Spacecraft inter-satellite closest approach time calculation method based on neural network

Abstract

The application discloses a spacecraft inter-satellite closest time moment calculation method based on a neural network, and comprises the following steps: acquiring different initial state data of a spacecraft, calculating corresponding inter-satellite closest time moments, and jointly forming an inter-satellite closest time moment data set; constructing a spacecraft inter-satellite closest time moment calculation neural network model according to the inter-satellite closest time moment data set and performing neural network training; substituting target initial state data of the spacecraft into the trained spacecraft inter-satellite closest time moment calculation neural network model to perform calculation, and obtaining a spacecraft inter-satellite closest time moment calculation result. The spacecraft inter-satellite closest time moment calculation model constructed by the application can quickly calculate the spacecraft inter-satellite closest time moment with a small calculation error through the network trained in advance after acquiring the initial state parameters of the target spacecraft.

Description

Technical Field

[0001] This invention belongs to the field of aerospace space safety early warning technology, and relates to a method for calculating the closest time between spacecraft based on neural networks. Background Technology

[0002] With the rapid development and widespread application of aerospace technology, the number of spacecraft is constantly increasing, mission capabilities are rapidly improving, the space environment is becoming more complex, the process of space militarization is accelerating, a space combat system has been initially established, space countermeasure weapons and equipment have emerged and developed rapidly, and attack tests against space systems are frequently conducted, posing a great threat to space security.

[0003] Meanwhile, with the increase in human space activities, the amount of waste released during space missions, debris from spacecraft disintegration or collisions, and the number of abandoned spacecraft are continuously increasing, posing a significant challenge to the safety of space systems. Space debris, also known as orbital debris, is junk generated by human activities in space, mainly including rocket bodies used to launch satellites, spacecraft that have exceeded their operational lifespan, and fragments generated by collisions between objects in space. Currently, a large proportion of spacecraft have deorbited due to launch failures or the expiration of their service life, becoming space debris and a major source of pollution to the space environment. Furthermore, with the continued increase in the number of human space activities, the amount of space debris will further increase, posing a serious threat to spacecraft operating normally in orbit and creating a significant threat to space safety.

[0004] The escalating space confrontations and the increasing amount of space debris both demonstrate the significant threats to current space security, making attention to space safety issues essential. Avoiding collisions with other space targets is a fundamental requirement for spacecraft orbiting during space missions. During close relative motion, the short distances between spacecraft increase the risk of collision, placing even greater demands on trajectory safety. To achieve this basic requirement of avoiding collisions with other space targets, the calculation of relative distances is extremely important, with the calculation of the minimum inter-spacecraft distance and the closest point of inter-spacecraft proximity being particularly critical issues that need to be addressed.

[0005] Currently, the problem of calculating the minimum inter-satellite distance is typically solved using intelligent search algorithms (genetic algorithms, particle swarm optimization, etc.) and iterative algorithms. However, these methods cannot simultaneously balance computational efficiency and accuracy, and the results may be locally optimal. Calculating the closest inter-satellite moment is also quite complex. On the one hand, errors in the minimum inter-satellite distance calculation may lead to errors in the calculated closest inter-satellite moment; on the other hand, in some cases, the closest inter-satellite moment problem may have multiple solutions, resulting in calculation errors. Summary of the Invention

[0006] The purpose of this invention is to provide a method for calculating the closest time between spacecraft based on neural networks, which solves the problems of low calculation efficiency and accuracy and certain errors in existing technologies.

[0007] To achieve the above objectives, the present invention employs the following technical solution:

[0008] A method for calculating the closest inter-satellite moment for spacecraft based on neural networks includes the following steps:

[0009] Acquire data on different initial states of the spacecraft, calculate the corresponding inter-satellite closest moments, and compile an inter-satellite closest moment dataset.

[0010] Based on the inter-satellite closest moment dataset, a neural network model for calculating the inter-satellite closest moment of a spacecraft was constructed and trained.

[0011] The initial state data of the spacecraft target is substituted into the trained neural network model for calculating the closest time between spacecraft and satellites to obtain the calculation result of the closest time between spacecraft and satellites.

[0012] Furthermore, the calculation process for the inter-satellite closest moment is as follows:

[0013] Choosing a reference spacecraft orbit and assuming a near-circular orbit, we obtain the analytical solution of the CW equation in coordinate component form:

[0014]

[0015] Where n represents the orbital angular velocity of the primary star around the Earth, x0 represents the initial position component of the spacecraft along the x-axis, y0 represents the initial position component of the spacecraft along the y-axis, and z0 represents the initial position component of the spacecraft along the z-axis. This represents the initial velocity component along the x-axis of the orbiting spacecraft. This represents the initial velocity component along the y-axis of the orbiting spacecraft. This represents the initial velocity component along the z-axis of the orbiting spacecraft;

[0016] Interstellar distance is defined as Substituting the analytical solution of the coordinate component form of the CW equation into the inter-satellite distance formula, we obtain the relationship between the inter-satellite distance of the spacecraft and the initial state of the target spacecraft and time t.

[0017] The initial state parameters of the target spacecraft are randomly generated, denoted as... The time t corresponding to the minimum inter-satellite distance is obtained by iterating through the inter-satellite distance D using the orbital recursion method. Dmin .

[0018] Furthermore, the dataset of the closest inter-satellite moments is as follows:

[0019]

[0020] Where x represents the radial position component of the orbit in the relative coordinate system, y represents the directional position component in the relative coordinate system, and z represents the directional position component of the orbit's angular momentum in the relative coordinate system. This represents the radial velocity component of the orbit in the relative coordinate system. This represents the velocity component in the direction of flight in a relative coordinate system. t represents the velocity component in the direction of the orbital angular momentum in the relative coordinate system. Dmin This indicates the closest inter-satellite moment after the initial state parameters of the target spacecraft have been determined.

[0021] Furthermore, the construction process of the neural network model for calculating the closest inter-satellite moment is as follows:

[0022] The inter-satellite closest moment dataset is divided into training set, validation set and test set, and the data in the inter-satellite closest moment dataset is normalized according to category.

[0023] Determine the information and number of input layer nodes, hidden layer nodes, and output layer nodes of the neural network, as well as the activation functions between each layer.

[0024] Furthermore, the ratio of the training set, validation set, and test set is 90:5:5.

[0025] Furthermore, the normalization process is as follows:

[0026] The data in the dataset is transformed into values ​​between [-1, 1] according to their categories, using the min-max method, as shown in the following formula:

[0027]

[0028] Where x represents the input data, x max x represents the maximum value in the data sequence. min y represents the minimum value in the data sequence. min y represents the minimum value in the normalized data sequence. max This represents the maximum value in the normalized data sequence.

[0029] Furthermore, the input layer nodes of the neural network contain relative position and relative velocity information.

[0030] Furthermore, the output layer node represents the closest moment between satellites, and both the hidden layer activation function and the output layer activation function employ the Sigmoid function.

[0031] Furthermore, the training process of the neural network model for calculating the closest inter-satellite moment is as follows:

[0032] The neural network is trained and its parameters are updated using the training set data. The validation set is used for verification. If the preset requirements are met, the next step is performed; otherwise, the iteration count is updated and the iteration continues.

[0033] After the neural network is trained, the neural network parameters are fixed to obtain the neural network model for calculating the closest time between spacecraft and satellites.

[0034] Furthermore, the steps for training the neural network are as follows:

[0035] The neural network parameters are initialized, and the training data is processed through the neural network structure to obtain the output value. The error between the output value and the corresponding labeled data in the labeled dataset is calculated using the MSE loss function. The error is then backpropagated to the neural network using the chain rule. At the same time, the weights and bias parameters of the neural network are updated using the gradient descent method.

[0036] Compared with the prior art, the present invention has the following beneficial effects:

[0037] This invention provides a neural network-based method for calculating the closest inter-satellite distance between spacecraft. It calculates the initial state parameters of the target spacecraft and outputs the closest inter-satellite distance. By setting different weight parameters, training, validation, and test datasets are established. Using the constructed spacecraft closest inter-satellite distance calculation model, the initial state parameters of the target spacecraft are calculated and the closest inter-satellite distance is output. This neural network-based method obtains the relationship between the initial state parameters of the target spacecraft and the closest inter-satellite distance through network training, enabling rapid calculation of the minimum inter-satellite distance even in complex situations.

[0038] The inter-satellite closest moment calculation model constructed in this invention can quickly calculate the inter-satellite closest moment after obtaining the initial state parameters of the target spacecraft through a pre-trained network, with relatively small calculation errors. Furthermore, due to the characteristics of neural network methods, the trained inter-satellite closest moment calculation model actually provides an approximate "analyzed" functional relationship between the initial state of the target spacecraft and the closest moment under natural evolution. Therefore, the model's computational efficiency can be guaranteed under any circumstances. Moreover, because it is an approximate "analyzed" functional relationship, the model has lower computational requirements, thus reducing calculation errors to some extent while improving computational efficiency.

[0039] Furthermore, by normalizing the data in the dataset, that is, transforming the data into data between [-1, 1], the difference in magnitude between the data in each dimension can be eliminated, thus avoiding large prediction errors in the network due to large differences in the magnitude of the input data. Attached Figure Description

[0040] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0041] Figure 1 This is a flowchart of the method for calculating the closest inter-satellite moment of a spacecraft based on a neural network, according to the present invention.

[0042] Figure 2 The relative motion trajectory curve provided for an embodiment of the present invention after giving relevant parameters.

[0043] Figure 3 A schematic diagram of the closest inter-satellite moment provided for embodiments of the present invention.

[0044] Figure 4 The neural network loss curve provided for an embodiment of the present invention.

[0045] Figure 5 Flowchart for constructing the inter-satellite closest moment calculation model of the present invention; Detailed Implementation

[0046] The following description, in conjunction with the accompanying drawings, illustrates exemplary embodiments of this application, including various details to aid understanding. These should be considered merely exemplary. Therefore, those skilled in the art will recognize that various changes and modifications can be made to the embodiments described herein without departing from the scope and spirit of this application. Similarly, for clarity and brevity, descriptions of well-known functions and structures are omitted in the following description.

[0047] Obviously, the described embodiments are only some, not all, of the embodiments in this application. All other embodiments obtained by those skilled in the art based on the embodiments in this application without inventive effort are within the scope of protection of this application.

[0048] Furthermore, the term "and / or" in this article is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, or B existing alone. Additionally, the character " / " in this article generally indicates that the preceding and following related objects have an "or" relationship.

[0049] The present invention will now be described in further detail with reference to the accompanying drawings:

[0050] See Figure 1 This invention provides a method for calculating the closest inter-satellite moment based on neural networks, comprising the following steps:

[0051] S1: Acquire data on different initial states of the spacecraft, calculate the corresponding inter-satellite closest moments, and combine them to form an inter-satellite closest moment dataset.

[0052] Initial state data is generated for different initial states of the target spacecraft, and an inter-satellite closest moment dataset is constructed. The specific steps are as follows:

[0053] After selecting a reference spacecraft orbit, assuming a near-circular orbit, we obtain the analytical solution of the CW equation in coordinate component form:

[0054]

[0055] Where n represents the orbital angular velocity of the primary star around the Earth, x0 represents the initial position component of the spacecraft along the x-axis, y0 represents the initial position component of the spacecraft along the y-axis, and z0 represents the initial position component of the spacecraft along the z-axis. This represents the initial velocity component along the x-axis of the orbiting spacecraft. This represents the initial velocity component along the y-axis of the orbiting spacecraft. This represents the initial velocity component along the z-axis surrounding the spacecraft.

[0056] Interstellar distance is defined as Substituting the analytical solution of the coordinate components of the CW equation into the inter-satellite distance formula, we obtain the relationship between the inter-satellite distance of the spacecraft and the initial state of the target spacecraft and time t.

[0057] Randomly generate initial state parameters for the target spacecraft, and denote these randomly generated initial state parameters as follows: Then, the time t corresponding to the minimum inter-satellite distance is obtained by iterating through the inter-satellite distance D using the orbital recursion method. Dmin .

[0058] Constructing a dataset of interstellar closest moments:

[0059]

[0060] Where x represents the radial position component of the orbit in the relative coordinate system, y represents the directional position component in the relative coordinate system, and z represents the directional position component of the orbit's angular momentum in the relative coordinate system. This represents the radial velocity component of the orbit in the relative coordinate system. This represents the velocity component in the direction of flight in a relative coordinate system. t represents the velocity component in the direction of the orbital angular momentum in the relative coordinate system. Dmin This indicates the closest inter-satellite moment after the initial state parameters of the target spacecraft have been determined.

[0061] S2: As Figure 5 As shown, a neural network model for calculating the closest inter-satellite moment is constructed based on the inter-satellite closest moment dataset, and the neural network is trained.

[0062] Data was randomly selected from the inter-satellite closest moment dataset to construct training, validation and test sets, with a ratio of 90:5:5.

[0063] The training data is obtained by normalizing the data in the dataset. The specific steps are as follows:

[0064] The data in the dataset is transformed into values ​​between [-1, 1] according to their categories. The data normalization method used is the min-max method, and the formula is as follows:

[0065]

[0066] Where x is the input data, x max Let x be the maximum value in the data sequence. min Let y be the minimum value in the data sequence. min Let y be the minimum value in the normalized data sequence. max It represents the maximum value in the normalized data sequence.

[0067] The specific steps for determining the information and number of input layer nodes, hidden layer nodes, and output layer nodes of a neural network, as well as the activation functions between each layer, are as follows:

[0068] The input nodes of the neural network model for determining the minimum inter-satellite distance are relative position and relative velocity information, with 6-dimensional nodes. The hidden layer consists of three layers, each with 25 nodes, for a total of 75 nodes. The output node is the closest moment between the two satellites, with 1-dimensional nodes. The activation functions for both the hidden and output layers are Sigmoid functions.

[0069] The specific steps for training a neural network on the training set data and updating the neural network parameters are as follows:

[0070] The neural network parameters are initialized, and the training data is processed through the neural network structure to obtain the output value. The error between the output value and the corresponding labeled data in the labeled dataset is calculated using the MSE loss function. The error is then backpropagated to the neural network using the chain rule. At the same time, the weights and bias parameters of the neural network are updated using the gradient descent method.

[0071] The validation set is used for verification. If the preset requirements are met, the next step is continued; otherwise, the iteration count is updated and the iteration continues.

[0072] Complete the neural network training, solidify the neural network parameters, and obtain the neural network model for calculating the closest inter-satellite moment.

[0073] S3: Substitute the initial state data of the spacecraft target into the trained spacecraft inter-satellite closest moment calculation neural network model to obtain the calculation result of the spacecraft inter-satellite closest moment.

[0074] Example 1:

[0075] The method for calculating the closest inter-satellite moment provided in this embodiment includes the following steps:

[0076] Data on different initial states of spacecraft are acquired, and the corresponding inter-satellite closest moments are calculated to form an inter-satellite closest moment dataset.

[0077] Based on the different initial state parameters of the target spacecraft, corresponding data are generated, and the closest inter-satellite moments are calculated to construct an inter-satellite closest moment dataset (DataSet).

[0078] The reference spacecraft orbit is selected as a GEO orbit with an altitude of h = 35786 km. The distance between the target spacecraft and the reference spacecraft is much smaller than the reference orbit altitude. Assuming a near-circular orbit, the analytical solution of the CW equation in coordinate component form is obtained as follows:

[0079]

[0080] Given the relevant parameters, the relative motion trajectory curve is as follows: Figure 2 As shown, the interstellar distance is defined as Substituting the analytical solution of the coordinate components of the CW equation into the inter-satellite distance formula, we obtain the relationship between the inter-satellite distance of the spacecraft and the initial state of the target spacecraft and time t.

[0081] One million sets of initial state parameters for the target spacecraft were randomly generated. To approximate reality, the initial relative position parameters of the target spacecraft in the three coordinate directions were randomly generated between [-100km, 100km], satisfying the close-range applicability conditions of the CW equation. The one million sets of initial relative position information are as follows: Figure 3As shown; the initial relative velocity parameters in the three coordinate directions are randomly generated between [-1 m / s, 1 m / s]. The randomly generated initial state parameters of the target spacecraft are denoted as... Then, using the orbital recursion method, the inter-satellite closest moments corresponding to 1 million sets of initial state parameters are traversed and calculated within the time range of [-10T, 10T] to obtain the corresponding inter-satellite closest moment t. Dmin data.

[0082] Constructing a minimum interstellar distance dataset:

[0083]

[0084] Where x represents the radial position component of the orbit in the relative coordinate system, y represents the directional position component in the relative coordinate system, and z represents the directional position component of the orbit's angular momentum in the relative coordinate system. This represents the radial velocity component of the orbit in the relative coordinate system. This represents the velocity component in the direction of flight in a relative coordinate system. t represents the velocity component in the direction of the orbital angular momentum in the relative coordinate system. Dmin This indicates the closest inter-satellite moment under the determined initial state parameters of the target spacecraft.

[0085] Based on the inter-satellite closest moment dataset, a neural network model for calculating the inter-satellite closest moment was constructed and trained.

[0086] Data was randomly selected from the inter-satellite closest moment dataset (DataSet) in a 90:5:5 ratio to construct the training dataset, validation dataset, and test dataset. There are a total of 1 million sets of minimum inter-satellite distance data. 900,000 sets were randomly selected as training data for network training, and 50,000 sets were used as validation data to verify the network training effect. Training was completed ahead of schedule when the preset conditions were met, and the 50,000 sets were used as test data to test the network's prediction ability.

[0087] Before training, the training set data is normalized to transform it into data within the range of [-1, 1], thus eliminating the difference in magnitude between different dimensions. The data normalization method used is the min-max method, and the formula is as follows:

[0088]

[0089] Where x is the input data, x max Let x be the maximum value in the data sequence. min Let y be the minimum value in the data sequence. minLet y be the minimum value in the normalized data sequence. max It represents the maximum value in the normalized data sequence.

[0090] Determine the information and number of input layer nodes, hidden layer nodes, and output layer nodes of the neural network, as well as the activation functions between each layer;

[0091] The neural network model for calculating the minimum inter-satellite distance of spacecraft has "relative position" and "relative velocity" as input nodes, with 6-dimensional nodes. The hidden layer is divided into three layers, each with 25 nodes, for a total of 75 nodes. The output node is the closest moment between the two satellites, with 1-dimensional nodes. The activation functions of both the hidden layer and the output layer are Sigmoid functions.

[0092] The training dataset (Train dataset) is used for neural network training and parameter updates. The neural network parameters are initialized, and the training data is processed through the neural network structure to obtain the output value. The error between the output value and the corresponding labeled data in the labeled dataset is calculated using the MSE loss function. The error is then backpropagated to the neural network using the chain rule. At the same time, the gradient descent method is used to update the weights and bias parameters of the neural network, thus completing one training cycle.

[0093] The validation set is used for verification. If the preset requirements are met, the next step is performed; otherwise, the iteration count is updated and the iteration continues.

[0094] After completing the neural network training and fixing the neural network parameters, a calculation model for the closest inter-satellite moment between spacecraft is obtained. For example... Figure 4 As shown, the mean squared error (MSE) is related to the number of iterations. As the number of iterations increases, the MSE decreases. When the number of iterations increases to a certain value, the MSE converges.

[0095] The initial state data of the spacecraft target is substituted into the trained neural network model for calculating the closest time between spacecraft and satellites to obtain the calculation result of the closest time between spacecraft and satellites.

[0096] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A method for calculating the closest inter-satellite moment for spacecraft based on neural networks, characterized in that, Includes the following steps: Acquire data on different initial states of the spacecraft, calculate the corresponding inter-satellite closest moments, and compile an inter-satellite closest moment dataset. Based on the inter-satellite closest moment dataset, a neural network model for calculating the inter-satellite closest moment of a spacecraft was constructed and trained. The target initial state data of the spacecraft is substituted into the trained spacecraft inter-satellite closest moment calculation neural network model to obtain the spacecraft inter-satellite closest moment calculation result. Any set of data in the inter-satellite closest moment dataset is represented as follows: in, Used to represent the initial state data of a spacecraft This represents the radial position component of the orbit in a relative coordinate system. This represents the position component of the flight direction in a relative coordinate system. This represents the position component of the orbital angular momentum direction in the relative coordinate system. This represents the radial velocity component of the orbit in the relative coordinate system. This represents the velocity component in the direction of flight in a relative coordinate system. This represents the velocity component in the direction of the orbital angular momentum in the relative coordinate system. This indicates the closest inter-satellite moment after the initial state data of the target spacecraft has been determined.

2. The method for calculating the closest inter-satellite time based on a neural network according to claim 1, characterized in that, The calculation process for the closest inter-satellite moment is as follows: Choosing a reference spacecraft orbit and assuming a near-circular orbit, we obtain the analytical solution of the CW equation in coordinate component form: in, This represents the orbital angular velocity of the primary star around the Earth. This represents the initial position component of the orbiting spacecraft along the x-axis. This represents the initial position component of the orbiting spacecraft along the y-axis. This represents the initial position component of the spacecraft along the z-axis. This represents the initial velocity component along the x-axis of the orbiting spacecraft. This represents the initial velocity component along the y-axis of the orbiting spacecraft. This represents the initial velocity component along the z-axis of the orbiting spacecraft; Interstellar distance is defined as Substituting the analytical solution of the coordinate components of the CW equation into the inter-satellite distance formula, we obtain the relationship between the inter-satellite distance of the spacecraft and the initial state of the target spacecraft and time t. Randomly generate the initial state data of the target spacecraft, denoted as The time corresponding to the minimum inter-satellite distance is obtained by iterating through the inter-satellite distance D using the orbital recursion method. .

3. The method for calculating the closest inter-satellite time based on a neural network according to claim 1, characterized in that, The construction process of the neural network model for calculating the closest inter-satellite moment is as follows: The inter-satellite closest moment dataset is divided into training set, validation set and test set, and the data in the inter-satellite closest moment dataset is normalized according to category. Determine the information and number of input layer nodes, hidden layer nodes, and output layer nodes of the neural network, as well as the activation functions between each layer.

4. The method for calculating the closest inter-satellite time based on a neural network according to claim 3, characterized in that, The ratio of the training set, validation set, and test set is 90:5:

5.

5. The method for calculating the closest inter-satellite time based on a neural network according to claim 3, characterized in that, The normalization process is as follows: The data in the dataset is transformed into values ​​between [-1, 1] according to their categories, using the min-max method, as shown in the following formula: in, Indicates input data, Represents the maximum value in a data sequence. This represents the minimum value in the data sequence. This represents the minimum value in the normalized data sequence. This represents the maximum value in the normalized data sequence.

6. The method for calculating the closest inter-satellite time based on a neural network according to claim 3, characterized in that, The input layer nodes of the neural network contain relative position and relative velocity information.

7. The method for calculating the closest inter-satellite time based on a neural network according to claim 3, characterized in that, The output layer node represents the closest moment between satellites, and both the hidden layer activation function and the output layer activation function use the Sigmoid function.

8. The method for calculating the closest inter-satellite time based on a neural network according to claim 1, characterized in that, The training process of the neural network model for calculating the closest inter-satellite moment is as follows: The neural network is trained and its parameters are updated using the training set data. The validation set is used for verification. If the preset requirements are met, the next step is performed; otherwise, the iteration count is updated and the iteration continues. After the neural network is trained, the neural network parameters are fixed to obtain the neural network model for calculating the closest time between spacecraft and satellites.

9. The method for calculating the closest inter-satellite time based on a neural network according to claim 8, characterized in that, The steps for training the neural network are as follows: The neural network parameters are initialized, and the training data is processed through the neural network structure to obtain the output value. The error between the output value and the corresponding labeled data in the labeled dataset is calculated using the MSE loss function. The error is then backpropagated to the neural network using the chain rule. At the same time, the weights and bias parameters of the neural network are updated using the gradient descent method.

Images