Navigation satellite high-precision orbit forecasting method based on bidirectional long short-term memory network

Abstract

The invention discloses a navigation satellite high-precision orbit forecasting method based on a bidirectional long short-term memory network, and relates to the technical field of satellite orbit forecasting, and the method comprises the following steps: (1) obtaining a reference orbit; (2) extrapolating a dynamic orbit; (3) constructing an orbit forecast error sequence; (4) training a network model; (5) predicting orbit forecast errors at future moments; and (6) compensating a forecast result. According to the method, the orbit prediction error sequence is constructed to describe the difference between the dynamic model and the real space environment, and the change rule of the orbit prediction error is captured and learned by adopting the bidirectional long-short-term memory network, so that the orbit error at the future moment is predicted, and the orbit prediction result based on the dynamic model is corrected; therefore, the defects of dynamic modeling in comparison with a real space environment are compensated, the trend that orbit errors are rapidly diverged along with the increase of forecasting time is inhibited, and a high-precision orbit forecasting task of a navigation satellite is effectively realized.

Description

Technical Field

[0001] The present invention relates to the technical field of satellite orbit prediction, and in particular to a high-precision orbit prediction method for a navigation satellite based on a bidirectional long short-term memory network. Background Art

[0002] High-precision orbit prediction is an important basis for satellites to carry out various applications in orbit. At present, the development trend of the new generation of global satellite navigation systems requires navigation satellites to have the function of high-precision autonomous orbit determination, that is, to be able to autonomously generate navigation messages and maintain the normal operation of the entire system without the support of the ground station operation and control system. As the prior information for satellite autonomous orbit determination, the accuracy of orbit prediction determines the accuracy of the final orbit determination to a certain extent.

[0003] Generally, to improve the accuracy of orbit prediction, it is necessary to fully analyze the various perturbations that the satellite is subject to in orbit and establish a more accurate satellite dynamics model. However, the refinement of the dynamics model requires the support of long-term on-orbit observation data, which is a long and difficult process, and the satellite's motion state is complex and changeable due to the influence of the space environment. Therefore, it is difficult for the idealized satellite dynamics model to fully and accurately describe the effects of space perturbations, resulting in rapid divergence of orbit errors over the prediction time, and the accuracy of satellite orbit prediction is difficult to meet the needs of actual applications.

[0004] In summary, it is necessary to seek a high-precision orbit prediction method for navigation satellites that can suppress the error divergence trend and improve orbit accuracy without relying on the refinement of the dynamic model. Summary of the invention

[0005] In response to the above-mentioned problems in navigation satellite orbit prediction, the present invention proposes a high-precision orbit prediction method for navigation satellites based on a bidirectional long short-term memory network, which constructs an orbit prediction error sequence to describe the difference between the dynamic model and the real space environment, and uses a bidirectional long short-term memory network to capture and learn the changing law of the orbit prediction error, so as to predict the orbit error at future times and correct the orbit prediction results based on the dynamic model, thereby compensating for the shortcomings of the dynamic modeling compared to the real space environment, suppressing the trend of rapid divergence of the error with the increase of the prediction time, and effectively realizing the high-precision orbit prediction task of the navigation satellite.

[0006] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0007] A method for high-precision orbit prediction of a navigation satellite based on a bidirectional long short-term memory network comprises the following steps:

[0008] Step 1: Obtain the reference orbit, and extract precise orbit determination data from the IGS precise ephemeris as the reference orbit for the navigation satellite's in-orbit motion;

[0009] Step 2: Dynamic orbit extrapolation: By analyzing and modeling the perturbations of the navigation satellite in orbit, a satellite dynamics model is constructed to extrapolate the satellite's future orbit.

[0010] Step 3: Construct an orbit prediction error sequence and compare the difference between the dynamically extrapolated orbit and the reference orbit in the precise ephemeris to describe the difference between the dynamic model and the real space environment.

[0011] Step 4: Train the network model to extract and learn the changing rules of the orbit prediction error sequence through the bidirectional long short-term memory network;

[0012] Step 5: Predict the orbit prediction error at future times, and use the trained neural network model to predict the orbit prediction error at future times;

[0013] Step 6: Compensate the prediction results. Use the network prediction error to compensate the orbit prediction results based on the dynamic model to obtain the corrected final satellite orbit prediction results.

[0014] A high-precision orbit prediction device for navigation satellites based on a bidirectional long short-term memory network includes the following modules:

[0015] The reference orbit acquisition module obtains the reference orbit and extracts the precise orbit determination data from the IGS precise ephemeris as the reference orbit for the navigation satellite's on-orbit motion;

[0016] The motion orbit extrapolation module and dynamic orbit extrapolation module analyze and model the perturbations of the navigation satellite in orbit, build a satellite dynamics model, and extrapolate the satellite's motion orbit in the future.

[0017] Error sequence construction module, which constructs orbit prediction error sequence and compares the difference between the dynamic extrapolated orbit and the reference orbit in the precise ephemeris, so as to describe the difference between the dynamic model and the real space environment;

[0018] Network training module: training network model, extracting and learning the changing rules of orbit prediction error sequence through bidirectional long short-term memory network;

[0019] The prediction module predicts the orbit prediction error at future times and uses the trained neural network model to predict the orbit prediction error at future times;

[0020] The compensation module compensates the prediction results and uses the network prediction error to compensate the orbit prediction results based on the dynamic model to obtain the corrected final satellite orbit prediction results.

[0021] An electronic device comprises a memory, a processor and a computer program stored in the memory and executable on the processor. When the processor executes the program, the steps of a method for high-precision orbit prediction of a navigation satellite based on a bidirectional long short-term memory network are implemented.

[0022] A non-transitory computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps of a method for high-precision orbit prediction of a navigation satellite based on a bidirectional long short-term memory network.

[0023] Beneficial effects:

[0024] (1) The present invention proposes a high-precision orbit prediction method for navigation satellites based on a bidirectional long short-term memory network, which can complete the high-precision orbit prediction task of navigation satellites without refining the dynamic model.

[0025] (2) The bidirectional long short-term memory network is used to mine the deep features of the orbit prediction error time series data, capture and learn the changing patterns of the orbit prediction error, and thus predict the orbit error at future moments.

[0026] (3) Effectively compensate for the shortcoming of the dynamic model that the difference between the dynamic model and the real space environment gradually increases over time, and suppress the rapid divergence of errors. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 A flow chart of a method for high-precision orbit prediction of a navigation satellite based on a bidirectional long short-term memory network of the present invention;

[0028] Figure 2 The bidirectional long short-term memory network structure diagram of the present invention;

[0029] Figure 3 The figure is a comparison diagram of orbit prediction errors before and after the bidirectional long short-term memory network compensation of the present invention; wherein, (a) is the orbit prediction X-axis error, (b) is the orbit prediction Y-axis error, (c) is the orbit prediction Z-axis error, and (d) is the three-dimensional position prediction error in the inertial system. DETAILED DESCRIPTION

[0030] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0031] The present invention will be further described below in conjunction with specific embodiments.

[0032] like Figure 1 As shown, a navigation satellite high-precision orbit prediction method based on a bidirectional long short-term memory network of the present invention specifically includes the following steps:

[0033] Step 1: Obtain the reference orbit, and extract precise orbit determination data from the IGS precise ephemeris as the reference orbit for the navigation satellite's in-orbit motion;

[0034] Step 2: Dynamic orbit extrapolation: By analyzing and modeling the perturbations of the navigation satellite in orbit, a satellite dynamics model is constructed to extrapolate the satellite's future orbit.

[0035] Step 3: Construct an orbit prediction error sequence and compare the difference between the dynamically extrapolated orbit and the reference orbit in the precise ephemeris to describe the difference between the dynamic model and the real space environment.

[0036] Step 4: Train the network model to extract and learn the changing rules of the orbit prediction error sequence through the bidirectional long short-term memory network;

[0037] Step 5: Predict the orbit prediction error at future times, and use the trained neural network model to predict the orbit prediction error at future times;

[0038] Step 6: Compensate the prediction results. Use the network prediction error to compensate the orbit prediction results based on the dynamic model to obtain the corrected final satellite orbit prediction results.

[0039] Specifically, the step 1 includes:

[0040] Obtain the reference orbit and extract the precise orbit determination data of the navigation satellite based on the precise ephemeris released by the IGS organization as the reference orbit for satellite motion analysis ;

[0041] Specifically, the step 2 includes:

[0042] Dynamic orbit extrapolation: The on-orbit operation of a navigation satellite will be affected by a variety of perturbation factors. The dynamic model of the navigation satellite is established based on the EGM2008 Earth gravitational field model, the sun-moon three-body gravity under the JPL DE403 ephemeris, the solid tidal perturbation, and the spherical solar light pressure model. In the inertial system, the satellite's perturbed motion equation can be obtained from Newton's second law:

[0043] ,

[0044] in, is the resultant force vector of the perturbation force acting on the satellite in orbit, is the mass of the satellite, is the acceleration vector of the satellite motion.

[0045] Convert it into a first-order differential equation and solve it jointly with the first-order differential equation of satellite position, that is,

[0046] ,

[0047] in, is the satellite position vector, is the satellite velocity vector,

[0048] Known at a certain moment Initial position of satellite and initial velocity , the position and velocity of the satellite at any time can be solved by the RKF7(8) numerical integration method, and the extrapolated orbit based on the dynamic model can be obtained ;

[0049] Specifically, the step 3 includes:

[0050] Construct an orbit prediction error sequence, and make a difference between the reference orbit obtained in step 1 and step 2 and the dynamic extrapolated orbit to obtain the orbit prediction error based on the dynamic model under the J2000 geocentric inertia, that is,

[0051] ,

[0052] in, is the orbit prediction error, is the reference orbit extracted from the precise ephemeris, is the predicted orbit obtained by extrapolation based on the dynamic model.

[0053] Specifically, the step 4 includes:

[0054] Train the network model and construct a bidirectional long short-term memory network to extract the change law of the orbit prediction error sequence obtained in step 3. The bidirectional long short-term memory network is composed of two independent forward LSTMs and backward LSTMs, and the hidden states in the two directions are spliced ​​and output, such as Figure 2 As shown. The two LSTMs are responsible for processing the input time series data from the forward and reverse directions respectively, so as to better mine the associated features of the time series data and capture the contextual information in the sequence. Each of the long short-term memory units uses the cell state to accumulate past information in time as long-term memory, and uses the hidden state to transmit the information of the most recent unit as short-term memory. At the same time, the gate structure is introduced to add or delete information in the cell state, weigh the proportion of long-term and short-term memory, and control the effective flow of information. Its working principle is as follows:

[0055] ,

[0056] ,

[0057] ,

[0058] ,

[0059] ,

[0060] ,

[0061] in, express The input vector at time instant, , , Respectively Always forget the output values ​​of the gate, input gate, and output gate; , , Respectively moment-to-moment temporary cell state, output cell state, and hidden state; , , , is the weight coefficient of each gate, , , , is the bias term; is the sigmoid activation function, is the hyperbolic tangent activation function.

[0062] Set the number of hidden units, batch size, maximum number of iterations, initial learning rate, input sequence length, output sequence length and other parameters of the network, use the MSE function as the loss function, and perform back propagation iterative training through the Adam optimizer. The calculation method of the MSE loss function is as follows:

[0063] ,

[0064] in, To predict the sample size, , Respectively The predicted value and the true value of the predicted time series orbit error.

[0065] The working principle of Adam optimizer is:

[0066] ,

[0067] ,

[0068] ,

[0069] ,

[0070] ,

[0071] in, is the gradient at the current moment, , denote the first-order integral and second-order integral of the gradient, respectively. , Respectively , An unbiased estimate of represents the learning rate, , are hyperparameters that control the decay rates of the first-order moment and the second-order moment, , Indicates The hyperparameters of time steps, is a small positive number used to prevent the denominator from being zero.

[0072] Through the above steps, the bidirectional long short-term memory network can be used to mine the deep features of the orbit prediction error time series data, capture and learn the changing laws of the orbit prediction error, and thus predict the orbit error at future moments.

[0073] Specifically, the step 5 includes:

[0074] Predicting the orbit prediction error at future moments, based on the trained bidirectional long short-term memory network, The starting time is Historical true orbit prediction error data As input, it is obtained through a bidirectional long short-term memory network The orbit error prediction value at time , and one-step prediction is now completed. Next, the input sequence moves back one time series, and the orbit error prediction value obtained in the previous time series is Add it to the input sequence of this time series, and then get it through the bidirectional long short-term memory network The orbit error prediction value at time And so on, until all time series prediction tasks are completed.

[0075] Through the above steps, the high-precision orbit prediction task of the navigation satellite can be completed without refining the dynamic model.

[0076] Specifically, the step 6 includes:

[0077] Compensate the prediction result and get the orbit error value predicted by the network from step 5 , and compensate it to the extrapolated orbit based on the dynamic model at the corresponding time, and then the corrected satellite prediction orbit can be obtained. The principle of this process is as follows:

[0078] ,

[0079] in, is the satellite orbit corrected by the bidirectional long short-term memory network compensation, is the predicted orbit extrapolated based on the dynamic model, It is the track error value predicted by the bidirectional long short-term memory network output.

[0080] Through the above steps, the deficiency of the dynamic model that the difference between the dynamic model and the real space environment gradually increases with time can be effectively compensated, and the rapid divergence of errors can be suppressed.

[0081] The orbit prediction error before and after compensation by the bidirectional long short-term memory network is as follows: Figure 3 As shown. Among them, Figure 3 (a) is the orbit prediction X-axis error, Figure 3 (b) is the Y-axis error of orbit prediction, Figure 3 (c) is the Z-axis error of orbit prediction, Figure 3 (d) is the three-dimensional position prediction error in the inertial system. The dashed curve is the orbit prediction error obtained directly using the dynamic model, and the solid curve is the orbit prediction error after compensation and correction based on the bidirectional long short-term memory network.

[0082] The comparison of the maximum orbit error of a navigation satellite high-precision orbit prediction method based on a bidirectional long short-term memory network and a direct use of a dynamic model is shown in Table 1:

[0083] Table 1

[0084]

[0085] It should be understood by those skilled in the art that the embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program codes. The solutions in the embodiments of the present invention may be implemented in various computer languages, for example, object-oriented programming language Java and interpreted scripting language JavaScript, etc.

[0086] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0087] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0088] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0089] Although the preferred embodiments of the present invention have been described, those skilled in the art may make other changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention.

[0090] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

Claims

1. A navigation satellite high-precision orbit prediction method based on a bidirectional long short-term memory network, characterized in that: The steps include: Step 1: Obtain the reference orbit, and extract precise orbit determination data from the IGS precise ephemeris as the reference orbit for the navigation satellite's in-orbit motion; Step 2: Dynamic orbit extrapolation: By analyzing and modeling the perturbations of the navigation satellite in orbit, a satellite dynamics model is constructed to extrapolate the satellite's future orbit. Step 3: Construct an orbit prediction error sequence and compare the difference between the dynamically extrapolated orbit and the reference orbit in the precise ephemeris to describe the difference between the dynamic model and the real space environment. Step 4: Train the network model to extract and learn the changing rules of the orbit prediction error sequence through the bidirectional long short-term memory network; Step 5: Predict the orbit prediction error at future times, and use the trained neural network model to predict the orbit prediction error at future times; Step 6: Compensate the prediction results. Use the network prediction error to compensate the orbit prediction results based on the dynamic model to obtain the corrected final satellite orbit prediction results.

2. According to claim 1, a navigation satellite high-precision orbit prediction method based on a bidirectional long short-term memory network is characterized in that: In the dynamic orbit extrapolation of step 2, the navigation satellite in-orbit operation process will be affected by a variety of perturbation factors. The dynamic model of the navigation satellite is established using the 36th-order EGM2008 Earth gravitational field model, the sun-moon three-body gravity under the JPL DE403 ephemeris, the solid tidal perturbation, and the spherical solar light pressure model. In the inertial system, the satellite's perturbed motion equation can be obtained from Newton's second law: ， in, is the resultant force vector of the perturbation force acting on the satellite in orbit, is the mass of the satellite, is the acceleration vector of satellite motion; Convert it into a first-order differential equation and solve it jointly with the first-order differential equation of satellite position, namely: ， in, is the satellite position vector, is the satellite velocity vector, Known at a certain moment Initial position of satellite and initial velocity , the position and velocity of the satellite at any time can be solved by the RKF7(8) numerical integration method, and the extrapolated orbit based on the dynamic model can be obtained .

3. According to claim 1, a navigation satellite high-precision orbit prediction method based on a bidirectional long short-term memory network is characterized in that: The orbit prediction error sequence constructed in step 3 is obtained by subtracting the reference orbit and the dynamic extrapolated orbit obtained in steps 1 and 2 to obtain the orbit prediction error based on the dynamic model under the J2000 geocentric inertia, that is: ， in, is the orbit prediction error, is the reference orbit extracted from the precise ephemeris, is the predicted orbit obtained by extrapolation based on the dynamic model.

4. According to claim 3, a navigation satellite high-precision orbit prediction method based on a bidirectional long short-term memory network is characterized in that: The training network model in step 4 constructs a bidirectional long short-term memory network to extract and learn the changing law of the orbit prediction error sequence obtained in step 3; the bidirectional long short-term memory network is composed of two independent forward LSTMs and backward LSTMs, and the hidden states in two directions are spliced ​​and output; the two LSTMs are responsible for processing the input time series data from the forward and reverse directions respectively, so as to better mine the associated features of the time series data and capture the context information in the sequence; each long short-term memory unit uses the cell state to accumulate past information in time as long-term memory, and uses the hidden state to transmit the information of the nearest unit as short-term memory; at the same time, the gate structure is introduced to add or delete information in the cell state, weigh the proportion of long and short-term memory, and control the effective flow of information; Here’s how it works: ， ， ， ， ， ， in, express The input vector at time instant, , , Respectively Always forget the output values ​​of the gate, input gate, and output gate; , , Respectively moment-to-moment temporary cell state, output cell state, and hidden state; , , , is the weight coefficient of each gate, , , , is the bias term; is the sigmoid activation function, is the hyperbolic tangent activation function; Set the number of hidden units, batch size, maximum number of iterations, initial learning rate, input sequence length, output sequence length and other parameters of the network, use the MSE function as the loss function, and perform back-propagation iterative training through the Adam optimizer; the calculation method of the MSE loss function is as follows: ， in, To predict the number of samples, , Respectively The predicted value and true value of the predicted time series orbit error; The working principle of Adam optimizer is: ， ， ， ， ， in, is the gradient at the current moment, , denote the first-order integral and second-order integral of the gradient, respectively. , Respectively , An unbiased estimate of represents the learning rate, , are hyperparameters that control the decay rates of the first-order moment and the second-order moment, , Indicates The hyperparameters of time steps, is a small positive number used to prevent the denominator from being zero.

5. According to claim 4, a navigation satellite high-precision orbit prediction method based on a bidirectional long short-term memory network is characterized in that: The predicted orbit prediction error at the future time in step 5 is based on the trained bidirectional long short-term memory network. The starting time is Historical true orbit prediction error data As input, it is obtained through a bidirectional long short-term memory network The orbit error prediction value at time , at this point one step of prediction is completed, and then the input sequence moves back one time series, and the orbit error prediction value obtained in the previous time series is Add it to the input sequence of this time series, and then get it through the bidirectional long short-term memory network The orbit error prediction value at time ; And so on, until all time series prediction tasks are completed.

6. The method for high-precision orbit prediction of navigation satellites based on a bidirectional long short-term memory network according to claim 5 is characterized in that: The compensation prediction result in step 6 is the orbit error value predicted by the network obtained in step 5 , and compensate it to the extrapolated orbit based on the dynamic model at the corresponding time, and then the corrected satellite prediction orbit can be obtained. The principle of this process is as follows: ， in, is the satellite orbit corrected by the bidirectional long short-term memory network compensation, is the predicted orbit extrapolated from the dynamical model, It is the track error value predicted by the bidirectional long short-term memory network output.

7. A high-precision navigation satellite orbit prediction device based on a bidirectional long short-term memory network, characterized in that: Includes the following modules: The reference orbit acquisition module obtains the reference orbit and extracts the precise orbit determination data from the IGS precise ephemeris as the reference orbit for the navigation satellite's on-orbit motion; The motion orbit extrapolation module and dynamic orbit extrapolation module analyze and model the perturbations of the navigation satellite in orbit, build a satellite dynamics model, and extrapolate the satellite's motion orbit in the future. Error sequence construction module, which constructs orbit prediction error sequence and compares the difference between the dynamic extrapolated orbit and the reference orbit in the precise ephemeris, so as to describe the difference between the dynamic model and the real space environment; Network training module: training network model, extracting and learning the changing rules of orbit prediction error sequence through bidirectional long short-term memory network; The prediction module predicts the orbit prediction error at future times and uses the trained neural network model to predict the orbit prediction error at future times; The compensation module compensates the prediction results and uses the network prediction error to compensate the orbit prediction results based on the dynamic model to obtain the corrected final satellite orbit prediction results.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, the steps of a method for high-precision orbit prediction of a navigation satellite based on a bidirectional long short-term memory network as described in any one of claims 1 to 6 are implemented.

9. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of a method for high-precision orbit prediction of a navigation satellite based on a bidirectional long short-term memory network as described in any one of claims 1 to 6 are implemented.

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