sample point and the external gravity acceleration measurement value.

5. An electronic device, characterized in that: The electronic device includes a processor, the processor is coupled to a memory, at least one computer program is stored in the memory, and the at least one computer program is loaded and executed by the processor so that the electronic device implements the method for predicting the external gravity acceleration of a small celestial body based on an interpolation neural network as described in any one of claims 1 to 3.

6. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores at least one computer program, and the at least one computer program is loaded and executed by the processor so that the computer-readable storage medium implements the method for predicting the external gravity acceleration of small celestial bodies based on the interpolation neural network as described in any one of claims 1 to 3.

Images