A method for compensating for satellite predicted orbit errors

Abstract

The application discloses a satellite predicted orbit error compensation method, and utilizes fast Fourier transform to analyze satellite predicted orbit error, identifies and extracts the periodic characteristics of the satellite predicted orbit error, establishes a periodic term model of the predicted orbit error, obtains residual error of the predicted orbit error, and then utilizes a pre-trained long short-term memory network to output a fitting residual error of prediction, finally, the periodic term model and the neural network model are used to respectively predict and compensate the orbit error, so that the precision of the satellite predicted orbit is improved. The application integrates error processing, frequency domain analysis and neural network technologies, slows down the attenuation trend of the satellite predicted orbit, and improves the precision of the predicted orbit.

Description

Technical Field

[0001] This invention belongs to the field of satellite positioning and orbit determination technology, and relates to a method for compensating for satellite orbit prediction errors, particularly a method for compensating for satellite orbit prediction errors that integrates spectral analysis and neural networks. Background Technology

[0002] High-precision satellite orbits are the foundation and prerequisite for Precise Point Positioning (PPP). The International GNSS Services (IGS) collects satellite orbit results from its multiple analysis centers, processes them comprehensively, and generates integrated orbit products, which are then released to the public. These products include orbit information from final precise ephemeris, rapid ephemeris, and ultra-rapid ephemeris. Among these orbit products, taking GPS as an example, the final precise ephemeris and rapid ephemeris have time delays of 12–18 days and 17–41 hours, respectively. Only ultra-rapid ephemeris can provide real-time satellite orbits to users, meeting the positioning requirements of real-time PPP. The predicted orbits in ultra-rapid ephemeris can be used for real-time positioning. The accuracy of the predicted orbit depends on the accuracy of the orbit determination and the prediction model. Large errors in orbit determination and perturbation modeling will both affect the accuracy of the predicted orbit. Currently, high-precision orbit prediction is mainly based on mechanical models, while perturbation models, primarily based on solar radiation pressure models, are not accurate enough, leading to a rapid decay in the accuracy of satellite predicted orbits, thus affecting the performance of real-time PPP positioning.

[0003] To mitigate the decay trend of predicted satellite orbits and improve their accuracy, one approach is to enhance orbit determination accuracy, and another is to improve the accuracy of the prediction model. However, both methods rely on accurate modeling of the perturbations acting on the satellite. But for satellites, the perturbation factors in their space operating environment are complex, and progress in improving the accuracy of perturbation modeling is slow. This is especially true for my country's BeiDou Navigation Satellite System (BDS), which only completed its global network in 2020, resulting in relatively limited satellite orbit data accumulation, further hindering the accurate construction of perturbation models. Summary of the Invention

[0004] To address the aforementioned issues in the prior art, the present invention aims to provide a satellite orbit prediction error compensation method that integrates spectral analysis and neural networks. This method utilizes spectral analysis to model the periodic characteristics of satellite orbit prediction errors and employs neural networks to model the fitting residuals within these errors. By combining the periodic model and the fitting residual model, a satellite orbit prediction error model is obtained. Based on this model, error compensation is applied to the satellite orbit prediction, mitigating the decay trend of the predicted orbit and improving its accuracy.

[0005] To solve the above-mentioned technical problems, the present invention provides a satellite prediction orbit error compensation method, comprising the following steps:

[0006] Step 1: Obtain the satellite predicted orbit error based on the first difference between the satellite reference orbit data and the predicted orbit data;

[0007] Step 2: Perform a fast Fourier transform on the predicted orbit error to identify and extract the periodic terms of the predicted orbit error data;

[0008] Step 3: Establish the orbital error periodic term model Y(t) based on the periodic term described in Step 2. x ), t x The time is represented by the least squares method to fit the satellite predicted orbit error obtained in step 1, and the coefficients of the periodic term model are obtained. Then, according to the model Y(t) x The predicted orbital error sequence Y(t) of the periodic term model was calculated. n +l·t0), l=1,2,3,…,L, L is the predicted data length, t0 represents the time interval; the orbital error value Y(t) calculated by the periodic term model is... x The satellite orbit prediction error obtained in step 1 is subtracted from x = 1, 2, ..., n to obtain the fitted residual sequence, which is then normalized to obtain X. n Using the fitted residual sequence X k Train the neural network using the formula k∈{1,2,3,…,n-1};

[0009] Step 4: Fit the residual sequence t n The residual value x at time step n The neural network, pre-trained and fed with the data to be predicted, predicts t. n The predicted value of the fitted residual at time +t0 is x. n+1 , and as the next moment t n The input is +2t0, where t0 represents the time interval of the residual sequence; after one prediction is completed, the input sequence is shifted one step forward until the set prediction sequence length is reached;

[0010] Step 5: Predicted orbital error value Y(t) for the periodic term model n The error prediction result is obtained by summing the predicted values ​​of the fitted residuals at the corresponding times (l = 1, 2, 3, ..., L) and l·t0), and then using this sum to compensate for the predicted orbit data in step 1.

[0011] Furthermore, before performing a fast Fourier transform on the predicted orbit error, the method further includes: determining whether there is a trend term in the original orbit error; if there is a trend term, removing the trend term and then performing a fast Fourier transform on the data; if there is no trend term, then directly performing a fast Fourier transform on the data.

[0012] Furthermore, step 2, which involves performing a fast Fourier transform on the predicted orbit error to identify and extract the periodic terms of the predicted orbit error data, includes:

[0013] The predicted orbit error is converted from the time domain to the frequency domain using a fast Fourier transform:

[0014]

[0015] In the formula: x[n] represents the orbital error; X[k] is the frequency domain representation. Solve for the magnitude of X[k], and select the frequencies f corresponding to the M largest magnitudes of X[k]. m , m=1,2,…,M.

[0016] Furthermore, the step of establishing the orbital error periodic term model based on the periodic term described in step 2 includes:

[0017] The periodic term model is as follows:

[0018]

[0019] In the formula: Y(t) x ) represents a periodic term model; M represents the number of periodic terms; a m For model coefficients; f m The frequency obtained from the Fast Fourier Transform; t x φ represents the time point for fitting the data; φ0 represents the initial phase.

[0020] Furthermore, the neural network is a long short-term memory network.

[0021] Furthermore, step 3 involves using the fitted residual sequence X k Training a neural network for k∈{1,2,3,…,n-1} includes:

[0022] Using the fitted residual sequence X k k∈{1,2,3,…,n-1} is used as the input to the Long Short-Term Memory (LSTM) network. Each LSM layer has three gate structures to control the cell state. The output of the LSM network is the predicted value of the fitted residual at the next time step after the input fitted residual. The predicted value of the fitted residual is compared with the true fitted residual X. kBackpropagation is performed on k∈{2,3,4,…,n} to update the weight matrix and bias matrix. The predicted values ​​are corrected in the next training. A set of input residual sequences and the next prediction results constitute the training data for one step. After completing one training step, the input sequence and output sequence will be shifted back one time point until the entire training data is completed.

[0023] The beneficial effects of this invention are as follows: To improve the accuracy of satellite orbit prediction, most current research focuses on accurately modeling the perturbations experienced by satellites. To mitigate the decay trend of satellite orbit prediction and improve its accuracy, this invention provides a satellite orbit prediction error compensation method that integrates spectral analysis and neural networks. It utilizes spectral analysis to extract the periodic characteristics of orbit errors, establishes a periodic term model of orbit errors, and uses a Long Short-Term Memory (LSTM) network to train the residuals of the periodic term model, establishing a fitted residual model. To improve error modeling efficiency, the length of the training data is selected based on the periodic characteristics of the orbit error data, avoiding the use of large amounts of data for training. The invention predicts orbit errors by integrating the periodic term model and the fitted residual model, and then compensates for the satellite orbit prediction. This invention integrates error processing, frequency domain analysis, and neural network technologies. It uses Fast Fourier Transform (FFT) to analyze satellite orbit prediction errors, mines and extracts the periodic features of these errors, establishes a periodic term model of the predicted orbit errors, obtains the residuals of the predicted orbit errors, and then uses an LSM network for training. Finally, it integrates the periodic term model and the neural network model to predict and compensate for orbit errors, thereby improving the accuracy of satellite orbit prediction. Attached Figure Description

[0024] Figure 1 This is a schematic diagram illustrating the implementation of the comprehensive spectral analysis and neural network satellite prediction orbit error compensation method of the present invention. Detailed Implementation

[0025] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0026] The present invention is implemented as follows:

[0027] Step 1: Collect satellite reference orbit and predicted orbit data, obtain satellite predicted orbit error data by the first difference between the two orbits, and perform data preprocessing;

[0028] Step 2: Perform a Fast Fourier Transform (FFT) on the predicted orbit error to identify and extract the periodic terms of the predicted orbit error data, and determine the changes in the periodicity of the predicted orbit error data;

[0029] First, determine if there is a trend term in the original orbital error. If a trend term exists, remove it and perform frequency domain analysis on the data. If no trend term exists, perform frequency domain analysis directly on the data. By performing a Fast Fourier Transform on the predicted orbital error data, calculate the amplitude-frequency characteristics of the orbital error and extract the periodic terms that have a significant impact on the radial, tangential, and normal directions of the orbital error.

[0030] Step 3: Based on the periodic terms extracted from the satellite predicted orbit error, establish a predicted orbit error periodic term model; fit the original predicted orbit error using the least squares method to obtain the coefficients of the periodic term model; subtract the original predicted orbit error from the orbit error data obtained through the periodic term model to obtain the fitting residual of the predicted orbit error;

[0031] A periodic term model is established based on the periodic term extracted in step 2. The satellite predicted orbit error obtained in step 1 is fitted using the least squares fitting method to obtain the coefficients of the periodic term model. Then, the orbit error data calculated based on the model is subtracted from the satellite predicted orbit error obtained in step 1 to obtain the fitting residual.

[0032] Step 4: Use the fitted residual samples obtained in Step 3 to train the neural network, and use the trained neural network to predict the fitted residuals.

[0033] Considering that recurrent neural networks tend to forget information from distant time periods and have a long-term dependence on training data, a Long Short-Term Memory (LSTM) network is used for training. During training, the first n-1 samples of the fitted residual (n samples) are used as input, and the last n-1 samples are used as output. This ensures that the output of the trained neural network is a prediction of the residual at the next time step after the input. The trained neural network then predicts the sample points after the last n samples of the fitted residual.

[0034] Step 5: Extrapolate the orbital error using the periodic term model to obtain the predicted orbital error data, and sum it with the predicted data of the fitting residual obtained in Step 4 to obtain the final predicted orbital error data.

[0035] The final prediction result is obtained by summing the prediction results of the periodic term model and the neural network, which enables the prediction of the predicted orbit error and is used to compensate for the predicted orbit after step 1, thereby improving the accuracy of the predicted orbit.

[0036] Combination Figure 1 The present invention includes the following steps:

[0037] Step 1: Collect BeiDou satellite reference orbit and predicted orbit data, obtain satellite predicted orbit error data by the first difference between the two orbits, and perform data preprocessing;

[0038] Step 2: Perform FFT on the orbit prediction error to identify and extract the periodic term of the orbit error;

[0039] Transforming the predicted orbit error from the time domain to the frequency domain, the expression for the Discrete Fourier Transform (DFT) is as follows:

[0040]

[0041] In the formula: x[n] represents the orbital error data; X[k] represents the frequency domain representation of the data. The original N-point sequence is decomposed into a series of short sequences using FFT. The symmetry and periodicity of the exponential factor in the DFT calculation are utilized to reduce multiplication operations. The magnitude of X[k] is solved, and the frequencies f corresponding to the M largest magnitudes of X[k] are selected. m , m=1,2,…,M.

[0042] Step 3: Based on the satellite predicted orbit error periodic term extracted in Step 2, establish a predicted orbit error periodic term model; then fit the original orbit prediction error data using the periodic term model, and subtract the fitted data from the original data to obtain the fitting residual;

[0043] A periodic term model is established based on the periodic term of the satellite predicted orbit error extracted in step 2:

[0044]

[0045] In the formula: Y(t) x ) represents a periodic term model; M represents the number of periodic terms; a m For model coefficients; f m The frequency obtained from the Fast Fourier Transform; t x φ represents the time of the fitted data; φ0 represents the initial phase. The model coefficients α are solved using the least squares method. m Then, the fitted data is subtracted from the original data to obtain the fitting residual.

[0046] Step 4: Train the long short-term memory network obtained in step 3 to obtain a trained neural network, and use the trained neural network to predict the residuals.

[0047] First, the fitted residual sequence X is... m Normalization is performed to obtain X n The processed data is restricted to the range [0,1]. Normalization can improve the convergence speed of network training. The normalized residual sequence X... n Training is performed using a Long Short-Term Memory (LSTM) network. Each LTM layer contains three gate structures to control cell states. When training the LTM network on the fitted residuals, the fitted residual sequence X is used.k k∈{1,2,3,…,n-1} is used as network input, and the residual sequence X is used. k The network output is k∈{2,3,4,…,n}, where n represents the length of the training residual sequence. This allows the output of the Long Short-Term Memory (LSTM) network to be a prediction of the residual at the next time step after the input. The weight and bias matrices are updated through backpropagation between the predicted values ​​and the actual residuals, and the predicted values ​​are corrected in the next training iteration. A set of input residual sequences and the next step's prediction results constitute one step of training data. After completing one training step, the input and output sequences are shifted forward by one time point until the entire training data is completed.

[0048] To predict the fitted residuals using the trained network, the final time step t of the residual sequence is required. n residual value x n As input to the prediction data, the trained network predicts t. n The residual value x at time +t0 n+1 , and as the next moment t n The input is +2t0, where t0 represents the time interval of the residual sequence. The predicted residual sequence length is set. After each prediction, the input sequence shifts one step forward, and the unknown residual data in the input is filled with the predicted value from the previous time step, until the pre-set prediction length is reached. Since the true error at future time steps is unknown, the entire prediction process does not perform backpropagation; only forward propagation is executed.

[0049] Step 5: Extrapolate the orbital error using the periodic term model to obtain the predicted orbital error data, and sum it with the predicted data of the fitting residual obtained in Step 4 to obtain the final predicted orbital error data. This data is then used to compensate for the predicted orbits after Step 1, thereby improving the accuracy of the predicted orbits.

[0050] In formula (2), all variables except time t and model output Y(t) are known. By shifting the time step by t0, the periodic term model can predict the orbital error, i.e., the final time of the original predicted orbital error sequence is t. n , t n +t0 is used as the input to the periodic term model, thus obtaining t n The model output at time +t0, t0 and t n All are the same as in step 4. Finally, Y(t) n +l·t0)+x n+l For the final predicted orbital error, Y(t) n +l·t0) periodic term model predicted value, x n+l The value is the neural network prediction, l∈{1,2,3,…,L}, where L is the length of the prediction data, and is used to compensate for the predicted orbit after step 1, thereby improving the accuracy of subsequent predicted orbits.

Claims

1. A method of compensating for satellite predicted orbit errors, characterized by, Includes the following steps: Step 1: Obtain the satellite predicted orbit error based on the first difference between the satellite reference orbit data and the predicted orbit data; Step 2: Perform a fast Fourier transform on the predicted orbit error to identify and extract the periodic terms of the predicted orbit error data; The periodic term model is as follows: ； wherein: is a periodic term model; M is the number of periodic terms; is a model coefficient; is a frequency obtained by a fast Fourier transform; is a time point of the fitted data; is an initial phase; Step 3: Establish a periodic term model for orbital errors based on the periodic term described in Step 2. , The time is represented by the least squares method to fit the satellite predicted orbit error obtained in step 1, obtaining the coefficients of the periodic term model. Then, based on the model... The calculated orbital error prediction sequence of the periodic term model was obtained. , , To predict data length, Indicates the time interval; the orbital error value calculated from the periodic term model. , The difference between the predicted satellite orbit error obtained in step 1 and the original error is used to obtain the fitted residual sequence, which is then normalized. Using the fitted residual sequence Train the neural network; Step 4: fitting residual sequence residual value at time t as the input of the to-be-predicted data, a pre-trained neural network is used to predict the fitting residual prediction value at time t , and as the input of the next time , the time interval of the residual sequence; after completing one prediction, the input sequence is shifted by one step, and the process is repeated until the set prediction sequence length is completed. Step 5: Periodic term model orbit error predictor , and the fitting residual predictor of the corresponding time are summed to obtain the error prediction result, and the predicted orbit data of step 1 is compensated.

2. The method of claim 1, wherein: Before performing a fast Fourier transform on the predicted orbit error, the method further includes: determining whether there is a trend term in the original orbit error; if there is a trend term, removing the trend term and then performing a fast Fourier transform on the data; if there is no trend term, then directly performing a fast Fourier transform on the data.

3. The method of claim 1, wherein: Step 2, which involves performing a Fast Fourier Transform on the predicted orbit error to identify and extract the periodic terms of the predicted orbit error data, includes: The predicted orbit error is converted from the time domain to the frequency domain using a fast Fourier transform: ； In the formula: is the track error; is the frequency domain representation, the modulus of is solved, and M larger modulus corresponds to the frequency , .

4. The method of claim 1, wherein: The neural network is a long short-term memory network.

5. The method of claim 4, wherein: using the fitted residual sequence of step 3 training the neural network comprises: Using fitted residual sequences As input to the Long Short-Term Memory (LSTM) network, each layer of the LTM network contains three gate structures to control the cell state. The output of the LTM network is the predicted value of the fitted residual at the next time step after the input fitted residual. This predicted value is then compared with the actual fitted residual. Backpropagation is performed to update the weight matrix and bias matrix. The predicted values ​​are corrected in the next training. A set of input residual sequences and the next prediction results constitute the training data for one step. After one training step is completed, the input sequence and output sequence will be shifted forward by one time point until the entire training data is completed.

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