A method and system for predicting errors in two-line element sets of Starlink satellites based on deep learning

Abstract

The application discloses a kind of based on deep learning's star chain satellite two-line element orbit prediction error compensation method and system, and prediction error compensation method includes: obtaining the star chain satellite two-line element sample data to be predicted;The sample data is input to error compensation prediction model, and obtains prediction result, wherein, the error compensation prediction model is constructed by neural network and is obtained by training set training, and the training set is star chain satellite two-line element data.The application is by the mining ability of data characteristics excellent of deep learning neural network, solves the randomness of error propagation, to batch star chain TLEs is carried out according to at least one period time interval, using actual reference orbit result and propagation orbit result carries out error compensation, and dynamically adjusts operation strategy according to error analysis result, to ensure the stability and applicability of model under different environmental conditions.

Description

Technical Field

[0001] This invention belongs to the field of space situational awareness technology, and in particular relates to a method and system for error compensation in the prediction of two rows of Starlink satellite element orbits based on deep learning. Background Technology

[0002] With the rapid development of aviation technology and the increasing number of satellites in orbit, the demand for orbit prediction methods is growing to obtain more accurate aircraft orbit data. Simultaneously, the increase in space debris is also leading to a rapid increase in the number of satellites in orbit, making satellite orbit prediction crucial for maintaining their normal operation.

[0003] With the continuous increase in space debris and the development of space debris management programs, more accurate orbit prediction is essential. Accurate prediction of low-Earth orbit (LEO) satellite orbits is crucial for ensuring safe satellite operation, optimizing mission scheduling, and improving service quality. However, traditional orbit prediction methods often have significant limitations when facing complex space environments, nonlinear orbital variations, and uncertain perturbations. Therefore, exploring new orbit prediction methods, especially deep learning-based methods, has become a current research hotspot.

[0004] Shortcomings of existing technology:

[0005] Current methods for predicting satellite orbits involve using a model built based on orbital dynamics, given the known state of the space target at a certain moment, to predict its orbital information over a subsequent period. Essentially, this involves solving the differential equations describing the motion of the space target. Analytical methods, based on Kepler's laws of motion and perturbation theory, describe the satellite's motion through analytical expressions, but these methods struggle to handle complex perturbations and nonlinear effects. Numerical methods predict orbits by solving the satellite's equations of motion; while they can consider more influencing factors, they involve a large computational load and are highly sensitive to initial conditions and model parameters. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention proposes a method and system for compensating for Starlink satellite two-row element orbit prediction errors based on deep learning. This method can fill the gap in existing methods regarding the accumulation of errors over time and solve the problem of the randomness of error propagation.

[0007] This invention provides a deep learning-based method for compensating for errors in the prediction of two-row element orbits of Starlink satellites, comprising:

[0008] Obtain two rows of element sample data for the Starlink satellites to be predicted;

[0009] The sample data is input into the error compensation forecasting model to obtain the forecast results. The error compensation forecasting model is constructed through a neural network and trained using a training set, which consists of two rows of Starlink satellite root data.

[0010] Optionally, obtaining the training set includes:

[0011] Obtain two rows of element data for Starlink satellites;

[0012] The two rows of Starlink satellite root data are processed and cleaned in batches to obtain the training set.

[0013] Optionally, batch processing and cleaning of the two rows of Starlink satellite root data includes:

[0014] The format of the two rows of element data for the Starlink satellites was standardized to obtain data with a unified format.

[0015] The data in the unified format is sorted according to the timestamp, invalid and missing data are removed after sorting, and the orbital parameter features after sorting are extracted.

[0016] Optionally, the sample data is input into the error-compensated prediction model to obtain the prediction results, including:

[0017] Based on the sample data, determine the optimal orbit prediction strategy;

[0018] Error compensation is performed based on the optimal orbit prediction strategy to obtain the prediction results.

[0019] Optionally, determining the optimal orbit prediction strategy based on the sample data includes:

[0020] The sample data is segmented into orbital data for different time periods;

[0021] Coordinate transformation is performed on orbital data from different time periods to obtain orbital data in the geocentric inertial coordinate system;

[0022] The orbital data in the geocentric inertial coordinate system is analyzed to obtain the optimal orbital prediction strategy.

[0023] Optionally, coordinate transformation can be performed on orbital data from different time periods to obtain orbital data in the geocentric inertial coordinate system, including:

[0024] Calculate the rotation matrix:

[0025]

[0026] Where, θ gmst This is the Earth's rotation angle;

[0027] By multiplying the coordinate vectors of the true equatorial vernal equinox coordinates by a rotation matrix, the orbital data in the geocentric inertial coordinate system is obtained:

[0028]

[0029] in, The coordinate vector in the true equatorial vernal equinox coordinate system. It is a coordinate vector in the geocentric inertial coordinate system.

[0030] Optionally, analyzing the orbital data in the geocentric inertial coordinate system to obtain the optimal orbital prediction strategy includes:

[0031] The acquired two rows of orbital root data are divided into three time periods, with each of the consecutive two rows of root data separated by at least one motion cycle. Each of these three time periods corresponds to a different Time Limit Expiration (TLE). Based on the start time of the second time period and the first timestamp of the third time period, several rows of orbital root data are extracted from each time period.

[0032] The SGP4 model was used to calculate the orbital parameters of several two-line orbital element data for each time period, and the calculation results were obtained.

[0033] Based on the calculation results, a reference orbit is obtained;

[0034] The orbit data for the second time period is predicted using the reference orbit for the first time period. The predicted orbit for the second time period is compared with the reference orbit to calculate the first prediction error.

[0035] The predicted orbit for the third time period is predicted using the predicted orbit for the second time period. The predicted orbit for the third time period is compared with the reference orbit to calculate the second prediction error.

[0036] Error analysis is performed based on the first and second forecast errors to obtain the optimal orbit forecasting strategy.

[0037] Optionally, training the error compensation prediction model using the training set includes:

[0038] Forward propagation is performed based on the input data in the training set to obtain the output data;

[0039] Based on a preset loss function, the loss value between the output data and the target value is calculated;

[0040] The gradients of each parameter in the error compensation prediction model are calculated based on the loss value, and the gradients are updated, i.e., backpropagation is performed.

[0041] The forward and backward propagation processes are performed alternately until the loss function meets a preset condition, at which point training stops.

[0042] The present invention also provides a Starlink satellite two-row element orbit prediction error compensation system based on deep learning, comprising: a data acquisition module, an orbit prediction module, an error analysis module, and a compensation module;

[0043] The data acquisition module is used to collect two rows of root sample data from Starlink satellites;

[0044] The orbit prediction module is used to obtain the optimal orbit prediction strategy based on the two rows of element sample data of the Starlink satellites;

[0045] The error analysis module is used to perform error analysis based on the optimal orbit prediction strategy;

[0046] The compensation module is used to perform error compensation based on the analysis results.

[0047] Compared with the prior art, the present invention has the following advantages and technical effects:

[0048] The method proposed in this invention improves accuracy by having time series processing capabilities, effectively capturing long-term dependencies in satellite orbit data, filling the gap in existing methods regarding the accumulation of errors over time, and solving the problem of randomness in error propagation.

[0049] This invention leverages the superior data feature mining capabilities of deep learning neural networks to address the randomness of error propagation. It uses batches of Starlink TLEs for prediction at at least one periodic time interval, employs actual reference orbit results and propagation orbit results for error compensation, and dynamically adjusts operational strategies based on error analysis results. Furthermore, it dynamically adjusts neural network model parameters, data cleaning, and preprocessing methods based on error performance to ensure the model's stability and applicability under different environmental conditions. Attached Figure Description

[0050] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings:

[0051] Figure 1 This is a flowchart of a method for compensating for errors in the two-row element orbit prediction of Starlink satellites based on deep learning, according to an embodiment of the present invention.

[0052] Figure 2 This is a structural diagram of a Starlink satellite two-row element orbit prediction error compensation system based on deep learning, according to an embodiment of the present invention. Detailed Implementation

[0053] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0054] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0055] This embodiment proposes a deep learning-based method for compensating for errors in the two-row element orbit prediction of Starlink satellites. Figure 1 As shown, the specific steps include:

[0056] Obtain two rows of element sample data for the Starlink satellites to be predicted;

[0057] The sample data is input into the error compensation forecast model to obtain the forecast results. The error compensation forecast model is constructed through a neural network and trained on a training set, which consists of two rows of Starlink satellite root data.

[0058] Specifically, step S1: Use a deep neural network to predict Starlink orbit samples, analyze the prediction effect under different parameter combinations (such as TLE time intervals) and different linear fitting functions to fit the orbit arc length, and determine the optimal orbit prediction strategy;

[0059] Step S2: Based on the strategy in S1, conduct batch forecast tests on Starlink TLEs, construct a deep neural network model, clean the TLE dataset, and construct a reasonable neural network structure according to the characteristics of the dataset.

[0060] Step S3: Optimize the parameters of the neural network structure (such as the number of neurons, the number of model layers, etc.) according to the S2 strategy to improve the prediction accuracy of the model;

[0061] Step S4: First, as shown in S1, analyze the sample orbit prediction results under different parameter combinations and linear fitting functions to determine the optimal orbit prediction strategy; then, as shown in S3, determine the error compensation prediction model based on a large amount of tested TLE data; finally, use the prediction results to perform error compensation to obtain the final prediction result.

[0062] More specifically, if the error continues to increase over time, it indicates that the model is drifting or accumulating errors. In this case, the training set size can be increased, more TLE data from different time periods can be introduced for training, the learning rate and batch size can be modified, and the model parameters can be optimized. If the error remains stable or decreases, it indicates that the current forecast strategy is stable, and no adjustment is needed. When the error fluctuates periodically, it indicates periodic perturbation or resonance, and periodic error compensation can be performed on the periodic parameters. The number of neurons can be adjusted according to the data fitting. Too few neurons can easily lead to underfitting of the data and failure to effectively learn trajectory patterns, while too many neurons can lead to overfitting of the data, and the performance on new data may be poor when batch processing TLE data. When the error fluctuates greatly, the model noise has a greater impact, so the data cleaning rules should be enhanced to remove abnormal TLE data. Secondly, the forecast duration can be dynamically adjusted, shortening or extending the forecast period according to the error situation.

[0063] Furthermore, obtaining the training set includes:

[0064] Obtain two rows of element data for Starlink satellites;

[0065] Batch processing and cleaning of two rows of Starlink satellite root data were performed to obtain a training set.

[0066] Furthermore, batch processing and cleaning of the two rows of Starlink satellite root data includes:

[0067] Standardize the format of the two rows of Starlink satellite root data to obtain data with a unified format;

[0068] The data with uniform format is sorted according to timestamp, invalid and missing data are removed after sorting, and the orbital parameter features are extracted after sorting.

[0069] Specifically, step S2 includes:

[0070] Step S21: Dataset analysis and cleaning;

[0071] TLE data contains orbital information for a series of satellites. Each TLE data entry includes satellite orbital parameters such as satellite catalog number, right ascension and declination of the ascending node, and orbital period. Before training a deep neural network, the TLE data needs to be batch-processed and cleaned. First, the TLE data format is standardized, and the TLE data is sorted according to timestamps. The orbital parameters in the TLE data are extracted as independent features, including eccentricity, orbital period, and right ascension of the ascending node. Since TLE data may contain gross errors caused by human observation, invalid and missing data are removed to ensure that there are no null values ​​or corrupted records.

[0072] Step S22: Perform large-scale testing on the deep neural network model;

[0073] Batch forecasts are made for all Starlink TLEs statistically analyzed within a certain time period, and the forecast results are analyzed and the forecast error is calculated.

[0074] Furthermore, the sample data is input into the error-compensated forecast model to obtain the forecast results, including:

[0075] Based on sample data, determine the optimal orbit prediction strategy;

[0076] Error compensation is performed based on the optimal orbit prediction strategy to obtain prediction results.

[0077] Furthermore, based on sample data, the optimal orbit prediction strategy is determined as follows:

[0078] The sample data was divided into orbital data for different time periods;

[0079] Coordinate transformation is performed on orbital data from different time periods to obtain orbital data in the geocentric inertial coordinate system;

[0080] We analyze orbital data in the geocentric inertial coordinate system to obtain the optimal orbital prediction strategy.

[0081] Specifically, step S1 includes:

[0082] Step S11: Collect TLE data from Starlink satellites. The sample data is divided into orbital data for different time periods (such as the first time period, the second time period, the third time period, etc.) according to the time interval.

[0083] Step S12: Convert the Starlink orbit in the True Equator Mean Equinox (TEME) coordinate system to the Earth Center Inertial Coordinates (ECI) coordinate system. TME is suitable for TLE data, but in practice, orbital data is generally expressed in ECI. The main difference between the TME and ECI coordinate systems is that the coordinate axes change over time. The coordinate axes in the TME coordinate system are based on the position of the Earth's equator and vernal equinox, while the coordinate axes in the ECI coordinate system are fixed and do not change with the Earth's rotation.

[0084] To convert the TME coordinate system to the ECI coordinate system, the Earth's rotation angle needs to be calculated, usually expressed as the Earth's rotation angle (GMST). The current GMST value is obtained, which can typically be calculated from the current UTC (Coordinated Universal Time) or obtained using astronomical calculation tools such as the SPICE library. The current TME coordinates (X...) are then used... teme ,Y teme Z temeThe Greenwich Mean Time (GMST) for calculating the time is converted using equations (1) and (2):

[0085] 1) Calculate the rotation matrix:

[0086]

[0087] In the formula, θ gmst This is the Earth's rotation angle.

[0088] 2) By multiplying the coordinate vectors in the TEE coordinate system by the rotation matrix, the coordinates in the ECI coordinate system are obtained:

[0089]

[0090] Step S13: Analyze the forecast performance under different TLE time intervals and determine the optimal orbit forecast strategy;

[0091] Furthermore, the analysis of orbital data in the geocentric inertial coordinate system to obtain the optimal orbital prediction strategy includes:

[0092] The acquired two rows of orbital root data are divided into three time periods, with each of the consecutive two rows of root data separated by at least one motion cycle. Each of these three time periods corresponds to a different Time Limit Expiration (TLE). Based on the start time of the second time period and the first timestamp of the third time period, several rows of orbital root data are extracted from each time period.

[0093] The SGP4 model was used to calculate the orbital parameters of several two-line orbital element data for each time period, and the calculation results were obtained.

[0094] Based on the calculation results, a reference orbit is obtained, including converting the orbital parameters calculated by the SGP4 model and the semi-major axis, eccentricity, inclination, right ascension of the ascending node, argument of perigee, and mean perigee angle from the two rows of orbital elements into Keplerian orbital elements to obtain the reference orbit.

[0095] The orbit data for the second period is predicted using the reference orbit for the first period. The predicted orbit for the second period is compared with the reference orbit to calculate the first prediction error.

[0096] The predicted orbit for the third time period is predicted using the predicted orbit for the second time period. The predicted orbit for the third time period is compared with the reference orbit to calculate the second prediction error.

[0097] Error analysis is performed based on the first and second forecast errors to obtain the optimal orbit forecasting strategy.

[0098] Specifically, step S13: Divide the data of TLE at least one period apart into three time periods. Based on the start time of the second time period and the first timestamp of the third time period, extract the relevant data from the data of the first time period. Use the reference orbit of the first time period to predict the orbit data of the second time period using the designed deep learning neural network model method. Compare the predicted orbit of the second time period with the reference orbit to calculate the prediction error. Then, use the predicted orbit of the second time period to predict the orbit of the third time period and calculate the prediction error. Perform error analysis on the error between the predicted orbit of the second time period and the predicted orbit of the third time period, and perform error compensation.

[0099] Statistical analysis of the prediction errors of different parameter combinations was performed using root mean square error (RMSE), mean absolute error (MAE), and standard deviation (STD) to compare the impact of different strategies on the accuracy of orbit prediction, as shown in formulas (3), (4), and (5).

[0100] Calculate the error index:

[0101]

[0102] In the formula, O pred,i For the i-th predicted orbit; O true,i Let be the i-th actual reference orbit; n is the total number of samples.

[0103] The smaller the RMSE and MAE, the smaller the difference between the propagation trajectory and the reference actual trajectory; STD is used to measure the degree of error fluctuation and can help evaluate the stability of the model. Based on the loss functions RMSE, MAE, and STD, the trajectory prediction strategy is determined. Step S13 can be repeated to determine the optimal trajectory prediction strategy.

[0104] More specifically, based on the first and second forecast errors, and through a comprehensive evaluation of error trends and characteristics, error analysis is conducted, and the strategy with the smaller error is selected as the optimal orbit prediction strategy, including:

[0105] Commonly used error analysis indicators include, but are not limited to: position error (the difference between the reference orbit and the predicted orbit); velocity error (the difference between the actual velocity and the predicted velocity); orbital parameter error (the deviation of orbital elements such as semi-major axis, eccentricity, and inclination from the reference orbit); average error (the average value of errors over different time periods); maximum error (the maximum deviation value); and root mean square error.

[0106] By comparing the first and second forecast errors, error trend analysis is performed to check: the trend of error change over time. If the error gradually increases over time, it indicates that the accuracy of the strategy model decreases in long-term forecasts. If the error remains stable or decreases, it indicates that the forecast effect is good. Periodic changes in error: If the error shows periodic fluctuations, it may be related to satellite orbital resonance or periodic perturbations. Periodicity can be detected by Fourier transform or autocorrelation analysis. Error convergence or divergence: If the error gradually converges, it indicates that the strategy has good convergence and good stability. If the error diverges, it indicates that the strategy has cumulative bias or drift.

[0107] Furthermore, training the error compensation prediction model using the training set includes:

[0108] Forward propagation is performed based on the input data in the training set to obtain the output data;

[0109] Based on a preset loss function, calculate the loss value between the output data and the target value;

[0110] The gradients of each parameter in the error compensation prediction model are calculated based on the loss value, and the gradients are updated, i.e., backpropagation is performed.

[0111] The forward and backward propagation processes are performed alternately until the loss function meets the preset conditions, at which point training stops.

[0112] Specifically, the S3 steps include:

[0113] Step S31: Adjust the number of neurons. Too few neurons may lead to underfitting and an inability to effectively learn the patterns in the data; too many neurons may lead to overfitting. The optimal number of neurons can be automatically selected through grid search or random search. The learning rate controls the step size of each gradient update. If the learning rate in the model is too large, it may lead to unstable training and poor fitting of the training results. If the learning rate is too small, the training efficiency will decrease and it may lead to failure to converge. To optimize the learning rate, adaptive learning rate optimizers such as Adam and RMSprop can be used, or learning rate decay can be used. The batch size needs to balance training speed and accuracy / generalization ability.

[0114] Step S32: Establish an evaluation mechanism;

[0115] The process of feeding the input data from the training set into the model to obtain the model's output is called forward propagation. Next, based on a predetermined loss function, the difference between the model's output and the target value (i.e., the loss between the predicted and true values) is calculated, and the gradients of each parameter are calculated based on this loss. Then, the network parameters are updated using these gradients to minimize the loss as much as possible; this process is called backpropagation. Forward and backpropagation are performed alternately until the loss function converges or a preset stopping condition is met. To avoid situations where gross errors have a significant impact and to measure the model's fitting ability, mean squared error (MSE) and the coefficient of determination (R²) are introduced. 2 As a loss function:

[0116]

[0117] In the formula, O pred,i For the i-th predicted orbit; O true,i Let be the i-th actual reference orbit; n is the total number of sample data participating in the propagation. This is the average value of the actual reference orbit.

[0118] R 2 R is an indicator that measures the goodness of fit of a model, representing the correlation between the model's predicted values ​​and the actual values. 2 The value of is between 0 and 1; the closer to 1, the better the model fit. It is standardized, thus facilitating comparisons between different linear fitting functions. MSE is highly sensitive to large errors and can be effective when the goal is to reduce large errors. It has a strong penalty effect on large errors, which may make the model performance appear poor, but it can avoid situations where gross errors have a significant impact and measures the model's fitting ability. According to R... 2 The performance of hyperparameters is measured by MSE, and step S31 can be repeated to determine the optimal parameter configuration.

[0119] Step S4 includes:

[0120] Step S41: Analyze the optimal prediction strategy for Starlink orbit samples under different parameter combinations and different linear fitting functions for fitting orbit arc lengths;

[0121] Step S42: Clean the TLE dataset and perform batch prediction tests on all Starlink TLEs;

[0122] Step S43: Optimize the parameters of the neural network structure;

[0123] Based on the results of S42, the parameters of the neural network were optimized by adjusting the number of neurons, controlling the learning rate, establishing an evaluation mechanism, and introducing mean squared error (MSE) and coefficient of determination (R²). 2 ) as the loss function;

[0124] Step S44: Use the forecast results to perform error compensation to obtain the final forecast result.

[0125] Specifically, the error compensation strategy is as follows: by continuously updating the training data, the error pattern is learned by using a deep learning neural network, and the orbit is calculated by combining the deep learning predicted orbit with the SGP4 model to compensate for the error, avoid the accumulation of error from a single model, and improve the accuracy of long-term orbit prediction.

[0126] For nonlinear orbit parameters that are stable but susceptible to disturbances, a deep learning neural network is used for error compensation. The temporal characteristics of the error are learned, such as orbit inclination, eccentricity and air resistance. The deep learning neural network model is used to learn the orbit evolution error pattern. Historical orbit data errors are used as model input to correct future orbit prediction errors and compensate for long-term prediction errors.

[0127] For orbital parameters that exhibit periodic changes, such as the right ascension of the ascending node, the argument of perigee, and the mean perigee angle, the prediction of these parameters using deep learning neural network models is prone to significant errors due to the periodic variations in orbital angles, such as the mean perigee angle cyclically changing between 0° and 360°. In such cases, linear fitting functions can be used for error compensation. This involves concatenating the periodic data, merging the 0° and 360° data, and then applying a linear fitting function to the concatenated data to correct and compensate for the angle parameters.

[0128] A linear fitting function can be achieved using a polynomial regression formula:

[0129] f(x) = c0 + c1x + c2x 2 +…+c n x n

[0130] Where n is the order of the polynomial, c i is the regression coefficient, and x is the input angle parameter.

[0131] Finally, the predicted orbit compensated by the deep neural network model is fused with the correction angle parameters of the linear fitting function to generate the final predicted orbit.

[0132] This embodiment also provides a Starlink satellite two-row element orbit prediction error compensation system based on deep learning, including: a data acquisition module, an orbit prediction module, an error analysis module, and a compensation module;

[0133] The data acquisition module is used to collect two rows of root sample data from Starlink satellites;

[0134] The orbit prediction module is used to obtain the optimal orbit prediction strategy based on two rows of Starlink satellite root sample data;

[0135] The error analysis module is used to perform error analysis based on the optimal orbit prediction strategy.

[0136] The compensation module is used to compensate for errors based on the analysis results.

[0137] Specifically, such as Figure 2 As shown, the system in this embodiment includes: a data processing module: acquiring Starlink TLE data, standardizing the TLE data format, sorting the TLE data according to timestamps, extracting orbital parameters from the TLE data into independent features (such as first time period, second time period, third time period, etc.), including eccentricity, orbital period, right ascension of the ascending node, etc.; since TLE data may have gross errors caused by human observation during observation, invalid data and missing data are removed to ensure that there are no null values ​​or damaged records in the TLE data, and performing TME→ECI coordinate transformation;

[0138] Orbit prediction module: Trains neural network model, analyzes TLEs dataset, designs reasonable neural network structure; performs orbit propagation, and generates orbit prediction data;

[0139] Error Analysis and Compensation Module: Performs statistical analysis of prediction errors for different parameter combinations using root mean square error (RMSE), mean absolute error (MAE), and standard deviation (STD). Compares the impact of different strategies on orbit prediction accuracy, introducing mean square error (MSE) and coefficient of determination (R²). 2 The loss function is used to evaluate model performance; error compensation is performed to adjust the model's prediction strategy.

[0140] Optimization and Decision Module: Adjust the number of neurons by automatically selecting the optimal number through grid search or random search; optimize the learning rate using adaptive learning rate optimizers such as Adam and RMSprop, or use learning rate decay; batch size should balance training speed and accuracy / generalization ability; determine the optimal parameter configuration to improve propagation accuracy.

[0141] Output module: Utilizes the forecast results to perform error compensation and derives the final forecast result. This embodiment relates to the field of space situational awareness and is applicable to aerospace monitoring or Starlink management applications.

[0142] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for compensating for errors in the prediction of two-row element orbits of Starlink satellites based on deep learning, characterized in that, include: Obtain two rows of element sample data for the Starlink satellites to be predicted; The sample data is input into the error compensation prediction model to obtain the prediction result. The error compensation prediction model is constructed through a neural network and trained on a training set, which consists of two rows of Starlink satellite root data. The sample data is input into the error compensation prediction model to obtain the prediction results, including: Based on the sample data, determine the optimal orbit prediction strategy; Error compensation is performed based on the optimal orbit prediction strategy to obtain the prediction results; Based on the sample data, the optimal orbit prediction strategy is determined as follows: The sample data was divided into orbital data for different time periods; Coordinate transformation is performed on orbital data from different time periods to obtain orbital data in the geocentric inertial coordinate system; The orbital data in the geocentric inertial coordinate system is analyzed to obtain the optimal orbital prediction strategy; Analyzing the orbital data in the geocentric inertial coordinate system to obtain the optimal orbital prediction strategy includes: The acquired two rows of orbital root data are divided into three time periods, with each of the three time periods corresponding to a different two rows of root data, which are at least one motion cycle apart. Based on the start time of the second time period and the first timestamp of the third time period, extract several two-line track element data for each time period; The SGP4 model was used to calculate the orbital parameters of several two-line orbital element data for each time period, and the calculation results were obtained. Based on the calculation results, a reference orbit is obtained; the orbit data for the second time period is predicted using the reference orbit for the first time period, and the predicted orbit for the second time period is compared with the reference orbit to calculate the first prediction error; The predicted orbit for the third time period is predicted using the predicted orbit for the second time period. The predicted orbit for the third time period is compared with the reference orbit to calculate the second prediction error. Based on the first and second forecast errors, and through a comprehensive evaluation of error change trends and error characteristics, error analysis is conducted, and the strategy with the smaller error is selected as the optimal orbit forecasting strategy.

2. The method for compensating for Starlink satellite two-row element orbit prediction errors based on deep learning according to claim 1, characterized in that, Obtaining the training set includes: Obtain two rows of element data for Starlink satellites; The two rows of Starlink satellite root data are processed and cleaned in batches to obtain the training set.

3. The method for compensating for Starlink satellite two-row element orbit prediction errors based on deep learning according to claim 2, characterized in that, Batch processing and cleaning of the two rows of Starlink satellite root data includes: The format of the two rows of element data for the Starlink satellites was standardized to obtain data with a unified format. The data in the unified format is sorted according to the timestamp, invalid and missing data are removed after sorting, and the orbital parameter features after sorting are extracted.

4. The method for compensating for Starlink satellite two-row element orbit prediction errors based on deep learning according to claim 1, characterized in that, Coordinate transformation is performed on orbital data from different time periods to obtain orbital data in the geocentric inertial coordinate system, including: Calculate the rotation matrix: in, This is the Earth's rotation angle; By multiplying the coordinate vectors of the true equatorial vernal equinox coordinates by a rotation matrix, the orbital data in the geocentric inertial coordinate system is obtained: in, The coordinate vector in the true equatorial vernal equinox coordinate system. It is a coordinate vector in the geocentric inertial coordinate system.

5. The method for compensating for Starlink satellite two-row element orbit prediction errors based on deep learning according to claim 1, characterized in that, Training the error compensation prediction model using the training set includes: Forward propagation is performed based on the input data in the training set to obtain the output data; Based on a preset loss function, the loss value between the output data and the target value is calculated; The gradients of each parameter in the error compensation prediction model are calculated based on the loss value, and the gradients are updated, i.e., backpropagation is performed. The forward and backward propagation processes are performed alternately until the loss function meets a preset condition, at which point training stops.

6. A deep learning-based Starlink satellite two-row element orbit prediction error compensation system, used to implement the method as described in any one of claims 1-5, characterized in that, include: Data acquisition module, orbit prediction module, error analysis module, and compensation module; The data acquisition module is used to collect two rows of root sample data from Starlink satellites; The orbit prediction module is used to obtain the optimal orbit prediction strategy based on the two rows of element sample data of the Starlink satellites; The error analysis module is used to perform error analysis based on the optimal orbit prediction strategy; The compensation module is used to perform error compensation based on the analysis results.

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