Intelligent method for determining initial orbit of space target with ultra-short arc

Abstract

The application discloses a kind of space target ultra-short arc initial orbit intelligent determination method, belong to aerospace technology field.The application is based on artificial intelligence technology to realize space target ultra-short arc initial orbit determination, there is no strict requirement to complex nonlinear problem, and can develop more complex perturbation condition and initial orbit determination under the operation law of multiple body, coverage is wider;The application generates multiple groups of target orbits randomly and calculates the observation and state quantity of each visible arc segment, constructs the sample data set with ultra-large capacity, which is helpful for neural network to learn the nonlinear relationship between observation and state quantity using rich samples;The application builds and trains long short-term memory network model, determines the optimal network model weight parameter by designing and adjusting hyperparameter, can obtain the fast prediction solution of unknown space target ultra-short arc initial orbit according to observation;The application can meet more space target ultra-short arc initial orbit determination tasks by considering different inputs and outputs.

Description

TECHNICAL FIELD

[0001] The present application relates to a kind of space target ultra-short arc initial orbit intelligent determination method, belong to aerospace technical field. BACKGROUND

[0002] With the continuous development of aerospace technology, space situation awareness has become the focus of attention of countries around the world. Space target orbit determination is becoming a research hotspot involving space field, especially near-earth non-cooperative target and deep space limited field of view high dynamic target and other space targets are facing urgent awareness needs. In the field of space target orbit determination, an important problem is the space target initial orbit determination problem. The space target initial orbit determination problem is a typical orbit dynamics problem, generally adopts two-body model or polynomial fitting method considering only J2 term influence, and determines the initial orbit of space target through observation data. According to the improvement idea, the initial orbit determination and precise orbit determination constitute the space target orbit determination problem. The initial orbit determination is a prerequisite for precise orbit determination, and its accuracy directly determines whether the convergence and convergence speed of precise orbit determination calculation. Too short observation arc will greatly increase the difficulty of space target initial orbit determination, but it is particularly important to determine the target orbit parameters as soon as possible using less observation data for space situation awareness mission. Therefore, it is necessary to study the space target ultra-short arc initial orbit determination problem.

[0003] In the developed space target ultra-short arc initial orbit intelligent determination method, online technology [1] (see: Ansalone L, Curti F. A genetic algorithm for initial orbit determination from a too short arc optical observation [J]. Advances in Space Research, 2013, 52 (3): 477-489.) considers introducing genetic algorithm into initial orbit determination, and proposes an initial orbit determination method using short-time observation optical data, selects the slant range at the beginning and end time as the preferred variable, and inversely calculates the orbit element solution. This method is novel and has high calculation accuracy, but the algorithm has poor geometric interpretation.

[0004] Prior art [2] (see: Zhang Zhengyuan, Sang Jizhang, Chen Junyu. Application of neural network in very short arc initial orbit determination problem [J / OL]. Surveying and mapping geographic information: 1-5 [2022-10-05].) considers the problem of very short arc initial orbit determination according to a set of rough orbit elements obtained from single arc segment limited observation information, and designs a neural network algorithm for solving the precise mathematical equation between a set of angle observation values and the corresponding true orbit element solution by using the "universal approximation property" of neural network algorithm, which improves the solution accuracy of traditional initial orbit determination, but still needs to give a set of rough orbit elements obtained by solving the very short arc observation data by some method, that is, only used for orbit element solution accuracy improvement, and is prone to non-convergence problem, and has poor robustness.

[0005] With the continuous development of artificial intelligence technology, recurrent neural networks are proposed and used to process time series problems, but when the nodes of the neural network are calculated through many stages, the features of the previous long time slice will be covered. Long short-term memory neural networks can solve this common long-term dependence problem and more fully and effectively utilize long historical information. SUMMARY

[0006] The space target ultra-short arc initial orbit intelligent determination method disclosed by the application solves the technical problem of realizing the intelligent determination of the space target ultra-short arc initial orbit based on the ultra-short arc observation data, using the rapid prediction performance of the neural network and the long historical information utilization ability of the long short-term memory network, learning the complex nonlinear relationship between the observation data and the orbit parameters, and has the advantages of wide coverage, strong robustness and high reliability, high solution efficiency, strong flexibility and high expansibility.

[0007] The object of the application is realized by the following technical scheme:

[0008] The application discloses a kind of space target ultra-short arc initial orbit intelligent determination method, establishes the geocentric inertial coordinate system, on this basis, establish observation, state quantity representation and only consider the J2 term influence two-body dynamics model;Randomly generate multiple sets of target orbits, construct with observation as input, state quantity as label sample dataset, and build long short-term memory network model, design observation embedding layer, state quantity embedding layer, state quantity decoding layer;According to predetermined proportion, sample dataset is divided and data normalization processing is carried out, based on state quantity output, design the loss function expressed in mean square deviation and dynamic descending learning rate, set predetermined round to carry out network model training and verification;According to loss adjustment hyperparameter, design error index, comprehensive loss function and error index, select the optimal long short-term memory network model for space target ultra-short arc initial orbit intelligent determination.The application can be based on a large number of space target ultra-short arc observation data samples, train long short-term memory network model to learn the complex nonlinear relationship between observation data and orbit parameters, obtain the optimal network model to reliably and quickly predict the initial orbit of space target, and the prediction result is used as initial value for precise orbit determination.The application can be used for target selection, target approaching planning guidance control and multiple task scenarios, and is favorable to improve task efficiency and effect.

[0009] The application discloses a kind of space target ultra-short arc initial orbit intelligent determination method, including the following steps:

[0010] Step one: establish the geocentric inertial coordinate system for space target ultra-short arc initial orbit determination.

[0011] The center of the earth is selected as the coordinate origin O to establish the geocentric inertial coordinate system. The x-axis points to the equinox point, the z-axis is along the earth's rotation axis and points to the north pole. The y-axis and the x and z two axes form a right-handed rectangular coordinate system, that is, the establishment of the geocentric inertial coordinate system for space target ultra-short arc initial orbit determination is realized.

[0012] Step two: establish observation and state quantity representation for space target ultra-short arc initial orbit determination under the geocentric inertial coordinate system, the observation considers the ground station azimuth converted from Cartesian position coordinates, the space target line-of-sight angle and its rate of change, and the state quantity considers the relative distance modulus and relative velocity modulus of the space target relative to the ground station. The two-body dynamics model requires fewer parameters than the multi-body dynamics model but can still reflect the dynamics state of the space target, and the main perturbation parameter of the two-body dynamics model is the J2 term gravity perturbation of the earth, which has the greatest influence on the dynamics of the space target, that is, a two-body dynamics model of the space target is established considering only the influence of the J2 term gravity perturbation of the earth.

[0013] Step 2.1: Establish the observation and state quantity representation of the initial trajectory of the space target in the geocentric inertial coordinate system. The observation considers the azimuth of the ground station, the line-of-sight angle of the space target and its rate of change, which are converted from Cartesian position coordinates to spherical coordinates. The state quantity considers the relative distance modulus and relative velocity modulus of the space target relative to the ground station.

[0014] In the geocentric inertial coordinate system, the 7×1 dimensional observations of a space target by a ground station are represented as follows:

[0015]

[0016] in, This represents the counterclockwise azimuth angle of the ground station's location on the xy plane, measured from the x-axis of the geocentric inertial coordinate system. and These represent the line-of-sight angle of the space target relative to the ground station in the geocentric inertial coordinate system and its rate of change, respectively. Where r... t =[x t y t z t ] T and r s =[x s y s z s ] T Let represent the position coordinates of the space target and the ground station in the geocentric inertial coordinate system, respectively, and Δr = r t -r s Δr = ||Δr|| represents the relative position vector of the space target with respect to the ground station and its magnitude, respectively. 3×3 It is a 3×3 identity matrix, where the subscript t represents a space target and the subscript s represents a ground station.

[0017] The 2×1 dimensional state variables of a space target observed by a ground station in a geocentric inertial coordinate system are represented as follows:

[0018]

[0019] Where, △v=||△v||=||v t -v s || represents the magnitude of the relative velocity vector of a space target relative to a ground station, v t =[vx t vy t vz t ] T and v s =[vx s vy s vz s ] Trespectively represent the velocity coordinates of the space object and ground station in the geocentric inertial coordinate system.

[0020] Step 2.2: The two-body dynamics model requires fewer parameters than the multi-body dynamics model but can still reflect the dynamics state of the space object, and the main perturbation parameter of the two-body dynamics model is the J2 term gravity perturbation of the Earth which has the greatest impact on the dynamics of the space object, that is, to establish a two-body dynamics model of the space object considering only the influence of the J2 term gravity perturbation of the Earth.

[0021] Considering only the influence of the J2 term gravity perturbation of the Earth, the two-body dynamics model of the space object is expressed as:

[0022]

[0023] where dr t and dv t respectively represent the rate of change of the position vector and the rate of change of the velocity vector of the space object in the geocentric inertial coordinate system, subscript e represents the Earth, μ e represents the Earth's gravitational constant, r t = ||r t || represents the length of the position vector of the space object, represents the J2 term gravity perturbation of the Earth related to the position vector of the space object. Where J2 is the J2 term gravity perturbation coefficient of the Earth, R e is the average radius of the Earth.

[0024] Step three: Generate multiple sets of target orbit elements combining Latin hypercube sampling and the given upper and lower bounds of the interval of the space object orbit elements; use the two-body dynamics model considering only the influence of the J2 term established in step two to obtain the orbit evolution through dynamics integration; calculate the observation and state quantity of each visible arc segment of each set of sampled orbits represented by step 2.1, and continuously update the upper and lower bounds of the interval of both; take the observation as input, the state quantity as label, and introduce the upper and lower bounds of the interval of both, and construct a sample data set for intelligent determination of the super-short-arc initial orbit of the space object. Considering the observation and state quantity represented by step two as input and output respectively, build a long short-term memory network model for intelligent determination of the super-short-arc initial orbit of the space object; combine the multilayer perception model and the linear function and nonlinear excitation function to design the observation embedding layer to extract the features of the 7-dimensional observation input; design the state quantity embedding layer to extract the features of the S-dimensional state quantity input; design the state quantity decoding layer to extract the features of the state quantity embedding layer output as input and obtain the 2-dimensional state quantity output.

[0025] Step 3.1: Generate multiple sets of target orbit elements by combining Latin hypercube sampling and given upper and lower bounds of a set of spatial target orbit elements; obtain the orbit evolution by dynamics integration using the two-body dynamics model considering only the J2 term influence established in step 2.2; calculate the observations and state quantities of each visible arc segment of each set of sampled orbits represented by step 2.1, and continuously update the upper and lower bounds of both; construct a sample data set for intelligent determination of super-short arc initial orbit of spatial targets by taking observations as input and state quantities as label, and introducing the upper and lower bounds of both.

[0026] The orbit elements of spatial targets are 6-dimensional, including semi-major axis a, eccentricity e, inclination i, ascending node right ascension Ω, argument of perigee ω, and true anomaly θ. Latin hypercube sampling method with uniform distribution is adopted to divide the 0-1 sample space into n layers, so that each layer has 6-dimensional sample space, and the elements in each dimension are randomly arranged. On the basis of sampling, the upper bound e u =[a u e u i u Ω u ω u θ u ] and the lower bound e l =[a l e l i l Ω l ω l θ l ] of the orbit elements of spatial targets are further given, and the n sets of spatial target orbit elements satisfying the limits are represented as:

[0027] e=e s ·(e u -e l )+e l (4)

[0028] where e s represents the n x 6-dimensional Latin hypercube sampling result, and the symbol "·" represents dot product.

[0029] The two-body dynamics model of spatial targets considering only the J2 term influence in equation (3) is used to take the position vector r0 and velocity vector v0 of the orbit elements in the Earth-centered inertial coordinate system as the initial value of integration, set the integration interval [t0, t f ] and the integration step size dt, and obtain the orbit state evolution of multiple sets of spatial target position vectors and velocity vectors by integration. Calculate and record the visible arc segments of each set of sampled orbits, and solve the observations and state quantities of each visible arc segment in each set of sampled orbits. Given a set of observation interval upper and lower bound initial values o u0 , o l0 and state quantity interval upper and lower bound initial values su0 l0 , comparing each solution and constantly updating, obtaining the upper and lower bounds of the observation interval o u and o l , and the upper and lower bounds of the state quantity interval s u and s l .

[0030] To achieve intelligent determination of the super-short-arc initial orbit of the space target, consider taking the observation quantity as the input and the state quantity as the label, and introduce the upper and lower bounds of the two intervals to build a sample data set.

[0031] Step 3.2: Consider taking the observation quantity represented in step 2.1 as the input and the state quantity as the output, and build a long short-term memory network model for intelligent determination of the super-short-arc initial orbit of the space target; combine the multi-layer perception model and the linear function and nonlinear excitation function to design the observation quantity embedding layer, extract the features of the 7-dimensional observation quantity input; design the state quantity embedding layer to extract the features of the S-dimensional state quantity input; design the state quantity decoding layer to extract the features of the state quantity embedding layer output as input and obtain the 2-dimensional state quantity output.

[0032] Set the input feature dimension of the long short-term memory network model for intelligent determination of the super-short-arc initial orbit of the space target to 7 dimensions, the hidden layer state dimension to H dimensions, the network stacking number to L layers, and the batch processing dimension to B dimensions.

[0033] To represent and extract the 7-dimensional observation quantity feature information, use multiple layers of linear functions and nonlinear excitation functions to design the observation quantity embedding layer. The linear function of the first layer expands the 7-dimensional observation quantity input to K o dimensions, multiple linear functions in the middle layer perform multiple feature processing, and the linear function of the last layer finally maps the features to D o dimensions. Use an activation function between every two linear functions to introduce a nonlinear factor, so that the neural network can arbitrarily approximate any nonlinear function. Select the LeakyReLU function as the nonlinear excitation function of the observation quantity embedding layer, which is represented as:

[0034]

[0035] where λ is a very small normal number. Thus, it reduces the possibility of gradient disappearance and gradient explosion during subsequent network training, has the advantages of low computational complexity and fast convergence speed, and is more inclined to activate than to die in the negative number region relative to the ReLU function.

[0036] To obtain the final 2-dimensional state quantity, design the state quantity embedding layer and the state quantity decoding layer with a structure similar to the observation quantity embedding layer. Similarly, use multiple layers of linear functions and LeakyReLU nonlinear excitation functions of formula (5) to map the S-dimensional state quantity to D​s The state quantity decoding layer embeds the state quantity into the D output by the state quantity embedding layer. s The state quantity embedding layer embeds the state quantity into the D output by the state quantity embedding layer.

[0037] The long short-term memory network represents the variables recording the previous state by the hidden layer state h(t) and the neuron state c(t), and changes with the new input x(t). The hidden layer state h(t) records more recent information and changes faster; the neuron state c(t) records more distant information and changes slower. To solve the spatial target super-short-arc initial orbit determination problem, the dimension of the initial hidden layer state h0 of the network is set as the number of network stacking layers x batch processing dimension x hidden layer state dimension, i.e. (L x B x H) dimensions; the initial neuron state c0 is a zero tensor with the same dimension as the initial hidden layer state h0.

[0038] Step four: according to the predetermined proportion, the sample data set for intelligent determination of the initial orbit of the spatial target super-short-arc is divided into a training set and a validation set; in order to facilitate data processing, speed up the solution and improve the accuracy, the upper and lower bounds of the updated observation and state quantity in step 3.1 are used to normalize the observation and state quantity in the training set and test set respectively. Pay attention to the state quantity output, design the loss function represented by the mean square error; considering the problem that too high or too low constant learning rate may lead to divergence or slow convergence of the loss function in the later training period, design a continuously decreasing learning rate based on the exponential function; set a certain number of rounds, train the long short-term memory network model built by forward propagation, loss calculation, gradient zero, back propagation and parameter update, and verify it without calculating the gradient and updating the parameters; learn the nonlinear relationship between the observation and the state quantity, so as to determine the initial orbit of the spatial target by updating the super-short-arc observation and the model parameters.

[0039] Step 4.1: according to a certain proportion, the sample data set for intelligent determination of the initial orbit of the spatial target super-short-arc is divided into a training set and a validation set, and 0.8:0.2 can be preferred; in order to facilitate data processing, speed up the solution and improve the accuracy, the upper and lower bounds of the updated observation and state quantity in step 3.1 are used to normalize the observation and state quantity in the training set and test set respectively.

[0040] In order to select the optimal long short-term memory network model to realize intelligent determination of the initial orbit of the spatial target super-short-arc, the sample data set is divided into a training set and a validation set according to a certain proportion. The training set is used to train the network model and determine the model weight, and the validation set is used to evaluate the network model and determine the model structure and adjust the model hyperparameters. 0.8:0.2 can be preferred as the division ratio.

[0041] Because the observation and state of the super short arc orbit determination of space targets have different dimensions and orders of magnitude, the features between different dimensions are considered to be comparable and weighted in value, the data of the training set and the test set are normalized to ensure the reliability of the results, which is beneficial to speed up the solution of the optimal solution and improve the accuracy. The Min-Max normalization method is used to linearly transform the original observation and state data in the sample data set using the upper and lower bounds of the observation and state, so that the results fall into the interval [0, 1]. The normalized observation and state are represented as:

[0042]

[0043] wherein subscript n represents normalization.

[0044] Step 4.2: Focus on the state output, design a loss function represented by mean square error; consider that too high or too low constant learning rate may lead to divergence or slow convergence of the loss function in the later training, design a constantly decreasing learning rate based on the exponential function; set a certain number of rounds, train the long short-term memory network model built in step 3.2 through forward propagation, loss calculation, gradient zero, back propagation and parameter update, and verify without calculating gradient and updating parameters; learn the nonlinear relationship between the observation and the state, and determine the initial orbit of the space target using the super short arc observation and the model parameter update.

[0045] Considering the state output in the intelligent determination of the super short arc initial orbit of space targets, the mean square error between the state prediction value and the true value s of the state is taken as a clue, and the optimal weight parameter is found by minimizing this index, which has the advantages of facilitating gradient descent and fast convergence. The loss function of the long short-term memory network model is designed and represented as:

[0046]

[0047] wherein N represents the number of samples, l i represents the loss value of the i-th sample.

[0048] Because too high constant learning rate may lead to divergence of the loss function in the later training, and too low constant learning rate will lead to slow convergence of the loss function, a gradually decreasing learning rate is designed to make the loss function for intelligent determination of the super short arc initial orbit of space targets stable convergence. The exponential function is selected to realize the learning rate decay, that is, a higher learning rate is used to quickly obtain a better solution, and then the learning rate is gradually reduced with the iteration of the training rounds, so that the network model is more stable in the later training. The learning rate updated based on the exponential function is represented as:

[0049] lr=lr0×γ epoch(8)

[0050] where lr0 represents the initial learning rate, γ represents the exponential decay rate in the interval [0, 1], and epoch represents the training round.

[0051] Set a certain number of round upper limit N e , train and verify the long short-term memory network model for intelligent determination of the initial orbit of a space target in a short arc. In each round, using the training set data, first, forward propagation is performed by inputting the observation input into the network model to predict the state output; second, the loss function is calculated according to the state prediction value and the true value of the state; then the gradient is initialized to 0, and the past gradient is cleared; then the loss value is back-propagated to the input side to calculate the current gradient; finally, according to the gradient, all network model parameters are updated. Using the validation set data, forward propagation is performed and the loss function is calculated, but gradient calculation is not performed, so the trained network model parameters are not changed, and only the training effect is evaluated. By training the network model, the nonlinear relationship between the observation input and the state output is learned, so that the initial orbit of the space target is determined using the short-arc observation and model parameter update.

[0052] Step five: according to the training loss and the validation loss, adjust the long short-term memory network model structure built and the dynamic change learning rate, training round and other hyperparameters set, check the model convergence and avoid underfitting or overfitting phenomenon; and take the difference between the state estimate value and the true value as the error indicator, and perform mean and standard deviation statistics on all errors of the entire validation set in each round; select the round with the minimum validation loss in the process of continuously decreasing training loss, if the error statistical value of the corresponding round is lower than the given threshold, then the network model of this round is taken as the optimal long short-term memory network model for intelligent determination of the initial orbit of the space target in a short arc.

[0053] According to the change of the training loss function and the validation loss function with the round, adjust the long short-term memory network model for intelligent determination of the initial orbit of the space target in a short arc, including the structure of the hidden layer state dimension, the batch dimension, the observation embedding layer, the state embedding layer and the state decoding layer; and adjust the dynamic change learning rate, the training round and other hyperparameters set. Make the loss function of the network model quickly and stably converge, and avoid underfitting or overfitting phenomenon.

[0054] To evaluate the effect of the long short-term memory network on the determination of the initial orbit of the space target in a short arc, the difference between the state prediction value and the true value in the validation process is taken as the error indicator, which is represented as:

[0055]

[0056] The mean and standard deviation statistics are performed according to all errors of the entire verification set in each round. The mean of the errors is error mean The smaller, the closer the initial orbit prediction result of the space target under the super-short-arc observation condition is to the true result, and the better the overall prediction effect is; the standard deviation of the error is error std The smaller, the smaller the discrete degree of the initial orbit prediction result of the space target under the super-short-arc observation condition corresponding to different observation quantities and the true result, and the more concentrated the prediction distribution is. The subscripts mean and std represent the mean and the standard deviation, respectively.

[0057] The optimal long short-term memory network model is selected by comprehensively utilizing the loss function and the error index to realize the intelligent determination of the initial orbit of the space target under the super-short-arc. In the process of continuously reducing the training loss, the round of the verification loss minimum of the non-underfitting or overfitting is found, and the determination criterion of the optimal model is represented as:

[0058]

[0059] Wherein, th mean And th std Respectively represent the error mean threshold and the error standard deviation threshold. When and only when the two inequalities of the determination criterion are established, the network model of the round is selected as the optimal long short-term memory network model for the intelligent determination of the initial orbit of the space target under the super-short-arc.

[0060] Step six, the optimal long short-term memory network model obtained in step five is utilized to determine the initial orbit of the space target under the super-short-arc, and the initial orbit is taken as the initial value for the refined orbit estimation, so that the high-precision orbit state of the space target is quickly obtained, the orbit prediction precision is improved, and the basis information is provided for the subsequent target selection, target approaching planning guidance control, and the efficiency and effect are improved.

[0061] Beneficial effects:

[0062] 1. The space target initial orbit determination method under the super-short-arc disclosed in the application realizes the determination of the initial orbit of the space target under the super-short-arc based on the artificial intelligence technology, has no strict requirement for complex nonlinear problems, can not only complete the solution of the space target initial orbit determination problem under the super-short-arc considering the two-body operation law, but also can develop the initial orbit determination under more complex perturbation conditions and multi-body operation law, and has a wider coverage.

[0063] 2. The space target initial orbit determination method under the super-short-arc disclosed in the application randomly generates multiple groups of target orbits, calculates the observation quantities and state quantities of each visible arc segment, and constructs a super-large-capacity sample data set, which is helpful for the neural network to learn the nonlinear relationship between the observation quantities and the state quantities by using rich samples, and to produce good prediction effect, and the robustness is strong and the reliability is high.

[0064] 3. The space target ultra-short arc initial orbit intelligent determination method disclosed by the application can quickly predict the solution of the initial orbit of the unknown space target according to the observation, can solve the convergence problem, and has higher solving efficiency compared with the traditional initial orbit solving method.

[0065] 4. The space target ultra-short arc initial orbit intelligent determination method disclosed by the application can meet more space target ultra-short arc initial orbit determination task scenarios by considering different inputs and outputs, can further realize precise orbit determination by taking the predicted solution as the initial value, is suitable for subsequent various task scenarios, has strong flexibility and high expansibility. BRIEF DESCRIPTION OF DRAWINGS

[0066] Figure 1 is a flowchart of the space target ultra-short arc initial orbit intelligent determination method of the application;

[0067] Figure 2 is a curve of the training loss and the validation loss changing with the number of rounds in the embodiment;

[0068] Figure 3 is a statistical distribution diagram of the error index in the embodiment. DETAILED DESCRIPTION

[0069] In order to better illustrate the purposes and advantages of the application, the following will make a detailed explanation of the application by simulating and analyzing a space target ultra-short arc initial orbit intelligent determination method.

[0070] As shown in Figure 1 , the space target ultra-short arc initial orbit intelligent determination method disclosed by the embodiment has the following specific steps:

[0071] Step 1: Establish the geocentric inertial coordinate system for space target ultra-short arc initial orbit determination.

[0072] The center of the earth is selected as the coordinate origin O to establish the geocentric inertial coordinate system. The x-axis points to the equinox point, the z-axis is along the earth rotation axis and points to the north pole. The y-axis and the x-axis and the z-axis form a right-handed rectangular coordinate system, that is, the establishment of the geocentric inertial coordinate system for space target ultra-short arc initial orbit determination is completed.

[0073] Step Two: Establish the observation and state quantity representations for the initial ultra-short arc trajectory of the space target in the geocentric inertial coordinate system. The observations consider the azimuth angle of the ground station, the line-of-sight angle of the space target, and their rate of change, converted from Cartesian position coordinates to spherical coordinates. The state quantities consider the relative distance modulus and relative velocity modulus of the space target relative to the ground station. The two-body dynamics model requires fewer parameters than the multi-body dynamics model but still reflects the dynamic state of the space target. Furthermore, the main perturbation parameter of the two-body dynamics model is the Earth's J2 gravitational perturbation, which has the greatest impact on the space target's dynamics. Therefore, a two-body dynamics model of the space target is established that only considers the influence of the Earth's J2 gravitational perturbation.

[0074] Step 2.1: Establish the observation and state quantity representation of the initial trajectory of the space target in the geocentric inertial coordinate system. The observation considers the azimuth of the ground station, the line-of-sight angle of the space target and its rate of change, which are converted from Cartesian position coordinates to spherical coordinates. The state quantity considers the relative distance modulus and relative velocity modulus of the space target relative to the ground station.

[0075] In the geocentric inertial coordinate system, the 7×1 dimensional observations of a space target by a ground station are represented as follows:

[0076]

[0077] in, This represents the counterclockwise azimuth angle of the ground station's location on the xy plane, measured from the x-axis of the geocentric inertial coordinate system. and These represent the line-of-sight angle of the space target relative to the ground station in the geocentric inertial coordinate system and its rate of change, respectively. Where r... t =[x t y t z t ] T and r s =[x s y s z s ] T Let represent the position coordinates of the space target and the ground station in the geocentric inertial coordinate system, respectively, and Δr = r t -r s Δr = ||Δr|| represents the relative position vector of the space target with respect to the ground station and its magnitude, respectively. 3×3 It is a 3×3 identity matrix, where the subscript t represents a space target and the subscript s represents a ground station.

[0078] The 2×1 dimensional state variables of a space target observed by a ground station in a geocentric inertial coordinate system are represented as follows:

[0079]

[0080] where, Δv = ||Δv|| = ||v t -v s || represents the relative velocity vector module of the space target relative to the ground station, v t = [vx t vy t vz t ] T and v s = [vx s vy s vz s ] T respectively represent the velocity coordinates of the space target and the ground station in the geocentric inertial coordinate system.

[0081] Step 2.2: The two-body dynamic model requires fewer parameters than the multi-body dynamic model but can still reflect the dynamic state of the space target, and the main perturbation parameter of the two-body dynamic model is the J2 term gravitational perturbation of the Earth which has the greatest impact on the dynamics of the space target, that is, a two-body dynamic model of the space target is established considering only the influence of the J2 term gravitational perturbation of the Earth.

[0082] Considering only the influence of the J2 term gravitational perturbation of the Earth, the two-body dynamic model of the space target is expressed as:

[0083]

[0084] where, dr t and dv t respectively represent the position vector rate of change and the velocity vector rate of change of the space target in the geocentric inertial coordinate system, subscript e represents the Earth, μ e represents the Earth's gravitational constant, r t = ||r t || represents the position vector module of the space target, represents the J2 term gravitational perturbation of the Earth related to the position vector of the space target. Where, J2 is the J2 term gravitational perturbation coefficient of the Earth, R e is the average radius of the Earth.

[0085] Step three: generate multiple sets of target orbit elements by combining Latin hypercube sampling and the given upper and lower bounds of the set of spatial target orbit elements; obtain the orbit evolution by dynamics integration using the two-body dynamics model considering only the J2 term established in step 2.2; calculate the observation and state quantity of each visible arc segment of each set of sampled orbits represented by step 2.1, and continuously update the upper and lower bounds of both; construct a sample data set for intelligent determination of the initial orbit of the super-short arc of the spatial target by taking the observation as input, the state quantity as label, and introducing the upper and lower bounds of both; consider the observation represented by step 2.1 and the state quantity as input and output respectively, and build a long short-term memory network model for intelligent determination of the initial orbit of the super-short arc of the spatial target; design an observation embedding layer combining the multilayer perception model and the linear function and nonlinear excitation function to extract the features of the 7-dimensional observation input; design a state quantity embedding layer to extract the features of the S-dimensional state quantity input; design a state quantity decoding layer to extract the features of the state quantity embedding layer output as input and obtain a 2-dimensional state quantity output.

[0086] Step 3.1: generate multiple sets of target orbit elements by combining Latin hypercube sampling and the given upper and lower bounds of the set of spatial target orbit elements; obtain the orbit evolution by dynamics integration using the two-body dynamics model considering only the J2 term established in step 2.2; calculate the observation and state quantity of each visible arc segment of each set of sampled orbits represented by step 2.1, and continuously update the upper and lower bounds of both; construct a sample data set for intelligent determination of the initial orbit of the super-short arc of the spatial target by taking the observation as input, the state quantity as label, and introducing the upper and lower bounds of both.

[0087] The orbit elements of the spatial target are 6-dimensional, including semi-major axis a, eccentricity e, inclination i, ascending node right ascension Ω, perigee amplitude ω, and true anomaly θ. The Latin hypercube sampling method subject to uniform distribution is adopted to divide the 0-1 sample space into 2000 layers, making each layer sample dimension 6-dimensional, and the elements in each dimension are randomly arranged. On the basis of sampling, the upper bound e u =[a u e u i u Ω u ω u θ u ] and the lower bound e l =[a l e l i l Ω l ω l θ l ] of the orbit elements of the spatial target are further given, and the n sets of spatial target orbit elements generated to satisfy the limits are represented as:

[0088] e=e s• (e u - e l + e l (14)

[0089] where e s represents the 2000 x 6-dimensional Latin hypercube sampling result, and the symbol "·" represents the dot product.

[0090] Using the spatial target two-body dynamics model in formula (3) considering only the influence of the Earth J2 term gravitational perturbation, taking the position vector r0 and the velocity vector v0 of the orbit root number in the Earth-centered inertial coordinate system as the initial value of integration, setting the integration interval [t0, t f ] and the integration step size dt, the orbit state evolution of the position vector and the velocity vector of the spatial target is obtained by integration. The visible arc segment of each sampling orbit of the spatial target is calculated and recorded, and the observation and state quantity of each visible arc segment in each sampling orbit are solved. Given a set of observation interval upper and lower limit initial values o u0 , o l0 and state quantity interval upper and lower limit initial values s u0 , s l0 , the solving results are compared and continuously updated to obtain the observation interval upper and lower limits o u and o l , and the state quantity interval upper and lower limits s u and s l .

[0091] To realize the intelligent determination of the super-short-arc initial orbit of the spatial target, the observation is considered as the input, the state quantity is considered as the label, and the interval upper and lower limits of the two are introduced to construct the sample data set.

[0092] Step 3.2: Considering the observation and state quantity represented in step 2.1 as input and output respectively, a long short-term memory network model for intelligent determination of the super-short-arc initial orbit of the spatial target is built; combined with the multilayer perception model and linear function and nonlinear excitation function, the observation embedding layer is designed to extract the features of the 7-dimensional observation input; the state quantity embedding layer is designed to extract the features of the 6-dimensional state quantity input; the state quantity decoding layer is designed to extract the features of the state quantity embedding layer output as input, and obtain the 2-dimensional state quantity output.

[0093] The input feature dimension of the long short-term memory network model for intelligent determination of the super-short-arc initial orbit of the spatial target is set to 7 dimensions, the hidden layer state dimension is set to 256 dimensions, the network stacking number is set to 1 layer, and the batch dimension is set to 1 dimension.

[0094] To characterize and extract the feature information of 7-dimensional observation, a multi-layer alternating linear function and nonlinear activation function are used to design the observation embedding layer. The linear function of the first layer expands the 7-dimensional observation input to 256 dimensions, and the multiple linear functions of the middle layer perform multiple feature processing, and the linear function of the last layer finally maps the features to 256 dimensions. An activation function is used between every two linear functions to introduce nonlinearity, so that the neural network can arbitrarily approximate any nonlinear function. LeakyReLU function is selected as the nonlinear activation function of the observation embedding layer, which is expressed as:

[0095]

[0096] where λ is a very small positive number. Thus, it can reduce the possibility of gradient vanishing and gradient explosion during subsequent network training, has the advantages of low computational complexity and fast convergence speed, and is more inclined to activate than neuron necrosis in the negative number region compared with ReLU function.

[0097] To obtain the final 2-dimensional state quantity, a state quantity embedding layer and a state quantity decoding layer with similar structure to the observation embedding layer are designed. Similarly, a multi-layer alternating linear function and LeakyReLU nonlinear activation function of formula (5) are used, and the state quantity embedding layer maps the 6-dimensional state quantity to 256 dimensions; the state quantity decoding layer takes the 256-dimensional feature output by the state quantity embedding layer as input and maps it to 2-dimensional state quantity after multiple processing.

[0098] The long short-term memory network uses the hidden layer state h(t) and the neuron state c(t) to record the variables of the previous state, which changes with the new input x(t). The hidden layer state h(t) records more recent information and changes faster, while the neuron state c(t) records more distant information and changes slower. To solve the spatial target super-short arc initial orbit determination problem, the dimension of the initial hidden layer state h0 of the network is set to the number of network stacking layers × batch dimension × hidden layer state dimension, i.e. (1 × 1 × 256) dimensions; the initial neuron state c0 is a zero tensor with the same dimension as the initial hidden layer state h0.

[0099] Step four: Divide the sample data set for intelligent determination of the initial orbit of a space target in a certain proportion into a training set and a validation set, with 0.8:0.2 being preferred; in order to facilitate data processing, accelerate solution speed and improve accuracy, use the upper and lower bounds of the updated observations and state quantities in step 3.1 to normalize the observations and state quantities in the training set and the test set respectively. Focus on the state quantity output, and design a loss function represented by the mean square error; considering that a constant learning rate that is too high or too low may cause the loss function to diverge or converge slowly in the later training period, design a learning rate that decreases based on an exponential function; set a certain number of rounds, train the long short-term memory network model built in step 3.2 through forward propagation, loss calculation, gradient zeroing, back propagation and parameter updating, and verify it without calculating gradients and updating parameters; learn the nonlinear relationship between the observations and the state quantities, so as to determine the initial orbit of the space target by using the super-short-arc observations and model parameter updates.

[0100] Step 4.1: Divide the sample data set for intelligent determination of the initial orbit of a space target in a certain proportion into a training set and a validation set, with 0.8:0.2 being preferred; in order to facilitate data processing, accelerate solution speed and improve accuracy, use the upper and lower bounds of the updated observations and state quantities in step 3.1 to normalize the observations and state quantities in the training set and the test set respectively.

[0101] In order to select the optimal long short-term memory network model to achieve intelligent determination of the initial orbit of a space target, the sample data set is divided into a training set and a validation set in a certain proportion. The training set is used to train the network model and determine the model weight, and the validation set is used to evaluate the network model and determine the model structure and adjust the model hyperparameters. 0.8:0.2 can be preferred as the division ratio.

[0102] Since the observations and state quantities for the super-short-arc orbit determination of a space target have different dimensions and orders of magnitude, it is considered that the features between different dimensions are comparable and can be weighted in value. The data in the training set and the test set are normalized to ensure the reliability of the results and facilitate the acceleration of the solution speed and the improvement of the accuracy. Use the upper and lower bounds of the observations and state quantities to perform linear transformation on the original observations and state quantity data in the sample data set using the Min-Max normalization method, so that the results fall within the [0, 1] interval. The normalized observations and state quantities are represented as:

[0103]

[0104] where subscript n represents normalization.

[0105] Step 4.2: Focus on the state quantity output, design the loss function expressed in mean square error; consider that too high or too low constant learning rate may lead to loss function divergence or slow convergence in the later training period, design a constantly decreasing learning rate based on exponential function; set a certain number of rounds, train the long short-term memory network model built in step 3.2 through forward propagation, loss calculation, gradient zeroing, back propagation and parameter updating, and verify without calculating gradient and updating parameters; learn the nonlinear relationship between observation quantity and state quantity, and determine the initial orbit of space target by using ultra-short arc observation quantity and model parameter updating.

[0106] Considering the state quantity output focused on in the intelligent determination of the initial orbit of space target ultra-short arc, the mean square error between the predicted value of the state quantity and the true value of the state quantity s is taken as a clue, and the optimal weight parameter is found by minimizing this index, which has the advantages of facilitating gradient descent method and fast convergence speed. The loss function of the long short-term memory network model is designed and expressed as:

[0107]

[0108] Where N represents the number of samples, l i represents the loss value of the i-th sample.

[0109] Since too high constant learning rate may lead to loss function divergence in the later training period, and too low constant learning rate may lead to slow convergence of loss function, a gradually decreasing learning rate is designed to make the loss function for intelligent determination of the initial orbit of space target ultra-short arc stable convergence. Exponential function is selected to realize learning rate decay, that is, a higher learning rate is used to quickly obtain a better solution, and then the learning rate is gradually reduced with the iteration of training rounds, so that the network model is more stable in the later training period. The learning rate updated based on exponential function is expressed as:

[0110] lr = lr0 x γ epoch (18)

[0111] Where lr0 represents the initial learning rate, γ represents the exponential decay rate in the interval [0, 1], and epoch represents the training rounds.

[0112] Set a certain number of rounds upper limit N e, train and verify the long short-term memory network model for intelligent determination of the initial orbit of the space target under the super-short arc. In each round, using the training set data, first, forward propagation is carried out, and the state quantity output is predicted by inputting the observation quantity into the network model; second, the loss function is calculated according to the state quantity prediction value and the state quantity true value; then, the gradient is initialized to 0, and the past gradient is cleared; then, the loss value is back propagated to the input side, and the current gradient is calculated; finally, according to the gradient, all network model parameters are updated. Using the validation set data, forward propagation is carried out and the loss function is calculated, but the gradient is not calculated by back propagation, so the trained network model parameters are not changed, and are only used to evaluate the training effect. Through the training of the network model, the nonlinear relationship between the observation quantity input and the state quantity output is learned, so as to determine the initial orbit of the space target by using the super-short arc observation quantity and the model parameter update.

[0113] Step five: according to the training loss and the validation loss, adjust the long short-term memory network model structure built in step 3.2 and the dynamic change learning rate, training round and other hyperparameters set in step 4.2, check the model convergence and avoid underfitting or overfitting phenomenon; and take the difference between the state quantity estimated value and the true value as the error indicator, and perform mean and standard deviation statistics on all errors of the entire validation set in each round; select the round with the minimum validation loss in the process of continuously decreasing training loss, if the error statistical value of the corresponding round is lower than the given threshold, the network model of the round is taken as the optimal long short-term memory network model for intelligent determination of the initial orbit of the space target under the super-short arc.

[0114] According to the change of the training loss function and the validation loss function with the round, adjust the long short-term memory network model for intelligent determination of the initial orbit of the space target under the super-short arc, including the hidden layer state dimension, the batch processing dimension, the structure of the observation quantity embedding layer, the state quantity embedding layer and the state quantity decoding layer; and adjust the dynamic change learning rate, the training round and other hyperparameters. Make the loss function of the network model converge quickly and stably, and avoid underfitting or overfitting phenomenon.

[0115] In order to evaluate the effect of the long short-term memory network on the determination of the initial orbit of the space target under the super-short arc, the difference between the state quantity prediction value and the state quantity true value in the validation process is taken as the error indicator, which is represented as:

[0116]

[0117] According to all errors of the entire validation set in each round, the mean and standard deviation are calculated. The mean of the error error mean The smaller, the closer the initial orbit prediction result under the super-short arc observation condition of the space target to the true result, and the better the overall prediction effect; the standard deviation of the error error stdThe smaller, the smaller the dispersion degree of the initial orbit prediction result of the space target corresponding to different observations and the true result, and the more concentrated the prediction distribution. The subscripts mean and std represent the mean and standard deviation, respectively.

[0118] The loss function and the error index are comprehensively utilized to select the optimal long short-term memory network model to realize intelligent determination of the initial orbit of the space target. In the process of continuously reducing the training loss, the verification loss minimum round of non-underfitting or overfitting is found, and the determination criterion of the optimal model is represented as:

[0119]

[0120] th mean and th std respectively represent the error mean threshold and the error standard deviation threshold. When and only when the two inequalities of the determination criterion are both established, the network model of this round is selected as the optimal long short-term memory network model for intelligent determination of the initial orbit of the space target.

[0121] Step six is also included, that is, using the optimal long short-term memory network model obtained in step five, determining the initial orbit of the space target in the ultra-short arc, and using it as the initial value for refined orbit estimation, and then quickly obtaining the high-precision orbit state of the space target, improving the orbit prediction accuracy, and providing basic information for subsequent target selection, target approaching planning guidance control and improving efficiency and effect.

[0122] In order to verify the feasibility and effectiveness of the method, the basic parameters are selected as shown in Table 1.

[0123] Table 1 Basic parameters

[0124]

[0125] In this embodiment, the Latin hypercube sampling method conforming to the uniform distribution is adopted, the 0-1 sample space is equally divided into 2000 layers, and the two-body dynamics model integral considering only the J2 term is used to obtain the orbit state evolution. 13448 groups of observations and state quantities of each sampling orbit are calculated, and the upper and lower bounds of the observation interval are updated to o u = [180.00, 1.00, 1.00, 1.00, 6.45x10 -16 , 7.11x10 -16 , 5.59x10 -16 ] and o l = [-180.00, -1.00, -1.00, -0.86, -6.24x10 -16 , -6.18x10 -16 , -5.41x10 -16], the lower bound of the state quantity interval is s u = [8388.06, 0.01, 0.01, 5485.67, 13.61] and s l = [6569.66, -0.01, -0.01, 195.30, 11.85].

[0126] After the sample data set is constructed, a training set containing 10758 groups of data and a test set containing 2690 groups of data are divided in a ratio of 0.8:0.2 and rounded. After appropriate adjustment, the designed long short-term memory network model is trained and verified for 100 rounds using the sample data set, and the training loss and verification loss are as shown in Figure 2 . The training loss continuously decreases with the rounds, showing a rapid downward trend within 10 times, and the decline slows down after 10 times, with the minimum value being 0.0019523 at the 100th round. The verification loss also shows a rapid downward trend within 10 times, and the degree of decline remains almost unchanged after 10 times, with the minimum value being 0.0053111 at the 72nd round. Therefore, the error indicators of the 72nd round are counted, and the mean and standard deviation are calculated, and the error statistical histogram is as shown in Figure 3 . The mean error of the relative distance module length is -0.0010652, and the standard deviation is 0.0570349; the mean error of the relative speed module length is 0.0066679, and the standard deviation is 0.0764903. The loss function and the error indicators meet the determination criteria, so the long short-term memory network model of the 72nd round can be used as the optimal network model for intelligent determination of the super-short-arc initial orbit of the space target. In addition, for the observation quantity input in the verification set, the prediction time of the state quantity output of the model is less than 1.5 milliseconds.

[0127] This example demonstrates the feasibility and effectiveness of the method, as well as the robustness, solving efficiency and solving accuracy of the obtained space target super-short-arc initial orbit prediction results, which has potential applications in complex real-time task scenarios.

[0128] The above specific description further details the purpose, technical solutions and beneficial effects of the application. It should be understood that the above description is only a specific embodiment of the application, which is used to explain the application and does not limit the protection scope of the application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the application shall be included in the protection scope of the application.

Claims

1. A method for intelligent determination of initial orbit of space target with ultra-short arc, characterized in that: Comprising the following steps, Step one: Establish the geocentric inertial coordinate system for the initial orbit determination of the space target in the ultra-short arc; Step two: Establish the observation and state quantity representation of the initial orbit determination of the space target in the ultra-short arc in the geocentric inertial coordinate system, the observation considers the azimuth angle of the ground station converted from the Cartesian position coordinates, the line-of-sight angle of the space target and its rate of change, and the state quantity considers the relative distance and relative velocity of the space target relative to the ground station; the two-body dynamics model requires fewer parameters than the multi-body dynamics model but can still reflect the dynamics state of the space target, and the main perturbation parameter of the two-body dynamics model is the J2 term of the Earth's gravity perturbation which has the greatest impact on the dynamics of the space target, that is, to establish a two-body dynamics model of the space target considering only the influence of the J2 term of the Earth's gravity perturbation; The implementation method of step two is, Step 2.1: Establish the observation and state quantity representation of the initial orbit determination of the space target in the ultra-short arc in the geocentric inertial coordinate system, the observation considers the azimuth angle of the ground station converted from the Cartesian position coordinates, the line-of-sight angle of the space target and its rate of change, and the state quantity considers the relative distance and relative velocity of the space target relative to the ground station; The 7x1-dimensional observation of the space target by the ground station in the geocentric inertial coordinate system is represented as: wherein denotes the counterclockwise azimuth in the xy-plane measured from the x-axis of the geocentric inertial coordinate system of the position of the ground station, and denote the line-of-sight angle and its rate of change of the space object relative to the ground station in the geocentric inertial coordinate system, respectively; wherein r t = [x t y t z t ] T and r s = [x s y s z s ] T denote the position coordinates of the space object and the ground station in the geocentric inertial coordinate system, respectively, while Δr = r t - r s and ||Δr|| = ||Δr|| denote the relative position vector and its magnitude of the space object relative to the ground station, I 3×3 is a 3x3 dimensional identity matrix, and the subscript t stands for the space object and the subscript s stands for the ground station; The 2x1-dimensional state quantity of the space target observed by the ground station in the geocentric inertial coordinate system is represented as: where Δv = ||Δv|| = ||v t -v s || represents the relative velocity vector module of the space object with respect to the ground station, v t = [vx t vy t vz t ] T and v s = [vx s vy s vz s ] T are the velocity coordinates of the space object and the ground station in the geocentric inertial coordinate system, respectively. Step 2.2: The two-body dynamics model requires fewer parameters than the multi-body dynamics model but can still reflect the dynamics state of the space target, and the main perturbation parameter of the two-body dynamics model is the J2 term of the Earth's gravity perturbation which has the greatest impact on the dynamics of the space target, that is, to establish a two-body dynamics model of the space target considering only the influence of the J2 term of the Earth's gravity perturbation; Considering only the influence of the J2 term of the Earth's gravity perturbation, the two-body dynamics model of the space target is represented as: where dr t and dv t denote the position and velocity vector rate of change of the space object in the geocentric inertial coordinate system, respectively, and subscript e represents the Earth, μ e denotes the Earth gravitational constant, r t = ||r t || denotes the position vector module of the space object, denotes the Earth J2 term gravitational perturbation related to the position vector of the space object; where J2 is the Earth J2 term gravitational perturbation coefficient, R e is the average Earth radius Step three: Combine the Latin hypercube sampling and the given upper and lower bounds of a set of space target orbit elements to generate multiple sets of target orbit elements; use the two-body dynamics model considering only the J2 term established in step 2.2 to obtain the orbit evolution through dynamics integration; calculate the observation and state quantity of each visible arc segment of each set of sampled orbits represented in step 2.1, and continuously update the upper and lower bounds of the two; take the observation as the input, the state quantity as the label, and introduce the upper and lower bounds of the two, to construct a sample data set for the intelligent determination of the initial orbit of the space target in the ultra-short arc; considering the observation and state quantity represented in step two as input and output respectively, build a long short-term memory network model for the intelligent determination of the initial orbit of the space target in the ultra-short arc; combine the multilayer perception model and the linear function and nonlinear excitation function to design the observation embedding layer to extract the features of the 7-dimensional observation input; design the state quantity embedding layer to extract the features of the S-dimensional state quantity input; design the state quantity decoding layer to extract the features of the state quantity embedding layer output as input and obtain the 2-dimensional state quantity output; Step four: divide the sample data set for intelligent determination of the initial orbit of a space target in a super-short arc into a training set and a validation set in a predetermined ratio; for the convenience of data processing, acceleration of solving speed and improvement of accuracy, use the upper and lower bounds of the updated observation and state quantity in step 3.1 to normalize the observation and state quantity in the training set and the test set respectively; focus on the state quantity output, design a loss function represented by the mean square deviation; consider that a too high or too low constant learning rate may lead to divergence or slow convergence of the loss function in the later training period, and design a continuously decreasing learning rate based on an exponential function; set a certain number of rounds, train the built long short-term memory network model through forward propagation, loss calculation, gradient zeroing, back propagation and parameter updating, and verify it without calculating the gradient and updating the parameters; learn the nonlinear relationship between the observation and the state quantity, so as to determine the initial orbit of the space target by using the super-short arc observation and the model parameter update; Step five: according to the training loss and the validation loss, adjust the structure of the built long short-term memory network model and the set dynamic change learning rate, training rounds and other hyperparameters, check the model convergence and avoid underfitting or overfitting; and take the difference between the state quantity estimated value and the true value as the error indicator, and statistically analyze the mean and standard deviation of all errors of the entire validation set in each round; select the round with the minimum validation loss in the process of continuously decreasing training loss, and if the error statistical value of the corresponding round is lower than a given threshold, the network model of the round is taken as the optimal long short-term memory network model for intelligent determination of the initial orbit of a space target in a super-short arc.

2. The method of claim 1, wherein: the initial orbit of the space object is determined based on the at least one of the plurality of observations. Step six: use the optimal long short-term memory network model obtained in step five to determine the initial orbit of a space target in a super-short arc, and use it as the initial value for refined orbit estimation, so as to quickly obtain a high-precision space target orbit state and improve the orbit prediction accuracy.

3. The method of claim 1 or 2, wherein: The implementation method of step one is, The center of the earth is selected as the coordinate origin O to establish the geocentric inertial coordinate system; the x-axis points to the equinox point, the z-axis points to the north pole along the earth's rotation axis, and the y-axis forms a right-handed rectangular coordinate system with the x-axis and the z-axis, that is, the establishment of the geocentric inertial coordinate system for determining the initial orbit of a space target in a super-short arc is realized.

4. The intelligent method for determining the initial trajectory of a space target in an ultra-short arc as described in claim 1, characterized in that: The implementation method of step three is, Step 3.1: generate multiple groups of target orbit elements in combination with Latin hypercube sampling and a given set of upper and lower bounds of the space target orbit element intervals; use the two-body dynamics model considering only the J2 term established in step 2.2 to obtain the orbit evolution through dynamics integration; calculate the observation and state quantity of each visible arc segment of each group of sampled orbits represented by step 2.1, and continuously update the upper and lower bounds of the two intervals accordingly; take the observation as the input, the state quantity as the label, and introduce the upper and lower bounds of the two intervals to construct a sample data set for intelligent determination of the initial orbit of a space target in a super-short arc; The spatial target orbit root number is 6 dimensions, including semi-major axis a, eccentricity e, inclination i, ascending node right ascension Ω, perigee amplitude ω, and true perigee angle θ; the Latin hypercube sampling method subject to uniform distribution is adopted, the 0-1 sample space is equally divided into n layers, so that the sample dimension of each layer is 6 dimensions, and the elements in each dimension are randomly arranged; on the basis of sampling, the upper bound e u =[a u e u i u Ω u ω u θ u ] of the orbit root number of the spatial target and the lower bound e l =[a l e l i l Ω l ω l θ l ] of the orbit root number are further given, and the n groups of spatial target orbit root numbers generated to satisfy the limits are represented as: e = e s • (e u - e l ) + e l (4) where e s denotes the n x 6-dimensional Latin hypercube sampling result, and the symbol "•" denotes the dot product; The two-body dynamics model of the space target in formula (3) only considers the influence of the J2 term of the earth gravity perturbation, and the position vector r0 and the velocity vector v0 of the orbit root number in the earth-centered inertial coordinate system are used as the integral initial value, the integral interval [t0, t f ] and the integral step size dt are set, and a plurality of groups of the orbit state evolution of the position vector and the velocity vector of the space target are obtained by integration; the visible arc segments of each group of the sampling orbit of the space target are calculated and recorded, and the observation quantity and the state quantity of each visible arc segment in each group of the sampling orbit are solved; a group of the upper and lower initial values o u0 , o l0 of the observation quantity interval and the upper and lower initial values s u0 , s l0 of the state quantity interval are given, the solving results are compared each time and are constantly updated, and the upper and lower o u and o l of the observation quantity interval and the upper and lower s u and s l of the state quantity interval are obtained; To realize intelligent determination of the initial orbit of a space target in a super-short arc, consider taking the observation as the input, the state quantity as the label, and introducing the upper and lower bounds of the two intervals to construct a sample data set; Step 3.2: Considering the observation quantity and state quantity represented in step 2.1 as input and output respectively, a long short-term memory network model for intelligent determination of space target ultra-short-arc initial orbit is built; combined with multi-layer perception model and linear function and nonlinear excitation function, an observation quantity embedding layer is designed to extract the features of 7-dimensional observation quantity input; a state quantity embedding layer is designed to extract the features of S-dimensional state quantity input; a state quantity decoding layer is designed to extract the features of state quantity embedding layer output as input and obtain 2-dimensional state quantity output; The input feature dimension of the long short-term memory network model for intelligent determination of space target ultra-short-arc initial orbit is set to 7 dimensions, the hidden layer state dimension is H dimensions, the network stacking layer number is L layers, and the batch processing dimension is B dimensions; To characterize and extract the feature information of 7-dimensional observation, the observation embedding layer is designed by using multiple layers of linear functions and nonlinear activation functions. The linear function of the first layer expands the 7-dimensional observation input to K o dimensions, the multiple linear functions of the intermediate layers perform multiple feature processing, and the linear function of the last layer finally maps the features to D o dimensions; the activation function is used between each two linear functions, and the nonlinear factor is introduced to make the neural network arbitrarily approximate any nonlinear function; the LeakyReLU function is selected as the nonlinear activation function of the observation embedding layer, which is represented as: Where λ is a very small normal number; thus reducing the possibility of gradient disappearance and gradient explosion in subsequent network training, having the advantages of low computational complexity, fast convergence speed, etc., and being more biased towards activation than neuron necrosis in the negative number region relative to the ReLU function; To obtain the final 2-dimensional state quantity, a state quantity embedding layer and a state quantity decoding layer similar to the structure of the observation quantity embedding layer and the observation quantity decoding layer are designed; similarly, by using a plurality of linear functions and a LeakyReLU nonlinear excitation function of formula (5), the state quantity embedding layer maps the S-dimensional state quantity to D s dimensional features as input, and maps them to 2-dimensional state quantities after multiple processing. s dimensional features as input, and maps them to 2-dimensional state quantities after multiple processing. The long short-term memory network uses the hidden layer state h(t) and the neuron state c(t) to represent the variables recording the previous state, and changes with the new input x(t); the hidden layer state h(t) records more recent information and changes faster; the neuron state c(t) records more distant information and changes slower; in order to solve the space target ultra-short-arc initial orbit determination problem, the dimension of the network initial hidden layer state h0 is set to network stacking layer number x batch processing dimension x hidden layer state dimension, i.e. (L x B x H) dimensions; the initial neuron state c0 is a zero tensor with the same dimension as the initial hidden layer state h0.

5. The intelligent method for determining the initial trajectory of a space target in an ultra-short arc as described in claim 4, characterized in that: The implementation method of step four is, Step 4.1: According to a certain proportion, divide the sample data set for intelligent determination of space target ultra-short-arc initial orbit into training set and validation set; in order to facilitate data processing, speed up the solution and improve the accuracy, use the upper and lower bounds of the updated observation quantity and state quantity in step 3.1 to normalize the observation quantity and state quantity in the training set and test set respectively; In order to select the optimal long short-term memory network model to realize the intelligent determination of space target ultra-short-arc initial orbit, the sample data set is divided into training set and validation set according to a certain proportion; The training set is used to train the network model and determine the model weight, and the validation set is used to evaluate the network model and determine the model structure and adjust the model hyperparameters; Since the observation quantity and state quantity of space target ultra-short-arc orbit determination have different dimensions and orders of magnitude, consider making the features between different dimensions comparable and weighted in value, normalize the data of the training set and test set to ensure the reliability of the results and facilitate the speed of solving the optimal solution and improve the accuracy; use the Min-Max normalization method to linearly transform the original observation quantity and state quantity data in the sample data set, so that the results fall into the [0, 1] interval; the normalized observation quantity and state quantity are represented as: Where subscript n represents normalization; Step 4.2: Focus on the state quantity output, design the loss function expressed in mean square error; consider that too high or too low constant learning rate may lead to loss function divergence or slow convergence in the later training period, design a constantly decreasing learning rate based on exponential function; set a certain number of rounds, train the long short-term memory network model built in step 3.2 through forward propagation, loss calculation, gradient zeroing, back propagation, parameter updating, and verify without calculating gradient and updating parameters; learn the nonlinear relationship between observation and state quantity, and determine the initial orbit of space target by using ultra-short arc observation and model parameter updating; In the problem of intelligent determination of the initial trajectory of a space target in an ultra-short arc, the output of the state variables of interest is considered, and the predicted values ​​of the state variables are used as the basis for this problem. Using the mean squared error between the actual state value s and the mean squared error as a clue, the optimal weight parameters are found by minimizing this index. This approach has the advantages of being convenient for gradient descent and having a fast convergence speed. The loss function of the Long Short-Term Memory network model is designed as follows: where N represents the number of samples, l i represents the loss value of the i-th sample; Because too high constant learning rate may lead to loss function divergence in the later training period, and too low constant learning rate will lead to slow convergence of loss function, a gradually decreasing learning rate is designed to make the loss function for intelligent determination of space target ultra-short arc initial orbit stable convergence; exponential function is selected to realize learning rate decay, that is, a higher learning rate is used to quickly obtain a better solution, and then the learning rate is gradually reduced with the iteration of training rounds, so that the network model is more stable in the later training period; the learning rate updated based on exponential function is expressed as: lr = lr0 x γ epoch (8) Where lr0 represents the initial learning rate, γ represents the exponential decay rate in the interval [0, 1], and epoch represents the training rounds; Setting a certain number of rounds upper limit N e , train and verify long short-term memory network model for intelligent determination of initial orbit of space target with ultra-short arc; in each round, using training set data, first forward propagation, by passing into the network model observation input to predict state output; second, according to the state prediction value and the state true value, the loss function is calculated; then the gradient is initialized to 0, and the past gradient is cleared; then the loss value is back propagated to the input side, and the current gradient is calculated; finally, according to the gradient, update all network model parameters; using validation set data, forward propagation and loss function calculation, but no backward propagation to calculate gradient, so no change to the trained network model parameters, only for evaluating the training effect; through the training of network model, learning the nonlinear relationship between observation input and state output, so as to determine the initial orbit of space target by using ultra-short arc observation and model parameter update.

6. The method of claim 5, wherein: The implementation method of step five is, According to the change of training loss function and validation loss function with rounds, the long short-term memory network model for intelligent determination of space ultra-short arc initial orbit is adjusted, including the structure of hidden layer state dimension, batch dimension, observation embedding layer, state quantity embedding layer and state quantity decoding layer; and the dynamically changing learning rate, training rounds and other hyperparameters are adjusted; so that the loss function of the network model converges quickly and stably, and the underfitting or overfitting phenomenon is avoided; To evaluate the effect of long short-term memory network on the determination of space target ultra-short arc initial orbit, the difference between the state quantity predicted value and the true value in the verification process is taken as the error index, which is expressed as: The mean and standard deviation statistics are performed according to all errors of the entire validation set in each round; the mean of the errors error mean The smaller, the closer the initial orbit prediction result of the space target under the super-short-arc observation condition is to the true result, and the better the overall prediction effect; the standard deviation of the errors error std The smaller, the smaller the dispersion degree of the initial orbit prediction result of the space target under the super-short-arc observation condition and the true result corresponding to different observation quantities, and the more concentrated the prediction distribution; the subscripts mean and std represent the mean and standard deviation, respectively; By comprehensively utilizing the loss function and error index, the optimal long short-term memory network model is selected to realize the intelligent determination of space target ultra-short arc initial orbit; in the process of continuous decline of training loss, the round with the minimum validation loss without underfitting or overfitting is found, and the judgment standard of optimal model is expressed as: wherein th mean and th std respectively represent the error mean threshold and the error standard deviation threshold; the network model of this round is selected as the optimal long short-term memory network model for the intelligent determination of the super-short-arc initial orbit of the space target only when both inequalities of the determination criteria are established.

7. The method of claim 5 or 6, wherein: The ratio of training set to validation set is 0.8:0.2.

Images