Method and device for track prediction error correction based on arima-bilstm

Abstract

This specification provides a method and apparatus for correcting orbit prediction errors based on ARIMA-BiLSTM. The method includes: obtaining a time series dataset of orbit prediction errors by calculating the difference between the CPF ephemeris and the TLE+SGP4 model prediction; analyzing the time series dataset of orbit prediction errors using the Autoregressive Differential Moving Average (ARIMA) model to obtain processed data; constructing a Bi-directional Long Short-Term Memory (BiLSTM) neural network model, inputting the processed ARIMA data as features into the BiLSTM model, learning and predicting historical errors in SGP4 orbit predictions using the BiLSTM model, and correcting the orbit prediction errors of the SGP4 model based on the prediction results.

Description

Technical Field

[0001] This document relates to the fields of space target orbit prediction and deep learning technology, and in particular to a method and apparatus for orbit prediction error correction based on ARIMA-BiLSTM. Background Technology

[0002] With the increasing activity of space activities worldwide, the number of space targets in Earth orbit is growing exponentially. These include not only functional satellites and space stations, but also non-functional targets such as defunct satellites, rocket debris, and space junk. To ensure the safe operation of spacecraft in orbit and avoid collision risks, accurate monitoring and prediction of targets performing maneuvers such as orbit changes and collision avoidance have become core requirements in the field of space tracking, telemetry, and command (TT&C). However, existing orbit prediction technologies have significant shortcomings: traditional methods are difficult to adapt to complex dynamic scenarios, and single AI models cannot take into account multi-dimensional data characteristics. These technical bottlenecks are becoming increasingly prominent, necessitating the integration and optimization of new AI technologies to overcome these challenges.

[0003] Traditional orbit prediction methods are based on dynamic physical models, relying on the two-body problem theory and incorporating perturbations such as atmospheric drag and Earth's non-spherical shape to extrapolate orbits. However, these methods exhibit poor adaptability to orbital maneuvers, large correction errors, and weak resistance to data interference. When the temporal distribution of target observation data is sparse and affected by ionospheric delay and measurement noise, the physical model struggles to accurately invert orbital characteristics from limited data, resulting in insufficient prediction accuracy for weakly observed targets such as space debris.

[0004] In recent years, brain-inspired intelligence technology, as an emerging field of artificial intelligence, has demonstrated a strong ability to process complex spatiotemporal data, referencing the way the human brain processes information. Neural networks, as the core carrier of brain-inspired intelligence technology, have become a key technological direction for overcoming the shortcomings of traditional physical models, thanks to their powerful nonlinear approximation, long-term time-series dependency capture, and autonomous feature learning capabilities. They do not require pre-setting complex perturbation models and can directly extract dynamic evolution patterns from orbital observation data (position, velocity, orbital elements, etc.), showing significant advantages in orbit prediction for targets such as low-Earth orbit satellites and space debris. However, due to limitations in model structure design and feature adaptability, existing single or simply combined neural network models still have common shortcomings and cannot fully meet the high-precision, high-real-time, and robust requirements of spacecraft orbit prediction.

[0005] The Autoregressive Moving Average (ARIMA) model uses differencing to stabilize non-stationary sequences and relies on autoregressive and moving average components to capture linear time-series patterns. It has been preliminarily applied in short-term spacecraft orbit forecasting. However, this model is inherently linear and cannot adapt to the strong nonlinear fluctuations in spacecraft orbit data caused by perturbations such as solar radiation pressure and abrupt changes in atmospheric density. Furthermore, it is sensitive to sparse data, and interpolation processing for missing observations further amplifies errors, making it difficult to meet the demands of high-precision forecasting.

[0006] Long Short-Term Memory (LSTM) networks, through a gating mechanism consisting of forget gates, input gates, and output gates, have solved the gradient vanishing problem of traditional RNNs and possess the ability to capture long-term temporal dependencies, making them a mainstream AI method for nonlinear orbit prediction. However, existing applications have significant shortcomings: weak linear feature modeling capabilities, with stable linear components such as the long-term precession of the perigee argument in orbital elements easily overlooked; reliance solely on forward time-series propagation, making it impossible to utilize subsequent observation data to invert maneuver timing features, leading to delays in maneuver detection; and insufficient noise robustness.

[0007] Bidirectional neural networks, represented by Bi-LSTM, utilize both forward and backward memory units and historical and future temporal information, demonstrating advantages over LSTM networks in extracting orbital contextual features.

[0008] In summary, existing spacecraft orbit prediction technologies share significant common shortcomings: traditional physical models cannot cope with orbital maneuvers and data interference, ARIMA models struggle to handle nonlinear characteristics, and LSTM and bidirectional neural networks lack the ability to collaboratively model linear-nonlinear features. These issues mean that a single technology or simple combination cannot meet the demands for high-precision, high-real-time orbit prediction in complex scenarios. Summary of the Invention

[0009] The purpose of this invention is to provide a method and apparatus for correcting orbit prediction errors based on ARIMA-BiLSTM, aiming to solve the above-mentioned problems in the prior art.

[0010] This invention provides a method for correcting orbit prediction errors based on ARIMA-BiLSTM, comprising: By calculating the difference between the CPF ephemeris and the TLE+SGP4 model prediction, a time series dataset of orbit prediction error is obtained. The time series dataset of orbit prediction errors was analyzed using the autoregressive differential moving average (ARIMA) model to obtain processed data. A bidirectional long short-term memory (Bi-LSTM) neural network model was constructed. The processed data from ARIMA was used as features and input into the Bi-LSTM model. The Bi-LSTM model was used to learn and predict the historical errors of SGP4 orbit prediction, and the errors of SGP4 orbit prediction were corrected based on the prediction results.

[0011] This invention provides an apparatus for correcting orbit prediction errors based on ARIMA-BiLSTM, comprising: The dataset creation module is used to obtain a time series dataset of orbit prediction errors by calculating the difference between the CPF ephemeris and the TLE+SGP4 model prediction. The ARIMA model module is used to analyze the orbit prediction error time series dataset using the autoregressive differential moving average model ARIMA to obtain processed data. The Bi-LSTM model module is used to construct a bidirectional long short-term memory neural network (Bi-LSTM) model. Processed ARIMA data is used as features input into the Bi-LSTM model. The Bi-LSTM model learns and predicts the historical errors of SGP4 orbit prediction and corrects the errors in orbit prediction by the SGP4 model based on the prediction results.

[0012] This invention also provides an electronic device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor. When the computer program is executed by the processor, it implements the steps of the above-described method for correcting orbit prediction errors based on ARIMA-BiLSTM.

[0013] This invention also provides a computer-readable storage medium storing an information transmission implementation program, which, when executed by a processor, implements the steps of the above-described method for correcting orbit prediction errors based on ARIMA-BiLSTM.

[0014] By employing the embodiments of the present invention, the forecast results of the SGP4 model can be corrected, and the forecast accuracy of the SGP4 model can be improved. Attached Figure Description

[0015] To more clearly illustrate the technical solutions in one or more embodiments of this specification or in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this specification. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0016] Figure 1This is a flowchart of a method for correcting orbit prediction errors based on ARIMA-BiLSTM according to an embodiment of the present invention; Figure 2 This is a schematic diagram of coordinate system transformation and time alignment according to an embodiment of the present invention; Figure 3 This is a schematic diagram of a device for correcting orbit prediction errors based on ARIMA-BiLSTM according to an embodiment of the present invention; Figure 4 This is a schematic diagram of an electronic device according to an embodiment of the present invention. Detailed Implementation

[0017] To enable those skilled in the art to better understand the technical solutions in one or more embodiments of this specification, the technical solutions in one or more embodiments of this specification will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this specification, and not all of the embodiments. Based on one or more embodiments of this specification, all other embodiments obtained by those skilled in the art without creative effort should fall within the protection scope of this document.

[0018] Method Implementation Examples According to an embodiment of the present invention, a method for correcting orbit prediction errors based on ARIMA-BiLSTM is provided. Figure 1 This is a flowchart of a method for correcting orbit prediction errors based on ARIMA-BiLSTM according to an embodiment of the present invention, as shown below. Figure 1 As shown, the method for correcting orbit prediction errors based on ARIMA-BiLSTM according to an embodiment of the present invention specifically includes: Step S101 involves calculating the difference between the CPF ephemeris and the TLE+SGP4 model prediction to obtain the orbit prediction error time series dataset; specifically including: The TLE data of the spacecraft is acquired and combined with the SGP4 model to predict the position of the spacecraft in the future period of time, so as to obtain the position information of the spacecraft in orbit per second, and the position information is used as the TLE orbit prediction data. Acquire multiple consecutive CPF ephemeris files, concatenate the second day data from the multiple consecutive CPF files to obtain a precise ephemeris, and use the precise ephemeris as the true value data of the spacecraft orbit; To unify the spatiotemporal reference between the TLE orbit prediction data and the true data, a time series dataset of orbit prediction errors is constructed. Specifically, this includes: In terms of coordinate systems, the true value data in the ITRF geocentric fixed coordinate system is converted to the position in the J2000 coordinate system, wherein the TLE orbit prediction data is the position in the J2000 coordinate system; In terms of time, the satellite status is obtained at any time covered by the CPF file using a ten-point baseline Lagrange interpolator, and the midpoint between the two points with the highest interpolation accuracy is selected. The interval between the true data is reduced to 1 minute through interpolation, which is aligned with the TLE orbit prediction data.

[0019] Step S102 involves analyzing the orbit prediction error time series dataset using the Autoregressive Differential Moving Average (ARIMA) model to obtain processed data; specifically including: The time series dataset of orbit prediction errors is visualized by plotting time series graphs in three dimensions. A unit root test is performed on each dimension's time series graph. If the test indicates a non-stationary sequence, it is stationary through differencing using the differencing formula shown in Formula 1 until it passes the unit root test. The differencing order i for each sequence is recorded. If a column of data fails the unit root test, its differencing sequence is used as a feature input into the subsequent neural network. Formula 1; Where i represents the difference order, and t represents the time index, i.e., the time point in the time series. This represents the value of the original time series at difference order i and time point t. This represents the value of the i-th order difference at time point t; To perform ARIMA pattern recognition and order determination, the autoregressive order and moving average order of the model are determined for each stationary sequence: First, autocorrelation function and partial autocorrelation function analysis are performed. For cases that are difficult to judge through graphs, smaller p and q values ​​are traversed. The model that minimizes the Akaike information criterion or the Bayesian information criterion BIC is selected. The p, d, and q parameters of the determined ARIMA model are estimated, and model fitting is performed. Here, p represents the autoregressive order; d represents the differencing order, the minimum differencing order required for the series to be stationary; and q represents the moving average order. Parameter estimation is performed using maximum likelihood or nonlinear least squares methods, ultimately yielding the equations for three ARIMA models. The first dimension of the ARIMA model is as follows: Formula 2; in, It is a white noise sequence, c represents the constant term of the model, and j represents the long-term average value of the reaction time series; j represents the index variable of the lag order. This represents the j-th moving average component in the first dimension. This represents the error term of the first dimension at time tj; The residual for each dimension at each time point is calculated using Formula 3, which is the difference between the true value and the fitted value of the ARIMA model: for Formula 3; in It is the ARIMA model. The in-sample fit value, L depends on the difference order and lag order of the model, and N represents the total length of the time series; The residuals are used as new features and input into the neural network to represent nonlinear features that the ARIMA model has not been able to fit successfully. The residuals are checked to see if they are white noise, which determines whether the ARIMA model has fully extracted the sequence information. The fitted ARIMA model is used to make predictions for each dimension to obtain the predicted values.

[0020] Step S103: Construct a Bi-directional Long Short-Term Memory (Bi-LSTM) neural network model. The processed ARIMA data is input as features into the Bi-LSTM model. The Bi-LSTM model learns and predicts historical errors in SGP4 orbit prediction, and corrects the orbit prediction errors of the SGP4 model based on the prediction results. The construction of the Bi-LSTM model specifically includes: The residuals from the original data and the ARIMA model, along with the nth-order difference data of the non-stationary data, are used to form an enhanced feature vector: The feature dimension is expanded from 3 dimensions to 6 to 9 dimensions, where x t Represents the x-axis value at time t, y t This represents the value of the y-axis at time t; z t ε represents the value of the z-axis at time t. x ε represents the difference between the true value on the x-axis at time t and the fitted value of the ARIMA model. y ε represents the difference between the true value on the y-axis at time t and the fitted value of the ARIMA model. z This represents the difference between the true value on the z-axis at time t and the fitted value from the ARIMA model. This indicates the x-axis difference value obtained if the x-axis is non-stationary. This indicates the y-axis difference value obtained if the y-axis is non-stationary. This indicates the z-axis difference value obtained if the z-axis is non-stationary; Define a time window length T, and construct a sample for each time point k. The sample features of the sample include all enhanced feature vectors from time kT to k-1. Where k represents a future time point, The subscripts correspond to the sample feature matrix at time points; the sample labels of the samples are the ground truth values ​​at future time point k. ,in, These represent the true values ​​of the orbit prediction error in three dimensions; The constructed samples are divided into a training set, a validation set, and a test set in chronological order. Design the network structure of the Bi-LSTM model and train it using the constructed training set to obtain the final bidirectional long short-term memory neural network Bi-LSTM model.

[0021] The network structure of the Bi-LSTM model specifically includes: The input layer accepts tensors of shape (Batch_size, T, n); The forward and backward LSTM units of the bidirectional LSTM layer are calculated at each time step according to Equation 4-9:

[0022] in, It is the sigmoid function. It is the product of Hadamard f s The output of the forget gate controls the degree to which the previous memory cell is retained. W f Let h represent the forget gate weight matrix. s-1 m represents the hidden state at the previous time step. s Let b represent the input vector at the s-th time step. f Represents the forget gate bias vector, i s W represents the output of the input gate. i Let b represent the input gate weight matrix. i This represents the input gate bias vector. Represents a candidate memory cell, obtained from the current input and the previous hidden state, W. c The weight matrix representing candidate memory cells, b c C represents the bias vector of candidate memory cells. s C represents the memory cell updated at the current time step. s-1 This represents the state of the memory cells at the previous time step, o s Indicates the output gate output, W o b represents the output gate weight matrix. o h represents the output gate bias vector. s This indicates the hidden state at the current time step; The final output of the Bi-LSTM layer is the concatenation of the last hidden state in the forward pass and the last hidden state in the backward pass. The fully connected layer maps the output of the Bi-LSTM layer to the final predicted value according to Equation 10.

[0023] Formula 10; in, W represents the predicted value for the k-th output dimension. o Let h represent the weight matrix of the fully connected layer, and b represent the final hidden state of the bidirectional LSTM. o This represents the bias vector of the fully connected layer; According to Formula 11, the mean squared error (MSE) is used as the loss function: Formula 11; Where L represents the value of the loss function, Ntrain represents the total number of time points in the training set, and y k This represents the k-th true value. This represents the k-th predicted value; The optimizer uses Adam; Minimize the loss function on the training set and use the validation set for early stopping to prevent overfitting.

[0024] The method further includes: finally, comparing the final output of the ARIMA model plus Bi-LSTM model with the output of the ARIMA model and the output of the Bi-LSTM model using only the original data as features to verify the effect of the ARIMA model plus Bi-LSTM model.

[0025] In summary, this invention, based on the SGP4 (Simplified General Perturbations) analytical orbit prediction model, firstly utilizes an Autoregressive Differential Moving Average (ARIMA) model to analyze the historical errors of SGP4 orbit prediction. Secondly, it employs a bidirectional long short-term memory (Bi-LSTM) network, using data processed by the ARIMA model as features, to learn the historical errors of SGP4 orbit prediction. By predicting and correcting the errors in orbit prediction by the SGP4 model, the accuracy of short-term predictions by the SGP4 model is improved. The technical solution of this invention first constructs a time-series dataset of orbit prediction errors by calculating the difference between the CPF ephemeris and the TLE+SGP4 model predictions. Then, the dataset is analyzed using the ARIMA model to obtain the corresponding p, d, and q parameters of the model. The processed data is then used as features and input into a Bi-LSTM network for training, enabling the network to learn historical orbit prediction errors.

[0026] This invention is based on the actual needs of spacecraft orbit prediction, takes the innovative integration of AI technology as its core idea, and makes targeted optimizations to address the shortcomings of existing technologies. It combines the ARIMA model with a bidirectional neural network and proposes an orbit prediction algorithm based on an improved LSTM. This aims to break through the limitations of traditional methods and single AI models and improve the accuracy and robustness of orbit prediction and maneuver detection.

[0027] The technical solutions of the embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0028] A method for constructing a time series dataset of orbit prediction errors according to an embodiment of the present invention includes the following steps: S11. Obtain the TLE data of the spacecraft from the spacetrack website, and combine it with the SGP4 model to predict the position of the spacecraft in the future, so as to obtain the spacecraft's position information in orbit every second.

[0029] S12. Obtain the CPF (consolidated perdiction format) ephemeris file, which can be obtained from CDDIS or EUROLAS data centers. The obtained data serves as the true value for the spacecraft's orbit. A specific CPF file includes precise orbit predictions for 5 days, including the next 3 days and the past 2 days, with a step size of 4 minutes, expressed in the International Ground Reference System. Since the precise data for future moments is unknown in reality, the data from the second day of multiple consecutive CPF files is concatenated to form the precise ephemeris for the experiment, ensuring its accuracy.

[0030] S13. Unify the spatiotemporal reference between TLE orbit forecast data and true data, and construct a time series dataset of orbit forecast error.

[0031] Regarding the coordinate system, the data predicted by the TLE+SGP4 model is the spacecraft's position in the J2000 coordinate system, in kilometers; the true orbital data is the position in the ITRF geocentric fixed coordinate system, in meters, and needs to be unified to the J2000 coordinate system through coordinate transformation.

[0032] Regarding timing: The TLE+SGP4 model predicts the spacecraft's position in the J2000 coordinate system every minute; while the true orbital data is high-precision data at 4-minute intervals. According to official documents, the satellite's status can be obtained at any time covered by the CPF file using a ten-point baseline Lagrange interpolator, with the highest interpolation accuracy achieved by selecting the midpoint between two points. Through interpolation, the true data interval can be reduced to 1 minute, aligning it with the prediction data obtained from the TLE+SGP4 model.

[0033] Taking data from the Ajisai satellite (serial number 16908) from January 10th to 12th, 2019 as an example, after coordinate system transformation and time alignment, the results are obtained. Figure 2 As shown.

[0034] 2. Data analysis methods based on the ARIMA model, including the following steps: S21. Data visualization: Draw a time series graph in three dimensions to make a preliminary judgment on the trend.

[0035] S22. Perform a unit root test (e.g., ADF test) on the series for each dimension. The null hypothesis is that the series has a unit root, i.e., it is non-stationary; the alternative hypothesis is that the series is stationary. If the p-value obtained from the test is greater than the significance level, the null hypothesis cannot be rejected, and differencing is required. For non-stationary series, differencing is needed to make them stationary. The differencing formula is:

[0036] The difference order i of each sequence is recorded until the ADF test is passed. If a column of data fails the test, its difference sequence will be used as a feature input into the subsequent neural network.

[0037] S23. Perform ARIMA pattern recognition and order determination, identifying the autoregressive and moving average orders of the model for each stationary sequence. First, perform autocorrelation and partial autocorrelation function analysis. For cases where graphical analysis is difficult, iterate through smaller p and q values; then select the model that minimizes the Akaike information criterion or the Bayesian information criterion (BIC). The formulas for calculating AIC and BIC are as follows:

[0038]

[0039] Where k is the total number of model parameters and n is the sample size. It is the maximum likelihood value of the model.

[0040] S24. Parameter Estimation and Model Fitting: Estimate the parameters of the determined ARIMA model (p, d, q) and fit the model. Parameter estimation is performed using maximum likelihood estimation or nonlinear least squares methods, ultimately yielding the equations for the three ARIMA models. Taking the first dimension as an example, its ARIMA model is:

[0041] in, It is a white noise sequence.

[0042] The residual for each dimension at each time point is the difference between the true value and the fitted value of the ARIMA model: for

[0043] in It is the ARIMA model. The in-sample fit value, L, depends on the difference order and lag order of the model. The residuals, as new features, are input into the neural network, representing the nonlinear features that the ARIMA model failed to fit.

[0044] S25. Model diagnosis: Test whether the residuals are white noise to determine whether the model has adequately extracted sequence information. Perform Ljung-Box test on the residual sequences of the three models. The null hypothesis is that the residuals are white noise sequences. If the p-value is greater than the significance level, the null hypothesis cannot be rejected, and the model is considered to be adequately fitted.

[0045] S26. Prediction and Analysis: Predict the future using the fitted model. For each dimension, make predictions using the fitted model separately, obtaining predicted values. These predicted values ​​are then compared with subsequent experimental results.

[0046] 3. A Bi-LSTM-based orbit prediction method, comprising the following steps: S31. Feature Engineering and Dataset Construction The original data, ARIMA residuals, and nth-order difference data of non-stationary data are combined to form an enhanced feature vector: At this point, the feature dimension is expanded from 3 dimensions to 6 to 9 dimensions (hereinafter referred to as n, the three columns may not all be non-stationary sequence data).

[0047] S32, Constructing Supervised Learning Samples Define the time window length T, for each time point k ( Construct a sample.

[0048] Sample features: Contains all enhanced feature vectors from time kT to k-1.

[0049]

[0050] Sample label: is the true value of future time point k.

[0051]

[0052] Dataset partitioning: The above samples are divided into training set, validation set and test set in chronological order.

[0053] S33. Bi-LSTM Model Construction and Training: Design the network structure and train it using the pre-constructed dataset. The network structure is as follows: Input layer: Accepts tensors of shape (Batch_size, T, n).

[0054] Bidirectional LSTM layer: The core part, whose forward and backward LSTM units are computed at each time step as follows:

[0055] in It is the sigmoid function. It is the Hadamard product. The final output of Bi-LSTM is the concatenation of the last hidden state in the forward pass and the last hidden state in the backward pass.

[0056] Fully connected layer: Maps the output of the Bi-LSTM layer to the final prediction.

[0057]

[0058] Loss function: using mean squared error (MSE)

[0059] Optimizer: Adam.

[0060] Training loop: Minimize the loss function on the training set and use the validation set for early stopping to prevent overfitting.

[0061] S34. Model Evaluation and Comparative Analysis To demonstrate the effectiveness of the hybrid model, it needs to be compared with the following benchmark models: the ARIMA model and the Bi-LSTM model that uses only the raw data as features. Evaluation metrics such as root mean square error, mean absolute error, and mean absolute percentage error are calculated on the test set.

[0062] Device Example 1 According to embodiments of the present invention, an apparatus for correcting orbit prediction errors based on ARIMA-BiLSTM is provided. Figure 3 This is a schematic diagram of a device for correcting orbit prediction errors based on ARIMA-BiLSTM according to an embodiment of the present invention, as shown below. Figure 3 As shown, the apparatus for correcting orbit prediction errors based on ARIMA-BiLSTM according to an embodiment of the present invention specifically includes: The dataset creation module 30 is used to obtain a time series dataset of orbit prediction errors by calculating the difference between the CPF ephemeris and the TLE+SGP4 model prediction. ARIMA model module 32 is used to analyze the orbit prediction error time series dataset using the autoregressive differential moving average model ARIMA to obtain processed data; Bi-LSTM model module 34 is used to construct a bidirectional long short-term memory neural network Bi-LSTM model. The processed data of ARIMA is used as the feature input to the bidirectional long short-term memory neural network Bi-LSTM model. The Bi-LSTM model learns and predicts the historical errors of SGP4 orbit prediction, and corrects the errors of SGP4 model in orbit prediction based on the prediction results.

[0063] The embodiments of the present invention are device embodiments corresponding to the above method embodiments. The specific operation of each module can be understood with reference to the description of the method embodiments, and will not be repeated here.

[0064] Device Example 2 This invention provides an electronic device, such as... Figure 4 As shown, it includes: a memory 40, a processor 42, and a computer program stored in the memory 40 and executable on the processor 42, wherein the computer program, when executed by the processor 42, performs the steps as described in the method embodiment.

[0065] Device Example 3 This invention provides a computer-readable storage medium storing an information transmission implementation program, which, when executed by a processor 42, performs the steps described in the method embodiment.

[0066] The computer-readable storage media described in this embodiment include, but are not limited to, ROM, RAM, disk, or optical disk.

[0067] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for correcting orbit prediction errors based on ARIMA-BiLSTM, characterized in that, include: By calculating the difference between the CPF ephemeris and the TLE+SGP4 model prediction, a time series dataset of orbit prediction error is obtained. The time series dataset of orbit prediction errors was analyzed using the autoregressive differential moving average (ARIMA) model to obtain processed data. A bidirectional long short-term memory (Bi-LSTM) neural network model was constructed. The processed data from ARIMA was used as features and input into the Bi-LSTM model. The Bi-LSTM model was used to learn and predict the historical errors of SGP4 orbit prediction, and the errors of SGP4 orbit prediction were corrected based on the prediction results.

2. The method according to claim 1, characterized in that, By calculating the difference between the CPF ephemeris and the TLE+SGP4 model prediction, the orbit prediction error time series dataset is obtained, which specifically includes: The TLE data of the spacecraft is acquired and combined with the SGP4 model to predict the position of the spacecraft in the future period of time, so as to obtain the position information of the spacecraft in orbit per second, and the position information is used as the TLE orbit prediction data. Acquire multiple consecutive CPF ephemeris files, concatenate the second day data from the multiple consecutive CPF files to obtain a precise ephemeris, and use the precise ephemeris as the true value data of the spacecraft orbit; A time series dataset of orbit prediction error is constructed by unifying the spatiotemporal reference between the TLE orbit prediction data and the true data.

3. The method according to claim 2, characterized in that, The specific steps to unify the spatiotemporal reference between the TLE orbit prediction data and the true data include: In terms of coordinate systems, the true value data in the ITRF geocentric fixed coordinate system is converted to the position in the J2000 coordinate system, wherein the TLE orbit prediction data is the position in the J2000 coordinate system; In terms of time, the satellite status is obtained at any time covered by the CPF file using a ten-point baseline Lagrange interpolator, and the midpoint between the two points with the highest interpolation accuracy is selected. The interval between the true data is reduced to 1 minute through interpolation, which is aligned with the TLE orbit prediction data.

4. The method according to claim 1, characterized in that, The orbit prediction error time series dataset was analyzed using the Autoregressive Differential Moving Average (ARIMA) model, and the processed data specifically includes: The time series dataset of orbit prediction errors is visualized by plotting time series graphs in three dimensions. A unit root test is performed on each dimension's time series graph. If the test indicates a non-stationary sequence, it is stationary through differencing using the differencing formula shown in Formula 1 until it passes the unit root test. The differencing order i for each sequence is recorded. If a column of data fails the unit root test, its differencing sequence is used as a feature input into the subsequent neural network. Official 1; Where i represents the difference order, and t represents the time index, i.e., the time point in the time series. This represents the value of the original time series at difference order i and time point t. This represents the value of the i-th order difference at time point t; To perform ARIMA pattern recognition and order determination, the autoregressive order and moving average order of the model are determined for each stationary sequence: First, autocorrelation function and partial autocorrelation function analysis are performed. For cases that are difficult to judge through graphs, smaller p and q values ​​are traversed. The model that minimizes the Akaike information criterion or the Bayesian information criterion BIC is selected. The p, d, and q parameters of the determined ARIMA model are estimated, and model fitting is performed. Here, p represents the autoregressive order; d represents the differencing order, the minimum differencing order required for the series to be stationary; and q represents the moving average order. Parameter estimation is performed using maximum likelihood or nonlinear least squares methods, ultimately yielding the equations for three ARIMA models. The first dimension of the ARIMA model is as follows: Official 2; in, It is a white noise sequence, c represents the constant term of the model, and j represents the long-term average value of the reaction time series; j represents the index variable of the lag order. This represents the j-th moving average component in the first dimension. This represents the error term of the first dimension at time tj; The residual for each dimension at each time point is calculated using Formula 3, which is the difference between the true value and the fitted value of the ARIMA model: for Official 3; in It is the ARIMA model. The in-sample fit value, L depends on the difference order and lag order of the model, and N represents the total length of the time series; The residuals are used as new features and input into the neural network to represent nonlinear features that the ARIMA model has not been able to fit successfully. The residuals are checked to see if they are white noise, which determines whether the ARIMA model has fully extracted the sequence information. The fitted ARIMA model is used to make predictions for each dimension to obtain the predicted values.

5. The method according to claim 1, characterized in that, The construction of the Bi-LSTM (Bidirectional Long Short-Term Memory) neural network model specifically includes: The residuals from the original data and the ARIMA model, along with the nth-order difference data of the non-stationary data, are used to form an enhanced feature vector: The feature dimension is expanded from 3 dimensions to 6 to 9 dimensions, where x t Represents the x-axis value at time t, y t This represents the value of the y-axis at time t; z t ε represents the value of the z-axis at time t. x ε represents the difference between the true value on the x-axis at time t and the fitted value of the ARIMA model. y ε represents the difference between the true value on the y-axis at time t and the fitted value of the ARIMA model. z This represents the difference between the true value on the z-axis at time t and the fitted value from the ARIMA model. This indicates the x-axis difference value obtained if the x-axis is non-stationary. This indicates the y-axis difference value obtained if the y-axis is non-stationary. This indicates the z-axis difference value obtained if the z-axis is non-stationary; Define a time window length T, and construct a sample for each time point k. The sample features of the sample include all enhanced feature vectors from time kT to k-1. Where k represents a future time point, The subscripts correspond to the sample feature matrix at time points; the sample labels of the samples are the ground truth values ​​at future time point k. ,in, These represent the true values ​​of the orbit prediction error in three dimensions; The constructed samples are divided into a training set, a validation set, and a test set in chronological order. Design the network structure of the Bi-LSTM model and train it using the constructed training set to obtain the final bidirectional long short-term memory neural network Bi-LSTM model.

6. The method according to claim 5, characterized in that, The network structure of the Bi-LSTM model specifically includes: The input layer accepts tensors of shape (Batch_size, T, n); The forward and backward LSTM units of the bidirectional LSTM layer are calculated at each time step according to Equation 4-9: in, It is the sigmoid function. It is the Hadamard product, f s The output of the forget gate controls the degree to which the previous memory cell is retained. W f Let h represent the forget gate weight matrix. s-1 m represents the hidden state at the previous time step. s Let b represent the input vector at the s-th time step. f Represents the forget gate bias vector, i s W represents the output of the input gate. i Let b represent the input gate weight matrix. i This represents the input gate bias vector. Represents a candidate memory cell, obtained from the current input and the previous hidden state, W. c The weight matrix representing candidate memory cells, b c C represents the bias vector of candidate memory cells. s C represents the memory cell updated at the current time step. s-1 This represents the state of the memory cells at the previous time step, o s Indicates the output gate output, W o b represents the output gate weight matrix. o h represents the output gate bias vector. s This indicates the hidden state at the current time step; The final output of the Bi-LSTM layer is the concatenation of the last hidden state in the forward pass and the last hidden state in the backward pass. The fully connected layer maps the output of the Bi-LSTM layer to the final predicted value according to Equation 10. Official 10; in, W represents the predicted value for the k-th output dimension. o Let h represent the weight matrix of the fully connected layer, and b represent the final hidden state of the bidirectional LSTM. o This represents the bias vector of the fully connected layer; According to Formula 11, the mean squared error (MSE) is used as the loss function: Official 11; Where L represents the value of the loss function, Ntrain represents the total number of time points in the training set, and y k This represents the k-th true value. This represents the k-th predicted value; The optimizer uses Adam; Minimize the loss function on the training set and use the validation set for early stopping to prevent overfitting.

7. The method according to claim 1, characterized in that, The method further includes: The final output of the ARIMA model plus Bi-LSTM model is compared with the output of the ARIMA model and the output of the Bi-LSTM model using only the original data as features to verify the effectiveness of the ARIMA model plus Bi-LSTM model.

8. A device for correcting orbit prediction errors based on ARIMA-BiLSTM, characterized in that, include: The dataset creation module is used to obtain a time series dataset of orbit prediction errors by calculating the difference between the CPF ephemeris and the TLE+SGP4 model prediction. The ARIMA model module is used to analyze the orbit prediction error time series dataset using the autoregressive differential moving average model ARIMA to obtain processed data. The Bi-LSTM model module is used to construct a bidirectional long short-term memory neural network (Bi-LSTM) model. Processed ARIMA data is used as features input into the Bi-LSTM model. The Bi-LSTM model learns and predicts the historical errors of SGP4 orbit prediction and corrects the errors in orbit prediction by the SGP4 model based on the prediction results.

9. An electronic device, characterized in that, include: The memory, the processor, and the computer program stored in the memory and executable on the processor, wherein the computer program, when executed by the processor, implements the steps of the method for orbit prediction error correction based on ARIMA-BiLSTM as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores an information transmission implementation program, which, when executed by a processor, implements the steps of the method for correcting orbit prediction errors based on ARIMA-BiLSTM as described in any one of claims 1 to 7.

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