Space target orbit parameter determination method based on weighted loss function neural network

Abstract

The invention discloses a space target orbit parameter determination method based on a weighted loss function neural network. The problems that in an existing space target orbit parameter determination method, orbit determination precision is low and results are prone to divergence through an angle measurement mode are solved. According to the method, the end-to-end estimation from the input angle observed quantity to the space target orbit state is realized through the neural network, and the establishment process of the space target orbit parameter determination model is simplified. A weighted loss function is adopted to reduce the influence of speed and position errors on target state estimation precision, the fitting precision of a neural network on different orbit parameters of an observation target is adjusted according to actual task precision requirements, and the precision of space target orbit parameters can be improved.

Description

Technical Field

[0001] The present invention relates to a method for determining space target orbit parameters, and in particular to a method for determining space target orbit parameters based on a weighted loss function neural network. Background Art

[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 and space debris orbiting Earth. This has significantly increased the probability of space collisions and posed a serious 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 objects, such as space debris, to provide a basis for developing evasive maneuvers for spacecraft in orbit.

[0003] Traditionally, the determination of orbital parameters for non-cooperative space targets relies primarily on ground-based observation stations. However, due to constraints such as atmospheric and cloud obstruction and the distribution of observation stations, ground-based observation stations struggle to timely monitor space collision threats in blind spots. Compared to ground-based observation stations, space-based observation platforms have the advantages of a wide observation range and freedom from atmospheric and cloud obstruction, and are gradually gaining widespread attention in the field of space security. Optical imaging equipment on space-based observation platforms offers the advantages of low power consumption, small size, and high-resolution detection results, making them crucial for space-based orbit determination of non-cooperative targets such as space debris. However, existing algorithms for determining the orbit of space targets using angle measurement information from optical imaging equipment often suffer from low orbit determination accuracy and easily divergent results. Furthermore, they may face unobservability issues due to the positional relationship between the space target and the observation platform, making them difficult to adapt to complex actual orbit determination scenarios. Summary of the Invention

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

[0005] In order to achieve the above object, the present invention adopts the following technical solutions: A method for determining space target orbit parameters based on a weighted loss function neural network comprises the following steps: Step 1: Based on the initial orbital parameters of the given on-orbit spacecraft and the observation platform, solve the orbital dynamics differential equation of the given on-orbit spacecraft orbiting the Earth in the Earth-centered inertial system to obtain neural network training data; wherein the given on-orbit spacecraft is a space target with given parameters; Step 2: Construct a neural network based on a weighted loss function, train the neural network using the neural network training data, and obtain a space target orbit state estimation model; Step 3: Collect N sets of observation platform position and velocity values at equal time intervals, as well as the azimuth and pitch angles of the space target to be measured relative to the observation platform, and input them into the space target orbit state estimation model to obtain the initial orbit position and initial velocity of the space target to be measured, where N ≥ 3; Step 4: Calculate the position and velocity of the space target at any moment based on the initial orbital position and initial velocity of the space target.

[0006] Furthermore, step 1 is specifically as follows: Step 1.1. Based on the force conditions of the given on-orbit spacecraft, establish the orbital dynamics differential equation of the given on-orbit spacecraft orbiting the Earth in the Earth-centered inertial system, which can be expressed as: ; in, is the acceleration vector of an object orbiting the earth in the geocentric inertial system, is the position vector of the object orbiting the earth in the geocentric inertial system, is the Earth's gravitational constant, It is the perturbation acceleration of an object orbiting the Earth in the Earth's inertial system caused by factors such as the Earth's non-spherical shape and atmospheric resistance. is the 2-norm of the vector; Step 1.2: Based on the initial orbital parameters of the given on-orbit spacecraft and the observation platform, solve the differential equation of the orbital dynamics of the given on-orbit spacecraft orbiting the Earth in the Earth-centered inertial system 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 moments in time. Step 1.3: Convert the position and velocity values of the given on-orbit spacecraft and the observation platform at multiple moments in the geocentric inertial system into the position vector of the given on-orbit spacecraft relative to the observation platform at multiple moments in the observation platform orbital coordinate system, and bring them 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 angle of the given on-orbit spacecraft relative to the observation platform. The position and velocity values of the given on-orbit spacecraft, the position and velocity values of the observation platform, and the azimuth and pitch angle of the given on-orbit spacecraft relative to the observation platform at the corresponding moments serve as neural network training data.

[0007] Furthermore, step 1.2 is specifically as follows: Let the counting variable be To begin, take the initial position of the given on-orbit spacecraft and initial velocity and the initial position of the observation platform and the initial velocity , solve the orbital dynamics differential equation of a given spacecraft orbiting the Earth in the Earth-centered inertial system, and obtain the position and velocity values of the given spacecraft and the position and velocity values of the observation platform at multiple moments. The calculation formula is: ; ; Where, express The position of an on-orbit spacecraft or observation platform is given at any moment. express The speed of the spacecraft or observation platform on orbit is given at any moment, and Deltat represents a time step. express The position of an on-orbit spacecraft or observation platform is given at any moment. express The velocity of a spacecraft or observation platform in orbit is given at any moment.

[0008] Furthermore, step 1.3 is specifically as follows: Step 1.3.1: Given the Earth-centered inertial system The position of the spacecraft in orbit is given at any time Location of the observation platform , given the position vector of the on-orbit spacecraft relative to the observation platform for , combining the position of the given on-orbit spacecraft and the position of the observation platform at multiple moments, and calculating the position vector of the given on-orbit spacecraft relative to the observation platform at multiple moments; Step 1.3.2, based on Always observe the platform's location and speed value , the coordinate transformation matrix from the Earth-centered inertial system to the observation platform orbit coordinate system is constructed as ; Calculate the position vector of a given on-orbit spacecraft relative to the observation platform in the observation platform orbit coordinate system ;in, for The coordinates of the observation platform in the Earth-centered inertial system at all times; Step 1.3.3: Set the position vector of the given on-orbit spacecraft relative to the observation platform in the observation platform orbit coordinate system to The azimuth and pitch angle measurement model of the space target relative to the observation platform is introduced to calculate the azimuth and pitch angle of the given on-orbit spacecraft relative to the observation platform. The azimuth and pitch angle measurement model of the space target relative to the observation platform is: ; ; Where, for In the observation platform orbit coordinate system The axis weight, for In the observation platform orbit coordinate system The axis weight, for In the observation platform orbit coordinate system The axis's weight; Step 1.3.4: Use the position and velocity values of the given on-orbit spacecraft and the position and velocity values of the observation platform at each moment obtained in step 1.2, and the azimuth and pitch angles of the given on-orbit spacecraft relative to the observation platform obtained at the corresponding moment as a set of neural network training samples, and obtain multiple sets of neural network training samples to constitute neural network training data.

[0009] Furthermore, in step 2, the construction of a neural network based on a weighted loss function is specifically as follows: Step a: setting an input layer, an output layer, and multiple hidden layers between the input layer and the output layer in a neural network; Multiple hidden layers are connected in sequence. The first hidden layer is connected to the input layer to receive the output data of the input layer. The last hidden layer is connected to the output layer to output the prediction results. Each hidden layer linearly transforms the output data of the previous layer through the weight matrix and bias, and then performs nonlinear transformation through the activation function and inputs it to the next layer. The calculation formula of the hidden layer is: ; in, Indicates the l The output of the hidden layer, Indicates the l The weight matrix of the hidden layer, Indicates the l The bias vector of the hidden layer, represents the activation function; A (l-1) Indicates the l -The output of 1 hidden layer; Initialize the weight matrix of the hidden layer and the output layer to a random number matrix, and initialize the bias vector of the hidden layer and the output layer to 0; Step b: Set the parameters of the Adam optimizer in the neural network 、 、 and δ, where is the learning rate, and is the exponential decay rate of the Adam optimizer, and δ is a small parameter to prevent division by 0; Step c: Set the weighted loss function of the neural network, which is expressed as: ; in, is the weighted loss function, is the position error weight, is the mean square error of position, is the speed error weight, is the mean square error of velocity, is the regularization term.

[0010] described The calculation formula is: ; m is the sample size, is the regularization coefficient, is the weight matrix j weights; The activation function is the linear rectification function ReLU, which is expressed as: .

[0011] Furthermore, step 2 is specifically as follows: Step 2.1, construct a neural network based on a weighted loss function, set the total number of neural network cycle training times, and normalize the neural network training data to obtain normalized neural network training data; Step 2.2, inputting the position and velocity values of the corresponding observation platform in the normalized neural network training data and the azimuth and pitch angles of the given on-orbit spacecraft relative to the observation platform into the input layer; and outputting the predicted position and velocity values of the given on-orbit spacecraft in the output layer; Step 2.3: Based on the output of the output layer, the predicted position and velocity of the given on-orbit spacecraft are compared with the corresponding position and velocity of the given on-orbit spacecraft in the normalized neural network training data. The weighted loss function is calculated, and the gradient of the loss function with respect to the weights and biases of each layer is calculated using the chain rule. The weights and biases of each layer are updated using the Adam optimizer. Step 2.4: Determine whether the total number of neural network cycle training times has been reached. If not, return to step 2.2 and input the position and velocity values of the corresponding observation platform in 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 cycle training times reaches the total number of neural network cycle training times, the network parameters corresponding to the weights and biases of each layer when the loss function value is minimized are brought into the neural network to obtain a space target orbit state estimation model.

[0012] Furthermore, in step 2.3, the update formula for updating the weights and biases of each layer using the Adam optimizer is: , , , , , ; Where, t is the number of updates, is the gradient of the loss function with respect to the weight when the relevant parameters are updated for the tth time, is the first-order moment estimate of the weight gradient after the tth update, is the estimated value of the second-order moment of the weight gradient after the tth update, is the gradient of the loss function with respect to the bias when the relevant parameters are updated for the tth time, is the first-order moment estimate of the bias gradient after the tth update, is the estimated value of the second-order moment of the bias gradient after the tth update.

[0013] Furthermore, step 3 is specifically as follows: collecting N groups of observation platform position and velocity values at equal time intervals and the azimuth and pitch angles of the space target to be measured relative to the observation platform, normalizing them respectively, and inputting them into the space target orbit state estimation model to obtain the normalized initial orbit position and initial velocity of the space target to be measured, and denormalizing the normalized initial orbit position and initial velocity of the space target to be measured to obtain the initial orbit position and initial velocity of the space target to be measured, where N≥3.

[0014] Furthermore, step 4 is specifically as follows: Input the initial orbital position and initial velocity of the space target to be measured into the calculation formula in step 1.2 to obtain the position and velocity of the space target to be measured at any time.

[0015] Beneficial effects of the present invention: (1) The present invention provides a method for determining the orbital parameters of a space target based on a weighted loss function neural network. This method avoids the problem that traditional orbit determination methods require complex dynamic modeling. By using a neural network, the method achieves end-to-end estimation from input angle observations to the orbital state of the space target, thus simplifying the process of establishing a model for determining the orbital parameters of the space target.

[0016] (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 method uses a weighted loss function to reduce the influence of velocity and position errors on the target state estimation accuracy. The fitting accuracy of the neural network for different orbital parameters of the observed target is adjusted according to the actual mission accuracy requirements, which can improve the accuracy of the orbital parameters of the space target. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 A schematic diagram of the positions of the Earth, an observation platform, and a space target or a 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 of the present invention; Figure 2This is a flow chart of an embodiment of a method for determining space target orbit parameters based on a weighted loss function neural network according to the present invention.

[0018] Reference numerals: 1-Earth; 2-Observation platform; 3-Space target or given spacecraft in orbit. DETAILED DESCRIPTION

[0019] The following will clearly and completely describe the technical solutions of the present invention in conjunction with the accompanying drawings and embodiments. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0020] The positional relationship between the space target or the given on-orbit spacecraft 3 and the earth 1 and the observation platform 2 is as follows: Figure 1 As shown. In view of the problem that the existing space target orbit determination method based on neural network cannot meet the differentiated requirements of different tasks for the space target position and velocity estimation accuracy, this embodiment provides a space target orbit parameter determination method based on weighted loss function neural network, as shown Figure 2 As shown, the following steps are included: Step 1: Based on the initial orbital parameters of the given on-orbit spacecraft and the observation platform, solve the differential equation of the orbital dynamics of the given on-orbit spacecraft orbiting the Earth in the Earth-centered inertial system to obtain neural network training data; specifically: Step 1.1. Based on the force conditions of the given on-orbit spacecraft, establish the orbital dynamics differential equation of the given on-orbit spacecraft orbiting the Earth in the Earth-centered inertial system, which can be expressed as: ; in, is the acceleration vector of an object orbiting the earth in the geocentric inertial system, is the position vector of the object orbiting the earth in the geocentric inertial system, is the Earth's gravitational constant, It is the perturbation acceleration of an object orbiting the Earth in the Earth's inertial system caused by factors such as the Earth's non-spherical shape and atmospheric resistance. is the 2-norm of the vector; Step 1.2: Based on the initial orbital parameters of the given on-orbit spacecraft and the observation platform, solve the orbital dynamics differential equation of the given on-orbit spacecraft orbiting the Earth in the Earth-centered inertial system 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 moments. Specifically: The orbital dynamics differential equation of a given spacecraft orbiting the Earth in the geocentric inertial system is reduced to a first-order differential equation: ; Define Deltat to represent a time step, according to the given The position of the spacecraft in orbit is given at any time and speed , the Euler method is used to solve the first-order differential equation, and the result is obtained after a step length of Deltat seconds. The position of the spacecraft in orbit is given at any time and speed , and its calculation formula is: ; ; Let the counting variable be At the beginning, the initial position and velocity of the spacecraft on orbit are given And the initial position and velocity of the observation platform , based on the initial position and velocity of the given on-orbit spacecraft and observation platform 、 from The time is recursively deduced backward step by step to obtain the position and velocity values of the on-orbit spacecraft and the position and velocity values of the observation platform at multiple given moments.

[0021] Step 1.3: Convert the position and velocity values of the given on-orbit spacecraft and the observation platform at multiple moments in the geocentric inertial system into the position vector of the given on-orbit spacecraft relative to the observation platform at multiple moments in the observation platform orbital coordinate system, bring them into the azimuth and pitch angle measurement model of the given on-orbit spacecraft relative to the observation platform, calculate the azimuth and pitch angle of the given on-orbit spacecraft relative to the observation platform, and use the position and velocity values of the given on-orbit spacecraft and the position and velocity values of the observation platform and the azimuth and pitch angle of the given on-orbit spacecraft relative to the observation platform at the corresponding moments as the neural network training data. Specifically: Step 1.3.1: Given the Earth-centered inertial system The position of the spacecraft in orbit is given at any time Location of the observation platform , given the position vector of the on-orbit spacecraft relative to the observation platform for , combining the position of the given on-orbit spacecraft and the position of the observation platform at multiple moments, and calculating the position vector of the given on-orbit spacecraft relative to the observation platform at multiple moments; Step 1.3.2, based on Always observe the platform's location and speed value , the coordinate transformation matrix from the Earth-centered inertial system to the observation platform orbit coordinate system is constructed as ; Calculate the position vector of a given on-orbit spacecraft relative to the observation platform in the observation platform orbit coordinate system ;in,( )for The coordinates of the observation platform in the Earth-centered inertial system at all times; Step 1.3.3: Set the position vector of the given on-orbit spacecraft relative to the observation platform in the observation platform orbit coordinate system to The azimuth and pitch angle measurement model of the space target relative to the observation platform is introduced to calculate the azimuth and pitch angle of the given on-orbit spacecraft relative to the observation platform. The azimuth and pitch angle measurement model of the space target relative to the observation platform is: ; ; Where, for In the observation platform orbit coordinate system The axis weight, for In the observation platform orbit coordinate system The axis weight, for In the observation platform orbit coordinate system The axis's weight; Step 1.3.4: Use the position and velocity values of the given on-orbit spacecraft and the position and velocity values of the observation platform at each moment obtained in step 1.2, and the azimuth and pitch angles of the given on-orbit spacecraft relative to the observation platform obtained at the corresponding moment as a set of neural network training samples, and obtain multiple sets of neural network training samples to constitute neural network training data.

[0022] Step 2: Construct a neural network based on a weighted loss function, train the neural network using the neural network training data, and obtain a space target orbit state estimation model; specifically: Step 2.1: Build a neural network based on weighted loss function: Set up the input layer, output layer, and multiple hidden layers between the input layer and output layer in the neural network; Multiple hidden layers are connected in sequence. The first hidden layer is connected to the input layer to receive the output data of the input layer. The last hidden layer is connected to the output layer to output the prediction results. Each hidden layer linearly transforms the output data of the previous layer through the weight matrix and bias, and then performs nonlinear transformation through the activation function and inputs it to the next layer. The calculation formula of the hidden layer is: ; in, Indicates the l The output of the hidden layer, Indicates the lThe weight matrix of the hidden layer, Indicates the l The bias vector of the hidden layer, represents the activation function; A (l-1) Indicates the l -The output of 1 hidden layer; Initialize the weight matrix of the hidden layer and the output layer to a random number matrix, and initialize the bias vector of the hidden layer and the output layer to 0; Setting the parameters of the Adam optimizer in the neural network 、 、 and δ, where is the learning rate, and is the exponential decay rate of the Adam optimizer, and δ is a small parameter to prevent division by 0; Set the weighted loss function of the neural network, the expression is: ; in, is the weighted loss function, is the position error weight, is the mean square error of position, is the speed error weight, is the mean square error of velocity, is the regularization term.

[0023] The calculation formula is: ; m is the sample size, is the regularization coefficient, is the weight matrix j weights; The activation function is the linear rectification function ReLU, and the expression is: .

[0024] Step 2.2, setting the total number of neural network training cycles, and normalizing the neural network training data to obtain normalized neural network training data; Normalization is specifically: ,

[0025] In the formula is the normalized training data input value, is the input value of the training data before normalization, is the minimum input value of the training data before normalization, is the maximum input value of the training data before normalization; is the normalized training data output value, is the output value of the training data before normalization, is the minimum output value of the training data before normalization, is the maximum output value of the training data before normalization.

[0026] Step 2.3: Input the position and velocity values of the observation platform corresponding to the 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; and output the predicted position and velocity values of the given on-orbit spacecraft in the output layer; Step 2.4: Calculate the weighted loss function value based on the predicted position and velocity values of the given on-orbit spacecraft output 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 gradient of the loss function value with respect to the weights and biases of each layer using the chain rule, and use the Adam optimizer to update the weights and biases of each layer. The update formula for updating the weights and biases of each layer using the Adam optimizer is: , , , , , ; Where, t is the number of updates, is the gradient of the loss function with respect to the weight when the relevant parameters are updated for the tth time, b t is the bias vector after the tth update, is the first-order moment estimate of the weight gradient after the tth update, is the estimated value of the second-order moment of the weight gradient after the tth update, is the gradient of the loss function with respect to the bias when the relevant parameters are updated for the tth time, is the first-order moment estimate of the bias gradient after the tth update, is the estimated value of the second-order moment of the bias gradient after the tth update.

[0027] Step 2.5: Determine whether the total number of neural network training cycles has been reached. If not, return to step 2.3 and input the position and velocity values of the corresponding observation platform in 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 cycles reaches the total number of neural network training cycles, the network parameters corresponding to the weights and biases of each layer when the loss function value is minimized are brought into the neural network to obtain a space target orbit state estimation model.

[0028] Step 3: Collect N groups of observation platform position and velocity values at equal time intervals, as well as the azimuth and pitch angles of the space target to be measured relative to the observation platform, and normalize them respectively. Input them into the space target orbit state estimation model to obtain the normalized initial orbit position and initial velocity of the space target to be measured. Denormalize the normalized initial orbit position and initial velocity of the space target to be measured to obtain the initial orbit position and initial velocity of the space target to be measured, where N ≥ 3.

[0029] Step 4: Input the initial orbital position and initial velocity of the space target to be measured into step 1.2. 、 The calculation formula is used to obtain the position and velocity of the space target to be measured at any moment.

[0030] The data parameters of the space target orbit parameter determination method based on the weighted loss function neural network provided in this embodiment are shown in Table 1 during implementation.

[0031] According to Table 1, the relative errors between the predicted position and velocity of the space target at time 0s (initial time) in the geocentric inertial system [45582875, -12838948, -5887964, 440, 2063, 641] and the actual position and velocity of the space target at time 0s (initial time) in the geocentric inertial system [48626635, -12535853, -5917512, 436, 2050, 640] are [6.26%, 2.42%, 0.50%, 1.25%, 0.64%, 0.21%]. It can be seen that the orbit determination accuracy of the space target orbit parameter determination method based on the weighted loss function neural network provided by this embodiment is high.

[0032] Through the above method, the present invention provides a method for determining the orbital parameters of a space target based on a weighted loss function neural network. By weighting 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 constructing a more adaptable space target orbital state estimation model for specific mission scenarios.

[0033] Table 1

[0034] The above description is merely a specific embodiment of the present invention, and a comparison of the effects of the specific embodiment with the 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 shall be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention shall be based on the scope of protection of the claims.

Claims

1. A method for determining space target orbit parameters based on a weighted loss function neural network, characterized in that: The following steps are involved: Step 1: Based on the initial orbital parameters of the given on-orbit spacecraft and the observation platform, solve the differential equation of the orbital dynamics of the given on-orbit spacecraft orbiting the Earth in the Earth-centered inertial system to obtain neural network training data; Step 2: Construct a neural network based on a weighted loss function, train the neural network using the neural network training data, and obtain a space target orbit state estimation model; Step 3: Collect N sets of observation platform position and velocity values at equal time intervals, as well as the azimuth and pitch angles of the space target to be measured relative to the observation platform, and input them into the space target orbit state estimation model to obtain the initial orbit position and initial velocity of the space target to be measured, where N ≥ 3; Step 4: Calculate the position and velocity of the space target at any moment based on the initial orbital position and initial velocity of the space target.

2. The method for determining space target orbit parameters 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 force conditions of the given on-orbit spacecraft, establish the orbital dynamics differential equation of the given on-orbit spacecraft orbiting the Earth in the Earth-centered inertial system, which can be expressed as: ； in, is the acceleration vector of an object orbiting the earth in the geocentric inertial system, is the position vector of the object orbiting the earth in the geocentric inertial system, is the Earth's gravitational constant, It is the perturbation acceleration of an object orbiting the Earth in the Earth's inertial system caused by factors such as the Earth's non-spherical shape and atmospheric resistance. is the 2-norm of the vector; Step 1.2: Based on the initial orbital parameters of the given on-orbit spacecraft and the observation platform, solve the differential equation of the orbital dynamics of the given on-orbit spacecraft orbiting the Earth in the Earth-centered inertial system 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 moments in time. Step 1.3: Convert the position and velocity values of the given on-orbit spacecraft and the observation platform at multiple moments in the geocentric inertial system into the position vector of the given on-orbit spacecraft relative to the observation platform at multiple moments in the observation platform orbital coordinate system, and bring them 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 angle of the given on-orbit spacecraft relative to the observation platform; use the position and velocity values of the given on-orbit spacecraft, the position and velocity values of the observation platform, and the azimuth and pitch angle of the given on-orbit spacecraft relative to the observation platform at the corresponding moments as neural network training data.

3. The method for determining space target orbit parameters based on a weighted loss function neural network according to claim 2, characterized in that: Step 1.2 is as follows: Let the counting variable be To begin, take the initial position of the given on-orbit spacecraft and initial velocity and the initial position of the observation platform and the initial velocity , solve the orbital dynamics differential equation of a given spacecraft orbiting the Earth in the Earth-centered inertial system, and obtain the position and velocity values of the given spacecraft and the position and velocity values of the observation platform at multiple moments. The calculation formula is: ； ； Where, express The position of an on-orbit spacecraft or observation platform is given at any moment. express The speed of the spacecraft or observation platform on orbit is given at any moment, and Deltat represents a time step. express The position of an on-orbit spacecraft or observation platform is given at any moment. express The velocity of a spacecraft or observation platform in orbit is given at any moment.

4. The method for determining space target orbit parameters based on a weighted loss function neural network according to claim 3, characterized in that: Step 1.3 is as follows: Step 1.3.1: Given the Earth-centered inertial system The position of the spacecraft in orbit is given at any moment Location of the observation platform , given the position vector of the on-orbit spacecraft relative to the observation platform for , combining the position of the given on-orbit spacecraft and the position of the observation platform at multiple moments, and calculating the position vector of the given on-orbit spacecraft relative to the observation platform at multiple moments; Step 1.3.2, based on Always observe the platform's location and speed value , the coordinate transformation matrix from the Earth-centered inertial system to the observation platform orbit coordinate system is constructed as ; Calculate the position vector of a given on-orbit spacecraft relative to the observation platform in the observation platform orbit coordinate system ;in, for The coordinates of the observation platform in the Earth-centered inertial system at all times; Step 1.3.3: Set the position vector of the given on-orbit spacecraft relative to the observation platform in the observation platform orbit coordinate system to The azimuth and pitch angle measurement model of the space target relative to the observation platform is introduced to calculate the azimuth and pitch angle of the given on-orbit spacecraft relative to the observation platform. The azimuth and pitch angle measurement model of the space target relative to the observation platform is: ； ； Where, for In the observation platform orbit coordinate system The axis weight, for In the observation platform orbit coordinate system The axis weight, for In the observation platform orbit coordinate system The axis's weight; Step 1.3.4: Use the position and velocity values of the given on-orbit spacecraft and the position and velocity values of the observation platform at each moment obtained in step 1.2, and the azimuth and pitch angles of the given on-orbit spacecraft relative to the observation platform obtained at the corresponding moment as a set of neural network training samples, and obtain multiple sets of neural network training samples to constitute neural network training data.

5. The method for determining space target orbit parameters based on a weighted loss function neural network according to claim 4, characterized in that: In step 2, the construction of a neural network based on a weighted loss function is specifically as follows: Step a: setting an input layer, an output layer, and multiple hidden layers between the input layer and the output layer in a neural network; Multiple hidden layers are connected in sequence. The first hidden layer is connected to the input layer to receive the output data of the input layer. The last hidden layer is connected to the output layer to output the prediction results. Each hidden layer linearly transforms the output data of the previous layer through the weight matrix and bias, and then performs nonlinear transformation through the activation function and inputs it to the next layer. The calculation formula of the hidden layer is: ; in, Indicates the l The output of the hidden layer, Indicates the l The weight matrix of the hidden layer, Indicates the l The bias vector of the hidden layer, represents the activation function; A (l-1) Indicates the l -The output of 1 hidden layer; Initialize the weight matrix of the hidden layer and the output layer to a random number matrix, and initialize the bias vector of the hidden layer and the output layer to 0; Step b: Set the parameters of the Adam optimizer in the neural network 、 、 and δ, where is the learning rate, and is the exponential decay rate of the Adam optimizer, and δ is a small parameter to prevent division by 0; Step c: Set the weighted loss function of the neural network, which is expressed as: ； in, is the weighted loss function, is the position error weight, is the mean square error of position, is the speed error weight, is the mean square error of velocity, is the regularization term.

6. The method for determining space target orbit parameters based on a weighted loss function neural network according to claim 5, characterized in that: As described in step c The calculation formula is: ; m is the sample size, is the regularization coefficient, is the weight matrix j weights; The activation function is the linear rectification function ReLU, which is expressed as: 。 7. The method for determining space target orbit parameters based on a weighted loss function neural network according to claim 5, characterized in that: Step 2 is as follows: Step 2.1, construct a neural network based on a weighted loss function, set the total number of neural network cycle training times, and normalize the neural network training data to obtain normalized neural network training data; Step 2.2, inputting the position and velocity values of the corresponding observation platform in the normalized neural network training data and the azimuth and pitch angles of the given on-orbit spacecraft relative to the observation platform into the input layer; and outputting the predicted position and velocity values of the given on-orbit spacecraft in the output layer; Step 2.3: Based on the output of the output layer, the predicted position and velocity of the given on-orbit spacecraft are compared with the corresponding position and velocity of the given on-orbit spacecraft in the normalized neural network training data. The weighted loss function is calculated, and the gradient of the loss function with respect to the weights and biases of each layer is calculated using the chain rule. The weights and biases of each layer are updated using the Adam optimizer. Step 2.4: Determine whether the total number of neural network training cycles has been reached. If not, return to step 2.2 and input the position and velocity values of the corresponding observation platform in 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 neural network training cycles has been reached, then the network parameters corresponding to the weights and biases of each layer when the loss function value is minimized are brought into the neural network to obtain a space target orbit state estimation model.

8. The method for determining space target orbit parameters based on a weighted loss function neural network according to claim 7, characterized in that: In step 2.3, the update formula for updating the weights and biases of each layer using the Adam optimizer is: ， ， ， ， ， ； Where, t is the number of updates, is the gradient of the loss function with respect to the weight when the relevant parameters are updated for the tth time, is the first-order moment estimate of the weight gradient after the tth update, is the estimated value of the second-order moment of the weight gradient after the tth update, is the gradient of the loss function with respect to the bias when the relevant parameters are updated for the tth time, is the first-order moment estimate of the bias gradient after the tth update, is the estimated value of the second-order moment of the bias gradient after the tth update.

9. The method for determining space target orbit parameters based on a weighted loss function neural network according to claim 7, characterized in that: Step 3 is specifically as follows: collect N groups of observation platform position and velocity values at equal time intervals, as well as the azimuth and pitch angles of the space target to be measured relative to the observation platform, normalize them respectively, and input them into the space target orbit state estimation model to obtain the normalized initial orbit position and initial velocity of the space target to be measured; denormalize the normalized initial orbit position and initial velocity of the space target to be measured to obtain the initial orbit position and initial velocity of the space target to be measured, where N ≥ 3.

10. The method for determining space target orbit parameters based on a weighted loss function neural network according to claim 7, characterized in that: Step 4 is as follows: Input the initial orbital position and initial velocity of the space target to be measured into the calculation formula in step 1.2 to obtain the position and velocity of the space target to be measured at any time.

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