Method and device for determining orbit prediction error, storage medium and product

Abstract

This disclosure relates to a method, apparatus, storage medium, and product for determining orbit prediction errors, and pertains to the field of satellite technology. The method for determining orbit prediction errors includes: constructing a target model, wherein the target model represents the relationship between the covariance matrices of any two adjacent time points, the relationship being determined based on correction parameters, including a first correction parameter corresponding to the orbit prediction model and a second correction parameter corresponding to an initial covariance matrix, the covariance matrix describing the error in the orbit prediction data, which is generated by the orbit prediction model; determining the values ​​of the correction parameters based on the orbit prediction data and orbit observation data; and determining the covariance matrix at the target time based on the target model, the values ​​of the correction parameters, and the initial covariance matrix.

Description

Technical Field

[0001] This disclosure relates to the field of satellite technology, and in particular to a method, apparatus, storage medium, and product for determining orbit prediction errors. Background Technology

[0002] Due to factors such as measurement errors and model errors, there will always be some error in the prediction of the orbits of spacecraft or space targets. Analyzing the prediction errors can help improve prediction accuracy. Summary of the Invention

[0003] One of the technical problems this disclosure aims to solve is: how to improve the accuracy of determining orbit prediction errors.

[0004] According to a first aspect of some embodiments of this disclosure, a method for determining orbit prediction error is provided, comprising: constructing a target model, wherein the target model is used to represent the relationship between the covariance matrices of any two adjacent time points, the relationship being determined based on correction parameters, the correction parameters including a first correction parameter corresponding to the orbit prediction model and a second correction parameter corresponding to an initial covariance matrix, the covariance matrix being used to describe the error of the orbit prediction data, the orbit prediction data being generated by the orbit prediction model; determining the values ​​of the correction parameters based on the orbit prediction data and orbit observation data; and determining the covariance matrix at a target time based on the target model, the values ​​of the correction parameters, and the initial covariance matrix.

[0005] In some embodiments, determining the value of the correction parameter based on orbit prediction data and orbit observation data includes: generating a parameter sample of the correction parameter; processing the parameter sample through a target model to obtain an error sample, wherein the error sample represents the simulation error of the orbit prediction data; training a neural network model based on the parameter sample and the error sample; generating error data based on the orbit prediction data and orbit observation data, wherein the error data represents the actual error of the orbit prediction data; and processing the error data through the trained neural network model to determine the value of the correction parameter.

[0006] In some embodiments, generating parameter samples of the correction parameters includes: determining the parameter space of the correction parameters; generating parameter samples by sampling in the parameter space of the correction parameters, wherein the parameter samples include sample values ​​of the first correction parameter at multiple sample times and sample values ​​of the second correction parameter.

[0007] In some embodiments, processing parameter samples through a target model to obtain error samples includes: processing the sample values ​​of the first correction parameter and the sample values ​​of the second correction parameter at multiple sample times through the target model to obtain a covariance matrix sample, wherein the covariance matrix sample corresponds to the next time time of the sample time; and determining the error sample based on the covariance matrix sample.

[0008] In some embodiments, generating parameter samples by sampling in the parameter space of the modified parameters includes: obtaining candidate parameter samples by sampling in the parameter space of the modified parameters; and generating parameter samples after performing anomaly processing on the candidate parameter samples.

[0009] In some embodiments, the parameter space of the first correction parameter is determined based on at least one of atmospheric drag and light pressure perturbation.

[0010] In some embodiments, adjacent time points are a first time point and a second time point, with the second time point being the next time point after the first time point; the relationship is expressed as follows: the covariance matrix of the second time point is equal to the covariance matrix of the first time point based on the congruent transformation of the state transition matrix and the value of the first correction parameter at the first time point, and the covariance matrix of the initial time point is the product of the initial covariance matrix and the second correction parameter, wherein the initial covariance matrix is ​​predetermined.

[0011] In some embodiments, the covariance matrix is ​​determined based on the error in orbital position and orbital velocity; the value of the first correction parameter at the first moment is determined based on the error in orbital position and orbital velocity caused by the first correction parameter at the first moment.

[0012] According to a second aspect of some embodiments of this disclosure, an apparatus for determining orbit prediction error is provided, comprising: a construction module configured to construct a target model, wherein the target model is used to represent the relationship between covariance matrices of any two adjacent time points, the relationship being determined based on correction parameters, the correction parameters including a first correction parameter corresponding to the orbit prediction model and a second correction parameter corresponding to an initial covariance matrix, the covariance matrix being used to describe the error of the orbit prediction data, the orbit prediction data being generated by the orbit prediction model; a first determination module configured to determine the values ​​of the correction parameters based on the orbit prediction data and orbit observation data; and a second determination module configured to determine the covariance matrix of a target time point based on the target model, the values ​​of the correction parameters, and the initial covariance matrix.

[0013] According to a third aspect of some embodiments of the present disclosure, an apparatus for determining orbit prediction errors is provided, comprising: a processor; and a memory coupled to the processor for storing instructions, which, when executed by the processor, cause the processor to perform the orbit observation error determination method as described above.

[0014] According to a fourth aspect of some embodiments of the present disclosure, a computer-readable storage medium is provided having computer instructions stored thereon, wherein the instructions, when executed by a processor, implement the method for determining orbit prediction errors as described above.

[0015] According to a fifth aspect of some embodiments of the present disclosure, a computer program product is provided, including instructions that, when executed by a processor, cause the processor to perform a method for determining orbit prediction errors as described above.

[0016] This disclosure constructs an evolutionary model of the covariance matrix by modifying parameters, including modification parameters for the orbit prediction model and modification parameters for the initial covariance matrix. This reduces the impact of insufficient accuracy of the initial covariance matrix and the orbit prediction model on the determination of orbit prediction errors, improves the accuracy of the evolutionary model, and thus improves the accuracy of determining orbit prediction errors.

[0017] Other features and advantages of this disclosure will become clear from the following detailed description of exemplary embodiments with reference to the accompanying drawings. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of this disclosure or 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 of this disclosure. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 A flowchart illustrating a method for determining orbit prediction errors according to some embodiments of the present disclosure is shown.

[0020] Figure 2 A schematic diagram showing the determination results of orbit prediction results according to some embodiments of the present disclosure is illustrated.

[0021] Figure 3 A schematic diagram showing the determination results of orbit prediction results according to other embodiments of this disclosure is illustrated.

[0022] Figure 4 A schematic diagram of a device for determining orbit prediction errors according to some embodiments of the present disclosure is shown.

[0023] Figure 5 A schematic diagram of the structure of an apparatus for determining orbit prediction errors according to other embodiments of the present disclosure is shown.

[0024] Figure 6 A schematic diagram of the structure of a device for determining orbit prediction errors according to some embodiments of the present disclosure is shown. Detailed Implementation

[0025] The technical solutions of the embodiments of this disclosure will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this disclosure, and not all embodiments. The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit this disclosure or its application or use. All other embodiments obtained by those skilled in the art based on the embodiments of this disclosure without creative effort are within the scope of protection of this disclosure.

[0026] Predicting the orbits of space targets or spacecraft, such as satellites, is typically achieved using orbit prediction models. After determining the initial orbit information, the orbit prediction model can extrapolate future orbit information and make predictions. Therefore, errors in the initial orbit information and errors in the orbit prediction model are sources of orbit prediction errors.

[0027] Furthermore, these errors accumulate and change over time due to the influence of various perturbations. For example, in the short term, the satellite's velocity changes relatively smoothly, and the orbit prediction error is relatively small. As time goes on, factors such as perturbations gradually accumulate, and the position and velocity errors of the orbit gradually increase, leading to a gradual decrease in the accuracy of the orbit prediction.

[0028] Orbit prediction errors are unavoidable. In this case, analyzing the evolution of orbit prediction errors can be used to correct the orbit prediction results.

[0029] Currently, orbit prediction errors can be calculated using error extrapolation methods based on orbit dynamics models, suitable for scenarios where initial orbit error information is available. This method includes linear propagation and nonlinear propagation. The linear propagation method is an analytical solution algorithm based on the state transition matrix, which uses the initial covariance matrix of the orbit prediction error and the state transition matrix to obtain the covariance matrix of the future orbit prediction error. The nonlinear propagation method, also known as the unscented transformation method, uses the Monte Carlo method to predict the orbit by simulating the initial orbit values ​​with the error distribution, and then statistically analyzes the error distribution of the orbit prediction results at the corresponding epochs, using this as the result of covariance evolution. The calculation results of the linear propagation method and the unscented transformation method are not significantly different.

[0030] Both linear propagation and unscented transformation methods rely on the accuracy of the initial covariance matrix. However, during orbit determination, the parameters for solving the initial covariance matrix often include some measurement errors and mechanical model errors, resulting in error values ​​that are often too small. This makes the initial covariance matrix unable to accurately describe the actual orbit state. Furthermore, both linear propagation and unscented transformation methods do not consider the errors in the orbit prediction model itself during the prediction process, leading to a slow error divergence rate in the prediction, which does not match the actual error propagation level.

[0031] Based on this, this disclosure provides a method for determining orbit prediction errors.

[0032] Figure 1 A flowchart illustrating a method for determining orbit prediction errors according to some embodiments of this disclosure is shown. Figure 1 As shown, the method of this embodiment includes steps S11 to S13.

[0033] In step S11, a target model is constructed, wherein the target model is used to represent the relationship between the covariance matrices of any two adjacent time points. This relationship is determined based on correction parameters, which include a first correction parameter corresponding to the orbit prediction model and a second correction parameter corresponding to the initial covariance matrix. The covariance matrix is ​​used to describe the error of the orbit prediction data, which is generated by the orbit prediction model.

[0034] The target model refers to the evolution model of the covariance matrix of orbit prediction errors. The target model represents the relationship between the covariance matrices of any two adjacent time points. In other words, after determining the covariance matrix at the initial time point, the covariance matrix at any future time point can be determined based on the target model.

[0035] When determining the target model, a first correction parameter corresponding to the orbit prediction model and a second correction parameter corresponding to the initial covariance matrix were considered. In other words, when determining the evolution model of orbit prediction error, both the orbit prediction error caused by insufficient accuracy of the orbit prediction model and the orbit prediction error caused by insufficient accuracy of the initial covariance matrix were considered. This way, the determined evolution model of orbit prediction error can more accurately reflect the evolution law of orbit prediction error.

[0036] In other words, the target model is based on determining the covariance matrix of future time steps according to the initial covariance matrix and the state transition matrix, and then setting correction parameters.

[0037] The first correction parameter for the orbit prediction model is determined based on the sources of error in the model. For example, a space target is affected by various perturbations during its orbital operation. The orbit prediction model is built upon these perturbation models. Some of these models lack accuracy, meaning that some perturbations affecting the space target cannot be accurately determined. Therefore, the first correction parameter can be set by determining the errors these perturbations cause to the satellite's orbit prediction, thus compensating for the impact of these perturbations on the orbit prediction error.

[0038] The initial covariance matrix is ​​generated during the orbit estimation process. Due to orbit observation errors and linearization, the initial covariance matrix is ​​generally not accurate enough. Therefore, the correction parameter of the initial covariance matrix, i.e. the second correction parameter, can be determined by analyzing the error factors that determine the initial covariance matrix.

[0039] The covariance matrix is ​​used to describe orbit prediction error information. For example, the covariance matrix at a certain moment can be the covariance matrix of the orbit's state error at that moment. The state error can be represented as position and velocity error.

[0040] In step S12, the values ​​of the correction parameters are determined based on the orbit prediction data and orbit observation data.

[0041] The target model mentioned above includes correction parameters. Once the correction parameters are determined, the covariance matrix at any future time can be determined based on the target model.

[0042] Orbit observation data and orbit prediction data are used to determine orbit prediction error data. That is, orbit prediction error data is the error data of orbit prediction data relative to orbit observation data. For example, high-precision, widely distributed, and dense orbit observation data can be obtained through modern space tracking technology. This orbit observation data can be used as "true" data on orbital motion to determine the error of orbit prediction data.

[0043] The target model, including correction parameters, can be solved using orbit prediction error data to obtain the values ​​of the correction parameters. For example, by sampling orbit prediction error data, the orbit prediction errors at multiple times can be determined, and the target model can be solved using these multiple time-time orbit prediction errors. That is, the covariance matrix at these multiple time times is determined based on the orbit prediction errors at these multiple times, and the values ​​of the correction parameters can be obtained by substituting these multiple time-time covariance matrices into the target model.

[0044] In step S13, the covariance matrix at the target time is determined based on the target model, the values ​​of the correction parameters, and the initial covariance matrix.

[0045] After determining the values ​​of the correction parameters, the target model becomes a function of time, thus enabling the determination of the covariance matrix at any future time, i.e., the target time.

[0046] This disclosure constructs an evolutionary model of the covariance matrix by modifying parameters, including modification parameters for the orbit prediction model and modification parameters for the initial covariance matrix. This reduces the impact of insufficient accuracy of the initial covariance matrix and the orbit prediction model on the determination of orbit prediction errors, improves the accuracy of the evolutionary model, and thus improves the accuracy of determining orbit prediction errors.

[0047] This disclosure is equivalent to constructing a unified evolutionary model of the covariance matrix, which includes correction parameters. The values ​​of these correction parameters can be calculated by combining orbital error data. This orbital error data is determined based on orbital observation data and orbital prediction data. In other words, after acquiring orbital observation data and orbital prediction data over a period of time, a specific evolutionary model of the covariance matrix can be determined. Subsequently, this specific evolutionary model can be used to determine the error of future orbital prediction data, without having to rely on obtaining orbital observation data to determine the error of the orbital prediction data.

[0048] For example, adjacent time points are the first time point and the second time point, where the second time point is the next time point after the first time point. In some embodiments, the above relationship is expressed as follows: the covariance matrix of the second time point is equal to the covariance matrix of the first time point based on the congruence transformation of the state transition matrix and the value of the first correction parameter at the first time point, and the covariance matrix of the initial time point is the product of the initial covariance matrix and the second correction parameter, wherein the initial covariance matrix is ​​predetermined.

[0049] In other words, the second correction parameter can be regarded as a constant coefficient, and the first correction parameter can be regarded as a time-dependent function coefficient.

[0050] For example, the target model can be represented by the following formula.

[0051]

[0052] in, For the first moment, This is the second time step. i can take any non-negative integer value. Let the initial covariance matrix be... Let be the covariance matrix at the initial time. The covariance matrix at time step 1. Let be the covariance matrix at the second time step. The value of the first correction parameter at the first moment is used to reflect... Time's up Errors in the orbit prediction models between different orbits. This is the second correction parameter. Let be the state transition matrix of the orbit from the first time step to the second time step.

[0053] In the aforementioned target model, the initial covariance matrix and state transition matrix are known, and the covariance matrix at any given time can be obtained after determining the correction parameters. The state transition matrix is ​​determined based on the orbit prediction model. The initial covariance matrix is ​​determined through precise orbit determination or based on historical experience. In other words, multiple sets of nonlinear equations for correcting the parameters can be constructed using the observation data used in orbit determination. Therefore, the problem of extrapolating and correcting orbit prediction errors is transformed into solving a system of nonlinear equations for correcting the parameters.

[0054] The aforementioned target model, by determining the relationship between the covariance matrices of adjacent time points, can accurately compensate for the errors of the orbit prediction model down to the time step. In other words, by using the time interval between two adjacent time points as the step size, and treating the error of the orbit prediction model within that step size as a constant, this also aligns with the scenario of nonlinear propagation in which the covariance matrix is ​​calculated linearly.

[0055] In some embodiments, determining the value of the correction parameter based on orbital observation data includes: generating a parameter sample of the correction parameter; processing the parameter sample through a target model to obtain an error sample, wherein the error sample represents the simulation error of the orbital prediction data; training a neural network model based on the parameter sample and the error sample; generating error data based on the orbital prediction data and orbital observation data, wherein the error data represents the actual error of the orbital prediction data; and processing the error data through the trained neural network model to determine the value of the correction parameter.

[0056] By training a neural network model using parameter samples and error samples, and then using the trained neural network model to determine the values ​​of the correction parameters, the accuracy of the determined correction parameters can be improved by leveraging the neural network model's ability to approximate nonlinear functions.

[0057] For example, a neural network model can be a back propagation (BP) neural network model. A BP neural network is a typical feedforward network, with an input layer, an output layer, and at least one hidden layer. Neurons in adjacent layers are fully connected, and the connection strength constitutes the network's weight matrix.

[0058] The basic principle of a backpropagation (BP) neural network is as follows: the input signal acts on the output node through the hidden layer nodes, and the output signal is generated through a nonlinear transformation. During BP neural network training, each sample is an input-output pair consisting of an input vector and the desired output vector. Before training, for each input vector, there is a deviation between the network's output value and the expected value. By adjusting the network's weight matrix, this deviation is reduced along the gradient direction. Through repeated training, the deviation is made to meet the network's requirements. After training, the network can use its weight matrix to determine the output information corresponding to the input information.

[0059] In the scenario described in this disclosure, error samples and parameter samples are used as input-output pairs to train a neural network model. Error data is then input into the trained neural network model to obtain the values ​​of the correction parameters corresponding to the error data. This process is equivalent to solving a system of nonlinear equations using a neural network model. This disclosure is essentially a neural network-based extrapolation correction method for orbit prediction errors. Building upon existing linear propagation methods, this disclosure leverages the ability of neural networks to approximate nonlinear functions, corrects the initial covariance matrix, and introduces model errors during the prediction process to further correct the prediction error, thereby obtaining prediction results that closely approximate the actual prediction error.

[0060] The core idea behind using neural networks to solve nonlinear equations is to transform the problem into an optimization problem, with the goal of finding the variable values ​​that minimize the error in the equation system. For example, a neural network can employ a two-layer structure: the input layer receives the variables from the equation system, and the output layer outputs the calculated results. Training is then used to make the output as close as possible to the ideal solution.

[0061] In other words, the correlation between error samples and parameter samples can be learned using a neural network model, i.e., the neural network model can be trained. Then, the trained neural network model can be used to calculate the correction parameters corresponding to the actual orbit prediction error data.

[0062] Here, error samples represent simulation errors in orbit prediction data. That is, parameter samples are input into the target model, and error samples are generated based on the target model. Since the parameter samples are simulated, the error samples are also simulated. The process of inputting parameter samples into the target model and generating error samples based on the target model is, for example, as follows: determine multiple sample times, determine the covariance matrix corresponding to these multiple sample times based on the target model, and then determine the error data corresponding to these multiple sample times based on the covariance matrix, which serves as the error samples.

[0063] When generating parameter samples, random sampling can be performed in the parameter space to generate multiple sets of parameter samples. By generating random samples covering the solution space as training data, the error of the equation system corresponding to each sample is calculated as the loss. The backpropagation algorithm is used to update the network parameters to minimize the loss, resulting in a trained neural network model. The trained neural network model can then use optimization algorithms to find the input that makes the network output closest to the ideal solution, which is the approximate solution to the equation system.

[0064] In some embodiments, generating parameter samples of the correction parameters includes: determining the parameter space of the correction parameters; generating parameter samples by sampling in the parameter space of the correction parameters, wherein the parameter samples include sample values ​​of the first correction parameter at multiple sample times and sample values ​​of the second correction parameter.

[0065] The parameter space of the correction parameters refers to the range of values ​​for the correction parameters. The first correction parameter is the correction parameter corresponding to the orbit prediction model, so the parameter space of the first correction parameter refers to the range of errors in orbit prediction caused by the errors of the orbit prediction model.

[0066] For example, the error of the orbit prediction model mainly depends on the refinement of the models of various perturbations acting on the space target. Except for atmospheric drag and radiation pressure perturbations, other perturbations have relatively mature and refined models, and their model errors have a negligible impact on the orbit. Therefore, the parameter space of the first correction parameter can be determined based on atmospheric drag and radiation pressure perturbations. In other words, the parameter space of the first correction parameter is determined based on at least one of atmospheric drag and radiation pressure perturbations.

[0067] The first correction parameter is a time-dependent function, so when determining the sample value of the first correction parameter, the sample value of the first correction parameter at multiple sample times is determined. For each sample time, the sample value of the first correction parameter is the error generated by the orbit prediction model on the orbit prediction data. Since the target model describes the relationship between the covariance matrices of the orbit prediction errors at adjacent times, the sample value of the first correction parameter can be expressed as the covariance matrix generated by the orbit prediction model. For example, in formula (1), the covariance matrix of the orbit prediction error at the second time ( The covariance matrix of the trajectory prediction error at the first moment is equal to the state transition matrix after a congruent transformation. After that, the covariance matrix generated by the orbit prediction model ( ) and .

[0068] In some embodiments, the covariance matrix is ​​determined based on the errors in orbital position and orbital velocity. The value of the first correction parameter at a first moment is determined based on the errors in orbital position and orbital velocity caused by the first correction parameter at that first moment.

[0069] Based on the characteristics of atmospheric drag and light pressure, the direction of atmospheric drag depends on the relative velocity between the space target and the atmosphere, while the direction of light pressure perturbation depends on the direction of illumination. For low-Earth orbit satellites, the perturbation error mainly originates from atmospheric drag, and the maximum error caused by atmospheric drag can be determined based on atmospheric density, satellite orbital speed, etc. Atmospheric drag generally acts in the T-direction (i.e., along the track direction), therefore, by constructing the atmospheric drag error in the T-direction, a simplified error in the orbit prediction model can be obtained.

[0070] For high-orbit satellites, the perturbation error mainly originates from the radiation pressure perturbation force. The maximum error generated by the radiation pressure perturbation force can be determined based on factors such as the radiation pressure surface-to-mass ratio. The radiation pressure perturbation force generally acts in the direction of illumination; therefore, a simplified error in the orbit prediction model can be obtained by constructing the radiation pressure perturbation force error in the direction of illumination.

[0071] For example, for low-Earth orbit satellites, the error in determining atmospheric drag will result in an error in the satellite's position and velocity. Then the covariance matrix that needs to be compensated within one step size is: .

[0072] This approach does not consider systematic biases, assuming that the expected value of the error caused by atmospheric drag on the satellite's position and velocity is zero, and uses the standard deviation of the error caused by atmospheric drag on the satellite's position and velocity as the error vector. Therefore, it is possible to determine the error vector. Determine the covariance matrix that needs to be compensated. In other words, this... It can be represented in the form of a covariance matrix.

[0073] In addition, here This only represents the statistical form of the covariance matrix calculation; the actual value is derived from the simplified model error. For example, for atmospheric drag, the forces in the track, radial, and normal directions can be considered uncorrelated. Therefore, the off-diagonal elements of the covariance matrix in a coordinate system with these three directions as axes are considered to be 0. That is, the covariance matrix is ​​a diagonal matrix, which is then transformed to an inertial coordinate system through coordinate transformation, and then used to calculate the covariance matrix of the orbit prediction error.

[0074] Of course, besides describing the orbital state through position and velocity, other parameters can also be used, such as the orbital elements, semi-major axis, eccentricity, orbital inclination, right ascension of the ascending node, argument of perigee, and true anomaly (or mean anomaly). In this case, the covariance matrix is ​​determined based on the error of the orbital elements, and the value of the first correction parameter at the first moment is determined based on the error that the first correction parameter introduces to the orbital elements at the first moment.

[0075] The second correction parameter is used to correct the initial covariance matrix. The parameter space of the second parameter can be set by determining the magnitude of deviation from the initial covariance matrix through statistical data analysis. For example, it can be set to (0, 10). If the second correction parameter is denoted as k, then the range of k is (0, 10).

[0076] In some embodiments, processing parameter samples through a target model to obtain error samples includes: processing the sample values ​​of the first correction parameter and the sample values ​​of the second correction parameter at multiple sample times through the target model to obtain a covariance matrix sample, wherein the covariance matrix sample corresponds to the next time time of the sample time; and determining the error sample based on the covariance matrix sample.

[0077] By substituting the second correction parameter, the first correction parameter, and their corresponding sample times into the target model, the covariance matrix corresponding to the next time step of the sample time can be obtained, and the error corresponding to the covariance matrix can be determined and used as the error sample.

[0078] For example, the covariance matrix at the next time step after determining the sample time is: .

[0079] Then the error sample can be set to Here, systematic bias is not considered, and the expected value of the error is assumed to be 0. Therefore, the standard deviation of the error can be determined based on the diagonal elements of the covariance matrix, and this standard deviation can be used as the error sample vector.

[0080] The neural network model is trained using error samples and parameter samples. Finally, the trained neural network model is used to process the orbit prediction error data determined based on orbit observation data and orbit prediction data to obtain the values ​​of the correction parameters.

[0081] The process of generating parameter samples described above also includes steps such as anomaly handling. In some embodiments, generating parameter samples by sampling in the parameter space of the corrected parameters includes: obtaining candidate parameter samples by sampling in the parameter space of the corrected parameters; and generating parameter samples after anomaly handling of the candidate parameter samples.

[0082] Random sampling may result in outliers. For example, samples with errors exceeding a threshold, such as more than five times the residual, can be considered invalid and discarded. The residual here is set based on the historical orbit prediction error values.

[0083] The above embodiments describe the process of determining the target model in this disclosure. The accuracy of the target model is described below with reference to two specific cases. These two cases use a medium-high orbit satellite (denoted as Satellite 1) and a low orbit satellite (denoted as Satellite 2) as test subjects. The orbital parameters of the test satellites are shown in Table 1.

[0084] Table 1

[0085] The ephemeris data for Satellite 1 was selected from September 25, 2018 to September 3, 2018. The data from the first day was used for orbit determination, and the calculated orbital parameters are shown in Table 2.

[0086] Table 2

[0087] The initial covariance matrix is:

[0088] Satellite 2 uses ephemeris data from January 1, 2002 to January 3, 2002. The data from the first day is used for orbit determination. The calculated orbital parameters are shown in Table 3.

[0089] Table 3

[0090] The initial covariance matrix is:

[0091] Figure 2 A schematic diagram showing the determination results of orbit prediction results according to some embodiments of the present disclosure is illustrated. Figure 2 For the satellite 1 test scenario, Figure 2 21 in the figure is a comparison between the orbit prediction error calculated using existing theoretical methods and the actual orbit prediction error. Figure 2 22 in the figure is a comparison between the orbit prediction error calculated using the method of this disclosure and the actual orbit prediction error. Figure 2 In this context, 211 represents the actual orbit prediction error, 212 represents the orbit prediction error calculated using existing theoretical methods, and 213 represents the orbit prediction error calculated using the method of this disclosure.

[0092] Figure 3 A schematic diagram showing the determination results of orbit prediction results according to other embodiments of this disclosure is illustrated. Figure 3 For the Satellite 2 test scenario, Figure 3 31 in the figure is a comparison between the orbit prediction error calculated using existing theoretical methods and the actual orbit prediction error. Figure 3 32 in the figure is a comparison between the orbit prediction error calculated using the method of this disclosure and the actual orbit prediction error. Figure 3 In this context, 311 represents the actual orbit prediction error, 312 represents the orbit prediction error calculated using existing theoretical methods, and 313 represents the orbit prediction error calculated using the method of this disclosure.

[0093] It can be seen that the method disclosed in this paper is a significant improvement over the existing theoretical methods, and can basically approach the actual orbit prediction error with very high accuracy.

[0094] Figure 4 A schematic diagram of a device for determining orbit prediction errors according to some embodiments of the present disclosure is shown. Figure 4 As shown, the first determination device 4 for orbit prediction error includes: a construction module 41 configured to construct a target model, wherein the target model is used to represent the relationship between the covariance matrices of any two adjacent time points, the relationship being determined based on correction parameters, the correction parameters including a first correction parameter corresponding to the orbit prediction model and a second correction parameter corresponding to the initial covariance matrix, the covariance matrix being used to describe the error of the orbit prediction data, the orbit prediction data being generated by the orbit prediction model; a first determination module 42 configured to determine the values ​​of the correction parameters based on the orbit prediction data and the orbit observation data; and a second determination module 43 configured to determine the covariance matrix at the target time based on the target model, the values ​​of the correction parameters, and the initial covariance matrix.

[0095] In some embodiments, the first determining module 42 is configured to generate parameter samples of correction parameters; process the parameter samples through the target model to obtain error samples, wherein the error samples represent the simulated error of the orbit prediction data; train the neural network model based on the parameter samples and error samples; generate error data based on the orbit prediction data and orbit observation data, wherein the error data represent the actual error of the orbit prediction data; and process the error data through the trained neural network model to determine the value of the correction parameters.

[0096] In some embodiments, the first determining module 42 is configured to determine the parameter space of the correction parameter; and generate parameter samples by sampling the parameter space of the correction parameter, wherein the parameter samples include sample values ​​of the first correction parameter at multiple sample times and sample values ​​of the second correction parameter.

[0097] In some embodiments, the first determining module 42 is configured to process the sample values ​​of the first correction parameter and the sample values ​​of the second correction parameter at multiple sample times through the target model to obtain a covariance matrix sample, wherein the covariance matrix sample corresponds to the next time time of the sample time; and to determine an error sample based on the covariance matrix sample.

[0098] In some embodiments, the first determining module 42 is configured to obtain candidate parameter samples by sampling in the parameter space of the corrected parameters; and to generate parameter samples after anomaly processing of the candidate parameter samples.

[0099] In some embodiments, the parameter space of the first correction parameter is determined based on at least one of atmospheric drag and light pressure perturbation.

[0100] In some embodiments, adjacent time points are a first time point and a second time point, with the second time point being the next time point after the first time point; the relationship is expressed as follows: the covariance matrix of the second time point is equal to the covariance matrix of the first time point based on the congruent transformation of the state transition matrix and the value of the first correction parameter at the first time point, and the covariance matrix of the initial time point is the product of the initial covariance matrix and the second correction parameter, wherein the initial covariance matrix is ​​predetermined.

[0101] In some embodiments, the covariance matrix is ​​determined based on the error in orbital position and orbital velocity; the value of the first correction parameter at the first moment is determined based on the error in orbital position and orbital velocity caused by the first correction parameter at the first moment.

[0102] This disclosure constructs an evolutionary model of the covariance matrix by modifying parameters, including modification parameters for the orbit prediction model and modification parameters for the initial covariance matrix. This reduces the impact of insufficient accuracy of the initial covariance matrix and the orbit prediction model on the determination of orbit prediction errors, improves the accuracy of the evolutionary model, and thus improves the accuracy of determining orbit prediction errors.

[0103] The device for determining the orbit prediction error in the embodiments of this disclosure can be implemented by various computing devices or computer systems, as described below. Figure 5 as well as Figure 6 Describe it.

[0104] Figure 5 A schematic diagram of a device for determining orbit prediction errors according to other embodiments of this disclosure is shown. Figure 5 As shown, the second device for determining orbit prediction error in this embodiment includes: a first memory 51 and a first processor 52 coupled to the first memory 51. The first processor 52 is configured to execute the orbit prediction error determination method in any of the embodiments of this disclosure based on instructions stored in the first memory 51.

[0105] The first memory 51 may include, for example, system memory, fixed non-volatile storage medium, etc. The system memory stores, for example, the operating system, application programs, boot loader, database, and other programs.

[0106] Figure 6 A schematic diagram of a device for determining orbit prediction errors according to some embodiments of the present disclosure is shown. Figure 6As shown, the third device 6 for determining orbit prediction errors in this embodiment includes a second memory 61 and a second processor 62, which are similar to the first memory 51 and the first processor 52, respectively. It may also include an input / output interface 63, a network interface 64, a storage interface 65, etc. These interfaces 63, 64, 65, the second memory 61, and the second processor 62 can be connected, for example, via a bus 66. The input / output interface 63 provides a connection interface for input / output devices such as displays, mice, keyboards, and touchscreens. The network interface 64 provides a connection interface for various networked devices, such as database servers or cloud storage servers. The storage interface 65 provides a connection interface for external storage devices such as SD cards and USB flash drives.

[0107] Embodiments of this disclosure also provide a computer-readable storage medium having a computer program stored thereon, characterized in that, when the program is executed by a processor, it implements any of the aforementioned methods for determining orbit prediction errors.

[0108] Embodiments of this disclosure also provide a computer program product including instructions that, when executed by a processor, cause the processor to perform a method for determining orbit prediction errors according to any of the foregoing methods.

[0109] Those skilled in the art will understand that embodiments of this disclosure can be provided as methods, systems, or computer program products. Therefore, this disclosure can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this disclosure can take the form of a computer program product embodied on one or more computer-usable non-transitory storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0110] This disclosure is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this disclosure. It should be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create a machine for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0111] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0112] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0113] The above description is only a preferred embodiment of this disclosure and is not intended to limit this disclosure. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this disclosure should be included within the protection scope of this disclosure.

Claims

1. A method for determining orbit prediction error, comprising: A target model is constructed, wherein the target model is used to represent the relationship between the covariance matrices of any two adjacent time points, the relationship being determined based on correction parameters, the correction parameters including a first correction parameter corresponding to the orbit prediction model and a second correction parameter corresponding to the initial covariance matrix, the covariance matrix being used to describe the error of the orbit prediction data, the orbit prediction data being generated by the orbit prediction model; The value of the correction parameter is determined based on the orbit prediction data and orbit observation data; Based on the target model, the values ​​of the correction parameters, and the initial covariance matrix, the covariance matrix at the target time is determined.

2. The determination method according to claim 1, wherein, Determining the value of the correction parameter based on the orbital prediction data and the orbital observation data includes: Generate a parameter sample of the corrected parameters; The parameter samples are processed by the target model to obtain error samples, wherein the error samples represent the simulation error of the orbit prediction data; The neural network model is trained based on the parameter samples and the error samples; Error data is generated based on the orbit prediction data and the orbit observation data, wherein the error data represents the actual error of the orbit prediction data; The error data is processed by the trained neural network model to determine the value of the correction parameter.

3. The determination method according to claim 2, wherein, The parameter samples used to generate the corrected parameters include: Determine the parameter space of the correction parameters; The parameter sample is generated by sampling in the parameter space of the correction parameter, wherein the parameter sample includes the sample values ​​of the first correction parameter at multiple sample times and the sample values ​​of the second correction parameter.

4. The determination method according to claim 3, wherein, The error samples are obtained by processing the parameter samples through the target model, including: The target model processes the sample values ​​of the first correction parameter at multiple sample times and the sample values ​​of the second correction parameter to obtain a covariance matrix sample, wherein the covariance matrix sample corresponds to the next time time of the sample time. The error sample is determined based on the covariance matrix sample.

5. The determination method according to claim 3, wherein, Generating the parameter samples by sampling in the parameter space of the corrected parameters includes: Candidate parameter samples are obtained by sampling in the parameter space of the corrected parameters; After anomaly processing of the candidate parameter samples, the parameter samples are generated.

6. The determining method according to claim 3, wherein, The parameter space of the first correction parameter is determined based on at least one of atmospheric drag and light pressure perturbation.

7. The determining method according to any one of claims 1 to 6, wherein, The adjacent moments are the first moment and the second moment, and the second moment is the moment following the first moment; The relationship is expressed as follows: the covariance matrix at the second time step is equal to the covariance matrix at the first time step, which is the sum of the covariance matrix at the first time step based on the congruence transformation of the state transition matrix and the value of the first correction parameter at the first time step; and the covariance matrix at the initial time step is the product of the initial covariance matrix and the second correction parameter, wherein the initial covariance matrix is ​​predetermined.

8. The determination method according to claim 7, wherein, The covariance matrix is ​​determined based on the errors in orbital position and orbital velocity; The value of the first correction parameter at the first moment is determined based on the error in the orbital position and the orbital velocity caused by the first correction parameter at the first moment.

9. A device for determining orbit prediction error, comprising: The construction module is configured to construct a target model, wherein the target model is used to represent the relationship between the covariance matrices of any two adjacent time points, the relationship being determined based on correction parameters, the correction parameters including a first correction parameter corresponding to the orbit prediction model and a second correction parameter corresponding to the initial covariance matrix, the covariance matrix being used to describe the error of the orbit prediction data, the orbit prediction data being generated by the orbit prediction model; The first determining module is configured to determine the value of the correction parameter based on the orbit prediction data and the orbit observation data; The second determining module is configured to determine the covariance matrix at the target time based on the target model, the value of the correction parameter, and the initial covariance matrix.

10. A device for determining orbit prediction error, comprising: processor; as well as A memory coupled to the processor is used to store instructions that, when executed by the processor, cause the processor to perform the method for determining orbit prediction errors as described in any one of claims 1 to 8.

11. A computer-readable storage medium having computer instructions stored thereon, wherein, When executed by the processor, this instruction implements the method for determining the orbit prediction error as described in any one of claims 1 to 8.

12. A computer program product comprising instructions that, when executed by a processor, cause the processor to perform a method for determining orbit prediction error according to any one of claims 1 to 8.

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