A method for determining spatial target orbit parameters based on a weighted loss function neural network

Abstract

The application discloses a space target orbit parameter determination method based on a weighted loss function neural network, and solves the problem of low orbit determination precision and easy divergence of results in the existing space target orbit parameter determination method by means of angle measurement; the method is realized through a neural network to achieve end-to-end estimation from input angle observation to the space target orbit state, and simplifies the establishment process of the space target orbit parameter determination model. The weighted loss function is adopted to reduce the influence of speed and position errors on the target state estimation precision, the fitting precision of the neural network to different orbit parameters of the observation target is adjusted according to the actual task precision requirement, and the precision of the space target orbit parameter can be improved.

Description

Technical Field

[0001] This invention relates to a method for determining the orbital parameters of a space target, specifically a method for determining the orbital parameters of a space target based on a weighted loss function neural network. Background Technology

[0002] The emergence of large-scale networked spacecraft and the explosive growth of global space launch missions have led to a rapid increase in the number of spacecraft orbiting the Earth and space debris, greatly increasing the probability of space collisions and posing a severe challenge to the operational safety of spacecraft in orbit. To avoid space collisions, it is necessary to accurately determine the orbits of non-cooperative space targets such as space debris, thereby providing a basis for developing evasive maneuver strategies for spacecraft in orbit.

[0003] Traditional methods for determining the orbital parameters of non-cooperative space targets primarily rely on ground-based observation stations. However, due to constraints such as atmospheric and cloud cover obstruction and station distribution, ground-based stations struggle to monitor space collision threats in blind spots. Compared to ground-based stations, space-based observation platforms offer advantages such as a wide observation range and freedom from atmospheric and cloud cover obstruction, gradually gaining widespread attention in the space security field. Space-based observation platforms' optical imaging equipment boasts advantages such as low power consumption, small size, and high resolution, making it crucial for space-based orbit determination of non-cooperative targets like space debris. However, existing algorithms for orbit determination based on angle measurement information from optical imaging equipment often suffer from low accuracy and susceptibility to divergence. Furthermore, the positional relationship between the space target and the observation platform can lead to unobservability issues, making them unsuitable for complex real-world orbit determination scenarios. Summary of the Invention

[0004] The purpose of this invention is to solve the problems of low orbit determination accuracy and easy divergence of results in existing methods for determining the orbit parameters of space targets by angle measurement, and to provide a method for determining the orbit parameters of space targets based on a weighted loss function neural network.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] A method for determining the orbital parameters of a space target based on a weighted loss function neural network includes the following steps:

[0007] Step 1: Based on the initial orbital parameters of the given on-orbit spacecraft and observation platform, solve the differential equation of orbital dynamics of the given on-orbit spacecraft in the geocentric inertial frame to obtain neural network training data; where the given on-orbit spacecraft belongs to the space target with given parameters.

[0008] Step 2: Construct a neural network based on a weighted loss function, train the neural network using neural network training data, and obtain a space target orbit state estimation model;

[0009] Step 3: Collect N sets of observation platform positions and velocity values ​​at equal time intervals, as well as the azimuth and elevation angles of the space target relative to the observation platform, and input them into the space target orbital state estimation model to obtain the initial orbital position and initial velocity of the space target, where N≥3;

[0010] Step 4: Calculate the position and velocity of the target space at any given moment based on its initial orbital position and initial velocity.

[0011] Furthermore, step 1 specifically includes:

[0012] Step 1.1: Based on the given forces acting on the spacecraft in orbit, establish the differential equations of orbital dynamics for the given spacecraft orbiting the Earth in a geocentric inertial frame, as follows:

[0013] ;

[0014] in, Let be the acceleration vector of an object orbiting the Earth in a geocentric inertial frame. Let be the position vector of an object orbiting the Earth in a geocentric inertial frame. The gravitational constant of Earth, This refers to the perturbation acceleration of an object orbiting the Earth in a geocentric inertial frame, caused by factors such as the Earth's non-spherical shape and atmospheric drag. It is the 2-norm of the vector;

[0015] Step 1.2: Based on the initial orbital parameters of the given on-orbit spacecraft and observation platform, solve the differential equation of orbital dynamics of the given on-orbit spacecraft in the geocentric inertial frame to obtain the position and velocity values ​​of the given on-orbit spacecraft and the position and velocity values ​​of the observation platform at multiple times.

[0016] Step 1.3: Convert the given position and velocity values ​​of the on-orbit spacecraft and observation platform at multiple moments in the geocentric inertial frame into the position vectors of the given on-orbit spacecraft relative to the observation platform at multiple moments in the observation platform's orbital coordinate system. Substitute these values ​​into the azimuth and pitch angle measurement model of the given on-orbit spacecraft relative to the observation platform to calculate the azimuth and pitch angles of the given on-orbit spacecraft relative to the observation platform. The position and velocity values ​​of the given on-orbit spacecraft and the position and velocity values ​​of the observation platform, along with the corresponding azimuth and pitch angles of the given on-orbit spacecraft relative to the observation platform at the corresponding moments, are used as training data for the neural network.

[0017] Furthermore, step 1.2 specifically includes:

[0018] Let the count variable be from Begin by taking the initial position of the given spacecraft in orbit. and initial velocity and the initial position of the observation platform and initial velocity initial value Solving the orbital dynamics differential equations of a given on-orbit spacecraft in a geocentric inertial frame yields the position and velocity values ​​of the on-orbit spacecraft and the position and velocity values ​​of the observation platform at multiple time points. The calculation formula is as follows:

[0019] ;

[0020] ;

[0021] In the formula, express The position of the spacecraft or observation platform in orbit is given at all times. express Given the velocity of the spacecraft or observation platform in orbit, Deltat represents a time step. express The position of the spacecraft or observation platform in orbit is given at all times. express The speed of the spacecraft or observation platform in orbit is given at any given moment.

[0022] Furthermore, step 1.3 specifically includes:

[0023] Step 1.3.1, in a given geocentric inertial frame... The position of the spacecraft in orbit is given at all times. Location of the observation platform Given the position vector of the on-orbit spacecraft relative to the observation platform for By combining the positions of the on-orbit spacecraft and the observation platform at multiple given moments, the position vector of the on-orbit spacecraft relative to the observation platform at multiple given moments is calculated.

[0024] Step 1.3.2, based on The position of the observation platform at all times and speed value The coordinate transformation matrix from the geocentric inertial frame to the orbital coordinate system of the observation platform is constructed as follows: ; Calculate the position vector of a given on-orbit spacecraft relative to the observation platform in the observation platform's orbital coordinate system. ;in, for The coordinates of the platform in the geocentric inertial frame are constantly monitored;

[0025] Step 1.3.3: Assign the position vector of the on-orbit spacecraft relative to the observation platform in the observation platform's orbital coordinate system. Substituting the azimuth and elevation angle measurement model of the space target relative to the observation platform, calculate the azimuth and elevation angles of a given on-orbit spacecraft relative to the observation platform. The azimuth and elevation angle measurement model of the space target relative to the observation platform is as follows:

[0026] ;

[0027] ;

[0028] In the formula, for In the orbital coordinate system of the observation platform Components of the axis, for In the orbital coordinate system of the observation platform Components of the axis, for In the orbital coordinate system of the observation platform The components of the axis;

[0029] Step 1.3.4: Take the position and velocity values ​​of the on-orbit spacecraft and the position and velocity values ​​of the observation platform at each time obtained in Step 1.2, as well as the azimuth and pitch angles of the on-orbit spacecraft relative to the observation platform at the corresponding time, as a set of neural network training samples, and obtain multiple sets of neural network training samples to form neural network training data.

[0030] Furthermore, in step 2, the construction of the neural network based on the weighted loss function specifically involves:

[0031] Step a: Set up the input layer, output layer, and multiple hidden layers located between the input and output layers in the neural network;

[0032] Multiple hidden layers are connected sequentially. The first hidden layer connects to the input layer to receive its output data, and the last hidden layer connects to the output layer to output the prediction result. Each hidden layer linearly transforms the output data of the previous layer using a weight matrix and a bias, then performs a non-linear transformation using an activation function before inputting it to the next layer. The calculation formula for each hidden layer is as follows: ;

[0033] in, Indicates the first l The output of the hidden layer, Indicates the first l The weight matrix of the hidden layer, Indicates the first l The bias vector of the hidden layer. Indicates the activation function;A (l-1) Indicates the first l -1 hidden layer output;

[0034] Initialize the weight matrices of the hidden layer and the output layer to random number matrices, and initialize the bias vectors of the hidden layer and the output layer to 0;

[0035] Step b: Set the parameters of the Adam optimizer in the neural network. , , and δ, where For learning rate, and δ is the exponential decay rate of the Adam optimizer, and δ is a small parameter to prevent division by zero.

[0036] Step c: Define the weighted loss function for the neural network, expressed as:

[0037] ;

[0038] in, For weighted loss function, For position error weights, This is the mean square error of the position. As the speed error weight, For the mean square error of speed, This is a regularization term.

[0039] The The calculation formula is: ;

[0040] m For the sample size, The regularization coefficient is . The weight matrix is ​​the first j Each weight;

[0041] The activation function is the ReLU linear rectified function, expressed as follows:

[0042] .

[0043] Furthermore, step 2 specifically involves:

[0044] Step 2.1: Construct a neural network based on a weighted loss function, set the total number of training iterations for the neural network, and normalize the neural network training data to obtain normalized neural network training data;

[0045] Step 2.2: Input the position and velocity values ​​of the corresponding observation platform in the normalized neural network training data, as well as the azimuth and elevation angles of the given on-orbit spacecraft relative to the observation platform, into the input layer; and output the predicted position and velocity values ​​of the given on-orbit spacecraft into the output layer.

[0046] Step 2.3: Based on the predicted position and velocity values ​​of the given on-orbit spacecraft from the output layer and the corresponding position and velocity values ​​of the given on-orbit spacecraft in the normalized neural network training data, calculate the weighted loss function value, and calculate the gradient of the loss function value with respect to the weights and biases of each layer using the chain rule. Then, use the Adam optimizer to update the weights and biases of each layer.

[0047] Step 2.4: Determine whether the total number of training iterations for the neural network has been reached. If not, return to step 2.2 and input the position and velocity values ​​of the corresponding observation platform from another set of normalized neural network training data, as well as the azimuth and pitch angles of the given on-orbit spacecraft relative to the observation platform, into the input layer. When the number of training iterations reaches the total number of training iterations for the neural network, input the network parameters corresponding to the weights and biases of each layer when the loss function value is minimized into the neural network to obtain the space target orbital state estimation model.

[0048] Furthermore, in step 2.3, the update formula for updating the weights and biases of each layer using the Adam optimizer is as follows:

[0049] , , ,

[0050] , , ;

[0051] In the formula, t For update count, Let be the gradient of the loss function with respect to the weights when the relevant parameters are updated for the t-th time. Let be the first moment estimate of the weight gradient after the t-th update. Let be the estimated second moment of the weight gradient after the t-th update. Let be the gradient of the loss function with respect to the bias when updating the relevant parameters for the t-th time. Let be the estimated first moment of the bias gradient after the t-th update. Let be the estimated second moment of the bias gradient after the t-th update.

[0052] Further, step 3 specifically involves: collecting N sets of observation platform positions and velocity values ​​at equal time intervals, as well as the azimuth and elevation angles of the target space relative to the observation platform, normalizing them, and inputting them into the target space orbit state estimation model to obtain the normalized initial orbit position and initial velocity of the target space. Then, the normalized initial orbit position and initial velocity of the target space are inversely normalized to obtain the initial orbit position and initial velocity of the target space, where N≥3.

[0053] Furthermore, step 4 specifically involves:

[0054] Input the initial orbital position and initial velocity of the target space into the calculation formula in step 1.2 to obtain the position and velocity of the target space at any time.

[0055] The beneficial effects of this invention are:

[0056] (1) The present invention provides a method for determining the orbital parameters of a space target based on a weighted loss function neural network, which avoids the problem of complex dynamic modeling required by traditional orbit determination methods. It achieves end-to-end estimation of the orbital state of the space target from the input perspective through a neural network, simplifying the process of establishing a model for determining the orbital parameters of a space target.

[0057] (2) The present invention provides a method for determining the orbital parameters of a space target based on a weighted loss function neural network. The weighted loss function is used to reduce the impact of velocity and position errors on the accuracy of target state estimation. The accuracy of the fitting accuracy of the neural network to different orbital parameters of the observed target is adjusted according to the accuracy requirements of the actual mission, which can improve the accuracy of the orbital parameters of the space target. Attached Figure Description

[0058] Figure 1 This is a schematic diagram illustrating the positions of the Earth, observation platform, and space target or given on-orbit spacecraft in an embodiment of a method for determining orbital parameters of a space target based on a weighted loss function neural network according to the present invention.

[0059] Figure 2 This is a flowchart of an embodiment of the method for determining the orbital parameters of a space target based on a weighted loss function neural network according to the present invention.

[0060] Figure label:

[0061] 1-Earth; 2-Observation platform; 3-Space target or given spacecraft in orbit. Detailed Implementation

[0062] The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings and embodiments. 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.

[0063] The positional relationship between the space target or the given on-orbit spacecraft 3 and Earth 1 and observation platform 2 is as follows: Figure 1 As shown. To address the issue that existing methods for determining the orbit of space targets based on neural networks cannot meet the varying accuracy requirements of different tasks in estimating the position and velocity of space targets, this embodiment provides a method for determining the orbital parameters of space targets based on a weighted loss function neural network, such as... Figure 2 As shown, it includes the following steps:

[0064] Step 1: Based on the initial orbital parameters of the given on-orbit spacecraft and observation platform, solve the differential equations of orbital dynamics of the given on-orbit spacecraft in the geocentric inertial frame, and obtain neural network training data; specifically:

[0065] Step 1.1: Based on the given forces acting on the spacecraft in orbit, establish the differential equations of orbital dynamics for the given spacecraft orbiting the Earth in a geocentric inertial frame, as follows:

[0066] ;

[0067] in, Let be the acceleration vector of an object orbiting the Earth in a geocentric inertial frame. Let be the position vector of an object orbiting the Earth in a geocentric inertial frame. The gravitational constant of Earth, This refers to the perturbation acceleration of an object orbiting the Earth in a geocentric inertial frame, caused by factors such as the Earth's non-spherical shape and atmospheric drag. It is the 2-norm of the vector;

[0068] Step 1.2: Based on the initial orbital parameters of the given on-orbit spacecraft and observation platform, solve the differential equations of orbital dynamics of the given on-orbit spacecraft in the geocentric inertial frame, obtaining the position and velocity values ​​of the given on-orbit spacecraft and the position and velocity values ​​of the observation platform at multiple moments; specifically:

[0069] By reducing the order of the differential equations for the orbital dynamics of a given on-orbit spacecraft in a geocentric inertial frame, a first-order differential equation is constructed:

[0070] ;

[0071] Define Deltat as a time step, based on a given... The position of the spacecraft in orbit is given at all times. and speed The Euler method was used to solve the first-order differential equation, and the result was obtained after a step size of Deltat seconds. The position of the spacecraft in orbit is given at all times. With speed The formula for its calculation is:

[0072] ;

[0073] ;

[0074] Let the count variable be from Initially, the initial values ​​of the position and velocity of the spacecraft in orbit are given. and the initial values ​​of the position and velocity of the observation platform. Based on the given initial values ​​of the position and velocity of the spacecraft in orbit and the observation platform. , from By progressively pushing the timeline forward, we obtain the position and velocity values ​​of the on-orbit spacecraft and the position and velocity values ​​of the observation platform at multiple given times.

[0075] Step 1.3: Convert the given position and velocity values ​​of the on-orbit spacecraft and observation platform at multiple moments in the geocentric inertial frame into position vectors of the given on-orbit spacecraft relative to the observation platform at multiple moments in the observation platform's orbital coordinate system. Substitute these vectors into the azimuth and pitch angle measurement model of the given on-orbit spacecraft relative to the observation platform to calculate the azimuth and pitch angles of the given on-orbit spacecraft relative to the observation platform. The position and velocity values ​​of the given on-orbit spacecraft and the position and velocity values ​​of the observation platform, along with the corresponding azimuth and pitch angles of the given on-orbit spacecraft relative to the observation platform at the corresponding moments, are used as training data for the neural network. Specifically:

[0076] Step 1.3.1, in a given geocentric inertial frame... The position of the spacecraft in orbit is given at all times. Location of the observation platform Given the position vector of the on-orbit spacecraft relative to the observation platform for By combining the positions of the on-orbit spacecraft and the observation platform at multiple given moments, the position vector of the on-orbit spacecraft relative to the observation platform at multiple given moments is calculated.

[0077] Step 1.3.2, based on The position of the observation platform at all times and speed value The coordinate transformation matrix from the geocentric inertial frame to the orbital coordinate system of the observation platform is constructed as follows: ; Calculate the position vector of a given on-orbit spacecraft relative to the observation platform in the observation platform's orbital coordinate system. ;in,( )for The coordinates of the platform in the geocentric inertial frame are constantly monitored;

[0078] Step 1.3.3: Assign the position vector of the on-orbit spacecraft relative to the observation platform in the observation platform's orbital coordinate system. Substituting the azimuth and elevation angle measurement model of the space target relative to the observation platform, calculate the azimuth and elevation angles of a given on-orbit spacecraft relative to the observation platform. The azimuth and elevation angle measurement model of the space target relative to the observation platform is as follows:

[0079] ;

[0080] ;

[0081] In the formula, for In the orbital coordinate system of the observation platform Components of the axis, for In the orbital coordinate system of the observation platform Components of the axis, for In the orbital coordinate system of the observation platform The components of the axis;

[0082] Step 1.3.4: Take the position and velocity values ​​of the on-orbit spacecraft and the position and velocity values ​​of the observation platform at each time obtained in Step 1.2, as well as the azimuth and pitch angles of the on-orbit spacecraft relative to the observation platform at the corresponding time, as a set of neural network training samples, and obtain multiple sets of neural network training samples to form neural network training data.

[0083] Step 2: Construct a neural network based on a weighted loss function, and train the neural network using the training data to obtain a space target orbital state estimation model; specifically:

[0084] Step 2.1: Construct a neural network based on a weighted loss function:

[0085] Configure the neural network with an input layer, an output layer, and multiple hidden layers located between the input and output layers;

[0086] Multiple hidden layers are connected sequentially. The first hidden layer connects to the input layer, receiving its output data. The last hidden layer connects to the output layer, outputting the prediction result. Each hidden layer linearly transforms the output data from the previous layer using a weight matrix and bias, then performs a non-linear transformation using an activation function before inputting it into the next layer. The formula for calculating the hidden layer is: ;

[0087] in, Indicates the first l The output of the hidden layer, Indicates the first l The weight matrix of the hidden layer, Indicates the first l The bias vector of the hidden layer. Indicates the activation function; A (l-1) Indicates the first l -1 hidden layer output;

[0088] Initialize the weight matrices of the hidden layer and the output layer to random number matrices, and initialize the bias vectors of the hidden layer and the output layer to 0;

[0089] Setting parameters for the Adam optimizer in a neural network , , and δ, where For learning rate, and δ is the exponential decay rate of the Adam optimizer, and δ is a small parameter to prevent division by zero.

[0090] The weighted loss function of the neural network is defined as follows:

[0091] ;

[0092] in, For weighted loss function, For position error weights, This is the mean square error of the position. As the speed error weight, For the mean square error of speed, This is a regularization term.

[0093] The calculation formula is: ;

[0094] m For the sample size, The regularization coefficient is . The weight matrix is ​​the first j Each weight;

[0095] The activation function is the linear rectified function ReLU, and its expression is:

[0096] .

[0097] Step 2.2: Set the total number of training iterations for the neural network and normalize the neural network training data to obtain normalized neural network training data;

[0098] Normalization specifically means:

[0099] ,

[0100] In the formula Input values ​​for the normalized training data. Input values ​​for the training data before normalization. The minimum input value of the training data before normalization. The maximum input value of the training data before normalization; The output value is the normalized training data. The output values ​​are the training data before normalization. The minimum output value of the training data before normalization. This represents the maximum output value of the training data before normalization.

[0101] Step 2.3: Input the position and velocity values ​​of the corresponding observation platform in the normalized neural network training data, as well as the azimuth and elevation angles of the given on-orbit spacecraft relative to the observation platform, into the input layer; and output the predicted position and velocity values ​​of the given on-orbit spacecraft into the output layer.

[0102] Step 2.4: Based on the predicted position and velocity values ​​of the given on-orbit spacecraft from the output layer and the corresponding positions and velocity values ​​of the given on-orbit spacecraft in the normalized neural network training data, calculate the weighted loss function value. Then, calculate the gradient of the loss function value with respect to the weights and biases of each layer using the chain rule. Update the weights and biases of each layer using the Adam optimizer. The update formula for updating the weights and biases of each layer using the Adam optimizer is as follows:

[0103] , , ,

[0104] , , ;

[0105] In the formula, t For update count, Let be the gradient of the loss function with respect to the weights when the relevant parameters are updated for the t-th time. b t Let be the bias vector after the t-th update. Let be the first moment estimate of the weight gradient after the t-th update. Let be the estimated second moment of the weight gradient after the t-th update. Let be the gradient of the loss function with respect to the bias when updating the relevant parameters for the t-th time. Let be the estimated first moment of the bias gradient after the t-th update. Let be the estimated second moment of the bias gradient after the t-th update.

[0106] Step 2.5: Determine whether the total number of training iterations for the neural network has been reached. If not, return to step 2.3 and input the position and velocity values ​​of the corresponding observation platform from another set of normalized neural network training data, as well as the azimuth and pitch angles of the given on-orbit spacecraft relative to the observation platform, into the input layer. When the number of training iterations reaches the total number of training iterations for the neural network, input the network parameters corresponding to the weights and biases of each layer when the loss function value is minimized into the neural network to obtain the space target orbital state estimation model.

[0107] Step 3: Collect N sets of observation platform positions and velocity values ​​at equal time intervals, as well as the azimuth and elevation angles of the target space relative to the observation platform. Normalize these values ​​and input them into the target space orbit state estimation model to obtain the normalized initial orbit position and initial velocity of the target space. Then, perform inverse normalization on the normalized initial orbit position and initial velocity of the target space to obtain the initial orbit position and initial velocity of the target space, where N≥3.

[0108] Step 4: Input the initial orbital position and initial velocity of the target space object into step 1.2. , The calculation formula yields the position and velocity of the target in space at any given moment.

[0109] The data parameters for the space target orbit parameter determination method based on weighted loss function neural network provided in this embodiment are shown in Table 1.

[0110] As shown in Table 1, the relative errors between the predicted position and velocity of the spatial target at time 0s (initial time) in the geocentric inertial frame [45582875,-12838948,-5887964,440,2063,641] and the actual position and velocity of the spatial target at time 0s (initial time) in the geocentric inertial frame [48626635,-12535853,-5917512,436,2050,640] are [6.26%, 2.42%, 0.50%, 1.25%, 0.64%, 0.21%]. Therefore, it can be seen that the orbit determination method for spatial target orbit parameters based on a weighted loss function neural network provided in this embodiment has high orbit determination accuracy.

[0111] In this invention, a method for determining the orbital parameters of a space target based on a weighted loss function neural network is provided. By assigning weights to different state parameters of the target in the weighted loss function and adjusting their weight parameters, the fitting accuracy of the neural network for different orbital parameters of the observed target can be adjusted, thereby enabling the construction of a more adaptable space target orbital state estimation model for specific task scenarios.

[0112] Table 1

[0113]

[0114] The above description is merely a specific embodiment of the present invention and a comparison of the effects of the specific embodiments with relevant comparative examples. However, the scope of protection of the present invention is not limited thereto. Any changes or substitutions within the technical scope disclosed in the present invention should be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for determining the orbital parameters of a space target based on a weighted loss function neural network, characterized in that, Includes the following steps: Step 1: Based on the initial orbital parameters of the given on-orbit spacecraft and observation platform, solve the differential equation of orbital dynamics of the given on-orbit spacecraft in the geocentric inertial frame, and obtain neural network training data. Step 2: Construct a neural network based on a weighted loss function, train the neural network using neural network training data, and obtain a space target orbit state estimation model; The construction of the neural network based on the weighted loss function specifically involves: Step a: Set up the input layer, output layer, and multiple hidden layers located between the input and output layers in the neural network; Multiple hidden layers are connected sequentially. The first hidden layer connects to the input layer and receives the output data from the input layer. The last hidden layer connects to the output layer and outputs the prediction result. Each hidden layer linearly transforms the output data of the previous layer using a weight matrix and a bias, then performs a non-linear transformation using an activation function before inputting it to the next layer. The calculation formula for the hidden layer is: A (l) =f(W (l) ·A (l-1) +b (l) ); Among them, A (l) W represents the output of the l-th hidden layer. (l) Let b represent the weight matrix of the l-th hidden layer. (l) Let A represent the bias vector of the l-th hidden layer, and f represent the activation function; (l-1) This represents the output of the (l-1)th hidden layer; Initialize the weight matrices of the hidden layer and the output layer to random number matrices, and initialize the bias vectors of the hidden layer and the output layer to 0; Step b: Set the parameters α, β1, β2 and δ of the Adam optimizer in the neural network, where α is the learning rate, β1 and β2 are the exponential decay rates of the Adam optimizer, and δ is a small parameter to prevent division by zero. Step c: Define the weighted loss function for the neural network, expressed as: L=ω pos s pos +oh vel s vel +L2; Where L is the weighted loss function, ω pos σ is the position error weight. pos The mean square error of the position, ω vel For the velocity error weight, σ vel L2 is the mean square error of velocity, and L2 is the regularization term. Step 2 is as follows: Step 2.1: Construct a neural network based on a weighted loss function, set the total number of training iterations for the neural network, and normalize the neural network training data to obtain normalized neural network training data; Step 2.2: Input the position and velocity values ​​of the corresponding observation platform in the normalized neural network training data, as well as the azimuth and elevation angles of the given on-orbit spacecraft relative to the observation platform, into the input layer; and output the predicted position and velocity values ​​of the given on-orbit spacecraft into the output layer. Step 2.3: Based on the predicted position and velocity values ​​of the given on-orbit spacecraft from the output layer and the corresponding position and velocity values ​​of the given on-orbit spacecraft in the normalized neural network training data, calculate the weighted loss function value, and calculate the gradient of the loss function value with respect to the weights and biases of each layer using the chain rule. Then, use the Adam optimizer to update the weights and biases of each layer. Step 2.4: Determine whether the total number of training iterations for the neural network has been reached. If not, return to step 2.2 and input the position and velocity values ​​of the corresponding observation platform from another set of normalized neural network training data, as well as the azimuth and pitch angles of the given on-orbit spacecraft relative to the observation platform, into the input layer. If the total number of training iterations for the neural network has been reached, then input the network parameters corresponding to the weights and biases of each layer when the loss function value is minimized into the neural network to obtain the space target orbital state estimation model. Step 3: Collect N sets of observation platform positions and velocity values ​​at equal time intervals, as well as the azimuth and elevation angles of the space target relative to the observation platform, and input them into the space target orbital state estimation model to obtain the initial orbital position and initial velocity of the space target, where N≥3; Step 4: Calculate the position and velocity of the target space at any given moment based on its initial orbital position and initial velocity.

2. The method for determining the orbital parameters of a space target based on a weighted loss function neural network according to claim 1, characterized in that, Step 1 is as follows: Step 1.1: Based on the given forces acting on the spacecraft in orbit, establish the differential equations of orbital dynamics for the given spacecraft orbiting the Earth in a geocentric inertial frame, as follows: in, Let be the acceleration vector of an object orbiting the Earth in a geocentric inertial frame, r be the position vector of the object orbiting the Earth in a geocentric inertial frame, μ be the Earth's gravitational constant, and a be the acceleration vector of the object orbiting the Earth in a geocentric inertial frame. J Let || be the perturbation acceleration of an object orbiting the Earth in the geocentric inertial frame caused by the Earth's non-spherical shape and atmospheric drag, and || be the 2-norm of the vector. Step 1.2: Based on the initial orbital parameters of the given on-orbit spacecraft and observation platform, solve the differential equation of orbital dynamics of the given on-orbit spacecraft in the geocentric inertial frame to obtain the position and velocity values ​​of the given on-orbit spacecraft and the position and velocity values ​​of the observation platform at multiple times. Step 1.3: Convert the given position and velocity values ​​of the on-orbit spacecraft and observation platform at multiple moments in the geocentric inertial frame into position vectors of the given on-orbit spacecraft relative to the observation platform at multiple moments in the observation platform's orbital coordinate system. Substitute these vectors into the azimuth and pitch angle measurement model of the given on-orbit spacecraft relative to the observation platform to calculate the azimuth and pitch angles of the given on-orbit spacecraft relative to the observation platform. Use the position and velocity values ​​of the given on-orbit spacecraft and the position and velocity values ​​of the observation platform, along with the corresponding azimuth and pitch angles of the given on-orbit spacecraft relative to the observation platform in space, as training data for the neural network.

3. The method for determining the orbital parameters of a space target based on a weighted loss function neural network according to claim 2, characterized in that, Step 1.2 specifically involves: Let the counting variable start from n=0, taking the initial position of the given spacecraft in orbit. and initial velocity and the initial position of the observation platform and initial velocity initial value Solving the orbital dynamics differential equations of a given on-orbit spacecraft in a geocentric inertial frame yields the position and velocity values ​​of the on-orbit spacecraft and the position and velocity values ​​of the observation platform at multiple time points. The calculation formula is as follows: In the formula, r n Indicates t n The position of the spacecraft or observation platform in orbit is given at all times. Indicates t n Given the velocity of the spacecraft or observation platform in orbit at any given moment, Deltat represents a time step, r n+1 Indicates t n+1 The position of the spacecraft or observation platform in orbit is given at all times. Indicates t n+1 The speed of the spacecraft or observation platform in orbit is given at any given moment.

4. The method for determining the orbital parameters of a space target based on a weighted loss function neural network according to claim 3, characterized in that, Step 1.3 specifically involves: Step 1.3.1: Given t in the geocentric inertial frame... n The position of the spacecraft in orbit is given at all times. Location of the observation platform Given the position vector of the on-orbit spacecraft relative to the observation platform for By combining the positions of the on-orbit spacecraft and the observation platform at multiple given moments, the position vector of the on-orbit spacecraft relative to the observation platform at multiple given moments is calculated. Step 1.3.2, based on t n The position of the observation platform at all times and speed value Construct the coordinate transformation matrix from the geocentric inertial frame to the orbital coordinate system of the observation platform as follows: Calculate the position vector of a given on-orbit spacecraft relative to the observation platform in the observation platform's orbital coordinate system. in, For t n The coordinates of the platform in the geocentric inertial frame are constantly monitored; Step 1.3.3: Assign the position vector of the on-orbit spacecraft relative to the observation platform in the observation platform's orbital coordinate system. Substituting the azimuth and elevation angle measurement model of the space target relative to the observation platform, calculate the azimuth and elevation angles of a given on-orbit spacecraft relative to the observation platform. The azimuth and elevation angle measurement model of the space target relative to the observation platform is as follows: In the formula, for The components of the x-axis in the orbital coordinate system of the observation platform. for The components of the y-axis in the orbital coordinate system of the observation platform. for The z-axis components in the orbital coordinate system of the observation platform; Step 1.3.4: Take the position and velocity values ​​of the on-orbit spacecraft and the position and velocity values ​​of the observation platform at each time obtained in Step 1.2, as well as the azimuth and pitch angles of the on-orbit spacecraft relative to the observation platform at the corresponding time, as a set of neural network training samples, and obtain multiple sets of neural network training samples to form neural network training data.

5. The method for determining the orbital parameters of a space target based on a weighted loss function neural network according to claim 1, characterized in that, The formula for calculating L2 in step c is: m is the sample size, λ is the regularization coefficient, and ω is the regularization coefficient. j Let j be the weight of the weight matrix; The activation function is the ReLU linear rectified function, expressed as follows: f(W (l) ·A (l-1) +b (l) )=max(W (l) ·A (l-1) +b (l) ,0)。 6. The method for determining the orbital parameters of a space target based on a weighted loss function neural network according to claim 1, characterized in that, In step 2.3, the update formula for updating the weights and biases of each layer using the Adam optimizer is as follows: In the formula, t represents the number of updates, and gW t Let mW be the gradient of the loss function with respect to the weights when the relevant parameters are updated for the t-th time. t Let vW be the first moment estimate of the weight gradient after the t-th update. t Let gb be the estimated second moment of the weight gradient after the t-th update. t Let mb be the gradient of the loss function with respect to the bias when the relevant parameters are updated for the t-th time. t Let vb be the first moment estimate of the bias gradient after the t-th update. t Let be the estimated second moment of the bias gradient after the t-th update.

7. The method for determining the orbital parameters of a space target based on a weighted loss function neural network according to claim 1, characterized in that, Step 3 specifically involves: collecting N sets of observation platform positions and velocity values ​​at equal time intervals, as well as the azimuth and elevation angles of the target space relative to the observation platform, normalizing them, and inputting them into the target space orbit state estimation model to obtain the normalized initial orbit position and initial velocity of the target space. Then, the normalized initial orbit position and initial velocity of the target space are inversely normalized to obtain the initial orbit position and initial velocity of the target space, where N≥3.

8. The method for determining the orbital parameters of a space target based on a weighted loss function neural network according to claim 1, characterized in that, Step 4 is as follows: Input the initial orbital position and initial velocity of the target space into the calculation formula in step 1.2 to obtain the position and velocity of the target space at any time.

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