A Passive Angle Measurement Initial Orbit Determination Method for the Circum-Mars Orbit in the Mars Sampling Return Mission

Abstract

The present invention discloses a method for initial orbit determination by passive angle measurement in a circum-Mars orbit for Mars sample return, establishing an absolute dynamics model, obtaining the absolute motion state of the spacecraft and deriving the relative motion state X ; using the measured quantities H and X to construct a data set; then designing a network architecture, with the input data I being the position and velocity coordinates of the tracker in the Mars equatorial inertial coordinate system and the angle information converted from H, and the output data being X ; finally, adjusting the observation interval dt and the number of times k according to the circum-Mars observation conditions, training a physics-informed neural network with limited observation data, defining a total loss function F including a loss function F Y and a physical law penalty term F D , and optimizing the weight coefficients and biases by minimizing the loss function through the F gradient descent method. The present invention trains the neural network offline, constructs a network mapping model from the line-of-sight angle measurement sequence of the target to the target orbit, and solidifies it on the returner for online use, realizing fast orbit determination by short-arc passive measurement of the sampler.

Description

Technical Field

[0001] The present invention relates to the field of relative navigation of spacecraft, and specifically to a method for initial orbit determination by passive angle measurement in a circum-Mars orbit for Mars sampling and return. Background Art

[0002] In recent years, the number of human space launch missions has gradually increased, and deep space exploration activities have been further developed. China has formulated a three-step Mars exploration plan of "orbiting - landing - returning", and has now entered the stage of tackling key problems in the sampling and return mission. In order to achieve the Mars sampling and return mission, it is necessary to complete the rendezvous and docking of the return vehicle and the sampler in the circum-Mars orbit. Since there is no navigation satellite system deployed in the Mars orbit, the relative satellite navigation scheme commonly used in Earth orbit rendezvous cannot be adopted. At the same time, due to the extremely long distance between the Earth and Mars, the ground measurement and control delay is very large, so the rendezvous navigation method based on ground measurement and control cannot be used either. Moreover, the cost of launching and using active relative measurement sensors such as microwave radars, which are large in mass and high in power consumption, is too high and not suitable for the circum-Mars orbit rendezvous and docking of Mars sampling and return. Therefore, it is an inevitable choice to adopt a circum-Mars orbit rendezvous relative measurement scheme based on passive angle measurement by an optical camera.

[0003] However, passive angle measurement can only measure and obtain the line-of-sight angle information of the target, lacking distance information, and the relative orbital state of the target is weakly observable or even unobservable. At present, there is no report on the method for passive angle measurement relative navigation orbit determination in circum-Mars orbit rendezvous at home and abroad.

[0004] Traditional relative navigation orbit determination methods for Earth orbits have problems such as long measurement arc segments, large computational workload for solution, and the need for initial value guessing with a certain accuracy, and are difficult to be used for the autonomous rendezvous and docking mission of Mars sampling and return. Summary of the Invention

[0005] Aiming at the problem that the existing technology cannot solve the relative navigation problem in the Mars sampling and return mission, the present invention provides a method for initial orbit determination by passive angle measurement in a circum-Mars orbit for Mars sampling and return. This method uses a designed physics-informed neural network for offline training, constructs a network mapping model from the line-of-sight angle measurement sequence of the target to the target orbit, and solidifies it on the return vehicle for online use to achieve fast short-arc passive measurement orbit determination of the sampler.

[0006] Step 1: Establish an absolute dynamics model considering the influence of Mars non-spherical perturbation and solar gravitational perturbation, obtain the absolute motion state of the spacecraft through orbit integration, and deduce the relative motion state X;

[0007] Step 2: Use the measurement quantity H measured by the sensor in the orbital system and the relative motion state X to construct a data set for the physics-informed neural network;

[0008] Step 3: Design the architecture of the physics-informed neural network and construct the penalty term for physical laws , where the input data are the position and velocity coordinates of the tracker in the Mars equatorial inertial coordinate system and the angle information converted from the measured quantities, and the output is the relative motion state X;

[0009] Step 4: Adjust the observation interval dt and the number of times k according to the circum-Martian observation conditions, train the physics-informed neural network with limited observation data, and use the gradient descent method to minimize the loss function to optimize the weight coefficients and biases, so as to obtain the optimal parameter configuration.

[0010] Preferably, in Step 1, the relative motion state , where R and V represent the relative position and relative velocity vector between the target spacecraft and the tracker in the orbital system, , , where, , , and , , respectively represent the three-axis relative position coordinates and three-axis relative velocity coordinates of the target and the tracker in the local horizontal local vertical orbital coordinate system with the centroid of the tracker as the origin.

[0011] Preferably, in Step 2, according to the dynamic model and the measured quantity H, determine the target orbit parameters within the time period m through orbit integration; in order to increase the diversity of the training data, uniformly select the initial orbit parameters of the target within the dispersion range L of the initial orbit injection of the target; in addition, map the input and output of the neural network to the interval [-1, 1] through the minmax transformation to improve the efficiency of the neural network during the training and prediction processes.

[0012] Preferably, in Step 2, the measured quantity is expressed as , where , , is the relative position between the target and the observation spacecraft, and are the measurement noises of the pitch angle and the azimuth angle respectively.

[0013] Preferably, the penalty term for physical laws in Step 3 is the acceleration residual in the two-body mechanics, and its definition is where, is the known acceleration of the target spacecraft, while is the target acceleration estimated by the network. and Non-spherical perturbation and solar gravitational perturbation, is the Mars gravitational term, is the Mars gravitational constant.

[0014] Preferably, the data set includes output data X and input data , , where , , and , , are the three-axis position coordinates and three-axis velocity coordinates of the tracker in the Mars equatorial inertial system, respectively.

[0015] Preferably, for the nth training sample, the minmax transformation normalization process of the kth-dimensional feature of the ith sample data is as follows: In the formula, and are the maximum and minimum values in the kth-dimensional feature, respectively.

[0016] Preferably, in step 4, training the physics-informed neural network includes: according to the number of observations k, a set of measurement quantities at time i , , … and the corresponding motion state of the tracker at that time, that is, the position-velocity vector, are used as the input of the neural network, while the relative motion state at the initial observation time is used as the output of the network; in the forward propagation process, the weight coefficients w and biases b in the neural network structure are randomly initialized in advance, and the optimal parameters are determined by the gradient descent method of the loss function and ; the physics-informed neural network is trained separately to obtain the optimal angle-only circum-Mars orbit determination model under simulation conditions.

[0017] Preferably, the input layer of the physics-informed neural network only plays the role of transmitting data, the hidden layer performs a non-linear transformation on the input data by the activation function , and the output layer performs a weighted sum on the data of the hidden layer and then outputs; among them, the number of neurons in the input layer is determined by the number of input parameters N. Under the condition of n angle measurement sequences, .

[0018] Preferably, the activation function is a Gaussian kernel function, defined as: In the formula, let the rd sample be , the center of the ith hidden layer node is , is the width of the hidden layer kernel function; the hidden layer contains p neurons.

[0019] Preferably, the total loss function , where

[0020] The loss function is the mean square error between the predicted value and the true value of the target relative motion state by the network: In the formula, is the relative motion state of the tracker and the target estimated by the neural network, is the true value of the relative motion state of the tracker and the target;

[0021] The physical law penalty term is: In the formula, is the known acceleration of the target spacecraft, and are the non-spherical perturbation and the solar gravitational perturbation, is the Mars gravitational term, is the Mars gravitational constant.

[0022] Beneficial effects

[0023] (1) Through the physics-informed neural network, the present invention can perform initial orbit determination of Mars orbit under the sparse angle-only measurement condition, with short orbit determination time and good position estimation accuracy;

[0024] (2) Through the algorithm, the present invention can accurately estimate the target position in the initial orbit determination of the Mars-orbiting orbit, providing a basis for subsequent Mars rendezvous and docking missions;

[0025] (3) The present invention mainly aims at the Mars coplanar orbit, and has better generalization performance and a wide application range under the relative orbit configuration with better general observation conditions;

[0026] (4) By constructing an offline database, establishing a Mars orbit dynamics model, training the physics-informed neural network, and then applying it to real-time initial orbit determination, the present invention is convenient to apply and has a short calculation time; at the same time, offline training reduces the on-board computing resource requirements, reduces the dependence on computing resources in real time, and realizes highly reliable Mars rendezvous orbit determination;

[0027] (5) The present invention balances the observation data and physical laws to construct a total loss function. The physical law penalty term evaluates the performance of the neural network by comparing the difference between the target acceleration predicted by the neural network and the target acceleration calculated by known physical laws, ensuring the accuracy of the neural network prediction while ensuring its compliance with physical principles, and improving the reliability and practicability of the model. Description of the drawings

[0028] Figure 1Schematic diagram of quantity measurement and estimation trajectory for an embodiment of the present invention;

[0029] Figure 2 For an embodiment of the present invention, the measurement interval of the test set is 60 s, and the mean absolute percentage error of the orbit determination position for 3 angle measurements;

[0030] Figure 3 For an embodiment of the present invention, the measurement interval of the test set is 60 s, and the mean absolute percentage error of the orbit determination position for 6 angle measurements;

[0031] Figure 4 For an embodiment of the present invention, the measurement interval of the test set is 90 s, and the mean absolute percentage error of the orbit determination position for 3 angle measurements;

[0032] Figure 5 For an embodiment of the present invention, the measurement interval of the test set is 90 s, and the mean absolute percentage error of the orbit determination position for 6 angle measurements;

[0033] Figure 6 Histogram of the mean absolute percentage error of the orbit determination distance under four measurement conditions for an embodiment of the test set of the present invention. Detailed implementation manners

[0034] Next, in combination with the accompanying drawings in the embodiments of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0035] The present invention discloses a passive angle measurement and initial orbit determination method for a circum-Mars orbit for Mars sampling and return. Aiming at the challenges such as poor observation conditions and large telemetry and remote control time delays faced during the rendezvous and docking of the circum-Mars orbit, based on the existing historical measurement and orbit data, a physics-informed neural network orbit determination module suitable for long distances during rendezvous and docking is constructed and trained, which can quickly and relatively accurately estimate the position of the target relative to the tracker under the coplanar orbit under sparse measurements, and at the same time meet the initial orbit determination under the dispersion range of the target at the time of orbit injection.

[0036] As Figure 1 shown, a passive initial orbit determination method for a non-cooperative target in a circum-Mars orbit based on a physics-informed neural network includes the following steps:

[0037] Step 1, considering the non-spherical perturbation of Mars and the solar gravitational perturbation under the two-body problem, constructing an absolute dynamics model, obtaining the absolute motion state of the spacecraft by integrating the orbit of the absolute dynamics model, and further obtaining the relative motion state X in the orbit system.

[0038] Specifically, the non-spherical perturbations of Mars considered in this application include , , perturbation coefficients. and the solar gravitational perturbation Specifically, they are respectively: , where, is the gravitational constant of Mars; X, Y, and Z are the three-axis position coordinates of the spacecraft in the Mars equatorial inertial system; r is the distance from the spacecraft to the center of Mars; and are the considered perturbation coefficients is the auxiliary angle; is the mean equatorial radius of Mars.

[0039] ,

[0040] where, is the solar gravitational constant; is the position vector of the sun relative to Mars; is the position vector of the detector relative to the sun, .

[0041] Among them, the relative motion state is , where R and V represent the relative position and relative velocity vectors between the target spacecraft and the tracker in the orbital system, specifically: , , where x, y, and z represent the three-axis relative position coordinates of the target and the tracker in the local horizontal local vertical orbital coordinate system with the center of mass of the tracker as the origin, , , represent the three-axis relative velocity coordinates of the target and the tracker in the local horizontal local vertical orbital coordinate system with the center of mass of the tracker as the origin.

[0042] Step 2: Obtain the measurement H measured by the sensor in the orbital system, and construct the dataset required for the training and testing of the physical information neural network in combination with the relative motion state X in Step 1. The dataset includes: input data and output data; the position, velocity, measurement azimuth, and pitch angle of the tracker during the orbital integration time period; the position and velocity of the target. The initial position and velocity of the tracker and the target are obtained by converting the orbital parameters of the tracker and the target, and then all the training data during the time period are obtained by integration.

[0043] Specifically,

[0044] Step 2.1: Obtain the measurement H measured by the sensor in the orbital system, , where and They are the pitch angle and azimuth angle measured under the orbital system, and their specific forms are as follows: , , where x, y, and z are the relative positions of the target and the observing spacecraft, and are the measurement noises of the pitch angle and azimuth angle respectively.

[0045] According to the dynamic model and measurement quantity H described in step 1, the target orbit parameters within the time period m are determined through orbit integration (the training data time period is m seconds). In this embodiment, the length of the training period is taken as 10 times the tracker orbit period, which is 68226 seconds, that is, m is taken as 68226.

[0046] Step 2.2, according to the initial orbit dispersion range L of the target, by changing the initial orbit parameters of the target (that is, uniformly selecting the initial orbit parameters of the target within the dispersion range L), the training data is diversified. The specific target orbit dispersion range L is: the semi-major axis changes , the orbital inclination changes , the true anomaly changes , the right ascension of the ascending node changes , and the eccentricity changes . The output data of the neural network is the relative motion state X, and the input data is composed of the known motion state of the tracker and the sequence of measured pitch angle and azimuth angle, and its specific form is as follows: where X, Y, and Z are the three-axis position coordinates of the tracker in the Mars equatorial inertial system, , , are the three-axis velocity coordinates of the tracker in the Mars equatorial inertial system. and are the pitch angle and azimuth angle measured under the orbital system respectively, and are obtained from the measurement quantity .

[0047] Step 2.3, map the input and output of the neural network to the interval [-1, 1] through minmax transformation to improve the efficiency of the neural network during training and prediction.

[0048] For the nth training sample, the minmax transformation normalization processing of the kth-dimensional feature of the ith sample data is as follows: where and are the maximum and minimum values in the kth-dimensional feature respectively.

[0049] It should be noted that: for the input data For example, its dimension is 8 - dimensional. Among all the training data, there are maximum and minimum values for the target's position and velocity, as well as the observation angle.

[0050] Step 3: Construct a physics - informed neural network. The physics - informed neural network has a three - layer structure: an input layer, a hidden layer, and an output layer. The input layer only serves to transfer data. The hidden layer performs a non - linear transformation on the input data using an activation function and the output layer outputs the weighted sum of the data from the hidden layer. Among them, the number of neurons is determined by the number of input parameters N. The activation function selects a Gaussian kernel function, which is defined as: In the formula, let the th sample be , the center of the i - th hidden - layer node is , is the width of the hidden - layer kernel function. The hidden layer contains n neurons, and the connection weights are denoted as , and k is the number of output - layer neurons. The number of input parameters of the neural network is determined according to the number of angle - measurement times. Under the condition of n angle - measurement sequences, .

[0051] Step 4: Train the physics - informed neural network. In view of the limitations of the ring - fire observation conditions, the observation interval dt and the number of observations k are correspondingly changed. That is, under the condition of limited transmission bandwidth, the sampling frequency is reduced, the sparse measurement number is k, and the observation interval dt is dynamically adjusted to reserve redundancy.

[0052] According to the number of observations, a set of measurement quantities ( , , … ) and the motion state of the tracker at the corresponding time are used as the input of the neural network, while the relative motion state X at the initial observation time is used as the output of the network. Here, the subscript i represents the i - th measurement time, and the subscript k represents the number of measurements k. In the forward - propagation process, the weight coefficients w and biases b in the neural - network structure are randomly initialized in advance. The determination of their optimal parameters is achieved through the gradient - descent method of the total loss function F including the loss function and . The physics - informed neural network is separately trained to obtain the optimal angle - only ring - fire orbit - determination model under simulation conditions. In this embodiment, the observation intervals dt are taken as 60 seconds and 90 seconds respectively, and the number of observations k are taken as 3 times and 6 times respectively.

[0053] The weight coefficients w and biases b in the neural network are initially given by the following formula: Among them, and are the i - th weight coefficient and the i - th bias in the neural network respectively, and Command for generating uniformly distributed random numbers.

[0054] The total loss function for determining the optimal hyperparameters is defined as , where is the weight parameter. Among them, the loss function is the mean square error between the predicted value and the true value of the target relative motion state network, which is used to measure the difference between the predicted value and the true value, and is expressed as: In the formula, is the relative motion state between the tracker and the target estimated by the neural network, is the true value of the relative motion state between the tracker and the target.

[0055] Physical law penalty term is the physical law penalty term, which is used to ensure that the prediction result conforms to the known physical laws. The performance is evaluated by comparing the difference between the target acceleration predicted by the neural network and the target acceleration calculated by the known physical laws, and is expressed as: In the formula, is the known acceleration of the target spacecraft, and are the non-spherical perturbation and the solar gravitational perturbation, is the Mars gravitational term, is the Mars gravitational constant, is the target acceleration estimated by the neural network.

[0056] The total loss function combines the observed data and the physical laws. By minimizing this total loss function, the neural network can not only learn how to accurately predict the motion state of the target, but also ensure that its prediction result conforms to the known physical laws, thereby improving the reliability and practicality of the model.

[0057] Step 5, Passive initial orbit determination of the non-cooperative target around Mars. Obtain the dataset to be tested with the same operation as in Step 2, define the error index Q, and give the orbit determination error analysis of the physical information neural network. Among them, the error performance index is defined as the mean absolute percentage error and the root mean square error , specifically: In the formula is the i-th of the n estimated relative motion states of the target, is the true value corresponding to the estimated value.

[0058] The feasibility of the present invention is illustrated by the following examples.

[0059] Set the following calculation conditions and technical parameters:

[0060] 1) The initial orbital elements of the target spacecraft are as follows: semi-major axis 3996.190 km, eccentricity 0, orbital inclination 29°, right ascension of the ascending node 164°, argument of perigee 0°, and true anomaly 73°.

[0061] 2) The initial orbital elements of the chaser spacecraft are as follows: semi-major axis 3996.230 km, eccentricity 0, orbital inclination 30°, right ascension of the ascending node 165°, argument of perigee 0°, and true anomaly 60°.

[0062] 3) In the measurement H, the measurement noises of the pitch angle and azimuth angle are taken as Gaussian white noises of 10 -5 rad.

[0063] 4) The training orbit time period is taken as 68000 s, which is 10 times the orbital period of the chaser; the test orbit time period is taken as 13000 s, which is 2 times the orbital period of the chaser.

[0064] 5) The number of measurements is taken as 3 times and 6 times respectively; the observation intervals are taken as 60 seconds and 90 seconds respectively, and the corresponding number of measurement groups is 4 groups.

[0065] 6) The orbit error of the chaser is 5 km ( ), 0.5 m / s ( ), and the measurement distance of the optical camera is less than or equal to 1000 km.

[0066] Based on the angle data measured by the present invention and the absolute motion state of the chaser, relevant simulation verification is carried out with the above set calculation conditions and technical parameters, and the simulation duration is 13645 s. Figure 2 and Figure 3 respectively give the mean absolute percentage errors of orbit determination for angle measurement 3 times at 60 s and angle measurement 6 times at 60 s; Figure 4 and Figure 5 give the mean absolute percentage errors of angle measurement 3 times at 90 s and angle measurement 6 times at 90 s. As can be seen from the figure, in the target simulation orbits 1, 3, and 9, there are cases where the single-axis percentage error is relatively large. However, the relative motion in the y-axis and z-axis is a small amount within kilometers compared to the x-axis. When approaching within nearly 1000 km during rendezvous and docking, the chaser only needs to align in one direction to approach the target, and its influence can be ignored. Orbit 0 in the test set is the initial target orbit, and the orbit determination position error satisfies within 4%. The mean absolute percentage errors of the neural network position in the three axes x, y, and z within the target orbit injection dispersion range basically satisfy within 8%.

[0067] Figure 6 is the histogram of the overall orbit determination distance error, from which it can be intuitively seen that as the number of measurements increases, the overall orbit determination accuracy of PINN improves, and as the measurement interval increases, the overall orbit determination accuracy improves, and the accuracy satisfies within 6%.

[0068] Therefore, by adopting the method of the present invention, passive initial orbit determination of non-cooperative targets on the coplanar orbit of ring fire can be achieved only by using offline orbit data training. The orbit determination accuracy meets within 4%, and the prediction accuracy of the target position can meet within 8% when the target enters the orbit initially with uncertainty. The generalization performance is good.

[0069] Aiming at the weak observability of the coplanar orbit of Mars and the existence of a dispersion range when the target initially enters the orbit during rendezvous and docking, the present invention constructs a physical law penalty term by using a physics-informed neural network under the conditions of low angular measurement frequency and sparse angular measurement times, and integrates the absolute orbit random error of the tracker into the training process of the physics-informed neural network, realizing space-based passive fast and high-precision initial orbit determination for non-cooperative targets on the ring-fire orbit under angular measurement noise.

[0070] Finally, it should be noted that the above are only the 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 recorded in the foregoing embodiments, or perform equivalent replacements for some of the technical features. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A passive angle measurement and initial orbit determination method for the circum-Mars orbit in the Mars sampling and return mission, characterized in that, Including: Step 1: Establish an absolute dynamics model considering the influence of Mars' non-spherical perturbation and solar gravitational perturbation. Obtain the absolute motion state of the spacecraft through orbit integration and derive the relative motion state X; Step 2: Use the measurement H measured by the sensor in the orbital system and the relative motion state X to construct a dataset for the physics-informed neural network; Step 3: Design the architecture of the physics-informed neural network, where the input data I is the position and velocity coordinates of the tracker in the Mars equatorial inertial coordinate system and the angle information converted from the measurement, and the output data is the relative motion state X; Step 4: Adjust the observation interval dt and the number of times k according to the armature short - circuit observation conditions, and train the physics - informed neural network with limited observation data. Define the total loss function F including the loss function F Y and the physical law penalty term F D as F = F Y + λF D , where λ is the weight parameter, and F D is expressed as: In the formula, is the known acceleration of the target spacecraft, a N and a B are the non-spherical perturbation and the solar gravitational perturbation, is the Mars gravitational term, μ M is the Mars gravitational constant; Optimize the weight coefficients and biases by minimizing the loss function through the gradient descent method of the total loss function F, so as to obtain the optimal parameter configuration.

2. The initial orbit determination method according to claim 1, characterized in that In step 1, the relative motion state where R and V represent the relative position and relative velocity vectors between the target spacecraft and the tracker in the orbital system, and R = [x y z] T , V = [v x v y v z T , where x, y, z, and v x , v y , v z respectively represent the three-axis relative position coordinates and three-axis relative velocity coordinates of the target and the tracker in the local horizontal local vertical orbital coordinate system with the centroid of the tracker as the origin.​ 3. The initial orbit determination method according to claim 2, wherein In Step 2, according to the dynamics model and the measurement H, determine the target orbit parameters within the time period m through orbit integration; in order to increase the diversity of training data, uniformly select the initial orbit parameters of the target within the dispersion range L of the target's initial orbit injection; in addition, map the input I and output O of the neural network to the interval [-1, 1] through minmax transformation to improve the efficiency of the neural network during training and prediction.

4. The initial orbit determination method according to claim 3, characterized in that, In step 2, the measured quantity is expressed as H = [θ δ] T , where x, y, z are the relative positions of the target and the observing spacecraft, and ε θ and ε δ are the measurement noises of the pitch angle and the azimuth angle respectively.

5. The initial orbit determination method according to claim 3, characterized in that The data set includes output data X and input data I, I = [X Y Z V X V Y V Z θ δ] T , where X, Y, Z, and V X 、V Y 、V Z are the three-axis position coordinates and three-axis velocity coordinates of the tracker in the Mars equatorial inertial frame, respectively.

6. The initial orbit determination method according to claim 3, characterized in that For the nth training sample, the minmax transformation normalization process of the kth-dimensional feature of the ith sample data is as follows: In the formula, and are respectively the maximum value and the minimum value in the k-th dimensional feature.

7. The initial orbit determination method according to any one of claims 1-6, characterized in that, In step 4, training the physics-informed neural network includes: according to the number of observations k, a set of measurement quantities H at time i i+1 , H i+2 , H i+3 …H i+k and the motion state of the tracker at the corresponding time, that is, the position-velocity vector, are used as the input of the neural network, while the relative motion state X at the initial observation time is used as the output of the network; in the forward propagation process, the weight coefficients w and biases b in the neural network structure are randomly initialized in advance, and the optimal parameters are determined by the gradient descent method of F Y and F D ; the physics-informed neural network is trained separately to obtain the optimal angle-only loop fire orbit determination model under simulation conditions.

8. The initial orbit determination method according to claim 7, wherein The input layer of the physical information neural network only plays a role in transmitting data, and the hidden layer performs a non-linear transformation on the input data through the activation function f X and the output layer outputs the data of the hidden layer after weighted summation. Among them, the number of neurons in the input layer is determined by the number of input parameters N. Under the condition of n angle measurement sequences, N = 6 + 2 * n.

9. The initial orbit determination method according to claim 8, wherein The activation function f X is a Gaussian kernel function, defined as: In the formula, let the l-th sample be The center of the i-th hidden layer node is c i , σ i is the width of the hidden layer kernel function; the hidden layer contains p neurons.

10. The initial orbit determination method according to claim 7, wherein In step 4, in the total loss function, the loss function F Y is the mean square error between the predicted value and the true value of the target relative motion state network: In the formula, is the relative motion state of the tracker estimated by the neural network and the target, and y i is the true value of the relative motion state of the tracker and the target.

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