Low earth orbit satellite short-time orbit prediction method and device based on LSTM-Transform

Abstract

The invention discloses a low earth orbit satellite short-time orbit prediction method and device based on LSTM-Transformer, and the method comprises the steps: firstly, determining and obtaining an initial orbit state parameter of an LEO satellite based on a precise orbit, then generating orbit data of an observation arc segment and a prediction arc segment based on the initial orbit state parameter, and then, carrying out the prediction of the observation arc segment and the prediction arc segment. Observation segmental arc orbit data generated through kinetic model integration is compared with a precise scientific orbit, an orbit error sequence of an observation segmental arc is obtained through calculation, and the error sequence serves as input of an LSTM-Transformer hybrid model. Wherein the LSTM module is used for capturing short time sequence local disturbance characteristics, and the Transform module is used for modeling a long-term dependency relationship. The trained model is used for predicting the dynamic extrapolation error at the future moment, the predicted error serves as a correction term, compensation is carried out on the original dynamic orbit, and therefore the compensated high-precision prediction orbit is generated, and the precision and stability of LEO satellite orbit prediction are remarkably improved through the method.

Description

Technical Field

[0001] This invention relates to the field of satellite orbit prediction technology, and more specifically, to a method and apparatus for short-term orbit prediction of low-Earth orbit satellites based on LSTM-Transformer. Background Technology

[0002] With the rapid development of space technology and the rise of commercial spaceflight, the number of Low Earth Orbit (LEO) satellites has experienced an unprecedented explosive growth. Many internationally renowned commercial companies are planning and building their own large LEO constellations, such as OneWeb, Starlink, Boeing, and CentiSpace, with more than 15 LEO constellation plans already announced. Due to their low orbital altitude and high speed, LEO satellites can effectively improve the geometry of traditional GNSS satellites, thus significantly improving positioning accuracy and reliability. In this process, satellite orbital parameters, as the basis for navigation signal calculation, directly determine the signal propagation path and arrival time. Because there is a certain time delay in orbital information calculation, to compensate for the insufficient real-time nature of ephemeris data, high-precision prediction of LEO satellite orbits is necessary to support the generation of ephemeris data for future moments, thereby achieving high-precision positioning. However, the operating environment of LEO satellites is extremely complex, and their orbital state is easily affected by various disturbances, such as atmospheric drag, solar radiation pressure, the Earth's non-spherical gravitational field, satellite attitude adjustments, and orbital maneuvers. These factors lead to significant instability and uncertainty in LEO orbit changes, making it impossible to meet the requirements of high-precision positioning technology.

[0003] Existing orbit prediction technologies can be mainly categorized into three types: analytical methods and polynomial fitting methods, dynamic extrapolation methods, and machine learning-based prediction methods. Analytical methods and polynomial fitting methods have limited prediction accuracy and are suitable for applications with relatively low requirements for orbit accuracy, such as space environment monitoring. Dynamic extrapolation methods, by establishing a dynamic model of the satellite orbit and combining it with the Earth's gravitational field and major non-conservative perturbations (such as atmospheric drag and solar radiation pressure), perform orbit integral extrapolation and are currently the most widely used high-precision orbit prediction method. While it exhibits good prediction performance on short timescales, it is highly sensitive to modeling non-conservative forces, and prediction errors tend to accumulate rapidly, making it difficult to meet accuracy requirements. To overcome the technical limitations of traditional methods, such as strong dependence on model structure and insufficient generalization ability, data-driven machine learning methods have been gradually applied to the field of orbit prediction in recent years. Shallow models such as Support Vector Machines (SVM) and Artificial Neural Networks (ANN) have shown some potential in short-term prediction, but their feature extraction capabilities are limited, making it difficult to effectively model the nonlinear characteristics and multi-scale perturbation effects during orbit changes.

[0004] With the development of deep learning technology, Long Short-Term Memory (LSTM) networks have become a research hotspot in the field of orbit prediction due to their advantages in time series modeling. LSTM alleviates the gradient vanishing problem through gating mechanisms, improving orbit prediction accuracy to some extent. However, research shows that LSTM can fluctuate when dealing with anomalous events (such as sudden attitude adjustments and solar storms), and its ability to handle multi-scale dynamic evolution of orbital states is limited. Especially in LEO satellite orbits, the orbital state is often affected by the superposition of short-term disturbances and long-term trends. Using a single-structure model makes it difficult to meet the needs of multi-scale feature modeling, and cannot effectively guarantee the comprehensiveness and robustness of the prediction results. Summary of the Invention

[0005] To address the technical problem of inaccurate prediction results in existing technologies, this invention provides a method and apparatus for short-term orbit prediction of low-Earth orbit satellites based on LSTM-Transformer.

[0006] Specifically, the first aspect of this invention provides a short-term orbit prediction method for low-Earth orbit satellites based on LSTM-Transformer, comprising: The initial orbital state parameters of LEO satellites are obtained based on precise orbit determination; Based on the initial orbital state parameters of the LEO satellite, orbital data for the observed arc segment and the predicted arc segment are generated respectively. The generated predicted arc segment orbital data is the original dynamic orbit. The generated observation arc segment orbit data is compared with the preset precision scientific orbit, and the orbit error sequence of the observation arc segment is calculated. The orbital error sequence of the observed arc segment is input into a pre-constructed LSTM-Transformer hybrid model to obtain the predicted error. The LSTM-Transformer hybrid model includes an LSTM module, a Transformer module, and a fully connected layer. A direct mapping channel is constructed between the LSTM module and the Transformer module to unify the dimension of the LSTM hidden layer output and the Transformer input embedding. The LSTM module is used to extract temporal features, and the Transformer module is used to extract global features based on the output of the LSTM model to obtain a high-dimensional deep feature vector. The fully connected layer outputs the predicted error based on the high-dimensional deep feature vector. The predicted error is used as a correction term to compensate for the original dynamic trajectory.

[0007] In one implementation, orbital data for the observed arc segment and the predicted arc segment are generated based on the initial orbital state parameters of the LEO satellite, including: A dynamic model is constructed based on the initial orbital state parameters of the LEO satellite; The initial state is integrally calculated using a dynamic model to generate orbital data for the observed arc segment and the predicted arc segment, respectively.

[0008] In one implementation, the constructed dynamic model is as follows:

[0009] In the formula, This represents the acceleration vector of the satellite's center of mass; This represents the sum of conservative force accelerations, including the perturbation of the Earth's central gravitational acceleration on the satellite. Earth's non-spherical gravitational perturbation acceleration Gravitational perturbation acceleration of solid tides and ocean tides N-body gravitational perturbation acceleration of the Sun, Moon and planets and relativistic perturbations ; This represents the sum of non-conservative forces, including atmospheric drag and perturbation acceleration. Solar radiation pressure perturbation acceleration Earth's albedo pressure perturbation acceleration and thermal radiation perturbation acceleration ; It represents the empirical acceleration, which includes the perturbation model error and the unmodeled perturbation force.

[0010] In one implementation, the LSTM module captures short-term local perturbations and nonlinear details of the input trajectory error sequence by introducing memory cells, forget gates, input gates, and output gates.

[0011] In one implementation, the Transformer module processes the time series data transmitted by the LSTM module in parallel and captures the global dependencies at any position in the sequence through an attention mechanism to obtain a high-dimensional deep feature vector.

[0012] In one embodiment, the method further includes training an LSTM-Transformer hybrid model. During training, a unified supervision signal path is established using the fully connected layers at the end of the model to map deep features to the final error prediction value, and the end-to-end mean squared error loss between the predicted value and the actual error is calculated. The loss function is calculated as follows:

[0013] In the formula, N is the number of training samples. This represents the actual orbital error. The prediction error of the model output is minimized by the loss function L, and the error gradient passes through the fully connected layer, the Transformer module and the LSTM module from back to front.

[0014] In one implementation, the method further includes evaluating the compensated orbital results.

[0015] Based on the same inventive concept, a second aspect of the present invention provides a short-term orbit prediction device for low-Earth orbit satellites based on LSTM-Transformer, comprising: The initial orbital state parameter determination module is used to obtain the initial orbital state parameters of LEO satellites based on precise orbit determination. The orbit data generation module is used to generate orbit data for the observation arc segment and the prediction arc segment based on the initial orbit state parameters of the LEO satellite. The generated prediction arc segment orbit data is the original dynamic orbit. The error sequence calculation module is used to compare the generated observation arc segment orbit data with the preset precision scientific orbit and calculate the orbit error sequence of the observation arc segment; The error prediction module is used to input the orbital error sequence of the observed arc segment into a pre-constructed LSTM-Transformer hybrid model to obtain the predicted error. The LSTM-Transformer hybrid model includes an LSTM module, a Transformer module, and a fully connected layer. A direct mapping channel is built between the LSTM module and the Transformer module to unify the dimension of the LSTM hidden layer output and the Transformer input embedding. The LSTM module is used to extract temporal features, and the Transformer module is used to extract global features based on the output of the LSTM model to obtain a high-dimensional deep feature vector. The fully connected layer outputs the predicted error based on the high-dimensional deep feature vector. The error compensation module is used to compensate the original dynamic trajectory by using the predicted error as a correction term.

[0016] Based on the same inventive concept, a third aspect of the present invention provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, provides the LSTM-Transformer-based short-term orbit prediction method for low-Earth orbit satellites as described in the first aspect.

[0017] Based on the same inventive concept, the fourth aspect of the present invention provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the LSTM-Transformer-based short-term orbit prediction method for low-Earth orbit satellites described in the first aspect.

[0018] Compared with the prior art, the advantages and beneficial technical effects of the present invention are as follows: This invention proposes a short-term orbit prediction method for LEO satellites based on LSTM-Transformer. This scheme pre-constructs a novel hybrid deep learning architecture (LSTM-Transformer hybrid model), which combines the ability to capture short-term local features with the ability to model long-term dependencies, effectively overcoming the technical bottleneck of existing single models that cannot simultaneously consider multi-scale orbit features. Addressing the key technical bottleneck of error accumulation during dynamic extrapolation prediction, this invention employs an LSTM-Transformer hybrid model to model and predict dynamic extrapolation errors, thereby achieving orbit error compensation. The proposed deep learning method based on error modeling and compensation effectively integrates the physical mechanisms of dynamic models with the data-driven advantages of deep models, while avoiding the problem of excessive errors that may arise from directly predicting orbit states, significantly improving the accuracy and stability of LEO satellite orbit prediction.

[0019] This invention offers significant advantages in model structure, prediction accuracy, adaptability, and system stability. Traditional methods have limited modeling capabilities when facing complex perturbation environments of LEO satellites, especially prone to rapid error accumulation under conditions such as atmospheric drag fluctuations and enhanced solar activity. This invention, however, effectively enhances the modeling capability for orbital nonlinear dynamics and multi-scale temporal features by integrating a deep learning architecture combining LSTM and Transformer. The invention employs a "dynamic model + error compensation" prediction mechanism, balancing physical consistency with data-driven advantages. Compared to completely black-box prediction methods, its prediction results are more stable and physically interpretable. Furthermore, the constructed model training framework possesses strong versatility and transferability, adapting to LEO satellite data at different altitudes and of different types, and can be widely applied in fields such as LEO navigation enhancement. Attached Figure Description

[0020] 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 some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0021] Figure 1 This is a flowchart of the short-term orbit prediction method for low-Earth orbit satellites based on LSTM-Transformer in an embodiment of the present invention; Figure 2 This is a detailed technical roadmap of the short-term orbit prediction method for low-Earth orbit satellites based on LSTM-Transformer in this embodiment of the invention; Figure 3 This is a diagram of the LSTM model structure in an embodiment of the present invention; Figure 4 This is a structural diagram of the Transformer model in an embodiment of the present invention; Figure 5 This is a schematic diagram illustrating the variation trend of the P-value of the LSTM model under different sliding windows in an embodiment of the present invention; Figure 6 This is a schematic diagram comparing the orbital errors of different models on multiple satellites in an embodiment of the present invention; Figure 7 This is a schematic diagram illustrating the changes in the average P-value of different models within the prediction interval in an embodiment of the present invention; Figure 8 This is a schematic diagram comparing the RMS orbital errors of different models under different satellites in an embodiment of the present invention; Figure 9 This is a schematic diagram comparing the accuracy improvement effect of the deep learning model compared to the dynamic model in the embodiments of the present invention.

[0022] Figure 10 This invention provides an analysis of the orbital accuracy of the LSTM-Transformer model under generalization and standard sliding window conditions in an embodiment of the invention.

[0023] Figure 11 This is a schematic diagram illustrating the variation trend of P value and RMS error of the GRACE-C satellite during solar activity in an embodiment of the present invention. Figure 12 This is a schematic diagram comparing the improvement in relative dynamic accuracy of the model under different environments in the embodiments of the present invention. Detailed Implementation

[0024] Example 1 This embodiment provides a short-term orbit prediction method for low-Earth orbit satellites based on LSTM-Transformer. Please refer to [link to relevant documentation]. Figure 1 ,include: S1: Obtain the initial orbital state parameters of the LEO satellite based on precise orbit determination.

[0025] Specifically, Precise Orbit Determination (POD) involves initial orbital state parameters, including position, velocity, and dynamic parameters.

[0026] S2: Based on the initial orbital state parameters of the LEO satellite, orbital data for the observation arc segment and the prediction arc segment are generated respectively. The generated prediction arc segment orbital data is the original dynamic orbit.

[0027] S2 can be implemented in the following way: S2.1: Construct a dynamic model based on the initial orbital state parameters of the LEO satellite; S2.2: Use the dynamic model to perform integral calculations on the initial state to generate orbital data for the observed arc segment and the predicted arc segment, respectively.

[0028] In practice, the satellite's equation of motion is described by the initial orbital state parameters of the orbit to be estimated. This equation can be integrated to obtain the satellite's orbit at any given time. This equation of motion (dynamic model) is expressed as: (1) In the formula, This represents the acceleration vector of the satellite's center of mass; This represents the sum of conservative force accelerations, including the perturbation of the Earth's central gravitational acceleration on the satellite. Earth's non-spherical gravitational perturbation acceleration Gravitational perturbation acceleration of solid tides and ocean tides The gravitational perturbation acceleration of N-body objects such as the Sun, Moon, and planets. Relativistic perturbation wait; This represents the sum of non-conservative forces, including atmospheric drag and perturbation acceleration. Solar radiation pressure perturbation acceleration Earth's albedo perturbation acceleration thermal radiation perturbation acceleration wait; It represents the empirical acceleration, which includes the perturbation model error and the unmodeled perturbation force.

[0029] After linearization, it is transformed into a first-order differential equation: (2) In the formula, Represents the satellite's velocity vector. and denoted by and , respectively, the first derivatives of the position vector and velocity vector with respect to time, and p represents the estimated dynamic parameters of the satellite, such as atmospheric drag parameters, empirical force model parameters, etc. This implies that within the current integration step, it is assumed that the rate of change of these parameters over time is zero.

[0030] make Let be the extended state vector of the satellite, where , , Let represent position, velocity, and dynamic parameters, respectively. Then, the kinematic equations and initial state of the satellite can be expressed as: (3) In the formula, It represents the first derivative of the extended state vector x with respect to time (i.e., the rate of change of the satellite state with time). The nonlinear dynamic function that describes the change of satellite motion state over time is defined by the differential equation set containing velocity, acceleration and parameter change rate given by formula (2). Indicates the satellite at the initial moment The initial value of the extended state vector.

[0031] set up Indicates satellite The reference orbital state vector at time t, in the above equation After first-order linear expansion at each time step, we get: (4) make Let the state deviation vector be denoted by . Representing the Jacobian matrix, the above expression can be transformed into: (5) The solution can be expressed as: (6) In the formula, Indicates from arrive The state transition matrix at time t; express The initial state deviation vector at time (i.e., the initial time) The difference between the actual state and the reference state constitutes the initial condition for this system of linear differential equations. Substituting the above equation into the equation yields: (7) In the formula, Let I represent the first derivative of the state transition matrix with respect to time, and let I represent the identity matrix with the same dimension as the state vector. It can be represented as: (8) In the formula, and They represent The satellite's position and velocity vectors at any given moment; and Representing the initial time respectively Position vector and velocity vector; This represents the dynamic model parameters to be estimated.

[0032] The methods for solving the equations of motion of satellites mainly include analytical methods and numerical methods. Numerical methods for solving ordinary differential equations include single-step methods and multi-step methods. Among them, precise orbit determination usually chooses integration methods such as the Runge-Kutta (RK) single-step method and the Adamas multi-step method. First, a sufficient starting point is calculated using the single-step method, and then the multi-step method is used to quickly and accurately calculate the partial derivative information of the state transition matrix and the position and velocity of the satellite at any time. After the initial orbit is determined, orbit extrapolation prediction becomes a key step in obtaining the future position and velocity state of the satellite. In order to improve the extrapolation accuracy, dynamic methods usually combine high-precision integrators with short time steps (such as RKF7(8) and the Dormand-Prince method) and introduce dynamic parameter adjustment mechanisms in orbit advancement, such as using empirical drag coefficients to mitigate the impact of model uncertainty on the prediction results. However, in medium and long-term predictions, the error sources of dynamic models are still difficult to completely suppress, especially when human control factors such as attitude changes or orbital maneuvers cannot be obtained in real time, and the prediction error may grow exponentially.

[0033] S3: Compare the generated observation arc segment orbit data with the preset precision scientific orbit to calculate the orbit error sequence of the observation arc segment.

[0034] Specifically, a Precise Scientific Orbit (PSO) is preset, and the two are compared to obtain the orbital error sequence of the observed arc segment.

[0035] S4: Input the orbital error sequence of the observed arc segment into the pre-constructed LSTM-Transformer hybrid model to obtain the predicted error. The LSTM-Transformer hybrid model includes an LSTM module, a Transformer module, and a fully connected layer. A direct mapping channel is constructed between the LSTM module and the Transformer module to unify the dimension of the LSTM hidden layer output and the Transformer input embedding. The LSTM module is used to extract temporal features, and the Transformer module is used to extract global features based on the output of the LSTM model to obtain a high-dimensional deep feature vector. The fully connected layer outputs the predicted error based on the high-dimensional deep feature vector.

[0036] Specifically, existing technologies (such as DNN, Bi-LSTM, etc.) typically rely on a single model architecture for orbit prediction. However, LEO satellite orbital error data exhibits multi-scale characteristics, including both short-term dramatic fluctuations and long-term system evolution trends. A single model struggles to simultaneously model both of these characteristics, resulting in a bottleneck in multi-scale feature extraction and limited prediction accuracy. To overcome these shortcomings, this invention proposes a serially cascaded LSTM-Transformer hybrid deep learning architecture. This architecture is not a simple model stacking but rather constructs a "microscopic to macroscopic" feature extraction pyramid, aiming to efficiently capture the full-band features of orbital errors through the collaborative work of heterogeneous networks. In the specific processing flow: In the first stage, the observation arc error sequence generated by comparing the dynamically extrapolated orbit with the PSO is input into the LSTM module. Utilizing the recursive gating mechanism of LSTM, it focuses on capturing short-term local perturbations and nonlinear details in the error data. In the second stage, the time-series feature vector output by LSTM is used as the input to the Transformer module. Leveraging the self-attention mechanism of the Transformer, we further explore global dependencies and low-frequency evolution trends across long time periods based on local features. In the third stage, the high-dimensional deep feature vector output by the Transformer is input into a fully connected layer. As the final decision unit of the model, the fully connected layer is responsible for linearly mapping the abstract features that integrate long and short-term information to the target prediction space, thus completing the final regression prediction.

[0037] Figure 2 This is a detailed technical roadmap of the short-term orbit prediction method for low-Earth orbit satellites based on LSTM-Transformer of this invention.

[0038] LSTM is an improved Recurrent Neural Network (RNN) specifically designed to address long-term dependencies in time series data. Traditional RNNs are prone to vanishing or exploding gradients when processing long-term series, hindering their ability to effectively learn correlations between distant time steps. LSTM, by introducing memory units (cell states) and three gating mechanisms (forget gate, input gate, and output gate), dynamically retains and updates time series information, effectively capturing both short-term and long-term dependencies. The model structure is as follows... Figure 3 As shown in the figure, A represents the module unit of the neural network. The first A represents the network state at time t-1, and the second A represents the network state at time t+1.

[0039] LSTM memory cells It is the core of information storage, and its internal state is dynamically updated through a gating mechanism. The forget gate is used to determine the memory information from the previous time step. Whether to retain it can be expressed as follows: (9) in, This is the output of the forget gate, with a value ranging from 0 to 1, representing the proportion of memory information retained. It is the hidden state of the previous time step; This is the input for the current time step; and These are the weight matrix and the bias term, respectively. It uses the sigmoid activation function. Through the forget gate, LSTM can selectively discard information that is no longer important, avoiding the accumulation of invalid information.

[0040] The input gate controls the input information at the current time step. Whether to write to a memory cell is determined by the following formula: (10) in, It is the output of the input gate, used to control the proportion of new information written; It is the candidate memory state at the current time step, expressed by the hyperbolic tangent function. Mapped to [ The interval is [1,1]. LSTM updates the state of memory cells by combining the forget gate and the input gate. This update mechanism ensures that memory cells can simultaneously retain historical information and introduce new information, enabling dynamic modeling of time series data.

[0041] (11) The output gate is based on the current memory state. and output information The output result is determined jointly, and its formula is as follows: (12) in, It refers to the output of the output gate, controlling how the state of the memory cell affects the final output result. Through the output gate, LSTM can dynamically adjust the output features according to the current task requirements.

[0042] The Transformer is a deep learning model based on an attention mechanism, primarily used to solve sequence modeling problems in natural language processing tasks. Unlike traditional recurrent neural networks (RNNs), the Transformer completely eliminates the limitations of sequence computation, enabling parallel processing of time series data and efficiently capturing global dependencies at any position in the sequence through its attention mechanism. The model structure diagram is shown below. Figure 4 As shown.

[0043] Input sequence The mapping is represented as a vector of queries, keys, and values, denoted as Q, K, and V respectively: (13) in, , , It is a learnable weight matrix. Next, the dot product of the query and the key is calculated to obtain the similarity score: (14) To prevent excessively large scores from causing gradient instability, the score matrix is ​​normalized using a scaling operation: (15) in, This refers to the dimension of the key vector. Then, the scaled scores are normalized using the Softmax function to generate attention weights: (16) The value vector V is weighted and summed using attention weights to obtain the self-attention output. Through this process, the Transformer can effectively capture the global dependencies between any two time steps in the input sequence.

[0044] (17) To enhance the model's ability to express features, Transformer introduces a multi-head attention mechanism. This mechanism, through multiple independent self-attention calculations, not only captures features at different levels but also deepens the understanding of complex dynamics in the sequence. Each attention head is calculated independently: (18) in, , , This is the projection matrix of the i-th head. The outputs of multiple heads are concatenated and then mapped using a mapping matrix. Generate the final result: (19) The Transformer also compensates for its inability to directly interpret time series positional information through positional encoding. Positional encoding introduces temporal positional information using the following formula: (20) in, `i` is the position index of the sequence, and `i` is the dimension index. This is the total dimension of the input vector. The model can distinguish the positional information of each time step in the sequence using the encoding generated by the sine and cosine functions.

[0045] Preferably, the method further includes training an LSTM-Transformer hybrid model. During training, a unified supervision signal path is established using the fully connected layers at the end of the model to map deep features to the final error prediction value, and the end-to-end mean squared error loss between the prediction and the true error is calculated. The loss function is calculated as follows: (twenty one) In the formula, N is the number of training samples. This represents the actual orbital error. The prediction error of the model output is minimized by the loss function L, and the error gradient passes through the fully connected layer, the Transformer module and the LSTM module from back to front.

[0046] Specifically, to address the technical challenges in hybrid architectures, this invention adopts the following key strategies: (1) Feature Dimension Alignment and Lossless Connection: To address the differences in heterogeneous feature spaces, this invention constructs a direct mapping channel by unifying the dimensions of the LSTM hidden layer output and the Transformer input embedding. This design avoids cumbersome intermediate transformations, ensuring that temporal features can be losslessly transferred from the recursive feature space to the attention feature space, thus solving the problem of sequence and dimension alignment.

[0047] (2) End-to-end joint optimization based on fully connected layers: To address the collaborative convergence problem, a unified supervision signal path is established using fully connected layers at the end of the model. Specifically, this layer is responsible for mapping deep features to the final error prediction value and calculating the end-to-end mean squared error loss between the prediction and the actual error. The loss function calculation formula is shown above. This mechanism forces the two heterogeneous sub-modules to update their parameters under the constraint of the same optimization objective, thereby ensuring that the model can efficiently learn the complete mapping relationship from local fluctuations to global trends.

[0048] (3) Verification of the balance between computing power and accuracy: Although the introduction of the hybrid architecture slightly increases the computational cost during the model training phase, the complementary advantages of LSTM and Transformer effectively resolve the contradiction between local feature capture and long-term memory decay. This design significantly reduces the cumulative error over long arcs while maintaining millisecond-level online inference, achieving a substantial improvement in accuracy and robustness at a controllable computing cost.

[0049] S5: Use the predicted error as a correction term to compensate for the original dynamic trajectory.

[0050] Specifically, in this study, we use the evaluation index P to assess the predictive performance of the model, and its formula is as follows: (twenty two) In the formula, n represents the total number of samples participating in the evaluation (or the sequence length of the time series data), and i represents the index of the sample data. This indicates the original orbital error of the LEO satellite. This represents the error predicted by the model. The evaluation index P is used to measure the significance of the difference between the two. The smaller the P value, the smaller the difference between the model's prediction and the actual error, indicating better prediction performance. In this study, the P values ​​for the A, C, and R components of the orbit were calculated separately, and their average values ​​were further obtained to comprehensively evaluate the overall accuracy of the model in orbit error prediction.

[0051] Furthermore, to assess the accuracy of the prediction, the predicted trajectory error output by the model needs to be used to correct the original predicted trajectory, thereby obtaining the error-compensated trajectory position. Let the original predicted trajectory be... The corrected orbit is then represented as: (twenty three) in, This represents the orbit prediction result after error compensation. To evaluate the effectiveness of the correction, [the following will be used]. With precision scientific orbital products Compare the results and calculate the residuals: (twenty four) Ultimately, through the study of We conducted statistical analysis on the root mean square (RMS) error to quantify the actual effect of the model in improving the accuracy of orbit prediction.

[0052] In summary, this invention proposes a short-term orbit prediction method for LEO satellites based on an LSTM-Transformer hybrid architecture. It aims to address the limitations of existing methods in modeling nonlinear disturbances, multi-scale dynamic characteristics, and anomalies, thereby achieving high-precision and robust predictions of LEO satellite orbital states. This method offers advantages such as strong scalability, flexible structure, and wide adaptability, making it suitable for orbit prediction requirements of various types of LEO satellite systems in navigation, positioning, remote sensing, and formation flying missions.

[0053] The main protection points and key points include the following three aspects: (1) Hybrid Deep Learning Model Architecture Design. The special feature of this architecture is the adoption of a serial cascaded deep learning structure of "local encoding first, then global modeling". Specifically, the model first inputs the observation arc error sequence obtained by comparing the dynamic extrapolation orbit with the precise scientific orbit into the LSTM module. Utilizing the good sequence sensitivity and recursive mechanism of LSTM, preliminary feature extraction is performed on the original error data to accurately capture the local perturbations and nonlinear evolution laws within a short time series. Subsequently, the time series feature sequence extracted by LSTM is used as the input of the Transformer module. The self-attention mechanism of Transformer is used to further explore the global long-range dependencies across time steps based on these features. The core advantage of this design is that LSTM is used to make up for the shortcomings of Transformer in processing local temporal position information, while Transformer solves the problem of memory decay of LSTM in long sequences, thereby realizing a deep progressive modeling of LEO satellite orbit errors from microscopic local fluctuations to macroscopic long-term trends.

[0054] (2) Orbit Error Prediction and Correction Mechanism. Unlike the "black box" method that directly replaces the dynamic model, this invention proposes an error compensation mechanism. This mechanism constructs a deep learning model to model and predict orbit errors based on the predicted orbit obtained from the existing dynamic extrapolation model. This mechanism not only retains the advantages of traditional orbit dynamic models in terms of physical consistency and theoretical interpretability, but also effectively compensates for system errors and disturbances in perturbation modeling by introducing data-driven methods, thereby improving the accuracy, stability, and correction capability of the overall orbit prediction system.

[0055] (3) A versatile and adaptable model training framework. This invention establishes a generalized model training and fine-tuning process to address the operational characteristics of different orbital altitudes and various types of LEO satellites. This framework includes unified data standardization processing, a multi-source perturbation feature fusion strategy, and a transferable training mechanism. It is compatible with orbital data from multiple LEO satellites, including GRACE-C, SWARM-B, SENTINEL-3A, and SENTINEL-6A, and possesses cross-mission and cross-platform deployment capabilities. Without needing to rebuild the model structure, users can achieve rapid model adaptation to different satellite or orbital scenarios through minor adjustments, significantly improving the model's generalization ability, engineering practicality, and commercial deployment value.

[0056] The method and beneficial effects of the present invention will be further explained below through specific experiments.

[0057] 1. Sliding window parameter selection This embodiment first determines the optimal sliding window size based on the LSTM model and applies it to a comparative experiment between the LSTM and LSTM-Transformer models in a prediction interval of 10 to 120 minutes. Figure 5 The trend of P-values ​​for different satellites with varying sliding window sizes within the prediction interval is shown. It can be seen that the P-values ​​generally increase with the extension of the prediction time, indicating that the prediction error gradually increases over time. However, the impact of different window sizes on the P-values ​​still varies significantly. Taking the GRACE-C satellite as an example, when the window size is 20, the model's P-values ​​remain low at each prediction time point, indicating that this configuration performs optimally in short-term predictions. This trend is also reflected in other satellites; smaller windows are more conducive to capturing local features of orbital changes. Conversely, as the window length increases, the P-value increases more significantly, especially in long-term predictions (e.g., 120 minutes), where excessively large windows lead to information dilution, significantly reducing prediction accuracy. Table 1 lists the optimal sliding window configurations for LSTM and LSTM-Transformer models under different prediction durations.

[0058] Table 1 Optimal window configuration for different prediction durations

[0059] 2. Analysis of Model Prediction Results Based on the optimal sliding window for each satellite determined above, we will conduct a model prediction performance analysis. Figure 6The results show a comparison of orbital errors between the LSTM and LSTM-Transformer models on SENTINEL-6A. It can be observed that after a prediction time exceeding 30 minutes, the LSTM model's error gradually deviates from the actual orbit, particularly noticeable in the A and R directions. In contrast, the LSTM-Transformer model maintains higher accuracy over a longer prediction time, especially in the C and R directions, where its error fluctuations are significantly smaller. This indicates that the self-attention mechanism in the Transformer module effectively enhances the model's ability to model global orbital dependencies, improves overall prediction accuracy, and exhibits stronger robustness under complex perturbation conditions.

[0060] Figure 7 Further analysis was conducted on the average P-value changes of the four satellites within the 10–120 minute prediction interval. The results show that the LSTM-Transformer model exhibits more stable prediction performance compared to the LSTM model: as the prediction time increases, the upward trend of the former's P-value slows significantly, while the latter's P-value continues to rise. This result further validates the advantages of the LSTM-Transformer model in medium- to long-term predictions, especially in long-term scenarios, where it can effectively suppress error accumulation and maintain a low prediction error.

[0061] 3. Evaluation of the effectiveness of track error correction To further verify the effectiveness of the proposed model in improving orbit prediction accuracy, this embodiment uses the prediction results of LSTM and LSTM-Transformer models to correct the traditional dynamic extrapolation orbit, and evaluates the error changes and correction gains of different methods at various prediction time scales. Figure 8 This paper presents a comparison of the RMS orbital errors of four satellites—GRACE-C, SWARM-B, SENTINEL-3A, and SENTINEL-6A—obtained using different methods (dynamic model, LSTM, and LSTM-Transformer) within a 10–120 minute prediction interval. The figures show that the error of the traditional dynamic extrapolation method increases significantly with prediction time, exhibiting typical error accumulation characteristics. In contrast, the LSTM model demonstrates better correction capabilities in the short term, but its accuracy decreases significantly in prediction intervals longer than 60 minutes. The LSTM-Transformer model, however, exhibits lower orbital errors throughout the entire prediction interval, with a significantly slower error growth trend, demonstrating stronger long-term stability and correction capabilities.

[0062] To further quantify the effect of the correction, Figure 9The results demonstrate the accuracy improvement of the two deep learning models compared to the dynamics model. The results show that both models achieve over 90% accuracy improvement within the first 30 minutes; however, as the prediction time increases, the improvement of the LSTM model decreases rapidly, while the LSTM-Transformer model maintains a high correction rate even after 120 minutes. This result further validates the significant advantage of the LSTM-Transformer model in medium- to long-term trajectory correction.

[0063] 4. Model generalization analysis To evaluate the generalization ability of the proposed model, this embodiment directly applies the optimal sliding window parameters (window size of 20) determined in the GRACE-C satellite to the orbital error prediction tasks of the SWARM-B, SENTINEL-3A, and SENTINEL-6A satellites, and conducts a comparative analysis under a unified configuration. Figure 10 The performance comparison of the LSTM-Transformer hybrid model under different sliding window settings is presented. The comparison objects include: the generalized model with the GRACE-C optimal window (20) as the unified parameter configuration, and the standard model using its corresponding optimal window configuration for each satellite. The results show that in the four-satellite experiment, the P-value curves predicted by the model under the unified window are generally stable, and the trend of change is highly consistent with the optimal window model, especially in the short-to-medium-term prediction interval (10–60 minutes), where they almost completely overlap. This indicates that even without adjusting the window parameters for different satellites, the model still has good time series modeling stability. Further comparison of orbital RMS reveals that under the unified window configuration, the model can still maintain a prediction accuracy close to or slightly higher than that under the optimal window setting in most prediction periods, especially in the short-term prediction of 10–40 minutes, where the error difference is minimal, verifying the generalization ability of the proposed model in cross-satellite application scenarios.

[0064] 5. Analysis of model prediction performance during solar activity Solar activity (such as solar flares and geomagnetic storms) significantly disturbs Earth's atmospheric density, thus affecting the accuracy of orbit predictions. Because the GRACE-C satellite orbits at a relatively low altitude, it is more significantly affected by solar activity disturbances and was therefore selected as a case study for evaluating the predictive performance of LSTM and LSTM-Transformer models during periods of solar activity. Figure 11This paper presents the trends of P-values ​​and corresponding RMS errors for the two models on the GRACE-C satellite during solar activity. It can be seen that the prediction error increases significantly under the influence of solar activity, with both the P-value and RMS value of the LSTM model increasing rapidly, indicating its poor stability in strongly disturbed environments. In contrast, the LSTM-Transformer model shows a slower increase in RMS and a lower P-value within the same prediction interval, demonstrating stronger anti-interference capabilities. Figure 12 The orbital accuracy improvement rates of the two models compared to the traditional dynamic model were further compared under normal and solar activity conditions. The results show that under normal conditions, both the LSTM and LSTM-Transformer models exhibit excellent error correction capabilities; however, under the influence of solar activity, the performance of the LSTM model deteriorates significantly, with the correction rate plummeting from approximately 95% to around 10%. While the accuracy of the LSTM-Transformer model decreases somewhat, it still maintains a correction rate of over 20%, demonstrating stronger environmental adaptability and model robustness.

[0065] Example 2 Based on the same inventive concept, this embodiment discloses a short-term orbit prediction device for low-Earth orbit satellites based on LSTM-Transformer, comprising: The initial orbital state parameter determination module is used to obtain the initial orbital state parameters of LEO satellites based on precise orbit determination. The orbit data generation module is used to generate orbit data for the observation arc segment and the prediction arc segment based on the initial orbit state parameters of the LEO satellite. The generated prediction arc segment orbit data is the original dynamic orbit. The error sequence calculation module is used to compare the generated observation arc segment orbit data with the preset precision scientific orbit and calculate the orbit error sequence of the observation arc segment; The error prediction module is used to input the orbital error sequence of the observed arc segment into a pre-constructed LSTM-Transformer hybrid model to obtain the predicted error. The LSTM-Transformer hybrid model includes an LSTM module, a Transformer module, and a fully connected layer. A direct mapping channel is built between the LSTM module and the Transformer module to unify the dimension of the LSTM hidden layer output and the Transformer input embedding. The LSTM module is used to extract temporal features, and the Transformer module is used to extract global features based on the output of the LSTM model to obtain a high-dimensional deep feature vector. The fully connected layer outputs the predicted error based on the high-dimensional deep feature vector. The error compensation module is used to compensate the original dynamic trajectory by using the predicted error as a correction term.

[0066] Since the apparatus in Embodiment 2 of this invention is the same apparatus used in the LSTM-Transformer-based short-term orbit prediction method for low-Earth orbit satellites in Embodiment 1, those skilled in the art can understand the specific structure and variations of this apparatus based on the method described in Embodiment 1 of this invention, and therefore will not be repeated here. All apparatuses used in the method of Embodiment 1 of this invention fall within the scope of protection of this invention.

[0067] Example 3 Based on the same inventive concept, the present invention also provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the LSTM-Transformer-based short-term orbit prediction method for low-Earth orbit satellites according to Embodiment 1.

[0068] Since the computer-readable storage medium described in Embodiment 3 of this invention is the same computer-readable storage medium used in implementing the LSTM-Transformer-based short-term orbit prediction method for low-Earth orbit satellites in Embodiment 1 of this invention, those skilled in the art can understand the specific structure and variations of this computer-readable storage medium based on the method described in Embodiment 1 of this invention, and therefore will not be repeated here. All computer-readable storage media used in the method of Embodiment 1 of this invention fall within the scope of protection of this invention.

[0069] Example 4 Based on the same inventive concept, the present invention also provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the method described in Embodiment 1.

[0070] Since the computer device described in Embodiment 4 of this invention is the same computer device used to implement the LSTM-Transformer-based short-term orbit prediction method for low-Earth orbit satellites in Embodiment 1 of this invention, those skilled in the art can understand the specific structure and variations of this computer device based on the method described in Embodiment 1 of this invention, and therefore will not be repeated here. All computer devices used in the method of Embodiment 1 of this invention fall within the scope of protection of this invention.

[0071] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention 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.

[0072] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. 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 illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0073] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention. Clearly, those skilled in the art can make various modifications and variations to the embodiments of the invention without departing from the spirit and scope of the invention. Thus, if these modifications and variations of the embodiments of the invention fall within the scope of the claims of the invention and their equivalents, the invention also intends to include these modifications and variations.

Claims

1. A short-term orbit prediction method for low-Earth orbit satellites based on LSTM-Transformer, characterized in that, include: The initial orbital state parameters of LEO satellites are obtained based on precise orbit determination; Based on the initial orbital state parameters of the LEO satellite, orbital data for the observed arc segment and the predicted arc segment are generated respectively. The generated predicted arc segment orbital data is the original dynamic orbit. The generated observation arc segment orbit data is compared with the preset precision scientific orbit, and the orbit error sequence of the observation arc segment is calculated. The orbital error sequence of the observed arc segment is input into a pre-constructed LSTM-Transformer hybrid model to obtain the predicted error. The LSTM-Transformer hybrid model includes an LSTM module, a Transformer module, and a fully connected layer. A direct mapping channel is constructed between the LSTM module and the Transformer module to unify the dimension of the LSTM hidden layer output and the Transformer input embedding. The LSTM module is used to extract temporal features, and the Transformer module is used to extract global features based on the output of the LSTM model to obtain a high-dimensional deep feature vector. The fully connected layer outputs the predicted error based on the high-dimensional deep feature vector. The predicted error is used as a correction term to compensate for the original dynamic trajectory.

2. The method for short-term orbit prediction of low-Earth orbit satellites based on LSTM-Transformer as described in claim 1, characterized in that, Based on the initial orbital state parameters of the LEO satellite, orbital data for the observed and predicted arc segments are generated, including: A dynamic model is constructed based on the initial orbital state parameters of the LEO satellite; The initial state is integrally calculated using a dynamic model to generate orbital data for the observed arc segment and the predicted arc segment, respectively.

3. The method for short-term orbit prediction of low-Earth orbit satellites based on LSTM-Transformer as described in claim 2, characterized in that, The constructed dynamic model is as follows: In the formula, This represents the acceleration vector of the satellite's center of mass; This represents the sum of conservative force accelerations, including the perturbation of the Earth's central gravitational acceleration on the satellite. Earth's non-spherical gravitational perturbation acceleration Gravitational perturbation acceleration of solid tides and ocean tides N-body gravitational perturbation acceleration of the Sun, Moon and planets and relativistic perturbations ; This represents the sum of non-conservative forces, including atmospheric drag and perturbation acceleration. Solar radiation pressure perturbation acceleration Earth's albedo pressure perturbation acceleration and thermal radiation perturbation acceleration ; It represents the empirical acceleration, which includes the perturbation model error and the unmodeled perturbation force.

4. The method for short-term orbit prediction of low-Earth orbit satellites based on LSTM-Transformer as described in claim 1, characterized in that, The LSTM module captures short-term local perturbations and nonlinear details of the input trajectory error sequence by introducing memory cells, forget gates, input gates, and output gates.

5. The method for short-term orbit prediction of low-Earth orbit satellites based on LSTM-Transformer as described in claim 1, characterized in that, The Transformer module processes the time series data passed from the LSTM module in parallel and captures the global dependencies at any position in the sequence through an attention mechanism to obtain high-dimensional deep feature vectors.

6. The method for short-term orbit prediction of low-Earth orbit satellites based on LSTM-Transformer as described in claim 1, characterized in that, The method further includes training an LSTM-Transformer hybrid model. During training, a unified supervision signal path is established using the fully connected layer at the end of the model to map deep features to the final error prediction value, and the end-to-end mean squared error loss between the prediction and the true error is calculated. The loss function is calculated as follows: In the formula, N is the number of training samples. This represents the actual orbital error. The prediction error of the model output is minimized by the loss function L, and the error gradient passes through the fully connected layer, the Transformer module and the LSTM module from back to front.

7. The method for short-term orbit prediction of low-Earth orbit satellites based on LSTM-Transformer as described in claim 1, characterized in that, The method also includes evaluating the compensated orbital results.

8. A short-term orbit prediction device for low-Earth orbit satellites based on LSTM-Transformer, characterized in that, include: The initial orbital state parameter determination module is used to obtain the initial orbital state parameters of LEO satellites based on precise orbit determination. The orbit data generation module is used to generate orbit data for the observation arc segment and the prediction arc segment based on the initial orbit state parameters of the LEO satellite. The generated prediction arc segment orbit data is the original dynamic orbit. The error sequence calculation module is used to compare the generated observation arc segment orbit data with the preset precision scientific orbit and calculate the orbit error sequence of the observation arc segment; The error prediction module is used to input the orbital error sequence of the observed arc segment into a pre-constructed LSTM-Transformer hybrid model to obtain the predicted error. The LSTM-Transformer hybrid model includes an LSTM module, a Transformer module, and a fully connected layer. A direct mapping channel is built between the LSTM module and the Transformer module to unify the dimension of the LSTM hidden layer output and the Transformer input embedding. The LSTM module is used to extract temporal features, and the Transformer module is used to extract global features based on the output of the LSTM model to obtain a high-dimensional deep feature vector. The fully connected layer outputs the predicted error based on the high-dimensional deep feature vector. The error compensation module is used to compensate the original dynamic trajectory by using the predicted error as a correction term.

9. A computer-readable storage medium, characterized in that, It stores a computer program that, when executed by a processor, implements the LSTM-Transformer-based short-term orbit prediction method for low-Earth orbit satellites as described in any one of claims 1 to 7.

10. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the LSTM-Transformer-based short-term orbit prediction method for low-Earth orbit satellites as described in any one of claims 1 to 7.

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