Satellite orbit prediction method, system, device and medium based on gravity field vectorization calculation model

Abstract

The application discloses a satellite orbit prediction method, system, device and medium based on a gravity field vectorization calculation model, and the method comprises the following steps: establishing a motion equation of a satellite in an inertial system; constructing a gravity field fast calculation model; dividing a gradient formula of a gravity field potential position into a sum of a harmonic part and a non-harmonic part, and performing vectorization reconstruction to obtain a gravity field vectorization calculation model; obtaining a position and a velocity vector of the satellite at an initial moment, inputting the position and the velocity vector into the motion equation of the satellite in the inertial system, combining the gravity field vectorization calculation model, and solving the satellite orbit by using a numerical integration method. The gravity field vectorization calculation model is numerically equivalent to a traditional loop algorithm, the accuracy of the gravity field model is ensured without loss, the traditional double loop structure is replaced by matrix operation, the calculation efficiency of a high-order gravity field is significantly improved, and therefore, the satellite orbit prediction calculation efficiency is improved on the basis of ensuring the accuracy.

Description

Technical Field

[0001] This invention relates to the field of satellite orbit determination technology, and in particular to a satellite orbit prediction method, system, device and medium based on a gravity field vectorization calculation model. Background Technology

[0002] The provision of high-precision satellite orbit predictions plays a crucial role in fields such as remote sensing, meteorology, and satellite navigation systems. In satellite orbit dynamics models, the gravity field model is a core component. It describes the Earth's gravitational potential field and is the primary force considered in orbit prediction. The Earth's gravity field is an objective reflection of the spatial distribution, motion, and changes of Earth's matter, typically described using spherical harmonic function expansions, containing thousands or even millions of terms. The accuracy of the gravity field model directly affects the accuracy of satellite orbits. With advancements in measurement and data processing technologies, satellite-based gravity detection missions such as GRACE Follow-On and GOCE have become mainstream methods, and high-resolution and refined gravity field models are continuously being iterated and updated. Currently, leading international institutions have the capability to provide gravity field models of order 2160 or even higher precision. In precise satellite orbit determination, integration calculations are performed based on a given initial orbit, requiring the calculation of spatial gravitational effects based on a priori gravity field model. However, the double-nested loop structure in gravity field superposition calculations leads to a computational complexity increase on the order of O(n²), significantly reducing computational efficiency. Due to the characteristics of satellite orbit prediction, the gravity field calculation model needs to be repeatedly called in the right-hand integral function. In this case, the traditional double-loop-based calculation scheme becomes extremely time-consuming, significantly impacting the performance of numerical integration methods for extrapolating orbits. Therefore, the time spent on each calculation becomes a key bottleneck affecting overall performance.

[0003] To address the technical bottlenecks in gravity field model calculations for satellite orbit prediction, existing research primarily overcomes performance limitations through parallel computing techniques. Xiao Huadong's team proposed a domain decomposition and aggregation communication strategy based on the MPI architecture, combined with Fourier transform to accelerate Legendre function calculation; Li Hongwei used the Stokes integral method to construct a fast calculation model, achieving approximate calculations through discretization, but with slight deviations from the original integral model; Zou Xiancai's team designed a parallel data processing flow based on OpenMP, effectively improving the solution speed. These parallel solutions have all optimized the efficiency of gravity field model calculations to some extent. However, the aforementioned existing technical solutions still have the following structural defects:

[0004] 1. Inherent defects at the algorithm level. Traditional loop calculations contain a large number of redundant operations, such as the successive double loop calls of the gravity field coefficient matrix.

[0005] 2. Engineering limitations at the parallel computing implementation level. Existing parallel computing solutions generally suffer from high adaptation costs and strong architecture dependencies. The application of heterogeneous accelerators such as GPUs is limited by the R&D costs and energy efficiency of miniaturized parallel platforms, and has not yet achieved large-scale application in the field of geodesy.

[0006] 3. Shortcomings of Algorithm Optimization Schemes. On the one hand, existing methods mostly focus on the inversion of gravity field parameters by solving high-dimensional equations, emphasizing the performance improvement of the constructed normal equations and their solution process. However, there are still significant shortcomings in optimizing the efficiency of single-step calculations of high-order gravitational potentials. On the other hand, using approximate models to simplify the complexity of gravity field calculations also leads to a certain degree of loss in the accuracy of the gravity field model.

[0007] In summary, the existing gravity field models cannot balance computational accuracy and efficiency, resulting in satellite orbit prediction failing to improve computational efficiency while ensuring accuracy. Summary of the Invention

[0008] To address the shortcomings of the existing technologies, this invention provides a satellite orbit prediction method, system, device, and medium based on a gravity field vectorization calculation model. By constructing a gravity field vectorization calculation model that balances efficiency and accuracy, the invention aims to improve the efficiency of satellite orbit prediction calculations while ensuring accuracy.

[0009] Firstly, a satellite orbit prediction method based on a gravity field vectorization calculation model is provided, including the following steps:

[0010] Establish the equations of motion for the satellite in an inertial frame;

[0011] Constructing a fast calculation model for the gravitational field: The gradient formula for the position of the gravitational potential pair in the gravitational field is written as the sum of the harmonic part and the tandem harmonic part, and then vectorized and reconstructed to obtain a vectorized calculation model for the gravitational field.

[0012] The satellite's position and velocity vectors at the initial moment are obtained, input into the satellite's motion equations in the inertial frame, and combined with the gravity field vectorization calculation model, the satellite orbit is obtained by numerical integration.

[0013] Furthermore, the equations of motion of the satellite in the inertial frame are expressed as follows:

[0014]

[0015] in, and These represent the position of the satellite's center of mass and its acceleration vector in the inertial frame, respectively. The radial direction of the satellite in the inertial frame; The gravitational constant of a celestial body; Earth mass; For the gravitational acceleration of the central celestial body, For non-spherical gravitational acceleration in an inertial frame of reference, It is the sum of all perturbation accelerations except for the gravitational acceleration of the central celestial body and the non-spherical gravitational acceleration of the gravitational field.

[0016] Furthermore, the process of constructing a rapid calculation model for the gravitational field is as follows:

[0017] The gradient formula for the position of the gravitational potential in the gravitational field is written as the sum of the harmonic part and the tandem harmonic part, and is expressed as follows:

[0018]

[0019]

[0020]

[0021] In the formula, Point The gravitational potential at that location. and They represent the gravitational potentials in the gravitational field. The harmonic part and the field harmonic part; and Points The corresponding longitude, geocentric latitude, and radial distance; , and These are the spherical harmonic coefficients; This is the normalized nth-order Legendre polynomial; For the normalized nth order m-th order associated Legendre polynomial; ; ; ;

[0022] By vectorizing and reconstructing the harmonic and tandem harmonic components of the gradient formula for the position of gravitational potential pairs in the gravitational field, a vectorized calculation model of the gravitational field is obtained; the vectorized representations of the harmonic and tandem harmonic components are as follows:

[0023]

[0024]

[0025] in:

[0026]

[0027]

[0028]

[0029]

[0030]

[0031]

[0032]

[0033]

[0034]

[0035]

[0036]

[0037] In the formula, "Represents the Hadamard product of a matrix; for A column vector consisting entirely of 1s.

[0038] Furthermore, the process of calculating the gravitational potential gradient of the gravitational field using the vectorized calculation model of the gravitational field is as follows:

[0039] Input points in a three-dimensional Earth-solid system and introduce global gravity field coefficients, including spherical harmonic coefficients. and ;

[0040] Transform the point from the Earth-fixed coordinate system to the geocentric spherical coordinate system to obtain the point's longitude, geocentric latitude, and radius. ;

[0041] Calculate the Legendre function and its counterpart using a recursive algorithm. The partial derivatives of and the matrix formed by them are calculated. , , and ;

[0042] according to The matrix variables required for calculating the vectorized model of the gravitational field include , , , , , , and ;

[0043] Substitute the gravitational field into the vectorized calculation model to obtain the gravitational potential gradient at that point.

[0044] Furthermore, in the process of obtaining the satellite orbit using numerical integration:

[0045] The gravitational acceleration of the gravitational field at a point is expressed as the gravitational acceleration of the gravitational field at that point.

[0046] The gravitational acceleration at that point is converted to the inertial frame using a rotation matrix, resulting in the non-spherical gravitational acceleration in the inertial frame.

[0047] Secondly, a satellite orbit prediction system based on a gravity field vectorization calculation model is provided, including:

[0048] The equations of motion module is used to establish the equations of motion of a satellite in an inertial frame.

[0049] The fast gravity field calculation model construction module is used to construct a fast gravity field calculation model: the gradient formula of the position of the gravitational potential pair of the gravity field is written as the sum of the harmonic part and the tandem harmonic part, and then vectorized and reconstructed to obtain the vectorized gravity field calculation model.

[0050] The satellite orbit determination module is used to obtain the satellite's position and velocity vectors at the initial moment, input them into the satellite's motion equations in the inertial frame, and combine them with the gravity field vectorization calculation model to obtain the satellite orbit using the numerical integration method.

[0051] Thirdly, an electronic device is provided, comprising:

[0052] A memory on which computer programs are stored;

[0053] A processor is used to load and execute the computer program to implement the satellite orbit prediction method based on the gravity field vectorization calculation model as described above.

[0054] Fourthly, a computer-readable storage medium is provided, on which a computer program is stored, which, when executed by a processor, implements the satellite orbit prediction method based on the gravity field vectorization calculation model as described above.

[0055] Fifthly, a computer program product is provided, which stores computer instructions. When the computer instructions are executed by a processor, they implement the satellite orbit prediction method based on the gravity field vectorization calculation model as described above.

[0056] This invention proposes a satellite orbit prediction method, system, device, and medium based on a gravity field vectorization calculation model, which has the following beneficial effects:

[0057] (1) A gravity field calculation model based on vectorization reconstruction is proposed. The numerical equivalence between the vectorization model and the traditional loop algorithm is proved through rigorous mathematical derivation, ensuring that the accuracy of the gravity field model is not lost. The traditional double loop structure is replaced by matrix operation, which significantly improves the calculation efficiency of high-order gravity fields. Thus, the calculation efficiency of satellite orbit prediction is improved while ensuring accuracy.

[0058] (2) Constructing a native vectorization framework can be adapted to general numerical computing environments and can significantly improve the performance of satellite orbit prediction. Attached Figure Description

[0059] 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 these drawings without creative effort.

[0060] Figure 1 This is a flowchart of the satellite orbit prediction method based on the gravity field vectorization calculation model provided in this embodiment of the invention;

[0061] Figure 2 This is a flowchart of the gravitational potential gradient calculation in the gravitational field provided in an embodiment of the present invention;

[0062] Figure 3 This is a schematic diagram of the gravity field calculation efficiency test results provided in an embodiment of the present invention. Detailed Implementation

[0063] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be described in detail below. Obviously, the described embodiments are merely some embodiments of this invention, and not all embodiments. Based on the embodiments of this invention, all other implementation methods obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0064] like Figure 1 As shown, the present invention provides a satellite orbit prediction method based on a gravity field vectorization calculation model, comprising the following steps:

[0065] S1: Based on Newton's second law, establish the equations of motion for the satellite in the inertial frame.

[0066] The equations of motion for the satellite in the inertial frame are expressed as follows:

[0067]

[0068] in, and These represent the position of the satellite's center of mass and its acceleration vector in the inertial frame, respectively. The radial distance of the satellite in the inertial frame (the distance from the satellite to the Earth's center); The gravitational constant of a celestial body; The mass of Earth; the first term on the right side of the equation. For the gravitational acceleration of the central celestial body, the second term For the non-spherical gravitational acceleration in an inertial frame of reference, the third term... It is the sum of all perturbation accelerations except for the gravitational acceleration of the central celestial body and the non-spherical gravitational acceleration of the gravitational field.

[0069] If we can obtain an accurate mechanical model on the right side of the equation, then we only need to know the satellite's initial moment in the inertial frame. Location and velocity vector This allows us to obtain the satellite's position and velocity vector at any given time. Since the dynamic model on the right side of the equation is quite complex, numerical integration is typically used to solve the satellite's equations of motion. Single-step integrators, such as 7th-8th order Runge-Kutta integrators, or multi-step integrators, such as Adams integrators, can be used. This invention focuses on improving the gravity field calculation model; therefore, the gravity field calculation model will be discussed in detail later. The calculation is not the focus of this invention, and the calculation process can be carried out using existing mature technologies, which will not be elaborated here.

[0070] S2: Constructing a fast calculation model for the gravitational field: The gradient formula for the position of the gravitational potential pair in the gravitational field is written as the sum of the harmonic part and the tandem harmonic part, and then vectorized and reconstructed to obtain a vectorized calculation model for the gravitational field.

[0071] As one of the terms to be calculated in the right function of the integrator mentioned above, for the convenience of model description, the non-spherical acceleration of the gravitational field is... The calculations for the Earth-solid system are typically handled within the context of the two-body problem. In the classic two-body problem, the Earth is treated as an ideal sphere with a uniform mass distribution. However, the actual Earth is not a perfect sphere, and its mass distribution is not uniform. Furthermore, the Earth itself is not a rigid sphere; tidal forces from the Sun and Moon exert attraction on both the solid and fluid parts of the Earth, causing the mass distribution to change over time. This gravitational force caused by an irregularly shaped central celestial body is a conservative force and possesses a corresponding gravitational potential, denoted as . Its location at the midpoint of the Earth-solid system. Acceleration caused at the location It can be generated by gravitational potential The gradient is used to represent this, that is:

[0072]

[0073] In the formula, express The gradient in the Earth-fixed frame. The gravitational acceleration in the gravitational field can be obtained between the inertial frame and the Earth-fixed frame through a rotation matrix. To convert, that is:

[0074]

[0075] Wherein, rotation matrix The calculations are existing technology and will not be described in detail here.

[0076] The gravitational potential of the Earth-fixed system can be expressed by the following formula after dimensionless processing:

[0077]

[0078] In the formula, Point The gravitational potential at that location; the first term is a harmonic term, corresponding to... The gravitational potential at that time; the second term is the Tianhe term, corresponding to Gravitational potential at that time; The gravitational constant of a celestial body; Earth mass; The equatorial radius of the Earth's reference ellipsoid; and Points The corresponding longitude, geocentric latitude, and radial distance; , and The spherical harmonic coefficients, For harmonic coefficients, and For the coefficient of the harmonic term, and For sector harmonic coefficients; This is the normalized nth-order Legendre polynomial; This is the normalized nth order m-th order associated Legendre polynomial.

[0079] In this embodiment, an equivalent notation for the gravitational potential of a gravitational field is adopted, in which the gradient formula of the gravitational potential with respect to position is written as the sum of the harmonic part and the tandem harmonic part, as follows:

[0080]

[0081]

[0082]

[0083] In the formula, and Representing points respectively gravitational potential in a gravitational field The harmonic part and the field harmonic part; ; ; The following points should be noted regarding the expression of the gravitational potential of this equivalent gravitational field:

[0084] (1) The formula adopts a dimensionless expression. Dimensionlessness refers to the process of transforming all physical quantities in an equation, model, or expression with physical units into dimensionless quantities (divided by the corresponding dimension to obtain a unitless quantity) through mathematical transformation. In this embodiment, the dimension is set as: unit of length. Quality unit Time unit .

[0085] (2) The conversion relationship between spherical coordinates and rectangular coordinates has been eliminated, and instead the conversion relationship between spherical coordinates and rectangular coordinates is given directly. , , The partial derivatives of equal variables simplify the expression method.

[0086] (3) The partial derivatives of the Legendre function are relative to... of, rather than And there is .

[0087] By vectorizing and reconstructing the harmonic and tandem harmonic parts of the gradient formula for the position of the gravitational potential pair, it can be derived into the following expression:

[0088]

[0089]

[0090] in:

[0091]

[0092]

[0093]

[0094]

[0095]

[0096]

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[0098]

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[0100]

[0101]

[0102] In the formula, "Represents the Hadamard product of matrices, which means that when two matrices are being multiplied have the same dimensions, they are multiplied element by element." for A column vector of all 1s; where, the quadratic expression Representative to The summation of all elements in a matrix can be efficiently calculated in code by calling a built-in optimized matrix element summation function.

[0103] like Figure 2 As shown, the process of calculating the gravitational potential gradient of the gravitational field using the gravitational field vectorization calculation model is as follows:

[0104] Step 1: Input the points of the three-dimensional Earth-solid system and introduce the global gravity field coefficients. The global gravity field system includes spherical harmonic coefficients. and ;

[0105] Step 2: Transform the point from the Earth-fixed coordinate system to the geocentric spherical coordinate system to obtain the longitude, geocentric latitude, and radius vector of the point. ;

[0106] Step 3: Calculate the Legendre function and its relation using the recursive algorithm. The partial derivatives of and the matrix formed by them are calculated. , , and ;

[0107] Step 4: According to The matrix variables required for calculating the vectorized model of the gravitational field include , , , , , , and ;

[0108] Step 5: , , , , , , , , , , and Substitute the gravitational field into the vectorized calculation model to obtain the gravitational potential gradient at that point.

[0109] In the subsequent process of obtaining the satellite orbit using numerical integration, it is also necessary to convert the gravitational potential gradient of the gravitational field in the Earth-fixed frame into the non-spherical gravitational acceleration of the gravitational field in the inertial frame. The process is as follows:

[0110] The gravitational acceleration of the gravitational field at a point is expressed as the gravitational acceleration of the gravitational field at that point.

[0111] The gravitational acceleration at that point is converted to the inertial frame using a rotation matrix, resulting in the non-spherical gravitational acceleration in the inertial frame.

[0112] S3: Obtain the satellite's position and velocity vectors at the initial moment, input them into the satellite's motion equations in the inertial frame, and combine them with the gravity field vectorization calculation model to obtain the satellite orbit using the numerical integration method.

[0113] The specific process of solving the problem using the numerical integration method is a well-established technology and will not be elaborated further here.

[0114] The satellite orbit prediction method based on a gravity field vectorization calculation model provided in the above embodiments solves the following technical problems:

[0115] (1) Solving the bottleneck of computational efficiency. Breaking through the O(n²) complexity limitation of traditional loop algorithms, the linear complexity of gravity field calculation is optimized through matrix operations, which significantly improves the efficiency of high-order gravity field calculation and thus improves the efficiency of satellite orbit prediction calculation.

[0116] (2) By rigorously deriving the gravity field formula, the overall reconstruction scheme is made equivalent to the traditional algorithm, thus ensuring the numerical stability of the calculation. This technical solution will not cause any loss of accuracy in the gravity field model, thereby ensuring accuracy while improving the efficiency of satellite orbit prediction calculation.

[0117] (3) Solve the platform compatibility problem. Construct a native vectorized computing framework and flexibly use the optimization mechanism of matrix operation (such as implicit broadcasting, memory pre-allocation, etc.) to adapt to the general numerical computing environment, which can significantly improve the performance of satellite orbit prediction.

[0118] To further illustrate the improvement in computational efficiency of the gravity field vectorization calculation model proposed in this invention, a test experiment is presented below.

[0119] The algorithm was tested using the MATLAB numerical computation platform, software version 2024a, and the gravity field model was GOCO06s. Test single calculation of Earth-fixed system coordinates The gravitational field order was set from low to high at each location. The test results are as follows: Figure 3 As shown, the cyclic accumulation algorithm is the traditional gravity field calculation model, while the vectorization algorithm is the gravity field vectorization calculation model proposed in this invention.

[0120] In low-order computation scenarios (approximately ≤30 orders), the vectorization algorithm and the loop accumulation algorithm have comparable computation times. However, as the order increases, the performance difference between the two algorithms widens exponentially. When the gravity field order reaches 300, the traditional loop accumulation algorithm takes 0.009 seconds, while the vectorization algorithm only takes 0.002 seconds, representing a 4.5-fold increase in computational efficiency. Furthermore, the vectorization algorithm maintains approximately linear growth at order 300, while the loop accumulation algorithm shows a clear exponential growth trend.

[0121] The above results show that the gravity field vectorization calculation model can significantly improve the computational performance of a single gravity field, thereby reducing the computation time required for scenarios such as satellite orbit prediction that require a large number of repeated calculations of high-order gravity fields.

[0122] This invention also provides a satellite orbit prediction system based on a gravity field vectorization calculation model, comprising:

[0123] The equations of motion module is used to establish the equations of motion of a satellite in an inertial frame.

[0124] The fast gravity field calculation model construction module is used to construct a fast gravity field calculation model: the gradient formula of the position of the gravitational potential pair of the gravity field is written as the sum of the harmonic part and the tandem harmonic part, and then vectorized and reconstructed to obtain the vectorized gravity field calculation model.

[0125] The satellite orbit determination module is used to obtain the satellite's position and velocity vectors at the initial moment, input them into the satellite's motion equations in the inertial frame, and combine them with the gravity field vectorization calculation model to obtain the satellite orbit using the numerical integration method.

[0126] It should be understood that the functional unit modules in the various embodiments of the present invention can be concentrated in one processing unit, or each unit module can exist physically separately, or two or more unit modules can be integrated into one unit module, and can be implemented in hardware or software.

[0127] Furthermore, embodiments of the present invention also provide an electronic device, comprising:

[0128] A memory on which computer programs are stored;

[0129] A processor is used to load and execute the computer program to implement the satellite orbit prediction method based on the gravity field vectorization calculation model as described above.

[0130] Furthermore, embodiments of the present invention also provide a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the satellite orbit prediction method based on the gravity field vectorization calculation model as described above.

[0131] Furthermore, this embodiment of the invention also provides a computer program product, which stores computer instructions. When the computer instructions are executed by a processor, they implement the satellite orbit prediction method based on the gravity field vectorization calculation model as described above.

[0132] It is understood that the same or similar parts in the above embodiments can be referred to each other, and the contents not described in detail in some embodiments can be referred to the same or similar contents in other embodiments.

[0133] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0134] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0135] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1The function specified in one or more boxes.

[0136] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0137] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. A satellite orbit prediction method based on a gravity field vectorization calculation model, characterized in that, Includes the following steps: Establish the equations of motion for the satellite in an inertial frame; Constructing a fast calculation model for the gravitational field: The gradient formula for the position of the gravitational potential pair in the gravitational field is written as the sum of the harmonic part and the tandem harmonic part, and then vectorized and reconstructed to obtain a vectorized calculation model for the gravitational field. The satellite's position and velocity vectors at the initial moment are obtained, input into the satellite's motion equations in the inertial frame, and combined with the gravity field vectorization calculation model, the satellite orbit is obtained by numerical integration. The process of constructing a fast calculation model for the gravity field is as follows: The gradient formula for the position of the gravitational potential in the gravitational field is written as the sum of the harmonic part and the tandem harmonic part, and is expressed as follows: ； ； ； In the formula, Point The gravitational potential at that location. and They represent the gravitational potentials in the gravitational field. The harmonic part and the field harmonic part; and Points The corresponding longitude, geocentric latitude, and radial distance; , and These are the spherical harmonic coefficients; This is the normalized nth-order Legendre polynomial; For the normalized nth order m-th order associated Legendre polynomial; ; ; ; By vectorizing and reconstructing the harmonic and tandem harmonic components of the gradient formula for the position of gravitational potential pairs in the gravitational field, a vectorized calculation model of the gravitational field is obtained; the vectorized representations of the harmonic and tandem harmonic components are as follows: ； ； in: ; ； ； ； ； ； ； ； ； ； ； ； In the formula, " "Represents the Hadamard product of a matrix; for A column vector consisting entirely of 1s.

2. The satellite orbit prediction method based on the gravity field vectorization calculation model according to claim 1, characterized in that, The equations of motion for the satellite in the inertial frame are expressed as follows: ； in, and These represent the position of the satellite's center of mass and its acceleration vector in the inertial frame, respectively. The radial direction of the satellite in the inertial frame; The gravitational constant of a celestial body; Earth mass; For the gravitational acceleration of the central celestial body, For non-spherical gravitational acceleration in an inertial frame of reference, It is the sum of all perturbation accelerations except for the gravitational acceleration of the central celestial body and the non-spherical gravitational acceleration of the gravitational field.

3. The satellite orbit prediction method based on the gravity field vectorization calculation model according to claim 1, characterized in that, The process of calculating the gravitational potential gradient of the gravitational field using the vectorized calculation model of the gravitational field is as follows: Input points in a three-dimensional Earth-solid system and introduce global gravity field coefficients; Transform the point from the Earth-fixed coordinate system to the geocentric spherical coordinate system to obtain the point's longitude, geocentric latitude, and radius. ; Calculate the Legendre function and its counterpart using a recursive algorithm. The partial derivatives of and the matrix formed by them are calculated. , , and ; according to The matrix variables required for calculating the vectorized model of the gravitational field include , , , , , , and ; Substitute the gravitational field into the vectorized calculation model to obtain the gravitational potential gradient at that point.

4. The satellite orbit prediction method based on the gravity field vectorization calculation model according to claim 3, characterized in that, In the process of obtaining satellite orbits using numerical integration: The gravitational acceleration of the gravitational field at a point is expressed as the gravitational acceleration of the gravitational field at that point. The gravitational acceleration at that point is converted to the inertial frame using a rotation matrix, resulting in the non-spherical gravitational acceleration in the inertial frame.

5. A satellite orbit prediction system based on a gravity field vectorization calculation model, characterized in that, The system for implementing the satellite orbit prediction method based on the gravity field vectorization calculation model as described in any one of claims 1-4 includes: The equations of motion module is used to establish the equations of motion of a satellite in an inertial frame. The fast gravity field calculation model construction module is used to construct a fast gravity field calculation model: the gradient formula of the position of the gravitational potential pair of the gravity field is written as the sum of the harmonic part and the tandem harmonic part, and then vectorized and reconstructed to obtain the vectorized gravity field calculation model. The satellite orbit determination module is used to obtain the satellite's position and velocity vectors at the initial moment, input them into the satellite's motion equations in the inertial frame, and combine them with the gravity field vectorization calculation model to obtain the satellite orbit using the numerical integration method.

6. An electronic device, characterized in that, include: A memory on which computer programs are stored; A processor is configured to load and execute the computer program to implement the satellite orbit prediction method based on a gravity field vectorization calculation model as described in any one of claims 1-4.

7. 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 satellite orbit prediction method based on the gravity field vectorization calculation model as described in any one of claims 1-4.

8. A computer program product, characterized in that, The computer program product stores computer instructions, which, when executed by a processor, implement the satellite orbit prediction method based on a gravity field vectorization calculation model as described in any one of claims 1-4.

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