A method for calculating the orbit injection of a lunar orbiter based on a radial basis neural network

Abstract

The application discloses a kind of based on radial basis neural network's lunar orbiter orbit injection calculation method, it is related to spaceflight control field. Numerical calculation method is used to solve lunar orbiter dynamics equation, and the precise ephemeris of spacecraft in preset time length is obtained;According to remote sensing task demand and orbit characteristic division orbit fitting time period, the epoch and orbit root number of each group of injection parameters are obtained;Based on instantaneous orbit root number, through the mean anomaly extrapolation generation two-body ephemeris, the position deviation of each corresponding epoch in precise ephemeris and two-body ephemeris is calculated;Iterative calculation radial basis neural network parameter, and the position deviation in each direction is fitted by radial basis neural network.The calculation method of the application, when running on star, only executes simple two-body extrapolation superposition neural network deviation compensation, can avoid complex multi-perturbation term high-precision integration operation, adapts the power and power consumption limit of on-board low-performance chip.

Description

Technical Field

[0001] This invention relates to the field of aerospace telemetry and control, and more specifically, to a method for calculating orbit injection for lunar spacecraft based on radial basis function neural networks. Background Technology

[0002] Lunar spacecraft hold great promise for lunar scientific exploration, deep space communication and navigation, lunar resource exploration, and future manned lunar landings and the construction of lunar research stations. While in orbit, spacecraft rely on orbital parameters to determine their real-time position. However, due to onboard memory limitations, ground stations cannot directly feed ephemeris data for a future period onto the spacecraft. Furthermore, onboard computing efficiency is far lower than on the ground, preventing the spacecraft from employing complex integral algorithms and perturbation models for orbit extrapolation.

[0003] Therefore, there is an urgent need for a lightweight and high-precision orbital deviation compensation method to meet the orbit injection and autonomous extrapolation requirements of lunar orbiting spacecraft when performing high-precision remote sensing missions, without significantly increasing onboard computing and storage overhead. Summary of the Invention

[0004] In view of this, the present invention provides a method for calculating orbit injection of lunar spacecraft based on radial basis neural networks, which is adapted to the computing power and power consumption limitations of low-performance onboard chips.

[0005] To achieve the above objectives, the following solution is proposed: A method for calculating orbit injection for lunar spacecraft based on radial basis function neural networks includes: A pre-defined numerical calculation method was used to solve the dynamic model of the lunar orbiter and obtain the precise ephemeris of the spacecraft within a pre-defined time period. The orbit fitting time period is divided according to the remote sensing mission requirements and orbit characteristics to obtain the injection parameter epochs for each group of orbits; Based on instantaneous orbital elements, a two-body ephemeris is generated by extrapolating the mean anomaly angle, and the positional deviations of each corresponding epoch in the precise ephemeris and the two-body ephemeris are calculated. The parameters of the radial basis function neural network are calculated iteratively, and the positional deviations in each direction are fitted by the radial basis function neural network.

[0006] Preferably, the step of solving the dynamic model of the lunar orbiter using a preset numerical calculation method includes: Construct a dynamic model of a lunar orbiter in the lunar center inertial frame; Based on the dynamic model of the lunar orbiter, the first-order differential state equation of the spacecraft orbit is established. The precise ephemeris was obtained by solving the first-order differential state equation using the Runge-Kutta method.

[0007] Preferably, the step of dividing the orbit fitting time period according to the remote sensing mission requirements includes: The number of injection orbit parameter sets and the start time of injection orbit are set according to the on-board memory capacity and remote sensing mission. A cutoff time is introduced for each fitting period, resulting in several independent orbit fitting periods and determining the injection parameter epochs corresponding to each orbit. The total fitting time for a single orbit is the sum of the orbit period and twice the cutoff time.

[0008] Preferably, the step of generating a two-body ephemeris based on instantaneous orbital elements by extrapolating the mean anomaly angle, and calculating the positional deviation between the precise ephemeris and the corresponding epochs in the two-body ephemeris, includes: Based on the precise ephemeris, the precise position and velocity corresponding to each set of injected parameter epochs are extracted and converted into orbital elements; Using the orbital elements as the initial value, the mean aperimeter angle is extrapolated according to the preset step size, and the deviated aperimeter angle and the true aperimeter angle at each sampling time are solved. Convert the extrapolated orbital elements into two-body position and velocity, and generate two-body ephemeris; By subtracting the precise ephemeris from the two-body ephemeris, the three-axis position deviations corresponding to each epoch are obtained; The sampled time series is normalized and used as the input variable for the neural network.

[0009] Preferably, fitting the positional deviations in each direction using a radial basis function neural network includes: The sampling time was used as the independent variable to be fitted, and the positional deviation was used as the dependent variable of the radial basis function neural network for fitting.

[0010] Preferably, iteratively calculating the parameters of the radial basis function neural network includes: K-means clustering was used to determine the center vector of the radial basis neural network; The width factor of the radial basis function neural network is determined based on the clustering results; The output layer weights are determined using the least squares method. The evaluation error of the current number of hidden layer nodes is calculated using the five-fold cross-validation method. The radial basis function neural network is trained by traversing the number of hidden layer nodes within a preset range, and the target number of hidden layer nodes is determined based on the evaluation error of each hidden layer node number.

[0011] Preferably, using K-means clustering to determine the center vector of the radial basis neural network includes: The sampling time is divided into several clusters; Calculate the distance from each sample to each cluster center and assign it to the nearest cluster; Calculate the mean vector of each cluster to obtain the updated cluster centers; Based on the updated cluster centers, sample allocation and cluster center updates are performed iteratively until the change in cluster centers is less than a set threshold, thus obtaining the center vector.

[0012] Preferably, determining the width factor of the radial basis function neural network based on the clustering results includes: The width factor of the radial basis function neural network is calculated based on the average Euclidean distance from all samples in each cluster to the cluster center.

[0013] Preferably, the output layer weights are solved using the least squares method, including: Substitute the center vector and width factor into the hidden layer function to calculate the hidden layer output matrix; A fitting model for a radial basis function neural network is constructed based on the hidden layer output matrix, and the optimal extended weights are obtained by the least squares method.

[0014] Preferably, the evaluation error for calculating the current number of hidden layer nodes using the five-fold cross-validation method includes: The sampling time independent variable and the corresponding position deviation dependent variable to be fitted are randomly shuffled and divided into 5 non-overlapping subsets. Training and validation are performed 5 times in sequence, with the validation set being changed each time. The arithmetic mean of the five verification errors is taken as the final evaluation error of the current number of hidden layer nodes, and the number of hidden layer nodes with the smallest final evaluation error is selected as the target number of hidden layer nodes.

[0015] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects: The lunar orbit injection calculation method based on radial basis function neural network (RBN) provided by this invention employs a pre-defined numerical calculation method to solve the dynamic model of the lunar orbiter and obtain the precise ephemeris of the spacecraft within a preset time period. The orbit fitting time period is divided according to remote sensing mission requirements and orbital characteristics to obtain the injection parameter epochs for each group of orbits. Based on the instantaneous orbital elements, a two-body ephemeris is generated by extrapolating the mean anomaly angle, and the positional deviation between the precise ephemeris and the corresponding epochs in the two-body ephemeris is calculated. The RBN parameters are iteratively calculated, and the positional deviations in each direction are fitted using the RBN. The calculation method of this invention, when running on-board, only performs simple two-body extrapolation superimposed with neural network deviation compensation, which can avoid complex high-precision integration calculations with multiple perturbation terms and is adapted to the computing power and power consumption limitations of low-performance onboard chips. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the embodiments of the present invention 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 embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0017] Figure 1 A flowchart of a lunar orbit injection calculation method based on radial basis function neural network provided in this embodiment of the invention; Figure 2 This is a schematic diagram of the time period division for orbit fitting provided in an embodiment of the present invention; Figure 3 The deviation between the x-direction two-body ephemeris and the precise ephemeris provided in the embodiments of the present invention and the fitting of the radial basis neural network; Figure 4 This refers to the fitting deviation of the radial basis neural network in the x-direction according to an embodiment of the present invention. Figure 5 The deviation between the two-body ephemeris and the precise ephemeris in the y-direction provided in this embodiment of the invention and the fitting of the radial basis neural network; Figure 6 This refers to the fitting deviation of the radial basis neural network in the y-direction according to an embodiment of the present invention. Figure 7 The deviation between the z-direction two-body ephemeris and the precise ephemeris provided in the embodiments of the present invention and the fitting of the radial basis neural network; Figure 8 This represents the fitting deviation of the radial basis neural network in the z-direction according to an embodiment of the present invention. Detailed Implementation

[0018] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0019] First, combined Figure 1 The method for calculating the orbit injection of a lunar spacecraft based on a radial basis function neural network, as provided in this invention, is described below: Step S1: Integrate the dynamic equations of the lunar orbiter using numerical calculation methods to obtain the precise ephemeris of the spacecraft within a preset time period.

[0020] Step S11: Construct a dynamic model of the lunar orbiter in the lunar center inertial frame: , in, The gravitational acceleration at the center of the moon, The gravitational acceleration generated by the non-spherical part of the moon. The acceleration is caused by solar radiation pressure. Acceleration caused by the gravitational pull of large celestial bodies such as the Earth and the Sun.

[0021] Step S12: Based on the lunar orbiter dynamics model, establish the first-order differential state equations for the spacecraft's orbital dynamics:

[0022] in, The location of the lunar orbiter. The speed of the lunar orbiter.

[0023] Step S13: Solve the first-order differential state equation using the Runge-Kutta method to calculate the precise ephemeris.

[0024] Set the spacecraft's initial epoch Corresponding position and speed and integral step size λ The Longmen-Kutta method was used to calculate the precise ephemeris of lunar orbiters over a period of time.

[0025] Step S2: Based on the remote sensing mission requirements and orbital characteristics, obtain the number of injection parameter groups, the number of two-body orbital elements for each injection parameter group, and the corresponding epoch.

[0026] Step S21: Set the number of orbit parameter sets to be uploaded based on the onboard memory capacity and the remote sensing mission. num , Initial time of the upper orbit .

[0027] Step S22: Introduce a cutoff time for each fitting period, divide the time into several independent orbit fitting periods, and determine the injection parameter epochs corresponding to each orbit.

[0028] like Figure 2 As shown, the fitting error is relatively large at the beginning and end of the data segment when using a radial basis function neural network. To ensure the accuracy of the data fitting, a cutoff time is introduced at the beginning and end of the effective extrapolation segment of the orbit injection parameters for each group. These, together, constitute the fitting time period for the injected parameters in this group. Therefore, the fitting time length for each group of orbits... The sum of the orbital period and twice the cutoff time: , , in, For the first j The epoch of the orbital injection parameters of the group, and Each of the following dates The corresponding orbital period and semi-major axis, is the lunar gravitational constant.

[0029] The number of injection groups based on the overall set orbital parameters num and the first set of calendars The epochs of each set of orbital injection parameters can be obtained as follows:

[0030] Step S3: Based on the instantaneous orbital elements, generate a two-body ephemeris by extrapolating the mean aperimeter angle, and calculate the positional deviation between the precise ephemeris and the two-body ephemeris.

[0031] Step S31: Interpolate the precise ephemeris and extract the epochs of each set of injected parameters. Corresponding position velocity Convert position and velocity into orbital elements : , , , , , , , , , in, The distance from the spacecraft to the lunar center. For the speed of the lunar inertial frame, For position vectors, It is a velocity vector. Let be the component of the specific angular momentum in the z-direction. The magnitude of the specific angular momentum, For specific angular momentum, For the track inclination angle, The ascending intersection vector, Let be the component of the ascending intersection vector in the z-direction. For the ascending intersection vector at x directional components, For eccentricity, The eccentricity vector, For true near point angle, For the angle of near point, The approximate angle is obtained by solving Newton's iteration method.

[0032] Step S32: Using the orbital elements as the initial value, perform binary extrapolation on the mean aperimeter angle according to the preset step size, and solve for the mean aperimeter angle and the true aperimeter angle at each sampling time.

[0033] Will The orbital elements at time t are used as initial values, and the values ​​are calculated according to the step size. λ Perform a two-dimensional extrapolation, where other orbital elements remain constant, and the mean anomaly changes uniformly according to the average angular velocity and time: , , in, For the first k The mean aperitoneal angle at each sampling time point Let the initial angle be the mean anterior angle. It is a sampled time series. , n The number of sampling points within the fitting time period. b It is a constant. .

[0034] The angle of the corresponding sampling time is close to the point. The solution can be obtained using Newton's iterative method, yielding the corresponding true anterior angle at each moment. : , Step S33: Convert the extrapolated orbital elements into two-body position and velocity, and generate the two-body ephemeris: , , in, To bypass z axis The rotation matrix, To bypass x axis The rotation matrix, To bypass z axis The rotation matrix.

[0035] Step S34: Subtract the precise ephemeris from the two-body ephemeris to obtain the three-axis position deviations corresponding to each epoch.

[0036] Subtracting the precise ephemeris from the two-body ephemeris yields the three-axis position deviations for each epoch. .

[0037] in, , , The first j Group injection parameter sampling points k corresponding x, y, z Positional deviation in direction.

[0038] Step S35: Normalize the sampled time series and use it as the input variable for the neural network. Normalization : , in, The average value of the time-sampled sequence. and These are the maximum and minimum values ​​of the time-sampled sequence, respectively.

[0039] Step S4: Iteratively calculate the parameters of the radial basis function neural network and fit the positional deviations in each direction using the radial basis function neural network.

[0040] Specifically, the sampling time Position deviation will be used as the independent variable to be fitted. As the dependent variable of radial basis neural networks Perform fitting. .like Figure 3-8 The figure shows the fitting results of the radial basis function neural network fitting for the positional deviations in each direction according to an embodiment of the present invention. Wherein, Figure 3 , Figure 5 and Figure 7 These are the radial basis function neural network fitting examples from embodiments of the present invention. X , Y , Z The positional deviation in the direction, in which the two-body orbit and the precise ephemeris deviation and the directional deviation ephemeris fitted by the radial basis neural network are basically coincident. Figure 4 , Figure 6 and Figure 8 Slice bias is used to fit ephemeris biases to radial basis neural networks on the order of ten meters.

[0041] The lunar orbit injection calculation method based on radial basis function neural network provided in this invention uses radial basis function neural network to fit the deviation between the precise ephemeris and the two-body ephemeris of the lunar orbiting spacecraft over a period of time, and combines it with the on-board two-body extrapolation algorithm to provide technical support for the spacecraft to perform high-precision remote sensing missions.

[0042] Next, this embodiment of the invention will describe the iterative calculation process of the radial basis function neural network parameters. The iterative process includes: Step S40: Set the initial values ​​for the iteration.

[0043] Based on empirical methods, the number of hidden layer nodes can be determined. h Generally in Therefore, it can be This serves as the initial value for the number of hidden layer nodes in the network iteration.

[0044] Step S41: Use K-means clustering to determine the center vector of the radial basis neural network. .

[0045] Set a threshold ɛ to divide the sampling time into... h Cluster Calculate each sample The distance to each cluster center is used to assign the child to the nearest cluster. m =1,...., h Then, the mean vector of each cluster is recalculated to obtain the updated cluster centers.

[0046] Based on the updated cluster centers, sample allocation and cluster center updates are iteratively performed until the change in cluster centers is less than a set threshold α, at which point the center vector is obtained. .

[0047] Step S42: Determine the width factor of the radial basis function neural network based on the clustering results. .

[0048] , Where, σ m For the first m The width factor of each cluster. d m For the first m All samples within a cluster are sent to the center. c m The average Euclidean distance.

[0049] Step S43: Solve for the output layer weights using the least squares method. .

[0050] Using the Gaussian function as the radial basis function, i.e. the hidden layer function, the output of the function for each hidden layer node is calculated as follows:

[0051] in It is the center vector c The One portion, It is the first normalized time independent variable. k One portion, k =1,...., n .

[0052] Substituting the time variable into the neural network, the output matrix of the hidden layer nodes is calculated. :

[0053] in, ,in, m =1,...., h .

[0054] To facilitate the solution, the bias b is incorporated into the output matrix of the hidden layer node. : .

[0055] Meanwhile, the weight vector can be written as:

[0056] A fitting model for a radial basis function neural network is constructed based on the hidden layer output matrix, and the optimal extended weights are obtained by the least squares method.

[0057] The fitting model for the radial basis function neural network is as follows:

[0058] in, This is the output vector of the neural network, which represents the value of the fitted dependent variable.

[0059] The optimal extended weights can be obtained by using least squares: .

[0060] in, for transpose, Y This represents the actual output value during weight training.

[0061] Step S44: The number of hidden layer nodes is calculated iteratively using the five-fold cross-validation method.

[0062] The sampling time independent variable to be fitted The corresponding positional deviation dependent variable is randomly shuffled and divided into 5 non-overlapping subsets. The training and validation processes are performed five times in sequence, with the validation set changed each time. Finally, the arithmetic mean of the five validation errors is taken as the final evaluation error of the current number of hidden layer nodes, and the number of hidden layer nodes with the smallest final evaluation error is selected as the target number of hidden layer nodes.

[0063] First time: Training set is The validation set is Following steps S41-S43, train the radial basis function neural network to obtain the validation error. ; Second time: Training set is The validation set is Train the radial basis function neural network according to steps S41-S43 to obtain the validation error. ; Third time: Training set is The validation set is Train the radial basis function neural network according to steps S41-S43 to obtain the validation error. ; Fourth time: Training set is The validation set is Train the radial basis function neural network according to steps S41-S43 to obtain the validation error. ; 5th time: Training set is The validation set is Train the radial basis function neural network according to the above steps to obtain the validation error. .

[0064] The arithmetic mean of the five verification errors is used as the number of hidden layer nodes. h Final evaluation error: .

[0065] Step S45: Train the radial basis neural network by traversing the number of hidden layer nodes within a preset range.

[0066] Set the iteration step size λ m Within the preset iteration range Number of hidden nodes in inner traversal h The radial basis function neural network is trained by repeating steps S41-S44 based on the number of hidden layer nodes to obtain the final evaluation error of the number of hidden layer nodes.

[0067] The weights calculated above are used as the loss function for fitting, with the mean squared error (MSE) as the basis for training.

[0068] in, The first output of the radial basis function neural network k The fitted values ​​of each sampled sample, For the first k The true value of each sampled sample.

[0069] Iterate through all hidden layer nodes to obtain the final evaluation error corresponding to each hidden layer node number h. Ultimately, the smallest one is chosen. The corresponding number of hidden layer nodes h The target number of hidden layer nodes in a radial basis function neural network.

[0070] Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0071] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0072] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for calculating orbit injection for lunar spacecraft based on radial basis function neural networks, characterized in that, include: A pre-defined numerical calculation method was used to solve the dynamic model of the lunar orbiter and obtain the precise ephemeris of the spacecraft within a pre-defined time period. The orbit fitting time period is divided according to the remote sensing mission requirements and orbit characteristics to obtain the injection parameter epochs for each group of orbits; Based on instantaneous orbital elements, a two-body ephemeris is generated by extrapolating the mean anomaly angle, and the positional deviations of each corresponding epoch in the precise ephemeris and the two-body ephemeris are calculated. The parameters of the radial basis function neural network are calculated iteratively, and the positional deviations in each direction are fitted by the radial basis function neural network.

2. The method for calculating the orbital injection of a lunar spacecraft based on a radial basis function neural network according to claim 1, characterized in that, The method of solving the dynamic model of the lunar orbiter using a preset numerical calculation method includes: Construct a dynamic model of a lunar orbiter in the lunar center inertial frame; Based on the dynamic model of the lunar orbiter, the first-order differential state equation of the spacecraft orbit is established. The precise ephemeris was obtained by solving the first-order differential state equation using the Runge-Kutta method.

3. The method for calculating the orbital injection of a lunar spacecraft based on a radial basis function neural network according to claim 1, characterized in that, The process of dividing the orbit fitting time period according to the requirements of the remote sensing mission includes: The number of injection orbit parameter sets and the start time of injection orbit are set according to the on-board memory capacity and remote sensing mission. A cutoff time is introduced for each fitting period, resulting in several independent orbit fitting periods and determining the injection parameter epochs corresponding to each orbit. The total fitting time for a single orbit is the sum of the orbit period and twice the cutoff time.

4. The method for calculating the orbit injection of a lunar spacecraft based on a radial basis function neural network according to claim 1, characterized in that, The method of generating a two-body ephemeris based on instantaneous orbital elements by extrapolating the mean anomaly angle, and calculating the positional deviations of corresponding epochs between the precise ephemeris and the two-body ephemeris, includes: Based on the precise ephemeris, the precise position and velocity corresponding to each set of injected parameter epochs are extracted and converted into orbital elements; Using the orbital elements as the initial value, the mean aperimeter angle is extrapolated according to the preset step size, and the deviated aperimeter angle and the true aperimeter angle at each sampling time are solved. Convert the extrapolated orbital elements into two-body position and velocity, and generate two-body ephemeris; By subtracting the precise ephemeris from the two-body ephemeris, the three-axis position deviations corresponding to each epoch are obtained; The sampled time series is normalized and used as the input variable for the neural network.

5. The method for calculating the orbit injection of a lunar spacecraft based on a radial basis function neural network according to claim 1, characterized in that, Positional deviations in various directions are fitted using a radial basis function neural network, including: The sampling time was used as the independent variable to be fitted, and the positional deviation was used as the dependent variable of the radial basis function neural network for fitting.

6. The method for calculating the orbital injection of a lunar spacecraft based on a radial basis function neural network according to claim 1, characterized in that, Iterative calculation of radial basis function neural network parameters includes: K-means clustering was used to determine the center vector of the radial basis neural network; The width factor of the radial basis function neural network is determined based on the clustering results; The output layer weights are determined using the least squares method. The evaluation error of the current number of hidden layer nodes is calculated using the five-fold cross-validation method. The radial basis function neural network is trained by traversing the number of hidden layer nodes within a preset range, and the target number of hidden layer nodes is determined based on the evaluation error of each hidden layer node number.

7. The method for calculating the orbital injection of a lunar spacecraft based on a radial basis function neural network as described in claim 6, characterized in that, Determining the center vector of a radial basis neural network using K-means clustering includes: The sampling time is divided into several clusters; Calculate the distance from each sample to each cluster center and assign it to the nearest cluster; Calculate the mean vector of each cluster to obtain the updated cluster centers; Based on the updated cluster centers, sample allocation and cluster center updates are performed iteratively until the change in cluster centers is less than a set threshold, thus obtaining the center vector.

8. The method for calculating the orbital injection of a lunar spacecraft based on a radial basis function neural network according to claim 6, characterized in that, The width factor of the radial basis function neural network is determined based on the clustering results, including: The width factor of the radial basis function neural network is calculated based on the average Euclidean distance from all samples in each cluster to the cluster center.

9. The method for calculating the orbital injection of a lunar spacecraft based on a radial basis function neural network according to claim 6, characterized in that, Solving for the output layer weights using the least squares method includes: Substitute the center vector and width factor into the hidden layer function to calculate the hidden layer output matrix; A fitting model for a radial basis function neural network is constructed based on the hidden layer output matrix, and the optimal extended weights are obtained by the least squares method.

10. The method for calculating the orbital injection of a lunar spacecraft based on a radial basis function neural network according to claim 6, characterized in that, The evaluation error for calculating the current number of hidden layer nodes using the five-fold cross-validation method includes: The sampling time independent variable and the corresponding position deviation dependent variable to be fitted are randomly shuffled and divided into 5 non-overlapping subsets. Training and validation are performed 5 times in sequence, with the validation set being changed each time. The arithmetic mean of the five verification errors is taken as the final evaluation error of the current number of hidden layer nodes, and the number of hidden layer nodes with the smallest final evaluation error is selected as the target number of hidden layer nodes.

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