A low earth orbit constellation orbit prediction method and system fusing power law scale constraints

Abstract

The application relates to a low-orbit constellation orbit prediction method and system fusing a power law scale constraint, and the method comprises the following steps: acquiring low-orbit constellation orbit state data and inputting the pre-trained physical information neural network model to obtain orbit deviation and state data at a future time; the training process of the physical information neural network model comprises the following steps: acquiring orbit deviation data under different satellite quantities and at different times and performing pretreatment; based on the pretreated orbit deviation data, an orbit deviation data set is constructed; the pretreated orbit deviation data is statistically analyzed to obtain a power law relationship between the orbit deviation and the satellite quantity; based on the power law relationship, a total loss function comprising a global scale law constraint and a local dynamics constraint is calculated, and model parameters of the physical information neural network model are optimized until training convergence is achieved, so that a trained physical information neural network model is obtained. Compared with the prior art, the application has the advantage of high prediction accuracy.

Description

Technical Field

[0001] This invention relates to the field of satellite communication technology, and in particular to a method and system for predicting the orbit of a low-Earth orbit constellation that incorporates power-law scaling constraints. Background Technology

[0002] Orbit prediction is a core component of low-Earth orbit satellite operation and management, and existing technologies are mainly divided into three categories: Traditional dynamic extrapolation methods: These methods are based on orbital dynamic equations and incorporate perturbation models such as Earth's non-spherical shape, atmospheric drag, and lunar and solar gravitational forces. Orbit prediction is achieved through numerical integration or analytical models (such as SGP4), making it the mainstream approach in engineering applications. In scenarios with a small number of low-Earth orbit satellites, this method can provide reliable predictions. However, as constellation sizes increase, the long-term cumulative effects of inter-satellite gravitational interactions become increasingly significant. Traditional simplified models cannot effectively characterize this collective dynamic behavior, and the computational cost of large-scale N-body simulations is insufficient to support engineering requirements.

[0003] Machine learning-assisted orbit prediction methods: To compensate for the error accumulation shortcomings of dynamic methods, existing research combines machine learning methods such as Support Vector Machines (SVM), Backpropagation Neural Networks (BP Neural Networks), and LSTM with dynamic extrapolation, using orbital error time series to train models, which can improve accuracy in ultra-short-term orbit prediction. However, these methods rely solely on historical data for modeling and do not incorporate the physical priors of the multibody system. Their generalization ability is limited, and their prediction performance is unstable under different constellation sizes and orbital environments, making it difficult to support the overall evolutionary analysis of large-scale constellations.

[0004] Physical Information Neural Networks (PINNs) orbit prediction method: The PINN method introduces orbital dynamics equations as physical constraints into the neural network, improving computational efficiency while ensuring physical consistency, and has been applied to single-star orbit prediction scenarios. However, existing PINN methods only introduce local orbital dynamics equations as constraints, failing to consider the global statistical physics of large-scale many-body systems. They cannot capture the power-law scaling behavior of orbital deviations with constellation size and time, and are insufficient in characterizing the collective dynamic effects caused by interstellar gravity. Furthermore, they are difficult to meet the needs of large-scale, long-period orbit prediction; there is still considerable room for improvement in prediction accuracy and generalization ability.

[0005] With the large-scale deployment of mega constellations in low Earth orbit, the orbital environment is gradually forming a high-density gravitational many-body system, and existing methods have revealed obvious shortcomings: the computational cost of traditional dynamic methods increases sharply with the number of satellites; machine learning methods lack many-body physical constraints and have limited generalization ability.

[0006] The invention disclosed in CN121145644A presents a fast end-to-end hop count estimation method for a low-Earth orbit mega-constellation network. The method includes: preprocessing the raw orbital data of the space target to generate a continuous and uniformly time-series dataset; constructing a physical information neural network model representing the input and output in the form of time-series data, and using an automatic differentiation mechanism to perform differential calculations on the output sequence; designing and introducing an adaptive weighting loss function to dynamically balance the loss terms of the network modules and physical modules during training; training the physical information neural network model; setting the data subset sampling rate, constructing multi-scale data scenarios, and evaluating the performance of the physical information neural network model under different data scale conditions. This invention can improve the modeling ability for long-term orbital evolution processes and achieve dynamic adjustment of the weights of various loss terms. However, this scheme does not consider global statistical physical laws and is difficult to meet the needs of large-scale, long-period orbit prediction. Summary of the Invention

[0007] To address the technical problems existing in current technologies, it is necessary to provide a low-Earth orbit (LEO) constellation orbit prediction method that integrates power-law scaling constraints, organically combining the statistical physical laws of large-scale multibody systems with orbital dynamics equations. By introducing time-varying power-law scaling as an additional physical constraint, a dual-constraint physical information neural network is constructed to improve the accuracy and generalization ability of LEO mega-constellation orbit prediction.

[0008] The objective of this invention can be achieved through the following technical solutions: A method for predicting the orbits of low-Earth orbit constellations by incorporating power-law scaling constraints includes: The orbital state data of the low-Earth orbit constellation is acquired and input into a pre-trained physical information neural network model to obtain orbital deviation and state data at future moments. The training process of the physical information neural network model includes: acquiring orbital deviation data under different numbers of satellites and different times and preprocessing it; constructing an orbital deviation dataset based on the preprocessed orbital deviation data; and performing statistical analysis on the preprocessed orbital deviation data to obtain the power-law relationship between orbital deviation and the number of satellites. The orbital deviation dataset is input into the physical information neural network model, and the total loss function, including global scaling law constraints and local dynamic constraints, is calculated based on the power law relationship. Based on the calculated loss function value, the model parameters of the physical information neural network model are optimized until the training converges, and a trained physical information neural network model is obtained.

[0009] In some possible implementations, statistical analysis is performed on the orbital deviation data to obtain a power-law relationship between the orbital deviation and the number of satellites, with the corresponding expression being: in, The scaling index evolves over time, characterizing the collective dynamics of orbital deviations as they co-evolve with constellation size and time. For orbital deviation, For the number of satellites, This indicates a direct proportional relationship.

[0010] In some possible implementations, based on the power-law relationship, the total loss function, including global scaling constraints and local dynamic constraints, is calculated, and the corresponding calculation formula is as follows: in, For data fitting terms, For the total loss function, , These are the weighting coefficients for the corresponding items; For local dynamic constraints, This is a global scaling law constraint.

[0011] In some implementations, the preprocessing includes data cleaning, noise reduction, normalization, and time alignment of the orbital deviation data. The orbital deviation data includes historical orbital states, number of satellites, time stamps, and disturbance parameters.

[0012] Specifically, the orbital deviation dataset is divided into a training set, a validation set, and a test set; wherein the training set is used to train a physical information neural network model, and the validation set and test set are used to evaluate the performance of the model. Optionally, the conditions for training convergence include: the error of the physical information neural network model on the validation set meets a preset requirement, or the number of training iterations reaches a preset maximum number of rounds.

[0013] In some embodiments, the method further includes optimizing training hyperparameters during the training of the physical information neural network model. The optimization includes adjusting the learning rate, network structure, batch size, and loss weights.

[0014] The present invention also provides a system for predicting the orbit of a low-Earth orbit constellation by incorporating power-law scaling constraints, comprising a memory and a processor, wherein the memory stores a computer program and the processor calls the computer program to execute the steps of the method described above.

[0015] Compared with the prior art, the present invention has the following advantages: (1) This invention extracts the time-varying power-law relationship between orbital deviation and the number of satellites by conducting in-depth statistical analysis and scaling law fitting of orbital deviation data. This prior knowledge, which reflects the essential law of the collective behavior of a multi-body system, is embedded in the loss function of the physical information neural network model in the form of a constraint term. This allows the model to grasp the statistical law of the constellation system's evolution with scale during the training process. Thus, when faced with constellation sizes that have not appeared in the training data, the model can make reasonable predictions based on the power-law relationship. Compared with the traditional method that only relies on local dynamic equations, this method can more comprehensively characterize the collective dynamic effects of the constellation system, with high prediction accuracy and strong generalization ability.

[0016] (2) This invention constructs a dual constraint mechanism by simultaneously introducing local dynamic constraints and global scaling law constraints into the loss function of the physical information neural network model. It ensures the dynamic consistency of local orbital evolution based on the orbital motion equations; and by embedding the time-varying power-law scaling law into the model training process, it makes the model conform to the statistical physical characteristics unique to large-scale multibody systems at the overall level. The dual constraints complement and synergistically enhance the model's physical consistency at both the local microscale and the global macroscale, resulting in significantly higher prediction accuracy than data-driven black-box models or traditional methods with only a single physical constraint. This enables rapid prediction of large-scale constellation orbital evolution, with significantly higher efficiency than traditional N-body simulations and a significant reduction in computational costs. Attached Figure Description

[0017] Figure 1 This is a flowchart of a method for predicting the orbit of a low-Earth orbit constellation that incorporates power-law scaling constraints, provided in an embodiment of the present invention. Figure 2 This is an overall flowchart of a low-Earth orbit constellation orbit prediction method that incorporates power-law scaling constraints, provided in an embodiment of the present invention. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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 some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0019] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0020] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0021] Definitions: The Low Earth Orbit (LEO) Walker mega-constellation model refers to a large satellite constellation system model constructed using the Walker constellation configuration design method and operating in Low Earth Orbit (LEO, typically at an altitude between 300 km and 2000 km). The Walker constellation is a classic circular orbit constellation design method proposed by British scientists. Its core parameters include orbital altitude, orbital inclination, total number of satellites, and phase factor. Through the systematic configuration of these parameters, multiple continuous coverages of the globe or specific regions can be achieved.

[0022] Example 1 like Figure 1 and Figure 2 As shown, this embodiment provides a method for predicting the orbit of a low-Earth orbit constellation by incorporating power-law scaling constraints. The method includes the following steps: S1: Obtain the orbital state data of the low-Earth orbit constellation and input it into a pre-trained physical information neural network model to obtain orbital deviation and state data at future moments; In some implementations... Orbital state prediction and rapid simulation: Using the trained model, the orbital states of low-Earth orbit constellations of different scales and time spans can be predicted, enabling rapid interpolation and extrapolation of orbital states, and replacing traditional N-body simulation to complete large-scale, long-period orbital evolution analysis.

[0023] S2: The training process of the physical information neural network model includes: acquiring orbital deviation data under different numbers of satellites and different times and performing preprocessing; constructing an orbital deviation dataset based on the preprocessed orbital deviation data; and performing statistical analysis on the preprocessed orbital deviation data to obtain the power-law relationship between orbital deviation and the number of satellites. Statistical analysis of the orbital deviation data yielded a power-law relationship between orbital deviation and the number of satellites. The corresponding expression is: in, The scaling index evolves over time, characterizing the collective dynamics of orbital deviations as they co-evolve with constellation size and time. For orbital deviation, For the number of satellites, This indicates a direct proportional relationship.

[0024] In some implementations... The preprocessing process includes data cleaning, noise reduction, normalization, and time alignment of the orbital deviation data.

[0025] In some implementations... Orbital deviation data includes historical orbital status, number of satellites, time stamps, and disturbance parameters.

[0026] In some implementations... The orbital deviation dataset is divided into a training set, a validation set, and a test set. The training set is used to train the physical information neural network model. The validation set and the test set are used to verify and test the performance of the physical information neural network model.

[0027] In some implementations... A low-Earth orbit Walker mega-constellation model containing N satellites was established. Through large-scale N-body numerical simulation, orbital deviation data were obtained at different times (from short-term to long-term) with different numbers of satellites (N ranging from tens to tens of thousands) to construct an orbital deviation dataset.

[0028] S3: Input the orbital deviation dataset into the physical information neural network model, and calculate the total loss function, including global scaling law constraints and local dynamic constraints, based on the power law relationship; optimize the model parameters of the physical information neural network model based on the calculated loss function value until the training converges, and obtain the trained physical information neural network model.

[0029] In some implementations... Constructing a dual-constraint physical information neural network model: Construct a Physical Information Neural Network (PINNs) model, simultaneously introducing two types of physical constraints into the loss function: Local dynamic constraints: The orbital motion equations are used as conventional physical constraints to ensure the consistency of individual orbital dynamics in the model prediction results.

[0030] Global scaling law constraint: The extracted time-varying power-law scaling law is used as a new constraint term to ensure that the model prediction results conform to the statistical physical laws of multibody systems.

[0031] In some implementations... The generated orbital deviation dataset is used to train the constructed dual-constraint PINNs model, optimize the network parameters so that the model can simultaneously satisfy two types of physical constraints, and achieve high-precision fitting of the orbital state.

[0032] In some implementations... Based on the power-law relationship, the total loss function, including global scaling constraints and local dynamic constraints, is calculated using the following formula: In the formula, For data fitting terms, For the total loss function, , These are the weighting coefficients for the corresponding items; For local dynamic constraints, This is a global scaling law constraint.

[0033] In some implementations... The conditions for training convergence include: the error of the physical information neural network model on the validation set reaches the target or the number of training iterations reaches the preset maximum number of rounds.

[0034] In some implementations... The method also includes optimizing the training hyperparameters during the training of the physical information neural network model.

[0035] In some implementations... Optimize the training hyperparameters, including adjusting the learning rate, network structure, batch size, and loss weights.

[0036] Example 2 This embodiment provides a system for predicting the orbit of a low-Earth orbit constellation by incorporating power-law scaling constraints. The system includes a memory and a processor. The memory stores a computer program, and the processor calls the computer program to execute the steps of the method as described in Embodiment 1.

[0037] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A method for predicting the orbit of a low-Earth orbit constellation by incorporating power-law scaling constraints, characterized in that, include: The orbital state data of the low-Earth orbit constellation is obtained and input into a pre-trained physical information neural network model to obtain orbital deviation and state data at future moments. The training process of the physical information neural network model includes: acquiring orbital deviation data under different numbers of satellites and different times and preprocessing it; constructing an orbital deviation dataset based on the preprocessed orbital deviation data; and performing statistical analysis on the preprocessed orbital deviation data to obtain the power-law relationship between orbital deviation and the number of satellites. The orbital deviation dataset is input into the physical information neural network model, and the total loss function, including global scaling law constraints and local dynamic constraints, is calculated based on the power law relationship. Based on the calculated loss function value, the model parameters of the physical information neural network model are optimized until the training converges, and a trained physical information neural network model is obtained.

2. The method for predicting the orbit of a low-Earth orbit constellation by incorporating power-law scaling constraints according to claim 1, characterized in that, Statistical analysis of the orbital deviation data yielded a power-law relationship between orbital deviation and the number of satellites, with the corresponding expression being: in, The scaling index evolves over time, characterizing the collective dynamics of orbital deviations as they co-evolve with constellation size and time. For orbital deviation, For the number of satellites, This indicates a direct proportional relationship.

3. The method for predicting the orbit of a low-Earth orbit constellation by incorporating power-law scaling constraints according to claim 2, characterized in that, Based on the aforementioned power-law relationship, the total loss function, including global scaling constraints and local dynamic constraints, is calculated using the following formula: in, For data fitting terms, For the total loss function, , These are the weighting coefficients for the corresponding items; For local dynamic constraints, This is a global scaling law constraint.

4. The method for predicting the orbit of a low-Earth orbit constellation by incorporating power-law scaling constraints according to claim 1, characterized in that, The preprocessing process includes data cleaning, noise reduction, normalization, and time alignment of the orbital deviation data.

5. The method for predicting the orbit of a low-Earth orbit constellation by incorporating power-law scaling constraints according to claim 1, characterized in that, The orbital deviation data includes historical orbital status, number of satellites, time stamps, and disturbance parameters.

6. The method for predicting the orbit of a low-Earth orbit constellation by incorporating power-law scaling constraints according to claim 1, characterized in that, The orbital deviation dataset is divided into a training set, a validation set, and a test set; the training set is used to train the physical information neural network model; the validation set and the test set are used to verify and test the performance of the physical information neural network model.

7. The method for predicting the orbit of a low-Earth orbit constellation by incorporating power-law scaling constraints according to claim 1, characterized in that, The conditions for training convergence include: the error of the physical information neural network model on the validation set reaches the target or the number of training iterations reaches the preset maximum number of rounds.

8. The method for predicting the orbit of a low-Earth orbit constellation by incorporating power-law scaling constraints according to claim 1, characterized in that, The method further includes optimizing the training hyperparameters during the training of the physical information neural network model.

9. The method for predicting the orbit of a low-Earth orbit constellation by incorporating power-law scaling constraints according to claim 8, characterized in that, The optimization of training hyperparameters includes adjusting the learning rate, network structure, batch size, and loss weights.

10. A system for predicting the orbits of low-Earth orbit constellations by incorporating power-law scaling constraints, characterized in that, It includes a memory and a processor, the memory storing a computer program, the processor invoking the computer program to perform the steps of the method as described in any one of claims 1 to 9.

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