A Beidou satellite ephemeris prediction method based on frequency domain information enhancement

Abstract

The present invention provides a Beidou satellite ephemeris prediction method based on frequency domain information enhancement, including receiving broadcast ephemeris data with a receiver, and constructing an ephemeris historical error data set through the broadcast ephemeris data; constructing an ephemeris error compensation model based on a deep learning network; training the ephemeris error compensation model using the ephemeris historical error data set; predicting the ephemeris error using the trained ephemeris error compensation model, and then compensating the prediction result of the dynamic model. The present invention can achieve high-precision, strong generalization and long-term satellite ephemeris prediction; the present invention introduces a frequency attention mechanism for frequency, which can efficiently capture the periodic characteristics between ephemeris, and can reduce the dimension of time series information to eliminate the redundancy of time series information; the present invention inputs the splicing information of the target satellite time domain characteristics and frequency domain characteristics into a multi-layer convolutional network for interactive fusion, thereby improving the accuracy of ephemeris error compensation.

Description

Technical Field

[0001] The invention relates to the technical field of ephemeris prediction, and in particular to a Beidou satellite ephemeris prediction method based on frequency domain information enhancement. Background Art

[0002] Each satellite in the satellite constellation is equipped with precise ephemeris data, which is a detailed description of the satellite's trajectory, including key parameters such as the satellite's position and speed. These data are regularly transmitted to the ground in the form of broadcast ephemeris, providing basic information for positioning calculations for user terminals.

[0003] The ephemeris data in the BeiDou system not only supports positioning and solving, but is also closely related to the high-precision timing service provided by the system, ensuring high reliability of positioning and time synchronization. BeiDou satellites ensure that user terminals can accurately solve their own positions through real-time updates of ephemeris information, and can maintain high-precision positioning even under complex environmental conditions. The accuracy and timeliness of ephemeris data are the cornerstones for the BeiDou system to provide all-weather and all-day positioning services around the world, ensuring efficient operation in many application scenarios from emergency rescue to daily travel, from precision agriculture to smart city construction. The ground control center is responsible for collecting satellite observation data, calculating and updating satellite ephemeris based on this data, and monitoring the operating status of the entire system to ensure the accuracy of ephemeris information, thereby supporting the BeiDou system to provide stable and reliable positioning and communication services worldwide.

[0004] The Global Navigation Satellite System (GNSS) is the most widely used method among various positioning technologies. Ground receivers are indispensable in satellite navigation systems. The receiver calculates the broadcast ephemeris by receiving satellite signals, and then calculates the positioning through the pseudorange and satellite position through the dynamic satellite orbit prediction model inside the receiver.

[0005] However, it takes a certain amount of time for the receiver to receive the entire broadcast ephemeris. Even under strong signal conditions, it takes about 18-36 seconds to receive the complete broadcast ephemeris. When the receiver is in a complex environment such as urban streets or wild jungles, the satellite signal may be weakened or interrupted by the presence of buildings, walls, trees, etc., which seriously hinders the search and demodulation of the signal. At this time, it becomes very difficult to receive the complete broadcast ephemeris, especially for the cold start mode without any prior information assistance. The first positioning time may be as long as several minutes or even more than ten minutes. In addition, the satellite ephemeris calculated by the existing receiver dynamics model is only valid for 2-4 hours, so the receiver needs to receive satellite ephemeris regularly to update the satellite status, which results in a certain amount of time to receive the ephemeris data of multiple satellites after the satellite is shut down for a long time.

[0006] In order to extend the validity period of a single-received broadcast ephemeris, research on satellite ephemeris prediction has been ongoing. Most of the research focuses on the construction and optimization of dynamic models. The existing technology mainly improves the orbital dynamics model inside the receiver. On the basis of the existing dynamics model, more environmental variables are introduced and the integral order during orbit extrapolation is increased, which improves the accuracy of the overall ephemeris prediction to a certain extent. However, the parameter determination process of these improved methods is very complicated, and more environmental data or a large amount of historical data is required to assist in modeling; resulting in the need for more memory space and sensors to correct the model parameters in real time, and requiring greater computational effort and time, which places high demands on the receiver hardware. Moreover, these methods have insufficient fitting capabilities and fail to fully learn the long-term ephemeris prediction error law caused by complex perturbations, resulting in insufficient accuracy in long-term ephemeris prediction. Furthermore, these methods also have technical problems such as a short prediction range and low generalization performance of the model. Summary of the invention

[0007] In view of the deficiencies in the prior art, the present invention provides a Beidou satellite ephemeris prediction method based on frequency domain information enhancement, which can achieve high-precision, strong generalization and long-term satellite ephemeris prediction.

[0008] The technical solution of the present invention is: a Beidou satellite ephemeris prediction method based on frequency domain information enhancement, comprising the following steps:

[0009] S1), using a receiver to receive broadcast ephemeris data, and constructing an ephemeris historical error data set through the broadcast ephemeris data;

[0010] S2), constructing an ephemeris error compensation model based on a deep learning network;

[0011] S3), using the historical ephemeris error data set to train the ephemeris error compensation model;

[0012] S4), using the trained ephemeris error compensation model to predict the ephemeris error, and then compensating the prediction result of the dynamic model.

[0013] Preferably, in step S1), the receiver is a Beidou information acquisition module TD1050, and the Beidou information acquisition module TD1050 has a built-in Kepler dynamics model; the receiver samples the broadcast ephemeris data once an hour and then starts ephemeris extrapolation; each extrapolation obtains 672 node data; and the estimation period is 28 days.

[0014] Preferably, in step S1), the historical 28-day kinetic model is used to extrapolate the error and the epoch is selected at intervals of 24 hours.

[0015] Preferably, in step S1), the precise ephemeris corresponding to the satellite position set calculated by broadcast ephemeris is padded to the same length using the identifier padding.

[0016] As a preferred embodiment, in step S1), the historical error E of the ephemeris inferred by the dynamic model is calculated by using the broadcast ephemeris and the precise ephemeris. in .

[0017] Preferably, in step S2), the ephemeris error compensation model of the deep learning network constructed includes a compression layer Patch, a frequency enhancement layer FEB, a frequency domain attention layer FAL, a time domain attention layer TAL and a fusion layer Fusion.

[0018] Preferably, in step S3), the ephemeris error compensation model is trained using a gradient descent algorithm; and during the training process, the model hyperparameters that need to be determined are:

[0019] 1) The frequency enhancement layer FEB selects the number of frequencies TopK;

[0020] 2) The number of heads in its multi-head attention module is n;

[0021] 3) The number of MLP network layers λ of the prediction part after fusion;

[0022] 4) Selection of convolution kernel and step size of fusion layer.

[0023] Preferably, in step S3), the optimizer selects an Adam optimizer with an adaptive learning rate, and dynamically adjusts the learning rate of each parameter using the first-order moment estimation and the second-order moment estimation of the Adam optimizer gradient; the loss function adopts the MAE loss function Its expression is:

[0024]

[0025] Where N is the number of training samples, E is the actual orbital time estimation error, Indicates the correction value output by the ephemeris error compensation model; when the trained ephemeris error compensation model outputs the result The closer it is to E, the more accurate the final result of the hybrid prediction is.

[0026] Preferably, in step S3), the total number of training rounds of the ephemeris error compensation model is set to M. During the training process, the back propagation algorithm is used to obtain the gradient to update the weights and biases of the model. The update formula is:

[0027]

[0028] Among them, w represents weight, b represents bias, and α is the learning rate; Find the partial derivative of the loss on the corresponding parameters.

[0029] Preferably, in step S4), the historical error E of the ephemeris estimated by the dynamic model obtained in step S1) is in The input to the compression layer Patch divides the longer sequence into several batch lengths and compresses them. The compressed historical prediction errors are processed in the frequency domain and time domain respectively. In the frequency domain, the frequency enhancement layer FEB is used to enhance the random frequency to highlight the frequency domain characteristics of the ephemeris, making it easier for the frequency domain attention layer FAL to learn the random frequency characteristics. In the time domain, the time domain attention layer TAL is used to extract the time series features between different epochs from multiple scales. The time domain features and frequency domain features are fused through the fusion layer Fusion, and finally the perceptron is used to perform time series prediction and output the future prediction error results.

[0030] As a preferred embodiment, in step S4), the compression layer Patch converts the input ephemeris historical error matrix Reshape Then, through a linear transformation layer, layer normalization, and nonlinear function, the time series features are obtained.

[0031] As a preferred embodiment, in step S4), the frequency enhancement layer FEB transforms the time series feature E patch Transform to frequency domain using E f_patch ; Randomly sample the TopK frequencies and multiply them with the random matrix R; fill all frequencies except the filtered frequencies with 0 and convert them into time series frequency features E through inverse Fourier transform FEB ,Right now:

[0032]

[0033] In the formula, F -1 represents inverse Fourier transform, F represents fast Fourier transform, Padding represents padding operation, MLP represents multi-layer perceptron, and Sampling represents random sampling operation.

[0034] As a preferred embodiment, in step S4), in the frequency domain, F(E FEB ) The input frequency domain attention layer FAL is characterized by a multi-head attention mechanism to obtain the enhanced frequency domain information E FAL ;

[0035] In the time domain, the time series feature E ptach The input is then processed in the temporal attention layer TAL to obtain the enhanced temporal information E TAL .

[0036] As a preferred embodiment, in step S4), the enhanced time domain information E TAL and frequency domain information E FAL In the input fusion layer, a two-dimensional convolutional network with a convolution kernel of 2×2 and a step size of 2 is used to transform the time domain information E TAL and frequency domain information E FAL Merge into the feature information of one node, the output dimension is reduced to 1 / 4 of the original, and the fused feature E is obtained. fusion ; Then the fused feature E fusion After a fully connected layer and a nonlinear Relu activation function, the weights are normalized by the normalization function Softmax.

[0037] Finally, the fusion feature E fusion Through size adjustment and dimension conversion, the input is then input into the multi-layer perceptron and the final output result is converted into dimension. That is, the three-axis prediction error of the Kepler dynamics model within 28 days Then the prediction error Ephemeris data corresponding to the orbit extrapolated in the data set Make a difference and get the corrected orbit prediction value (p x ,p y ,p z ).

[0038] The beneficial effects of the present invention are:

[0039] 1. The present invention uses the time-frequency domain attention mechanism to learn the global and local trend characteristics of the ephemeris error in the time dimension; by using the frequency domain enhancement mechanism and the frequency domain attention mechanism to capture the global periodic information characteristics of the input multi-epoch, and effectively compress the long-term multi-epoch data; to achieve high-precision, strong generalization and long-term satellite ephemeris prediction;

[0040] 2. The present invention fully considers the time domain features and frequency domain features between multiple epochs, learns the correlation between data in multiple domains through the frequency enhancement layer and the attention mechanism, reasonably uses the multi-domain features and reduces the redundancy of data, and uses convolution in the fusion layer to effectively fuse the time domain data and the frequency domain data for satellite ephemeris error prediction;

[0041] 3. The present invention introduces a frequency attention mechanism for frequency, which can efficiently capture the periodic characteristics between ephemeris, and can reduce the dimension of time series information to eliminate the redundancy of time series information; using time domain attention, through the time series attention mechanism, by extracting direct time series features of different scales between different epochs, the model helps to pay more attention to the error trend characteristics between epochs; in the feature fusion stage, the present invention inputs the splicing information of the target satellite time domain characteristics and frequency domain characteristics into a multi-layer convolutional neural network for interactive fusion, thereby improving the accuracy of ephemeris error compensation. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 It is a process framework diagram of the present invention;

[0043] Figure 2 It is a framework diagram of the ephemeris error compensation model of the present invention;

[0044] Figure 3 It is a schematic diagram of the process of the frequency enhancement layer of the present invention;

[0045] Figure 4 A schematic diagram of the training process of the ephemeris error compensation model of the present invention. DETAILED DESCRIPTION

[0046] The specific implementation of the present invention will be further described below in conjunction with the accompanying drawings:

[0047] like Figure 1 As shown, this embodiment provides a Beidou satellite ephemeris prediction method based on frequency domain information enhancement, comprising the following steps:

[0048] S1) Receive broadcast ephemeris data using a receiver and construct an ephemeris historical error data set using the broadcast ephemeris data.

[0049] In this embodiment, the receiver is a Beidou information acquisition module TD1050, and the Beidou information acquisition module TD1050 has a built-in Kepler dynamic model; after the receiver is turned on, the receiver receives the Beidou broadcast ephemeris to update the dynamic model parameters every hour, and performs orbit extrapolation ephemeris data. The receiver samples the broadcast ephemeris data once an hour and then starts ephemeris extrapolation; each extrapolation obtains 672 node data; the estimation period is 28 days.

[0050] In this embodiment, the receiver starts to extrapolate the ephemeris after receiving the broadcast ephemeris every hour. However, due to the redundancy of the time series, the historical 28-day dynamic model is used to extrapolate the error and the epoch is selected at intervals of 24 hours. Therefore, the 28 reference epochs are used, and each node in the epoch is used. express; It indicates that the ephemeris information at time j is inferred through the dynamic model based on the broadcast ephemeris at time i, which contains the three-axis satellite position p based on the geodetic coordinate system. x ,p y ,p z ;use represents a set of satellite positions derived from 28 days of broadcast ephemeris; that is:

[0051]

[0052] In actual application, the precise ephemeris has a 12-hour delay, but in order to ensure alignment with the broadcast ephemeris, this embodiment uses the identifier padding to fill the precise ephemeris set Ψ corresponding to the satellite position set calculated by the broadcast ephemeris to the same length, that is:

[0053]

[0054] In the formula, express The corresponding precise ephemeris.

[0055] The historical error E of the ephemeris inferred by the dynamic model is calculated by using the broadcast ephemeris and the precise ephemeris. in ;Right now:

[0056]

[0057] In the formula, e i,j It indicates the ephemeris error estimated at the jth moment when the machine is turned on at the i-th moment.

[0058] S2) Construct an ephemeris error compensation model based on deep learning network

[0059] like Figure 2 As shown, the ephemeris error compensation model of the deep learning network constructed in this embodiment includes a compression layer Patch, a frequency enhancement layer FEB, a frequency domain attention layer FAL, a time domain attention layer TAL and a fusion layer Fusion.

[0060] S3) Use the historical ephemeris error data set to train the ephemeris error compensation model

[0061] like Figure 4 As shown, this embodiment uses a gradient descent algorithm to train the ephemeris error compensation model; and during the training process, the model hyperparameters that need to be determined are:

[0062] 1) The frequency enhancement layer FEB selects the number of frequencies TopK;

[0063] 2) The number of heads in its multi-head attention module is n;

[0064] 3) The number of MLP network layers λ of the prediction part after fusion;

[0065] 4) Selection of convolution kernel and step size of fusion layer.

[0066] The optimizer of this embodiment selects the Adam optimizer with adaptive learning rate, and dynamically adjusts the learning rate of each parameter using the first-order moment estimation and second-order moment estimation of the Adam optimizer gradient; the loss function adopts the MAE loss function Its expression is:

[0067]

[0068] Where N is the number of training samples, E is the actual orbital time estimation error, Indicates the correction value output by the ephemeris error compensation model; when the trained ephemeris error compensation model outputs the result The closer it is to E, the more accurate the final result of the hybrid prediction is.

[0069] In this embodiment, the total number of training rounds of the ephemeris error compensation model is set to M. During the training process, the back propagation algorithm is used to obtain the gradient to update the weights and biases of the model. The update formula is:

[0070]

[0071] Among them, w represents weight, b represents bias, and α is the learning rate; Find the partial derivative of the loss on the corresponding parameters.

[0072] S4), using the trained ephemeris error compensation model to predict the ephemeris error, and then compensating the prediction result of the dynamic model.

[0073] In this embodiment, the historical error E of the ephemeris inferred by the dynamic model obtained in step S1) is in The input to the compression layer Patch divides the longer sequence into several batch lengths and compresses them. The compressed historical prediction errors are processed in the frequency domain and time domain respectively. In the frequency domain, the frequency enhancement layer FEB is used to enhance the random frequency to highlight the frequency domain characteristics of the ephemeris, making it easier for the frequency domain attention layer FAL to learn the random frequency characteristics. In the time domain, the time domain attention layer TAL is used to extract the time series features between different epochs from multiple scales. The time domain features and frequency domain features are fused through the fusion layer Fusion, and finally the perceptron is used to perform time series prediction and output the future prediction error results.

[0074] In this embodiment, the compression layer Patch is used to convert the time series data into a form suitable for processing by the ephemeris error compensation model, which helps to improve the processing capability and prediction accuracy of the ephemeris error compensation model, and also optimizes the computational efficiency of the ephemeris error compensation model. The sequence processed by the compression layer Patch can focus on both the short-term time series characteristics of the sequence and the long-term time series characteristics of the sequence. The compression layer Patch converts the input ephemeris historical error matrix into Reshape

[0075] Then, through a linear transformation layer, layer normalization, and nonlinear function, the time series features are obtained.

[0076] This embodiment uses the frequency enhancement layer FEB to enhance the time series features and the time series features between epochs, fully exploits the global periodic features of the ephemeris error, and enables the subsequent frequency domain attention layer to better learn the global periodic features and achieve more accurate ephemeris prediction. Its structure is as follows: Figure 3 As shown. The frequency enhancement layer FEB transforms the time series feature E patch Transform to frequency domain using E f_patch ; Randomly sample the TopK frequencies and multiply them with the random matrix R; fill all frequencies except the filtered frequencies with 0 and convert them into time series frequency features E through inverse Fourier transform FEB ,Right now:

[0077]

[0078] In the formula, F -1 represents inverse Fourier transform, F represents fast Fourier transform, Padding represents padding operation, MLP represents multi-layer perceptron, and Sampling represents random sampling operation.

[0079] In this embodiment, it is necessary not only to learn the time series features between different epochs in the time domain, but also to characterize the sequence frequency features between epochs in the frequency domain.

[0080] In the frequency domain, F(E FEB ) The input frequency domain attention layer FAL is characterized by a multi-head attention mechanism to obtain the enhanced frequency domain information E FAL ; Where, F represents fast Fourier transform.

[0081] In the time domain, the time series feature E patch The input is then processed in the temporal attention layer TAL to obtain the enhanced temporal information E TAL .

[0082] The multi-head attention mechanism layer is built on the self-attention mechanism layer. The expression of the self-attention mechanism is:

[0083]

[0084] Where Q = W Q X, K = W K X, V = W V X represents the query matrix, key matrix and value matrix respectively; softmax is the normalization function, Represents the scaling factor in the attention mechanism; In order to improve the generalization performance of the ephemeris error compensation model, the ephemeris error compensation model adds a residual layer and normalization.

[0085] In this embodiment, the enhanced time domain information E TAL and frequency domain information E FAL In the input fusion layer, a two-dimensional convolutional network with a convolution kernel of 2×2 and a step size of 2 is used to transform the time domain information E TAL and frequency domain information E FAL Merge into the feature information of one node, the output dimension is reduced to 1 / 4 of the original, and the fused feature E is obtained. fusion ; Then the fused feature E fusion After a fully connected layer and a nonlinear Relu activation function, the weights are normalized by the normalization function Softmax.

[0086] Finally, the fusion feature E fusion Through size adjustment and dimension conversion, the input is then input into the multi-layer perceptron and the final output result is converted into dimension. That is, the three-axis prediction error of the Kepler dynamics model within 28 days Then the prediction error Ephemeris data corresponding to the orbit extrapolated in the data set Make a difference and get the corrected orbit prediction value (p x ,p y ,p z ).

[0087] The above embodiments and descriptions are only for illustrating the principles and best embodiments of the present invention. Without departing from the spirit and scope of the present invention, the present invention may be subject to various changes and improvements, all of which fall within the scope of the present invention to be protected.

Claims

1. A Beidou satellite ephemeris prediction method based on frequency domain information enhancement, characterized in that: The following steps are involved: S1), using a receiver to receive broadcast ephemeris data, and constructing an ephemeris historical error data set through the broadcast ephemeris data; The received broadcast ephemeris data is the historical 28-day broadcast ephemeris data. The precise ephemeris corresponding to the satellite position set estimated by the broadcast ephemeris is padded to the same length using the identifier padding. Then, the historical ephemeris error E estimated by the dynamic model is calculated using the broadcast ephemeris and the precise ephemeris. in ; S2), constructing an ephemeris error compensation model based on a deep learning network; The ephemeris error compensation model based on deep learning network includes compression layer Patch, frequency enhancement layer FEB, frequency domain attention layer FAL, time domain attention layer TAL and fusion layer Fusion; S3), using the historical ephemeris error data set to train the ephemeris error compensation model; S4), using the trained ephemeris error compensation model to predict the ephemeris error, and then compensate the prediction result of the dynamic model; the details are as follows: The historical error E of the ephemeris inferred by the dynamic model obtained in step S1) in The input to the compression layer Patch divides the longer sequence into several batch lengths and compresses them. The compressed historical prediction errors are processed in the frequency domain and time domain respectively; In the frequency domain, the frequency enhancement layer FEB is used to enhance the random frequency and highlight the frequency domain characteristics of the ephemeris, making it easier for the frequency domain attention layer FAL to learn the random frequency characteristics; In the time domain, the time domain attention layer TAL is used to extract temporal features between different epochs from multiple scales; The time domain features and frequency domain features are fused through the fusion layer, and finally the perceptron is used to perform time series prediction and output the future prediction error results; The frequency enhancement layer FEB transforms the time series features E patch Transform to frequency domain using E f_patch ; Randomly sample the TopK frequencies and multiply them with the random matrix R; fill all frequencies except the filtered frequencies with 0 and convert them into time series frequency features E through inverse Fourier transform FEB ,Right now: E FEB =F -1 (Padding(Sampling(F(MLP(E patch )))*R)); In the formula, F -1 represents inverse Fourier transform, F represents fast Fourier transform, Padding represents padding operation, MLP represents multi-layer perceptron; Sampling represents random sampling operation; In the frequency domain, F(E FEB ) The input frequency domain attention layer FAL is characterized by a multi-head attention mechanism to obtain the enhanced frequency domain information E FAL ; In the time domain, the time series feature E patch The input is then processed in the temporal attention layer TAL to obtain the enhanced temporal information E TAL ; The enhanced time domain information E TAL and frequency domain information E FAL In the fusion layer, the time domain information E is transformed into TAL and frequency domain information E FAL Merge into the feature information of one node to obtain the fused feature E fusion ; Then the fused feature E fusion After a fully connected layer and a nonlinear Relu activation function, the weights are normalized by the normalization function Softmax. Finally, the fusion feature E fusion Through size adjustment and dimension conversion, the output result is converted into the dimension of the multi-layer perceptron. That is, the three-axis prediction error of the Kepler dynamics model within 28 days Then the prediction error Ephemeris data corresponding to the orbit extrapolated in the data set Make a difference and get the corrected orbit prediction value (px, py, pz).

2. The Beidou satellite ephemeris prediction method based on frequency domain information enhancement according to claim 1, characterized in that: In step S2), the ephemeris error compensation model of the constructed deep learning network includes a compression layer Patch, a frequency enhancement layer FEB, a frequency domain attention layer FAL, a time domain attention layer TAL and a fusion layer Fusion.

3. The Beidou satellite ephemeris prediction method based on frequency domain information enhancement according to claim 1, characterized in that: In step S3), the ephemeris error compensation model is trained using a gradient descent algorithm; and during the training process, the optimizer selects an Adam optimizer with an adaptive learning rate, and dynamically adjusts the learning rate of each parameter using the first-order moment estimation and the second-order moment estimation of the Adam optimizer gradient; The loss function uses the MAE loss function Its expression is: Where N is the number of training samples, E is the actual orbital time estimation error, Indicates the correction value output by the ephemeris error compensation model; when the trained ephemeris error compensation model outputs the result The closer it is to E, the more accurate the final result of the hybrid prediction is.

4. The Beidou satellite ephemeris prediction method based on frequency domain information enhancement according to claim 3, characterized in that: In step S3), the total number of training rounds of the ephemeris error compensation model is set to M. During the training process, the back propagation algorithm is used to obtain the gradient to update the weights and biases of the model. The update formula is: Among them, w represents weight, b represents bias, and α is the learning rate; Find the partial derivative of the loss on the corresponding parameters.

5. The Beidou satellite ephemeris prediction method based on frequency domain information enhancement according to claim 1, characterized in that: In step S4), the compression layer Patch converts the input ephemeris historical error matrix Reshape Then, through a linear transformation layer, layer normalization, and nonlinear function, the time series features are obtained.

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