Satellite initial orbit determination method of embedded physical knowledge neural network

Abstract

The invention relates to a method for determining an initial orbit of a satellite with an embedded physical knowledge neural network, which is used for determining an initial orbit of a short arc segment under an optical observation condition and providing support for subsequent precise orbit determination. The network comprises an encoder-decoder structure, an encoder predicts the motion state of a satellite in an orbit according to observation information, the decoder converts the predicted satellite motion state into an observation value, the prediction accuracy of the encoder is evaluated, physical information of satellite orbit dynamics is introduced into a loss function, and the prediction accuracy of the satellite orbit is improved. And satellite orbit determination based on the neural network is realized. The input of the encoder is the observation angle quantity (namely azimuth angle and pitch angle) of the satellite relative to an observer, the observation time and the position information (namely longitude, latitude and altitude) of the observer; the output of the encoder, namely the input of the decoder, is the absolute motion state quantity (namely the position and the speed of the satellite in a geocentric inertial coordinate system) of the satellite in the orbit and the position information of an observer, and the output of the decoder is the observed quantity of the satellite relative to the observer. When the network is trained, firstly, a decoder is trained by taking a mean square error between a predicted observation value and a real observation value as a loss function, and a transformation relation from a satellite motion state to the observation value is learned; fixing the structure and parameters of a decoder, training the whole encoder-decoder network, calculating the derivative of the predicted satellite absolute state quantity relative to the observation time, and calculating the physical information loss of a speed item and an acceleration item; adding the physical information item loss and the mean square error of the observed quantity, constructing a total loss function, and optimizing network parameters through error back propagation; in the reasoning stage, an encoder network is used for reasoning, and the absolute motion state quantity, predicted by an encoder, of the satellite is converted into an orbit element form, namely, the initial orbit is determined.

Description

Technical Field

[0001] The present invention relates to the field of satellite initial orbit determination, and in particular to a satellite initial orbit determination method with a physical knowledge neural network embedded therein. Background Art

[0002] With the continuous advancement of aerospace technology, especially the significant improvement in carrying capacity, the number of satellites entering space has shown explosive growth. This has provided more opportunities for human exploration and utilization of space, but it has also brought about an increasingly complex operating environment. In this context, it is particularly important to accurately determine the orbital parameters of satellites. This is not only a key means to ensure the normal operation of satellites, it can monitor the health status of satellites in real time, and it also plays an important role in preventing potential spacecraft collisions and avoiding the generation of space debris. By optimizing the monitoring and management of orbital parameters, it is possible to more effectively maintain the order of space operations and ensure the safety of future human space activities.

[0003] Traditional orbit determination methods are based on satellite state modeling, mainly including the Gibbs method, Lambert method, and Newton iteration method. The Gibbs method uses cubic position vectors to determine the orbit and directly calculates the orbit parameters through vector operations. It is suitable for two-body problems, but the error will increase significantly when the measurement time interval is large, and it is not suitable for large disturbances. The Lambert method solves the orbit by giving two positions and time intervals. It is often used for orbit transfer calculations and can be applied to complex orbit designs, but the equation solving process is complicated and sensitive to the initial guess value, and convergence problems may occur. The Newton iteration method approximates the precise orbit solution through repeated iterations. It is suitable for high-precision orbit determination problems, but because it requires multiple iterations, the amount of calculation is large, and it may not converge or converge too slowly when the initial conditions are not selected properly.

[0004] With the rapid application of deep learning technology in many fields, data-driven neural network methods have been used to estimate the motion state of satellites in recent years. This type of method no longer relies on the precise modeling of perturbations, but extracts the relationship between observed quantities and satellite motion states from a large amount of data. However, neural network methods are sensitive to the quality of observation data and have insufficient generalization capabilities, making them difficult to be widely used in a variety of complex environments. Therefore, further improvement and optimization of satellite orbit determination technology still has important practical significance.

[0005] The existing initial orbit determination technology has some shortcomings in practical applications, which are mainly manifested in the following aspects: (1) The traditional algorithm has a large amount of calculation and a slow convergence speed; (2) The selection of initial values ​​is sensitive and can easily affect the accuracy and convergence of the algorithm; (3) The deep learning algorithm has high requirements on data quality and is difficult to achieve generalization application in various scenarios. Summary of the invention

[0006] The technical problem solved by the present invention is: to overcome the shortcomings of the existing technology, provide a method for determining the initial orbit of a satellite, combine physical knowledge and deep learning models, improve the efficiency and accuracy of orbit parameter estimation, and achieve high-precision orbit determination of the satellite.

[0007] The technical solution of the present invention is a method for determining the initial orbit of a satellite with a physical knowledge neural network embedded therein, comprising the following steps:

[0008] Step (1) construct a decoder whose structure is a multi-layer perceptron neural network. Its input is the absolute motion state of the satellite (i.e., its position and velocity in the geocentric inertial coordinate system) and the latitude, longitude and altitude of the observer. Its output is the observation of the satellite relative to the observer. The mean square error between the predicted observation value and the true observation value is used as the loss function to train this neural network. After the training process is completed, the structure and parameters of the decoder network are fixed.

[0009] Step (2) constructs an encoder whose structure is a transformer-structured neural network. Its input is the satellite's relative observation value, observation time, and the observer's latitude, longitude, and altitude. Its output is the satellite's absolute motion state (i.e., its position and velocity in the geocentric inertial coordinate system).

[0010] Step (3) connects the encoder in step (2) and the decoder with fixed structure and parameters in sequence, that is, the output of the encoder is used as the input of the decoder, and an encoder-decoder network for track determination is constructed.

[0011] Step (4) calculates the first-order derivative of the satellite absolute state quantity relative to the observation time for the satellite absolute state quantity predicted by the network in step (3), and calculates the physical information loss of the velocity term and the acceleration term according to the velocity equation and the acceleration equation.

[0012] Step (5) adds the calculated result of the physical information item loss in step (4) to the mean square error of the observed quantity to construct the total loss function. In the training phase, the network performs error back propagation to optimize the network parameters of the encoder. In the inference phase, the absolute motion state of the satellite predicted by the encoder is converted into the form of orbital elements.

[0013] Furthermore, the specific implementation method of step (1) is as follows:

[0014] The data is organized into the format of decoder input and output. The input includes the observer's position parameters: longitude lat, latitude lon and altitude alt, and the satellite's position and velocity in the geocentric inertial coordinate system:

[0015] r = [x, y, z]

[0016] v=[v x ,vy ,v z ]

[0017] The output is the observation value of the satellite relative to the observer, which can be expressed by the observation angle quantity, namely the pitch angle ele and the azimuth angle azi under optical observation conditions.

[0018] A multi-layer perceptron neural network is constructed as a decoder. Specifically, the decoder contains multiple sub-networks with the same structure and shared parameters. The number of sub-networks is the same as the number of measured data points in the observation arc. Each sub-network decodes a single measured data point, and the scale of parameters can be reduced by parameter sharing.

[0019] The loss function of the decoder is the mean square error between the predicted observation angle value and the true observation angle value:

[0020]

[0021] Among them, ele i andele i are the network predicted pitch angle value and the real observed pitch angle value of the i-th observation data point, respectively, i and azi i are the network predicted azimuth value and the actual observed azimuth value of the i-th observation point, respectively, and n is the number of measured data points in the arc segment.

[0022] The error is back-propagated to optimize the network parameters of this decoder.

[0023] Furthermore, the specific implementation method of step (2) is as follows:

[0024] A transformer structure neural network is constructed as an encoder to capture the relationship between sequence measurement data and predict the motion state. Its input is the satellite's pitch angle ele and azi relative to the observer, the observation time t, and the observer's longitude lat, latitude lon and altitude alt. The output is the satellite's position and speed in the geocentric inertial coordinate system, and both the input and output are serialized data in the observation arc:

[0025] r = [x, y, z]

[0026] v=[v x ,v y ,v z ]

[0027] Furthermore, the specific implementation method of step (3) is as follows:

[0028] The encoder in step (2) and the decoder with fixed structure and parameters after training in step (1) are connected in sequence, that is, the output of the encoder is used as the input of the decoder. A path is added between the input and output of the encoder, and the observer's longitude lat, latitude lon and altitude alt are used as part of the encoder output. A path is added between the input and output of the decoder, and the position r and velocity v of the satellite in the geocentric inertial coordinate system are used as part of the decoder output, to construct an encoder-decoder network for orbit determination. The input of this encoder-decoder network is the satellite's pitch angle ele and azi relative to the observer, the observation time t and the observer's longitude lat, latitude lon and altitude alt, and the output is the satellite's position r and velocity v in the geocentric inertial coordinate system and the satellite's pitch angle ele and azi relative to the observer.

[0029] Furthermore, the specific implementation method of step (4) is as follows:

[0030] For the absolute state of the satellite predicted by the network in step (3), the first-order derivatives of the satellite position r and velocity v relative to the observation time t are calculated. According to the dynamic equation of the satellite under the gravitational force of the center of the earth and the perturbation force of J2, it can be known that:

[0031]

[0032]

[0033] Where r is the size of position r, μ is the gravitational constant, J2 is the J2 perturbation coefficient, R e is the radius of the Earth.

[0034] Further, the specific implementation method of step (5) is as follows:

[0035] According to the first-order derivative equation of the satellite's position r and velocity v relative to the observation time t in step (4), the satellite position r and velocity v predicted by the neural network should satisfy the above velocity equation and acceleration equation. Therefore, the physical information term loss is constructed based on this equation to constrain the network output. The velocity term loss is in the form of:

[0036]

[0037] in and is the position component of the satellite in the geocentric inertial coordinate system predicted by the network, and is the velocity component of the satellite in the geocentric inertial coordinate system predicted by the network. The loss form of the acceleration term is:

[0038]

[0039] The total loss of the network includes the mean square error loss between the predicted observations and the true observations, the velocity term loss, and the acceleration term loss:

[0040] L=λ d L d +λ v L v +λ a L a

[0041] Among them, λ d , v and λ a are the weights of the three losses respectively.

[0042] During the training process, the network structure and weights of the decoder are kept unchanged, and the network parameters of the encoder are updated.

[0043] In the inference phase, the absolute motion state of the satellite predicted by the encoder is converted into the form of orbital elements.

[0044] Calculate the distance r from the center of the earth:

[0045] Calculate speed v size:

[0046] Calculate the total energy:

[0047] Calculate the semi-major axis a:

[0048] Calculate the component array of the angular momentum H = r × v:

[0049] Calculate the magnitude H of the moment of momentum:

[0050] Calculate the semi-diameter p:

[0051] Calculate the eccentricity e:

[0052] Calculate the ascending node vector b = k i ×H component array:

[0053]

[0054] where k i Yes i The unit vector of the axis, and

[0055] (k i ) i =(0,0,1) T

[0056] Calculate the eccentricity vector The component array

[0057]

[0058] Calculate the orbital inclination i:

[0059] Calculate the right ascension of the ascending node Ω:

[0060] Calculate the argument of perigee ω:

[0061] Calculate the latitude argument u:

[0062] Calculate the true anomaly θ: θ = u - ω

[0063] Calculate the eccentric anomaly angle E:

[0064] Calculate the mean anomaly angle M: ​​M = E-esinE

[0065] The advantages of the present invention compared with the prior art are:

[0066] (1) The present invention uses the learning and reasoning capabilities of neural networks to reduce the cumbersome calculations in traditional algorithms and can estimate orbital parameters more quickly.

[0067] (2) The present invention enhances the physical consistency of the model by introducing the physical information loss term in satellite orbit dynamics. This method ensures a close correlation between the network output and the physical equations, thereby significantly improving the prediction accuracy of the satellite motion state.

[0068] (3) The present invention adopts an encoder-decoder architecture and optimizes the loss by combining physical information and observation errors, so that the model not only has strong learning ability but also has good generalization ability, and is suitable for different types of satellites and observation environments.

[0069] (4) Compared with traditional orbit determination methods, the neural network method of the present invention does not rely on high-precision initial state modeling and can flexibly handle complex orbit environments and nonlinear perturbation effects, making its application scenarios more extensive.

[0070] In summary, the method adopted by the present invention is simple in principle and can achieve the purpose of quickly and accurately determining the satellite motion state and orbital parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1 This is a flow chart of a method for determining the initial orbit of a satellite with a physical knowledge neural network embedded in the present invention.

[0072] Figure 2 The present invention is a flow chart of the training phase of a method for determining the initial orbit of a satellite with a physical knowledge neural network embedded therein.

[0073] Figure 3 This is a flow chart of the reasoning phase of a satellite initial orbit determination method with a physical knowledge neural network embedded in the present invention.

[0074] Figure 4 This is a network structure diagram of an encoder and decoder for a satellite initial orbit determination method with an embedded physical knowledge neural network according to the present invention. DETAILED DESCRIPTION

[0075] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only 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 ordinary technicians in this field without creative work are within the protection scope of the present invention.

[0076] like Figure 1-4 As shown, a satellite initial orbit determination method with a physical knowledge neural network embedded in the present invention has the following specific implementation steps:

[0077] Step 1. Arrange the data into the format of decoder input and output. The input includes the observer's position parameters: longitude lat, latitude lon and altitude alt, and the satellite's position and speed in the geocentric inertial coordinate system:

[0078] r = [x, y, z]

[0079] v=[v x ,v y ,v z ]

[0080] The output is the observation value of the satellite relative to the observer, which can be expressed by the observation angle quantity, namely the pitch angle ele and the azimuth angle azi under optical observation conditions.

[0081] A multi-layer perceptron neural network is constructed as a decoder. Specifically, the decoder contains multiple sub-networks with the same structure and shared parameters. The number of sub-networks is the same as the number of measured data points in the observation arc. Each sub-network decodes a single measured data point, and the scale of parameters can be reduced by parameter sharing.

[0082] The loss function of the decoder is the mean square error between the predicted observation angle value and the true observation angle value:

[0083]

[0084] Among them, ele i andele i are the network predicted pitch angle value and the real observed pitch angle value of the i-th observation data point, respectively, i and azi i are the network predicted azimuth value and the actual observed azimuth value of the i-th observation point, respectively, and n is the number of measured data points in the arc segment.

[0085] The error is back-propagated to optimize the network parameters of this decoder.

[0086] Step 2: Build a transformer neural network as an encoder to capture the relationship between sequence measurement data and predict the motion state. Its input is the satellite's pitch angle ele and azi relative to the observer, the observation time t, and the observer's longitude lat, latitude lon and altitude alt. The output is the satellite's position and velocity in the geocentric inertial coordinate system, and both the input and output are serialized data in the observation arc:

[0087] r = [x, y, z]

[0088] v=[v x ,v y ,v z ]

[0089] Step 3: Connect the encoder in step 2 and the decoder with fixed structure and parameters after training in step 1 in sequence, that is, the output of the encoder is used as the input of the decoder. Add a path between the input and output of the encoder, and use the observer's longitude lat, latitude lon and altitude alt as part of the encoder output. Add a path between the input and output of the decoder, and use the satellite's position r and velocity v in the geocentric inertial coordinate system as part of the decoder output to build an encoder-decoder network for orbit determination. The input of this encoder-decoder network is the satellite's pitch angle ele and azi relative to the observer, the observation time t, and the observer's longitude lat, latitude lon and altitude alt. The output is the satellite's position r and velocity v in the geocentric inertial coordinate system and the satellite's pitch angle ele and azi relative to the observer.

[0090] Step 4: For the absolute state of the satellite predicted by the network in step 3, calculate the first-order derivative of the satellite's position r and velocity v relative to the observation time t. According to the dynamic equation of the satellite under the gravity of the center of the earth and the perturbation force of J2, it can be known that:

[0091]

[0092] Where r is the size of position r, μ is the gravitational constant, J2 is the J2 perturbation coefficient, R e is the radius of the Earth.

[0093] Step 5: According to the first-order derivative equation of the satellite position r and velocity v relative to the observation time t in step 4, the satellite position r and velocity v predicted by the neural network should satisfy the above velocity equation and acceleration equation. Therefore, a physical information term loss is constructed based on this equation to constrain the network output. The velocity term loss is in the form of:

[0094]

[0095] in and is the position component of the satellite in the geocentric inertial coordinate system predicted by the network, and is the velocity component of the satellite in the geocentric inertial coordinate system predicted by the network. The loss form of the acceleration term is:

[0096]

[0097] The total loss of the network includes the mean square error loss between the predicted observations and the true observations, the velocity term loss, and the acceleration term loss:

[0098] L=λ d L d +λ v L v +λ a L a

[0099] Among them, λ d , v and λ a are the weights of the three losses respectively.

[0100] During the training process, the network structure and weights of the decoder are kept unchanged, and the network parameters of the encoder are updated.

[0101] In the inference phase, the absolute motion state of the satellite predicted by the encoder is converted into the form of orbital elements.

[0102] Calculate the distance r from the center of the earth:

[0103] Calculate speed v size:

[0104] Calculate the total energy:

[0105] Calculate the semi-major axis a:

[0106] Calculate the component array of the angular momentum H = r × v:

[0107] Calculate the magnitude H of the moment of momentum:

[0108] Calculate the semi-diameter p:

[0109] Calculate the eccentricity e:

[0110] Calculate the ascending node vector b = k i ×H component array:

[0111]

[0112] where k i Yes i The unit vector of the axis, and

[0113] (k i ) i =(0,0,1) T

[0114] Calculate the eccentricity vector The component array

[0115]

[0116] Calculate the orbital inclination i:

[0117] Calculate the right ascension of the ascending node Ω:

[0118] Calculate the argument of perigee ω:

[0119] Calculate the latitude argument u:

[0120] Calculate the true anomaly θ: θ = u - ω

[0121] Calculate the eccentric anomaly angle E:

[0122] Calculate the mean anomaly angle M: ​​M = E-esinE

[0123] Contents not described in detail in the specification of the present invention belong to the common knowledge of professionals in the field. Although the above illustrative specific embodiments of the present invention are described to facilitate the understanding of the present invention by those skilled in the art, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention defined and determined by the attached claims, these changes are obvious, and all inventions and creations using the concept of the present invention are protected.

Claims

1. A method for determining the initial orbit of a satellite with a physical knowledge neural network embedded, characterized in that: The following steps are involved: Step (1) constructs a decoder whose structure is a multi-layer perceptron neural network. Its input is the absolute motion state of the satellite (i.e., its position and velocity in the geocentric inertial coordinate system) and the latitude, longitude and altitude of the observer. Its output is the observation of the satellite relative to the observer. The mean square error between the predicted observation value and the true observation value is used as the loss function to train this neural network. After the training process is completed, the structure and parameters of the decoder network are fixed. Step (2) constructs an encoder whose structure is a transformer-structured neural network. Its input is the satellite's relative observation value, observation time, and the observer's latitude, longitude, and altitude. Its output is the satellite's absolute motion state (i.e., its position and velocity in the geocentric inertial coordinate system). Step (3) connects the encoder in step (2) and the decoder with fixed structure and parameters in sequence, that is, the output of the encoder is used as the input of the decoder, and an encoder-decoder network for track determination is constructed. Step (4) calculates the first-order derivative of the satellite absolute state quantity relative to the observation time for the satellite absolute state quantity predicted by the network in step (3), and calculates the physical information loss of the velocity term and the acceleration term according to the velocity equation and the acceleration equation. Step (5) adds the calculated result of the physical information item loss in step (4) to the mean square error of the observed quantity to construct the total loss function. In the training phase, the network performs error back propagation to optimize the network parameters of the encoder. In the inference phase, the absolute motion state of the satellite predicted by the encoder is converted into the form of orbital elements.

2. The satellite initial orbit determination method with embedded physical knowledge neural network according to claim 1 is characterized by: The specific implementation method of step (1) is as follows: The data is organized into the format of decoder input and output. The input includes the observer's position parameters: longitude lat, latitude lon and altitude alt, and the satellite's position and velocity in the geocentric inertial coordinate system: r = [x, y, z] v=[v x ,v y ,v z ] The output is the observation value of the satellite relative to the observer, which can be expressed by the observation angle quantity, namely the pitch angle ele and the azimuth angle azi under optical observation conditions. A multi-layer perceptron neural network is constructed as a decoder. Specifically, the decoder contains multiple sub-networks with the same structure and shared parameters. The number of sub-networks is the same as the number of measured data points in the observation arc. Each sub-network decodes a single measured data point, and the scale of parameters can be reduced by parameter sharing. The loss function of the decoder is the mean square error between the predicted observation angle value and the true observation angle value: Among them, ele i andele i are the network predicted pitch angle value and the real observed pitch angle value of the i-th observation data point, respectively, i and azi i are the network predicted azimuth value and the actual observed azimuth value of the i-th observation point, respectively, and n is the number of measured data points in the arc segment. The error is back-propagated to optimize the network parameters of this decoder.

3. The satellite initial orbit determination method with embedded physical knowledge neural network according to claim 1 is characterized by: The specific implementation method of step (2) is as follows: A transformer structure neural network is constructed as an encoder to capture the relationship between sequence measurement data and predict the motion state. Its input is the satellite's pitch angle ele and azi relative to the observer, the observation time t, and the observer's longitude lat, latitude lon and altitude alt. The output is the satellite's position and speed in the geocentric inertial coordinate system, and both the input and output are serialized data in the observation arc: r = [x, y, z] v=[v x ,v y ,v z ] 4. The satellite initial orbit determination method with embedded physical knowledge neural network according to claim 1 is characterized by: The specific implementation method of step (3) is as follows: The encoder in step (2) and the decoder with fixed structure and parameters after training in step (1) are connected in sequence, that is, the output of the encoder is used as the input of the decoder. A path is added between the input and output of the encoder, and the observer's longitude lat, latitude lon and altitude alt are used as part of the encoder output. A path is added between the input and output of the decoder, and the position r and velocity v of the satellite in the geocentric inertial coordinate system are used as part of the decoder output, to construct an encoder-decoder network for orbit determination. The input of this encoder-decoder network is the satellite's pitch angle ele and azi relative to the observer, the observation time t and the observer's longitude lat, latitude lon and altitude alt, and the output is the satellite's position r and velocity v in the geocentric inertial coordinate system and the satellite's pitch angle ele and azi relative to the observer.

5. The satellite initial orbit determination method with embedded physical knowledge neural network according to claim 1 is characterized by: The specific implementation method of step (4) is as follows: For the absolute state of the satellite predicted by the network in step (3), the first-order derivatives of the satellite position r and velocity v relative to the observation time t are calculated. According to the dynamic equation of the satellite under the gravitational force of the center of the earth and the perturbation force of J2, it can be known that: Where r is the size of position r, μ is the gravitational constant, J2 is the J2 perturbation coefficient, R e is the radius of the Earth.

6. The satellite initial orbit determination method with embedded physical knowledge neural network according to claim 1 is characterized by: The specific implementation method of step (5) is as follows: According to the first-order derivative equation of the satellite's position r and velocity v relative to the observation time t in step (4), the satellite position r and velocity v predicted by the neural network should satisfy the above velocity equation and acceleration equation. Therefore, the physical information term loss is constructed based on this equation to constrain the network output. The velocity term loss is in the form of: in and is the position component of the satellite in the geocentric inertial coordinate system predicted by the network, and is the velocity component of the satellite in the geocentric inertial coordinate system predicted by the network. The loss form of the acceleration term is: The total loss of the network includes the mean square error loss between the predicted observations and the true observations, the velocity term loss, and the acceleration term loss: L=λ d L d +λ v L v +λ a L a Among them, λ d , v and λ a are the weights of the three losses respectively. During the training process, the network structure and weights of the decoder are kept unchanged, and the network parameters of the encoder are updated. In the inference phase, the absolute motion state of the satellite predicted by the encoder is converted into the form of orbital elements. Calculate the distance r from the center of the earth: Calculate speed v size: Calculate the total energy: Calculate the semi-major axis a: Calculate the component array of angular momentum H = r × v: Calculate the magnitude H of the moment of momentum: Calculate the semi-diameter p: Calculate the eccentricity e: Calculate the ascending node vector b = k i ×H component array: where k i Yes i The unit vector of the axis, and (k i ) i =(0,0,1) T Calculate the eccentricity vector The component array Calculate the orbital inclination i: Calculate the right ascension of the ascending node Ω: Calculate the argument of perigee ω: Calculate the latitude argument u: Calculate the true anomaly θ: θ = u - ω Calculate the eccentric anomaly angle E: Calculate the mean anomaly angle M: ​​M = E-esinE.

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