Very short arc segment space-based passive intelligent orbit determination method based on physical information neural network

Abstract

The application discloses a very short arc segment space-based passive intelligent orbit determination method based on a physical information neural network and belongs to the technical field of space situation awareness. The method only utilizes optical angle measurement data of an observation satellite, and realizes initial orbit determination for a very short arc segment of a low-orbit non-cooperative target with an observation time of less than 1 minute. The application establishes a spacecraft motion dynamics model containing the earth non-spherical gravity perturbation and a line-of-sight angle measurement model, constructs a target relative state residual loss function and an orbit acceleration residual loss function, embeds an orbit dynamics physical law driving term in neural network back propagation, forms a total loss function combined with data loss and physical loss joint constraints, optimizes model hyperparameters based on gradient descent, completes nonlinear mapping of a line-of-sight angle sequence to a target relative motion state, and realizes high-precision initial orbit determination of a very short arc segment. The application has the advantages of convenient deployment, high stability and strong robustness, and is suitable for space-based space target monitoring and cataloging.

Description

Technical Field

[0001] This invention relates to the field of space situational awareness technology, specifically to a space-based passive intelligent orbit determination method based on a physical information neural network. This method is applicable to space-based platforms performing initial orbit determination of non-cooperative space targets under very-short-arc (VSA) conditions (observation time ≤ 1 minute) using only line-of-sight angle measurement information acquired by optical cameras. Background Technology

[0002] With the rapid development of human space technology, global space launch missions are becoming increasingly frequent. The increase in Starlink, low-Earth orbit space debris, and defunct spacecraft has created space safety hazards. To reduce the collision risk of spacecraft in orbit, cataloging these non-cooperative space targets is particularly important, and initial orbit determination is the foundation of space cataloging. Space-based optical measurement has advantages such as wide dynamic range, broad coverage, and low power consumption, and is not affected by atmospheric conditions or terrain limitations, making it one of the important methods for detecting and tracking space targets. However, when the relative velocity between the non-cooperative space target and the observation platform is high and the observation duration is less than one minute, existing angle-only initial orbit determination methods, such as Gaussian and least squares methods, fail to solve for the target orbit. This is the very short arc initial orbit determination problem.

[0003] Currently, existing technical solutions for determining the initial orbit of very short arc space targets mainly fall into three categories: First, a short arc orbit determination method that constructs the allowable region of the target by observing the angle and the rate of change of angle, assuming the range of slant range and slant range rate; Second, a method that uses a heuristic search algorithm to iteratively optimize the initial target orbit under the condition of constructing an angle fitness function, given the initial target orbit boundary range; Third, a method that uses a neural network to complete a nonlinear mapping model from angle sequence to target orbit state after offline training, for online application after on-board deployment.

[0004] However, the aforementioned existing technical solutions have significant limitations: the method of constructing the target allowable domain essentially links multiple short arc data together, which does not solve the problem of uncertainty in the initial orbit when measurement information is insufficient; while search algorithms such as evolutionary algorithms and swarm algorithms require prior information on the initial boundary range of the orbit, and the computational iteration is time-consuming and computationally complex; and neural networks based solely on data have the problem that the black box model cannot be physically explained, resulting in limited generalization performance of the trained orbit determination model.

[0005] To address the shortcomings of the existing technologies, this invention proposes a very short arc space-based passive intelligent orbit determination method based on a physical information neural network. This method utilizes only the optical angle measurement data of observed satellites and embeds orbital dynamics equations into the structure of a deep neural network. Under the constraints of data and physical laws, it constructs an initial orbit determination model that maps the line-of-sight angle sequence to the target orbit, filling the gap in the field of very short arc space-based passive orbit determination. Summary of the Invention

[0006] This invention aims to provide a space-based passive intelligent orbit determination method for very short arc segments based on physical information neural networks, which solves the problems of instability in calculating the initial orbit of very short arc segments and limited generalization performance in existing technologies. It enables the determination of the initial orbit of low Earth orbit very short arc segments within one minute using only the optical angle measurement data of observation satellites.

[0007] To achieve the above-mentioned objectives, the technical solution provided by this invention is as follows: A very short arc segment space-based passive intelligent orbit determination method based on physical information neural networks. This method utilizes only optical angle measurement data from observation satellites. By embedding orbital dynamics equations into the structure of a deep neural network, and under the constraints of data combined with physical laws, an initial orbit determination model is constructed that maps the line-of-sight angle sequence to the target orbit. This enables the nonlinear mapping of the relative motion state of the target spacecraft from the sparse angle measurement sequence. The steps include: S1. Construct a spacecraft motion dynamics model based on the geocentric equatorial inertial coordinate system, incorporating the non-spherical gravitational perturbation of the Earth, and a line-of-sight observation model of the target spacecraft by the spaceborne optical camera; S2. Construct an initial orbit determination model based on a physical information neural network, using the observed star orbit information and line-of-sight angle sequence as input, and the target's relative motion state as output. This step specifically includes: Construct the relative state residual loss function and the orbital acceleration residual loss function of the target spacecraft to form a total loss function with joint constraints of data loss and physical loss; The physical laws of orbital dynamics are embedded as driving terms in the backpropagation of the neural network, and the hyperparameters of the model are optimized by gradient descent of the total loss function. S3. Construct a training dataset from the line-of-sight angle sequence to the relative motion state of the target spacecraft. Train the deep neural network using the training dataset and optimize the model hyperparameters based on gradient descent to complete the nonlinear mapping from the line-of-sight angle sequence to the relative motion state of the target spacecraft, thereby achieving high-precision initial orbit determination in very short arc segments.

[0008] Furthermore, the method utilizes only the optical angle measurement data of the observation satellite to solve the initial relative motion state of the low-orbit target spacecraft within a very short arc segment of less than 1 minute, thereby completing the initial orbit determination of the target spacecraft.

[0009] The spacecraft motion dynamics model described in step S1 is constructed based on the geocentric equatorial inertial coordinate system and takes into account the gravitational perturbations of the Earth's non-spherical J2, J3 and J4 terms; In the aforementioned line-of-sight observation model, the measurement noise of the actual observation equipment is modeled as zero-mean Gaussian white noise.

[0010] Furthermore, in step S2, the target spacecraft relative state residual loss function is constructed as the squared residual between the target spacecraft's predicted relative motion state and the true value, and its mathematical expression is:

[0011] In the formula, This represents the relative state residual loss function of the target spacecraft. This represents the true value of the relative motion state of the target spacecraft. This represents the relative motion state predicted by the neural network model. This indicates the number of samples in mini-batch gradient descent. Indicates the sample index number; The orbital acceleration residual loss function is calculated based on the spacecraft motion dynamics model constructed in step S1, which calculates the orbital acceleration term at any moment in the training target orbit. The second derivative term of the neural network is calculated from the target relative motion state estimated by weighted summation after nonlinear transformation of the input line-of-sight angle sequence through activation function, thereby deriving the orbital acceleration residual loss function. The expression is as follows:

[0012] In the formula It can be represented as a nonlinear implicit function of time in a deep neural network model. For the acceleration of the perturbed orbit, To observe the acceleration of spacecraft. , These represent the right ascension and declination of the target spacecraft in the geocentric equatorial inertial reference frame J2000, respectively. The total loss function is: In the formula and These are the weighting coefficients for the physical loss and data loss functions, respectively.

[0013] Furthermore, step S2, which embeds physics-driven terms into the backpropagation path during neural network training, is as follows: S21. Based on the line-of-sight observation model constructed in step S1, obtain the line-of-sight sequence observed by the observation satellite, and calculate the first and second derivatives of the relative line-of-sight vector with respect to time corresponding to the line-of-sight sequence. S22. After obtaining the derivative of the line-of-sight angle sequence of the network input with respect to time, the input of the physical information neural network is set to the line-of-sight angle sequence at three different times. Then, according to the chain-like compound differentiation rule of backpropagation in the neural network, the second derivative of the relative motion state of the target spacecraft predicted by the deep neural network with respect to time is solved. S23. Combining steps S21 and S22, the derivative term of the line-of-sight angle sequence is obtained, and then the physical acceleration term of the target state predicted by the neural network with respect to time is determined. The physical loss function is then constructed and combined with the data loss function to form the total loss function.

[0014] Based on the total loss function, the optimal hyperparameters of the initial orbit determination model are determined through gradient descent during backpropagation. The update equation is expressed as:

[0015] In the formula The hyperparameter is the learning rate. It is the total loss function.

[0016] Furthermore, the acquisition of the training dataset in step S3 includes the following process: The observation satellite and the target orbit are set in low Earth orbit, and the orbital elements of the observation satellite and the target at the initial moment are converted into the absolute motion state in the geocentric equatorial inertial coordinate system. Within at least two orbital periods of the observed target, the absolute motion state of the observed satellite and the target at any time is obtained through orbital propagation, and the relative line-of-sight vector at the corresponding time is obtained through the line-of-sight angle observation model of the target spacecraft.

[0017] Furthermore, the training data for the physical information neural network model includes normalizing the motion state vector and angle measurement sequence using a maximum-minimum normalization method. ; For the training samples, where the first... The first sample data The normalization process for the dimensional features is as follows:

[0018] In the formula: and They are the first The maximum and minimum values ​​of the sample features in dimension . It is the first The first sample data Normalized data for dimensional features.

[0019] Beneficial effects: Compared with existing technologies, the substantial features and significant advancements of this invention include: First, this invention enables initial orbit determination of very short arc segments using only observation satellite orbit information and optical camera angle measurement information. This reduces the requirements for observation equipment and makes it easy to deploy in existing space observation systems. Second, by embedding penalties based on the physical laws of orbital dynamics, the uncertainty problem of the neural network black-box model is improved, enhancing stability in initial orbit determination. Third, by training the network using a combination of physical loss functions and data loss functions, the generalization ability of the neural network is enhanced. Fourth, it has a wide range of applications, with broad requirements for target orbit types, observation arc segments, and observation noise. Attached Figure Description

[0020] Figure 1 This is a flowchart illustrating the algorithm logic of this invention. Figure 2 It is a structure diagram of a neural network model based on physical information; Figure 3 This is a flowchart of the process for obtaining the training dataset; Figure 4 This is an error curve diagram of the initial trajectory in the embodiment; Figure 5 This is a graph showing the mean absolute percentage error of the initial track in the embodiment. Figure 6 This is a graph showing the average absolute percentage error of the test track in the embodiment. Detailed Implementation

[0021] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0022] This invention provides a space-based passive intelligent orbit determination method for very short arc segments based on a Physical Information Neural Network (PINN). This method constructs data residuals and orbital acceleration residual functions using only observed angle data. The PINN, penalized by physical laws, can accurately solve for the relative motion state of a target in a very short arc segment. Compared to the data-driven approach used in traditional deep neural networks, this invention introduces an orbital dynamics model as a physical constraint to construct a comprehensive loss function that includes both data and physical losses. By training the network with a constructed training dataset, the PINN can nonlinearly map the relative motion state of the target from a sparse angle measurement sequence.

[0023] The following describes the problem to be solved by the present invention and the specific implementation process in the J2000 geocentric equatorial inertial coordinate system and the spacecraft orbital coordinate system.

[0024] The geocentric equatorial inertial coordinate system (ECI) has its origin at the Earth's center of mass, with the XY plane being the equatorial plane. The X-axis points to the vernal equinox, the Z-axis points to the North Pole, and the Y-axis, Z-axis, and X-axis form a right-handed rectangular coordinate system.

[0025] Combination Figure 1 As shown, the implementation steps of the present invention are as follows: Step S1: Construct a spacecraft motion dynamics model based on the geocentric equatorial inertial coordinate system, incorporating the non-spherical gravitational perturbation of the Earth. And a model for observing the line-of-sight angle of a target spacecraft using a spaceborne optical camera; This invention primarily studies the initial orbit determination problem of space-based passive very short arcs for non-cooperative targets such as low-Earth orbit space debris. Therefore, an absolute dynamic model considering the gravitational perturbations of the Earth's non-spherical J2, J3, and J4 terms is used for orbit generalization, and the construction form is as follows:

[0026] In the formula, Represents the absolute dynamic model function. This represents the motion state of the spacecraft in the Earth's equatorial inertial coordinate system. This indicates that the derivative of the state variables is calculated. and These are the spacecraft's position vector and velocity vector in the geocentric inertial coordinate system, respectively. For the central gravitational acceleration, The gravitational constant of Earth, It is the non-spherical perturbation acceleration of the Earth. This represents the calculation of the derivative of the spacecraft's position vector in the Earth's equatorial inertial coordinate system. Indicates to The derivative is calculated again, that is, the second derivative is performed on the spacecraft's position vector in the Earth's equatorial inertial coordinate system.

[0027] The aforementioned non-spherical perturbation acceleration of Earth The mathematical expression is:

[0028] Without loss of generality, assuming the optical camera is mounted at the center of mass of the observed spacecraft, the relative line-of-sight vector between the target and the observed spacecraft can be established in the geocentric equatorial inertial coordinate system. :

[0029] From relative position vector Then the azimuth angle obtained by the camera can be calculated separately. and pitch angle As shown in the following formula:

[0030]

[0031] In the formula: and It is the measurement noise for measuring azimuth and elevation angles.

[0032] Under passive space-based observation conditions, the input data for IOD consists of the line-of-sight angle sequence of the observed target and the orbital information of the observed spacecraft. After the optical camera acquires the pitch and azimuth angles, these can be converted into right ascension and declination in the geocentric equatorial inertial reference frame J2000. , The expression form of ) is:

[0033] Furthermore, the target-relative line-of-sight angle model is obtained as follows: .

[0034] In the formula, , These represent the target's positions along the three axes of the inertial coordinate system. , , These represent the three-axis positions of the tracker in the inertial coordinate system (the tracker's trajectory is known and can be accurately obtained through its own orbit measurement data). , The measurement noise for right ascension and declination are respectively. Considering the measurement noise of actual observation equipment, it is modeled as zero-mean Gaussian white noise, i.e. , and These are the standard deviations of the measurements of right ascension and declination, respectively. For observing the line-of-sight angle sequence.

[0035] Step S2: Construct an orbit determination model based on a physical information neural network.

[0036] Combination Figure 2 As shown, the physical information neural network constructed in step S2 is based on a data-driven neural network architecture, in which the orbital dynamics information of the low-Earth orbit spacecraft flying in space is embedded as a physical law penalty term. Therefore, the PINN (Physical Information Neural Network) structure can be mainly divided into a data-driven part and a physical-driven part.

[0037] The basic neural network structure is as follows: the input layer is used to observe the line-of-sight angle sequence; multiple hidden layers perform nonlinear transformations on the input data; the activation function in the neuron nodes is chosen as the hyperbolic tangent function, with the following form:

[0038] The neurons in the output layer perform a weighted sum of the outputs from the hidden layers, and the final output is:

[0039] In the formula, It is the number of neurons in the hidden layer. Given the input samples (motion state variables), the connection weights are represented as follows: ,and It represents the number of neurons in the output layer.

[0040] During training, a loss function is needed to evaluate the accuracy of the model construction. The loss function considered for data layer fitting in a physical information neural network is as follows:

[0041] In the formula, Represents the true value of the relative motion state. This represents the relative motion state predicted by the model. This represents the number of samples in mini-batch gradient descent. Clearly, the closer the MSE is to 0, the better the prediction performance of the neural network.

[0042] The total loss function is: In the formula and These are the weighting coefficients for the physical loss and data loss functions, respectively.

[0043] Based on the total loss function, the optimal hyperparameters of the initial orbit determination model are determined through gradient descent during backpropagation. :

[0044] In the formula The hyperparameter is the learning rate. It is the total loss function.

[0045] Furthermore, the PINN orbit determination model structure used in this invention for angle-only orbit determination is as follows: Figure 2 As shown, the dynamic explicit orbital acceleration is calculated from the output of the input observation line-of-sight sequence after forward propagation in the deep neural network. Then, the second derivative of the network's nonlinear model with respect to time constraints is used as the sum of the orbital accelerations of the observed satellites in the training dataset to approximate the physical laws. The physical loss function is obtained by comparing the two.

[0046] In the formula It can be represented as a nonlinear implicit function of time in a deep neural network model. For the acceleration of the perturbed orbit, To observe the acceleration of spacecraft. , These represent the right ascension and declination of the target spacecraft in the geocentric equatorial inertial reference frame J2000, respectively. The observation time.

[0047] Based on the aforementioned data-driven structure and the physical loss function that uses orbital acceleration dynamics for soft constraints, a set of network weights and biases can be determined after the training dataset is input into the model for forward propagation. However, the neural network requires optimal hyperparameters that nonlinearly map the observation line-of-sight sequence to the target's relative motion state model. Therefore, it is necessary to design the gradient descent portion of the physical loss function during backpropagation to achieve a balance between data fitting and physical law penalty in the total loss function.

[0048] Physical law-driven refers to the fact that the structure of a deep neural network model itself satisfies the laws of orbital dynamics, thereby avoiding overfitting of orbit determination networks based on objective physical information. The model expression of a deep neural network can be simplified to:

[0049] In the formula, X, These are the network's input and output, respectively. It is a non-linear activation layer function. This is the weight matrix. It is a hyperbolic tangent function. When the second derivative of the model output with respect to time approximates the predicted analytical orbital acceleration, it indicates that the model has learned the laws of orbital dynamics and possesses good physical interpretability. Therefore, in the physical driving part, it is necessary to calculate the analytical expression of the second derivative of the neural network model output with respect to time. Specifically, according to the chain rule of composite differentiation, solving for the second derivative of the model with respect to time requires the derivative of the model output with respect to the input line-of-sight angle sequence, and then the derivative of the line-of-sight angle sequence with respect to time.

[0050] The number of angle measurements is set to 3, and the neural network output sequence of line-of-sight angles is then given. , , The simplified forms of the first and second partial derivatives of ) are:

[0051]

[0052]

[0053] From the above observation model, the first derivative of the relative line-of-sight vector with respect to the observation time can be obtained:

[0054] In the formula, The distance is relative. Let be the first derivative of the relative line-of-sight vector with respect to time. Taking the derivative of with respect to time again yields the analytical expression for the second derivative of the relative line-of-sight vector with respect to time.

[0055] Let the derivative term of the line-of-sight angle sequence be:

[0056]

[0057] To suppress overfitting in the neural network, a backpropagation physics driving term is constructed, which is the physical acceleration term of the target state predicted by the neural network with respect to time, as follows:

[0058] For angle measurement times greater than The physical acceleration term can be simplified as follows: .

[0059] Step S3: Construct a training dataset for the physical information neural network.

[0060] Through the above process, we can obtain the input and output data of the PINN model used for initial orbit determination using only angle measurement in space-based very short arcs. Combining the known orbit information of the observed satellites and the information from the training target library, the training dataset is composed as follows:

[0061] In the formula, Indicates the observed motion state of the spacecraft. Indicates the motion state of the target spacecraft. , , This represents a sequence of line-of-sight angles at three different times. , and It is the first derivative of three different time-sequence line-of-sight angles. , and It is the second derivative of three different time-line angle sequences.

[0062] Furthermore, combined Figure 3As shown, step S3 first sets the orbits of the observation satellite and the target in low Earth orbit. The orbital elements of the observation satellite and the target at the initial moment can be converted into the absolute motion state in the ECI frame. , specific vector and The expression is as follows:

[0063] In the formula, , , , , and Represent the semi-major axis, eccentricity, inclination, right ascension of the ascending node, argument of perigee, and true perigee angle, respectively, of the six orbital roots; vector , Used to indicate the orientation of the near-focal coordinate system:

[0064]

[0065] Within two orbital periods of the observed target, the absolute motion state of the observed star and the target at any moment can be obtained through orbital propagation. Furthermore, the relative line-of-sight vector at the corresponding moment can be obtained from the observation model.

[0066] The above process yields a training sample set for the initial training target orbit. The initial motion state of the observed spacecraft and the measured pitch and azimuth angles serve as inputs to the PINN orbit determination model. Since the data volume varies and the value ranges differ significantly, normalization is required.

[0067] This invention uses a maximum and minimum value normalization method to normalize the motion state vector and angle measurement sequence to... For the first The training samples, where the th training sample is... The first sample data The normalization process for the dimensional features is as follows:

[0068] In the formula: and They are the first The maximum and minimum values ​​among the sample features of dimension.

[0069] This embodiment sets the following calculation conditions and technical parameters: 1) The initial orbital parameters of the target and tracker are shown in Table 1 below.

[0070] Table 1. Initial orbital numbers of the target and observation spacecraft

[0071] 2) The training method for the physical information neural network adopts mini-batch stochastic gradient descent, and its key parameter settings are shown in Table 2 below.

[0072] Table 2. Parameters of Physical Information Neural Network

[0073] 3) The track parameters for the training dataset are set as shown in Table 3 below.

[0074] Table 3. Orbital parameters of the training dataset

[0075] 4) The track parameters for the test dataset are set as shown in Table 4 below.

[0076] Table 4. Track parameters of the test dataset

[0077] 5) The training dataset sampling duration is 2 orbital periods, the duration of the very short observation arc segment is 20 seconds, the number of measurements is 3, and the standard deviation of the angular noise is taken as [value missing]. .

[0078] The very short arc space-based passive initial orbit determination method based on the physical information neural network of this invention was simulated and verified using the above-mentioned calculation conditions and technical parameters. The very short arc observation simulation duration was 20 seconds. After three angle measurements, the line-of-sight angle sequence and the observed spacecraft motion state were used as inputs to the physical information neural network. The model then predicted the relative motion state of the target. Figure 4 , Figure 5 and Figure 6 The figures show the error curves for the initial track, the mean absolute percentage error (MASE) plot, and the MASE plot for the test track, respectively, within the training dataset. Figure 4-6 It can be seen that, by means of the method described in this invention, the initial orbit determination position accuracy under sparse measurement conditions of very short arc segments is within 1%, the average position value of each axis is within 5km, and the average initial orbit determination position error of the test track set under very short arc segments of less than half a minute is within 2%, which shows good generalization performance.

[0079] Therefore, the method described in this invention breaks through the limitations of rapid orbit determination of very short arc segments of space-based non-cooperative targets under passive angle measurement conditions. It can perform initial orbit determination of very short arc segments of less than half a minute using only observed satellite orbit data and angle measurement data, thus solving the problem of rapid and high-precision orbit determination of very short arc segments on space that cannot be achieved by traditional methods.

[0080] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A very short arc segment space-based passive intelligent orbit determination method based on physical information neural networks, characterized in that, The method utilizes only satellite optical angle measurement data to solve for the initial relative motion state of a low-Earth orbit target spacecraft within a very short arc segment of less than one minute, thereby determining the initial orbit of the target spacecraft. By embedding orbital dynamics equations into the structure of a deep neural network, and under the constraints of data and physical laws, an initial orbit determination model is constructed that maps the line-of-sight angle sequence to the target orbit. This achieves nonlinear mapping of the relative motion state of the target spacecraft from a sparse angle measurement sequence. The steps include: S1. Construct a spacecraft motion dynamics model based on the geocentric equatorial inertial coordinate system, incorporating the non-spherical gravitational perturbation of the Earth, and a line-of-sight observation model of the target spacecraft by the spaceborne optical camera; S2. Construct an initial orbit determination model based on a physical information neural network, using the observed star orbit information and line-of-sight angle sequence as input, and the relative motion state of the target spacecraft as output. This step specifically includes: Construct the relative state residual loss function and the orbital acceleration residual loss function of the target spacecraft to form a total loss function with joint constraints of data loss and physical loss; The physical laws of orbital dynamics are embedded as driving terms in the backpropagation of the neural network, and the hyperparameters of the model are optimized by gradient descent of the total loss function. Step S2 involves embedding physics-driven terms into the backpropagation path during the neural network training process, as detailed below: S21. Based on the line-of-sight observation model constructed in step S1, obtain the line-of-sight sequence observed by the observation satellite, and calculate the first and second derivatives of the relative line-of-sight vector with respect to time corresponding to the line-of-sight sequence. S22. After obtaining the derivative of the line-of-sight angle sequence of the network input with respect to time, the input of the physical information neural network is set to the line-of-sight angle sequence at three different times. Then, according to the chain-like compound differentiation rule of backpropagation in the neural network, the second derivative of the relative motion state of the target spacecraft predicted by the deep neural network with respect to time is solved. S23. Combining steps S21 and S22, the derivative term of the line-of-sight angle sequence is obtained, and then the physical acceleration term of the target state predicted by the neural network with respect to time is determined. Thus, a physical loss function is constructed, and then the physical loss function is combined with the data loss function to form the total loss function. S3. Construct a training dataset from the line-of-sight angle sequence to the relative motion state of the target spacecraft. Train the deep neural network using the training dataset and optimize the model hyperparameters based on gradient descent to complete the nonlinear mapping from the line-of-sight angle sequence to the relative motion state of the target spacecraft, thereby achieving high-precision initial orbit determination in very short arc segments.

2. The very short arc segment space-based passive intelligent orbit determination method based on physical information neural network according to claim 1, characterized in that, The spacecraft motion dynamics model described in step S1 is constructed based on the geocentric equatorial inertial coordinate system and takes into account the gravitational perturbations of the Earth's non-spherical J2, J3 and J4 terms; In the aforementioned line-of-sight observation model, the measurement noise of the actual observation equipment is modeled as zero-mean Gaussian white noise.

3. The very short arc segment space-based passive intelligent orbit determination method based on physical information neural network according to claim 1, characterized in that, The target spacecraft relative state residual loss function described in step S2 is constructed as the squared residual between the target spacecraft's predicted relative motion state and the true value, and its mathematical expression is: In the formula, This represents the relative state residual loss function of the target spacecraft. This represents the true value of the relative motion state of the target spacecraft. This represents the relative motion state predicted by the neural network model. This indicates the number of samples in mini-batch gradient descent. Indicates the sample index number; The orbital acceleration residual loss function is calculated based on the spacecraft motion dynamics model constructed in step S1, which calculates the orbital acceleration term at any time in the training target orbit. The second derivative term of the neural network is calculated from the estimated relative motion state of the target spacecraft after the input line-of-sight angle sequence is weighted and summed through a nonlinear transformation of the activation function, thereby deriving the orbital acceleration residual loss function. The expression is as follows: In the formula It can be represented as a nonlinear implicit function of time in a deep neural network model. For the acceleration of the perturbed orbit, To observe spacecraft acceleration, , These represent the right ascension and declination of the target spacecraft in the geocentric equatorial inertial reference frame J2000, respectively. Indicates the observation time; The total loss function is: In the formula and These are the weighting coefficients for the physical loss and data loss functions, respectively.

4. The very short arc segment space-based passive intelligent orbit determination method based on physical information neural network according to claim 1, characterized in that, Based on the total loss function, the optimal hyperparameters of the initial orbit determination model are determined through gradient descent during backpropagation. The update equation is expressed as: In the formula The hyperparameter is the learning rate. It is the total loss function.

5. The very short arc segment space-based passive intelligent orbit determination method based on physical information neural network according to claim 1, characterized in that, The acquisition of the training dataset in step S3 includes the following process: The observation satellite is placed in low Earth orbit, and the target spacecraft's orbit is set to low Earth orbit. The orbital elements of the observation satellite and the target at the initial moment are converted into the absolute motion state in the geocentric equatorial inertial coordinate system. Within at least two orbital periods of the observed target, the absolute motion state of the observed satellite and the target at any time is obtained through orbital propagation, and the line-of-sight angle sequence at the corresponding time is obtained through the line-of-sight angle observation model of the target spacecraft.

6. The very short arc segment space-based passive intelligent orbit determination method based on physical information neural network according to claim 5, characterized in that, The training data for the initial orbit determination model based on the physical information neural network includes normalized motion state vectors and angle measurement sequences using a maximum-minimum-maximum normalization method. ; For the training samples, where the first... The first sample data Data with 3D features The normalization process is as follows: In the formula: and They are the first The maximum and minimum values ​​of the sample features in dimension . It is the first The first sample data Normalized data for dimensional features.

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