High-precision low-orbit satellite forecasting method and system

Abstract

The invention belongs to the technical field of spaceflight measurement and control and artificial intelligence, and particularly relates to a high-precision low-orbit satellite forecasting method and system, and the method comprises the steps: obtaining the observation data of a low-orbit satellite, and the parameter data of the earth center gravitational force and non-spherical gravitational force perturbation; the method comprises the following steps: decomposing observation data of a low-orbit satellite into long-term trend data, medium-term fluctuation data and short-term change data; constructing a long-term dynamic model, and fitting the long-term trend data and the long-term dynamic model to obtain a long-term fitting result; constructing a medium-term dynamic model, and fitting the medium-term fluctuation data and the long-term dynamic model to obtain a medium-term fitting result; constructing a short-term dynamic model, and fitting the short-term change data with the short-term dynamic model to obtain a short-term fitting result; fusing the fitting results to obtain a satellite orbit state fitting result; and updating parameters of all the dynamic models, and calculating orbit forecast information of the low-orbit satellite. And the orbit forecasting precision of the low-orbit satellite is effectively improved.

Description

Technical Field

[0001] The present invention belongs to the field of aerospace measurement and control and artificial intelligence technology, and in particular relates to a high-precision low-orbit satellite prediction method and system. Background Art

[0002] In recent years, the construction of LEO navigation augmentation systems using large-scale low-orbit satellite constellations has become a research hotspot. LEO satellites generally operate in low-Earth orbits of about 300~1500km, with fast flight speeds and fast changes in graphic structures relative to ground monitoring stations. LEO satellites can theoretically provide navigation signals with stronger signal power, shorten the ambiguity convergence time in precise single-point positioning, and provide users with real-time, high-precision positioning, navigation, and timing services.

[0003] At present, many institutions at home and abroad are conducting research or substantial construction on the LEO navigation augmentation system. The commonly used LEO orbit prediction methods are mainly polynomial fitting method, orbit element analysis method, etc. The polynomial fitting method performs polynomial fitting on discrete orbit points and extrapolates the orbit, while the analysis method obtains the orbit element at a certain moment and then directly extrapolates the orbit.

[0004] The polynomial fitting method is simple to implement, but due to the rapid changes in the LEO satellite orbit, the prediction accuracy is very limited. The analytical method also has the problem of low prediction accuracy. As a result, there is a general problem of low accuracy in LEO orbit prediction. Summary of the invention

[0005] In view of the above-mentioned deficiencies in the prior art, the present invention provides a high-precision low-orbit satellite prediction method and system to solve the above-mentioned technical problems.

[0006] In a first aspect, an embodiment of the present application provides a high-precision low-orbit satellite prediction method, comprising the following steps: S1, based on satellite monitoring equipment, obtains observation data of low-orbit satellites, obtains parameter data and dynamic change factor data of the Earth's center gravity and non-spherical gravitational perturbations; S2, based on empirical mode decomposition, decomposes the observation data of low-orbit satellites into long-term trend data, medium-term fluctuation data and short-term change data; S3, based on the observation data combined with the Earth's central gravity and non-spherical gravitational perturbations, a long-term dynamic model is constructed, and the long-term trend data is fitted with the long-term dynamic model to obtain the long-term fitting results; Based on the observation data, a medium-term dynamic model is constructed by combining the gravity of the Earth's center, non-spherical gravitational perturbations and dynamic change factors, and the medium-term fluctuation data is fitted with the long-term dynamic model to obtain the medium-term fitting results; A short-term dynamics model is constructed based on the observed data combined with the local weighted regression method, and the short-term variation data is fitted with the short-term dynamics model to obtain the short-term fitting results. S4, using a weighted summation method to fuse the long-term fitting result, the mid-term fitting result and the short-term fitting result to obtain the satellite orbit state fitting result; S5, based on the satellite orbit state fitting result at the current moment, update the parameters of all the dynamic models constructed in step S3, and calculate the orbit prediction information of the low-orbit satellite based on the updated dynamic models combined with the numerical calculation method.

[0007] Optionally, in step S3, the step of constructing a long-term dynamic model based on the observation data combined with the Earth's central gravity and non-spherical gravitational perturbations includes: Determine the position coordinates of the satellite based on the observation data; For the gravity at the center of the earth, according to Newton's law of universal gravitation, the acceleration it produces is:

[0008] in, =GM ​​is the Earth's gravitational constant, is the distance from the satellite to the Earth's center of mass, is the position vector of the satellite relative to the center of the Earth; For non-spherical gravitational perturbations, the perturbation acceleration is expressed in the form of spherical harmonic expansion, and the specific calculation is:

[0009]

[0010] in, is the Earth's gravitational potential, R is the Earth's average radius, and are the spherical harmonic coefficients, is an associated Legendre polynomial of order (n,m), where n is the order and m is the series. is the satellite co-latitude angle, is the satellite longitude angle; The long-term dynamic model is obtained: .

[0011] Optionally, in step S3, fitting the long-term trend data with the long-term kinetic model to obtain a long-term fitting result specifically includes: The fourth-order Runge-Kutta method is used to integrate and solve the long-term dynamic model. The set initial position and initial velocity data are used as the initial conditions of the integration. The calculation is gradually carried out according to the set time step to obtain the theoretical values ​​of the satellite orbit that conform to the long-term trend at different times. Calculate the error between the theoretical value and the long-term trend data based on the least squares method; The parameters of the long-term kinetic model are adjusted to minimize the error.

[0012] Optionally, the steps of constructing a medium-term dynamic model based on observational data combined with the Earth's central gravity, non-spherical gravitational perturbations and dynamic change factors include: Obtain the changes in atmospheric density at different altitudes and seasons; Calculate the acceleration of atmospheric drag based on the change in atmospheric density:

[0013] in, is the drag coefficient of the satellite, A is the cross-sectional area of ​​the satellite, is the satellite mass, is the atmospheric density, v is the satellite velocity vector; The acceleration based on atmospheric drag combined with the long-term dynamics model gives the medium-term dynamics model: + .

[0014] Optionally, the step of constructing a short-term kinetic model based on observed data combined with a local weighted regression method includes: Use the local weighted regression method to fit short-term fluctuations:

[0015] in, is the local regression function, is the fitting parameter vector, It is to find the value of parameter vector a so that the objective function reaches the minimum value. For all data points To sum, yes The weight value at the moment, The short-term volatility data is measured in The position vector at time, is the basis function at time The value of The second-order derivative of the fitted local regression function is calculated to obtain the short-term dynamic model:

[0016] in, is the k-th fitting parameter vector, is the kth basis function.

[0017] Optionally, in step S3, fitting the short-term variation data with the short-term kinetic model to obtain a short-term fitting result specifically includes: Obtain short-term satellite orbit theoretical values ​​based on short-term dynamics model; Calculate the mean square error between the short-term variation data and the short-term satellite orbit theoretical value; Adjust the parameters of the short-term satellite orbit theoretical value to minimize the mean square error.

[0018] Optionally, step S2 specifically includes: S2-1, obtaining all local maximum points and local minimum points in the observation data sequence based on the observation data; S2-2, the upper envelope and the lower envelope are fitted by cubic spline interpolation method, and the average of the two envelopes is taken as the average envelope; S2-3, subtract the mean envelope from the observed data to obtain a new data series; S2-4, returning to step S2-1 to repeatedly obtain a new data sequence, and obtaining a plurality of decomposed intrinsic mode functions and a residual term; S2-5, based on the frequencies of multiple intrinsic mode functions, the observed data are divided into long-term trend data, medium-term fluctuation data and short-term change data.

[0019] Optionally, in S4, the error value of the satellite orbit state fitting result is obtained based on the law of conservation of energy. When the error value is determined to be beyond a reasonable error range, the fitting result is incorrect, and each dynamic model is checked.

[0020] Optionally, S5 specifically includes: Re-evaluate the Earth's center gravity and non-spherical gravity perturbation factors based on the current satellite orbit state fitting results, and update the relevant parameters in the long-term dynamic model; Based on the current atmospheric density and the actual state of the satellite orbit, the atmospheric drag related parameters in the medium-term dynamic model are updated; Based on the current satellite orbit state fitting results, the current orbit change characteristics and data distribution are obtained, and the relevant parameters in the short-term dynamics model are updated; Taking the current satellite orbital state as the initial condition, the theoretical orbital position and velocity after a preset time step are calculated based on the long-term dynamic model. The theoretical orbital position and velocity after the preset time step are further adjusted based on the medium-term dynamic model to obtain the adjustment result. The adjustment result is finally adjusted based on the short-term dynamic model to obtain the orbital prediction information of the low-orbit satellite after the preset time step.

[0021] In a second aspect, an embodiment of the present application further provides a high-precision low-orbit satellite prediction system. When implemented, the system executes the above-mentioned high-precision low-orbit satellite prediction method, including: The data acquisition module acquires the observation data of low-orbit satellites based on satellite monitoring equipment, and acquires the parameter data and dynamic change factor data of the earth's center gravity and non-spherical gravitational perturbation; The scale decomposition module decomposes the observation data of low-orbit satellites into long-term trend data, medium-term fluctuation data and short-term change data based on empirical mode decomposition; The dynamic model building and fitting module builds a long-term dynamic model based on the observation data combined with the gravity of the Earth's center and non-spherical gravitational perturbations, and fits the long-term trend data with the long-term dynamic model to obtain the long-term fitting results; Based on the observation data, a medium-term dynamic model is constructed by combining the gravity of the Earth's center, non-spherical gravitational perturbations and dynamic change factors, and the medium-term fluctuation data is fitted with the long-term dynamic model to obtain the medium-term fitting results; A short-term dynamics model is constructed based on the observed data combined with the local weighted regression method, and the short-term variation data is fitted with the short-term dynamics model to obtain the short-term fitting results. The multi-scale fusion module uses a weighted summation method to fuse the long-term fitting results, the mid-term fitting results, and the short-term fitting results to obtain the satellite orbit state fitting results; The orbit prediction module updates the parameters of all the dynamic models constructed in step S3 based on the fitting results of the satellite orbit state at the current moment, and calculates the orbit prediction information of the low-orbit satellite based on the updated dynamic models combined with the numerical calculation method.

[0022] It can be seen from the above technical solutions that the present invention has the following advantages: In a high-precision low-orbit satellite prediction method and system provided by the present application, comprehensive data, including observation data as well as gravitational perturbation and dynamic change factor data, are obtained through satellite monitoring equipment, laying the foundation for accurate prediction. Empirical mode decomposition can effectively analyze the characteristics of observation data, construct and fit long-term, medium-term, and short-term dynamic models respectively, and fully consider the influencing factors at different time scales, so as to improve the adaptability and accuracy of the model to the changes in satellite orbital state. The weighted summation integrates multiple fitting results, combines the advantages of each model, and further improves the fitting accuracy of the orbital state. Based on the fitting results at the current moment, the dynamic model parameters are updated, and the orbital prediction information is calculated in combination with numerical calculation methods, so that the prediction results are more in line with the actual situation, which can effectively improve the accuracy of low-orbit satellite orbit prediction and enhance the ability to control the operating status of low-orbit satellites. It plays an important role in aerospace mission planning, satellite communications, space science research and other fields, and helps to improve the safety, reliability and efficiency of space activities. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] In order to more clearly illustrate the technical solution of the present invention, the accompanying drawings required for use in the description will be briefly introduced below. Obviously, the accompanying drawings in the following description are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative work.

[0024] Figure 1 The present invention is a schematic flowchart of a high-precision low-orbit satellite prediction method according to an embodiment of the present invention.

[0025] Figure 2 The present invention is a schematic block diagram of a high-precision low-orbit satellite prediction system according to an embodiment of the present invention. DETAILED DESCRIPTION

[0026] In the specific steps of a high-precision low-orbit satellite prediction method and system described in detail below, various embodiments of the present disclosure will be described more comprehensively. The present disclosure may have various embodiments, and adjustments and changes may be made therein. However, it should be understood that there is no intention to limit the various embodiments of the present disclosure to the specific embodiments disclosed herein, but rather the present disclosure should be understood to cover all adjustments, equivalents and / or alternatives that fall within the spirit and scope of the various embodiments of the present disclosure.

[0027] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0028] See also Figure 1 FIG. 1 is a flow chart of a high-precision low-orbit satellite prediction method in a specific embodiment, the method comprising: S1, based on satellite monitoring equipment, obtains observation data of low-orbit satellites, obtains parameter data and dynamic change factor data of the Earth's center gravity and non-spherical gravitational perturbations; Observation data directly reflects the actual operating status of the satellite and is the core basis for subsequent analysis and modeling. Gravitational perturbation parameter data helps to accurately consider the impact of the Earth's gravity on the satellite orbit, because when low-orbit satellites are operating, factors such as the Earth's non-spherical gravitational perturbation cannot be ignored. Accurate parameters can make orbit calculations more in line with actual conditions. The acquisition of dynamic change factor data (such as changes in atmospheric drag, changes in the gravity of the sun and the moon, etc.) can further take into account various external dynamic influences, making the constructed dynamic model more comprehensive and accurate, improving the prediction method's ability to describe satellite orbit changes in complex space environments, and laying a solid foundation for subsequent high-precision predictions.

[0029] S2, based on empirical mode decomposition, decomposes the observation data of low-orbit satellites into long-term trend data, medium-term fluctuation data and short-term change data; Being able to clearly analyze the changing characteristics of observation data on different time scales will help us to deeply understand the inherent laws of changes in satellite orbital states.

[0030] S3, based on the observation data combined with the Earth's central gravity and non-spherical gravitational perturbations, a long-term dynamic model is constructed, and the long-term trend data is fitted with the long-term dynamic model to obtain the long-term fitting results; Based on the observation data, a medium-term dynamic model is constructed by combining the gravity of the Earth's center, non-spherical gravitational perturbations and dynamic change factors, and the medium-term fluctuation data is fitted with the long-term dynamic model to obtain the medium-term fitting results; A short-term dynamics model is constructed based on the observed data combined with the local weighted regression method, and the short-term variation data is fitted with the short-term dynamics model to obtain the short-term fitting results. For long-term trend data, we can better grasp the overall direction and long-term change trend of satellite orbits, such as the slow decay or upward trend of orbits, and provide targeted data support for the construction of long-term dynamic models. Medium-term fluctuation data can reflect the periodic or non-periodic fluctuations of satellite orbits within a certain period of time, which may be related to factors such as periodic changes in the gravity of the sun and the moon, and help to build a more realistic medium-term dynamic model. Short-term change data can capture the rapid changes of satellite orbits in a relatively short period of time, such as small orbital disturbances caused by sudden changes in atmospheric drag, etc., providing accurate input for the construction of short-term dynamic models, thereby improving the targeted description capabilities of various dynamic models for satellite orbit changes, and ultimately improving the accuracy of the entire forecasting method.

[0031] S4, using a weighted summation method to fuse the long-term fitting result, the mid-term fitting result and the short-term fitting result to obtain the satellite orbit state fitting result; The long-term fitting results provide the overall trend information of the satellite orbit, the medium-term fitting results reflect the medium-term fluctuation characteristics, and the short-term fitting results capture the short-term rapid changes. Through reasonable weighting, the influence of different time scales can be balanced in the final orbit state fitting results, so that the fitting results can more comprehensively and accurately reflect the actual state of the satellite orbit. This fusion method avoids the limitations of a single model in describing satellite orbit changes, improves the overall grasp of the complex changes in satellite orbits, and thus provides a more accurate initial state for subsequent orbit predictions, further improving the accuracy and reliability of the entire prediction method, and enhancing the ability to predict orbit changes of low-orbit satellites.

[0032] S5, based on the satellite orbit state fitting result at the current moment, update the parameters of all the dynamic models constructed in step S3, and calculate the orbit prediction information of the low-orbit satellite based on the updated dynamic models combined with the numerical calculation method.

[0033] By continuously updating the model parameters with the latest orbit state fitting results, the dynamic model can timely adapt to the actual changes in the satellite orbit, such as orbit changes caused by changes in atmospheric drag, slight changes in the gravitational field, etc. It can accurately calculate the satellite's orbital position and speed in the future, improving the timeliness and accuracy of orbit prediction.

[0034] In an exemplary embodiment, step S2 specifically includes: S2-1, obtaining all local maximum points and local minimum points in the observation data sequence based on the observation data; S2-2, the upper envelope and the lower envelope are fitted by cubic spline interpolation method, and the average of the two envelopes is taken as the average envelope; S2-3, subtract the mean envelope from the observed data to obtain a new data series; S2-4, returning to step S2-1 to repeatedly obtain a new data sequence, and obtaining a plurality of decomposed intrinsic mode functions and a residual term; S2-5, based on the frequencies of multiple intrinsic mode functions, the observed data are divided into long-term trend data, medium-term fluctuation data and short-term change data.

[0035] Generally speaking, the decomposed intrinsic mode functions (IMFs) are arranged in order from high to low frequency, where high-frequency IMFs correspond to the scale of short-term changes, reflecting the characteristics of rapid changes in satellite orbits in a short time interval, such as small-amplitude high-frequency fluctuations in the orbit caused by factors such as short-term atmospheric micro-disturbance and slight adjustments in the satellite's own attitude. The low-frequency IMFs and the final residual terms are related to long-term trends. The residual terms often reflect the most macroscopic and stable changes in the satellite orbit over a long period of time, such as the slow migration of the overall orbit dominated by the gravity of the center of the earth. The IMF at an intermediate frequency can roughly correspond to the scale of medium-term fluctuations, which reflects the regular changes in satellite orbits over a medium time span, such as seasonal changes in atmospheric density and periodic effects of solar activity.

[0036] In an exemplary embodiment, in step S3, the step of constructing a long-term dynamic model based on observation data combined with the Earth's central gravity and non-spherical gravitational perturbations includes: Determine the initial position (x, y, z) and initial velocity of the satellite based on the observation data at the initial time; The position vector and velocity vector of the satellite in the spatial rectangular coordinate system are selected as state variables; Based on Newton's second law combined with the Earth's central gravity and non-spherical gravitational perturbation parameter data, a set of second-order ordinary differential equations is established as a long-term dynamic model.

[0037] For the gravity at the center of the earth, according to Newton's law of universal gravitation, the acceleration it produces is:

[0038] in, =GM ​​is the Earth's gravitational constant, is the distance from the satellite to the Earth's center of mass, is the position of the satellite relative to the center of the Earth.

[0039] For non-spherical gravitational perturbations, refer to the Earth's gravity field model (such as the EGM2008 model) and express the perturbation acceleration in the form of spherical harmonic expansion ;

[0040] The non-spherical gravitational perturbation acceleration is calculated from the gradient of the Earth's gravitational potential: ; in, is the Earth's gravitational potential, R is the Earth's average radius, and are the spherical harmonic coefficients, is the associated Legendre polynomial of order (n,m) and is the main descriptor of the latitudinal variation. n is the order and represents the overall complexity of the spherical harmonics, mainly describing the radial variation of the Earth's mass distribution (variation with altitude and latitude). m is the order and represents the meridional variation characteristics under a given order nnn. The value range of the series is 0≤m≤n. is the satellite co-latitude angle, is the satellite longitude angle; Decomposing it into three components (radial, latitudinal, and longitudinal), we get: The radial acceleration is calculated as follows:

[0041]

[0042]

[0043] Combining the components in the three directions, we get the vector form of the non-spherical gravitational perturbation acceleration:

[0044] in, is the radial unit vector, is the zonal unit vector (perpendicular to the radial direction, along the sphere), is the meridional unit vector (along the longitude direction); The long-term dynamic model is obtained: ; In summary, the complete second-order ordinary differential equation system is constructed after considering these factors; The model parameters are obtained through long-term observation data (such as satellite orbit measurements), and the long-term trend data are separated using empirical mode decomposition (EMD). The long-term trend data are fitted and the spherical harmonic coefficients in the model are optimized to ensure the fitting accuracy.

[0045] In step S3, fitting the long-term trend data with the long-term kinetic model to obtain a long-term fitting result specifically includes: The fourth-order Runge-Kutta method is used to integrate and solve the long-term dynamic model. The set initial position and initial velocity data are used as the initial conditions of the integration. The calculation is gradually carried out according to the set time step to obtain the theoretical value of the satellite orbit that conforms to the long-term trend at different times; the step size set in this embodiment is 10s, and multiple intermediate calculations are performed in each time step.

[0046] Calculate the error between the theoretical value and the long-term trend data based on the least squares method; Adjust the parameters of the long-term dynamics model, such as the perturbation term correlation coefficient, to minimize the error.

[0047] In an exemplary embodiment, the steps of constructing a medium-term dynamic model based on observation data combined with the Earth's central gravity, non-spherical gravitational perturbations and dynamic change factors include: Obtain the changes in atmospheric density at different altitudes and seasons; the impact of seasonal changes in atmospheric density on orbits. First, it is necessary to obtain atmospheric density at different altitudes and seasons based on an atmospheric density model (such as the U.S. Standard Atmospheric Model, etc.); Calculate the acceleration of atmospheric drag based on the change in atmospheric density;

[0048] in, is the drag coefficient of the satellite (dimensionless, related to factors such as the satellite shape, usually obtained through experiments or experience), A is the cross-sectional area of ​​the satellite, is the satellite mass, is the atmospheric density, v is the satellite velocity vector; The acceleration based on atmospheric drag combined with the long-term dynamics model gives the medium-term dynamics model: + ; The fit of the medium-term volatility data is consistent with the fit of the long-term trend mentioned above.

[0049] In addition to changes in atmospheric density, if other dynamic factors that affect medium-term fluctuations are considered, such as the impact of periodic changes in solar activity on the ionization of the Earth's upper atmosphere, which in turn indirectly affects satellite orbits (by changing the atmospheric composition, the distribution of charged particles, etc., affecting the forces acting on the satellite), corresponding physical terms can be further added to the dynamic model. The specific form must be derived and modeled based on the relevant physical mechanisms, and the detailed complex physical process will not be repeated here.

[0050] In an exemplary embodiment, the step of constructing a short-term kinetic model based on observed data combined with a local weighted regression method includes: The empirical mode decomposition (EMD) is used to extract the high-frequency components, and the local data and weights are used to fit each moment. The second-order derivative of the fitting function is numerically calculated to obtain the acceleration.

[0051] Constructing a short-term dynamics model:

[0052] is the acceleration vector caused by short-term fluctuations, is the satellite's position vector, is the satellite’s velocity vector; are model parameters to be determined through regression fitting, is a regression function describing short-term dynamic effects; First, calculate the weight and define a kernel function , calculated as follows:

[0053] Smoothing parameter (bandwidth), which controls the width of the kernel function. The smaller the value, the stronger the emphasis on local fitting;

[0054]

[0055] in, is the parameter vector obtained by fitting, is the basis function, used to capture the characteristics of short-term disturbances; is the local regression function, The required fitting parameter vector is It is to find the value of the parameter vector a so that the objective function (the weighted sum of squares of errors) reaches the minimum value. For all data points To sum, The short-term volatility data is measured in The position vector at time, is the basis function at time The value of .

[0056] For the short-term changing data, in addition to directly using basic data such as satellite orbital position and velocity as input features, you can also consider adding some derivative features, such as the first-order difference of position (i.e. velocity), second-order difference (approximate acceleration), etc., to better capture the changing trends and characteristics of the data. The sorted data is divided into training set, validation set, and test set (usually in a certain ratio, such as 7:2:1) for subsequent model training, parameter selection, and performance evaluation.

[0057] In step S3, fitting the short-term variation data with the short-term dynamics model to obtain a short-term fitting result specifically includes: Obtain short-term satellite orbit theoretical values ​​based on short-term dynamics model; Calculate the mean square error between the short-term variation data and the short-term satellite orbit theoretical value; Adjust the parameters of the short-term satellite orbit theoretical value to minimize the mean square error.

[0058] In an exemplary embodiment, in S4, weights are allocated according to the importance of each part to the overall track description and error characteristics. For example, after preliminary analysis and verification, it is found that the long-term trend part is more critical in describing the overall track's macro trend, but the short-term change part is indispensable for capturing the minute changes in the track at the moment, and the medium-term fluctuation part plays a role in connection and supplementation. Then, weights can be allocated according to a certain ratio (such as the weight of the long-term trend part is set to 0.5, the weight of the medium-term fluctuation part is set to 0.3, and the weight of the short-term change part is set to 0.2. These are just example weights, and they need to be determined according to specific circumstances).

[0059] The error value of the satellite orbit state fitting result is obtained based on the law of conservation of energy. When the error value is judged to be beyond the reasonable error range, the fitting result is incorrect, and each dynamic model is checked. That is, if it is a fitting problem at a certain scale, it may be necessary to return to the model of the corresponding scale to readjust the parameters and optimize the fitting process; if the weight distribution is unreasonable, the importance of each scale is re-evaluated and the weight is adjusted, and then the combination operation is performed again. After multiple iterative verifications and adjustments, a more accurate and reasonable combination result is obtained, which can truly reflect the actual orbit state of the satellite at that moment.

[0060] In an exemplary embodiment, step S5 specifically includes: According to the fitting results of the satellite orbit state at the current moment, the factors of the gravity of the center of the earth and the non-spherical gravity perturbation are re-evaluated, and the relevant parameters in the long-term dynamic model are updated; for the long-term dynamic model, the gravity of the center of the earth and the non-spherical gravity perturbation are the key factors that dominate the long-term change trend of the satellite orbit, so it is of great significance to re-evaluate and update the relevant parameters according to the fitting results of the satellite orbit state at the current moment. In terms of the gravity of the center of the earth, its calculation is based on the law of universal gravitation. Although the mass of the earth and the gravitational constant are relatively fixed, the distance between the satellite and the center of mass of the earth is a variable that changes all the time and has a significant impact on gravity. With the help of the current accurate orbit state fitting results, this distance value can be accurately obtained and substituted into the gravity calculation formula, so that the effect of the gravity of the center of the earth on the satellite orbit can be more accurately quantified, laying an accurate foundation for the long-term model. As for the non-spherical gravitational perturbation, since the earth is not an ideal sphere, its uneven mass distribution leads to complex perturbations in the gravitational field. With the progress of scientific research, the Earth's gravity field model is constantly updated and optimized. The new model can provide more precise and accurate parameters such as spherical harmonic coefficients of various orders. The current precise position coordinates of the satellite (determined by the orbital state fitting results) are substituted into the calculation formula based on the new model to recalculate the perturbation components and update the corresponding parameters in the model, thereby ensuring that the model can truthfully reflect the real impact of the current non-spherical gravitational perturbations on the long-term direction of the satellite orbit. This is like equipping the long-term dynamic model with "precision navigation" to enable it to keep up with actual orbital changes and ensure the reliability of long-term forecasts.

[0061] Combined with the current atmospheric density and the actual state of the satellite orbit, the atmospheric drag-related parameters in the medium-term dynamic model are updated; the medium-term dynamic model focuses on orbital fluctuations caused by factors such as seasonal changes in atmospheric density, and atmospheric drag is a core element. First of all, obtaining accurate atmospheric density data is the key, which is in dynamic change under the influence of many factors. On the one hand, with the help of professional atmospheric density models, theoretical reference values ​​are obtained according to the current altitude and geographical location of the satellite. At the same time, it is better if real-time meteorological observation data (such as information provided by meteorological satellites and ground meteorological stations) can be combined. After all, actual observations are more in line with the current real atmospheric conditions, especially in special meteorological environments. In addition, the actual state of the satellite orbit has an impact on atmospheric drag that cannot be underestimated. The speed of the satellite directly determines the size of the drag. Different attitudes change the effective projection area of ​​the cross-sectional area in all directions, which in turn affects the direction and size of the drag. Changes in orbital altitude also cause it to enter different atmospheric density layers. After comprehensively analyzing the actual atmospheric drag faced by the satellite based on these factors, the atmospheric drag-related parameters in the medium-term dynamics model are updated. For example, the drag coefficient is appropriately adjusted according to the actual situation on the satellite surface, and the cross-sectional area is accurately calculated based on the attitude. This is like a "fine-tuning" of the model, allowing it to more accurately capture the medium-term orbital fluctuation characteristics and make the model output more consistent with the actual orbital changes.

[0062] Based on the current satellite orbit state fitting results, the current orbit change characteristics and data distribution are obtained, and the relevant parameters in the short-term dynamics model are updated; the short-term dynamics model focuses on the rapid changes of the satellite orbit in a short period of time, and the current satellite orbit state fitting results are an important basis for insight into these change characteristics and data distribution. By analyzing the fitting results, it can be clearly seen that in the current short time interval, the satellite orbit has produced rapid fluctuations due to its own short-term attitude adjustment, small interference in the surrounding area and other factors. For example, there are high-frequency small displacement changes in a certain direction, or the speed has a small increase or decrease in an instant, etc. These are all manifestations of orbit change characteristics. At the same time, data distribution, such as the degree of discreteness and change trend of position, speed and other data in a short period of time, can also be mastered. Based on the information obtained, the relevant parameters in the short-term dynamic model are updated. For example, when using the local weighted regression method, the parameters of the weight calculation function are adjusted according to the data distribution to make it more suitable for the current data characteristics and accurately capture rapid changes; or when using support vector machine regression, the kernel function parameters are optimized, etc., so that the model can better adapt to the dynamic changes of the orbit in a short period of time, as if to "inject new vitality" into the short-term model, so that it can more keenly track the subtle changes in the satellite orbit on a short time scale, and ensure that the model's fitting effect on short-term changes always remains at a high precision level.

[0063] Taking the current satellite orbital state as the initial condition, the theoretical orbital position and velocity after a preset time step are calculated based on the long-term dynamic model. The theoretical orbital position and velocity after the preset time step are further adjusted based on the medium-term dynamic model to obtain the adjustment result. The adjustment result is finally adjusted based on the short-term dynamic model to obtain the orbital prediction information of the low-orbit satellite after the preset time step.

[0064] During the forecasting process, the calculation results must be monitored in real time and the errors must be evaluated. If it is found that the error gradually increases over time and exceeds the preset accuracy requirements, it may be necessary to return to check the accuracy of each scale model, the rationality of the parameters, and the combination method, and make timely optimization and adjustments to ensure the high accuracy and reliability of the forecast results and realize high-precision forecasting functions for low-orbit satellites.

[0065] [Microsoft User 1] should understand that the order of execution of the steps in the above embodiments does not necessarily mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present invention.

[0066] like Figure 2As shown, the following is an embodiment of the high-precision low-orbit satellite prediction system provided by the embodiments of the present disclosure. The system and the high-precision low-orbit satellite prediction methods of the above-mentioned embodiments belong to the same inventive concept. For details not described in detail in the embodiments of the high-precision low-orbit satellite prediction system, please refer to the embodiments of the above-mentioned high-precision low-orbit satellite prediction method.

[0067] The system includes: a data acquisition module, which acquires observation data of low-orbit satellites based on satellite monitoring equipment, and acquires parameter data and dynamic change factor data of the earth's center gravity and non-spherical gravitational perturbations; The scale decomposition module decomposes the observation data of low-orbit satellites into long-term trend data, medium-term fluctuation data and short-term change data based on empirical mode decomposition; The dynamic model building and fitting module builds a long-term dynamic model based on the observation data combined with the gravity of the Earth's center and non-spherical gravitational perturbations, and fits the long-term trend data with the long-term dynamic model to obtain the long-term fitting results; Based on the observation data, a medium-term dynamic model is constructed by combining the gravity of the Earth's center, non-spherical gravitational perturbations and dynamic change factors, and the medium-term fluctuation data is fitted with the long-term dynamic model to obtain the medium-term fitting results; A short-term dynamics model is constructed based on the observed data combined with the local weighted regression method, and the short-term variation data is fitted with the short-term dynamics model to obtain the short-term fitting results. The multi-scale fusion module uses a weighted summation method to fuse the long-term fitting results, the mid-term fitting results, and the short-term fitting results to obtain the satellite orbit state fitting results; The orbit prediction module updates the parameters of all the dynamic models constructed in step S3 based on the fitting results of the satellite orbit state at the current moment, and calculates the orbit prediction information of the low-orbit satellite based on the updated dynamic models combined with the numerical calculation method.

[0068] The system operates through the collaboration of multiple modules. The data acquisition module collects key data, the scale decomposition module refines and analyzes the observed data into components of different time scales, the dynamic model construction and fitting module builds and fits models for each scale to obtain corresponding results, and the multi-scale fusion module fuses the results of each scale to obtain the orbital state fitting results. The orbital prediction module then updates the model and calculates the forecast information. Overall, it can fully consider various influencing factors and realize accurate analysis of the low-orbit satellite orbital characteristics from multiple dimensions, effectively improving the accuracy of orbital state fitting and prediction, and providing a reliable and valuable reference for low-orbit satellite operation monitoring, mission planning, etc.

[0069] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A high-precision low-orbit satellite prediction method, characterized in that: The following steps are involved: S1, based on satellite monitoring equipment, obtains observation data of low-orbit satellites, obtains parameter data and dynamic change factor data of the Earth's center gravity and non-spherical gravitational perturbations; S2, based on empirical mode decomposition, decomposes the observation data of low-orbit satellites into long-term trend data, medium-term fluctuation data and short-term change data; S3, based on the observation data combined with the Earth's central gravity and non-spherical gravitational perturbations, a long-term dynamic model is constructed, and the long-term trend data is fitted with the long-term dynamic model to obtain the long-term fitting results; Based on the observation data, a medium-term dynamic model is constructed by combining the gravity of the Earth's center, non-spherical gravitational perturbations and dynamic change factors, and the medium-term fluctuation data is fitted with the long-term dynamic model to obtain the medium-term fitting results; A short-term dynamics model is constructed based on the observed data combined with the local weighted regression method, and the short-term variation data is fitted with the short-term dynamics model to obtain the short-term fitting results. S4, using a weighted summation method to fuse the long-term fitting result, the mid-term fitting result and the short-term fitting result to obtain the satellite orbit state fitting result; S5, based on the satellite orbit state fitting result at the current moment, update the parameters of all the dynamic models constructed in step S3, and calculate the orbit prediction information of the low-orbit satellite based on the updated dynamic models combined with the numerical calculation method.

2. The high-precision low-orbit satellite prediction method according to claim 1, characterized in that: In step S3, the steps of constructing a long-term dynamic model based on observation data combined with the Earth's central gravity and non-spherical gravitational perturbations include: Determine the position coordinates of the satellite based on the observation data; For the gravity at the center of the earth, according to Newton's law of universal gravitation, the acceleration it produces is: in, =GM ​​is the Earth's gravitational constant, is the distance from the satellite to the Earth's center of mass, is the position vector of the satellite relative to the center of the Earth; For non-spherical gravitational perturbations, the perturbation acceleration is expressed in the form of spherical harmonic expansion, and the specific calculation is: in, is the Earth's gravitational potential, R is the Earth's average radius, and are the spherical harmonic coefficients, is an associated Legendre polynomial of order (n,m), where n is the order and m is the series. is the satellite co-latitude angle, is the satellite longitude angle; The long-term dynamic model is obtained: 。 3. The high-precision low-orbit satellite prediction method according to claim 2, characterized in that: In step S3, fitting the long-term trend data with the long-term kinetic model to obtain a long-term fitting result specifically includes: The fourth-order Runge-Kutta method is used to integrate and solve the long-term dynamic model. The set initial position and initial velocity data are used as the initial conditions of the integration. The calculation is gradually carried out according to the set time step to obtain the theoretical values ​​of the satellite orbit that conform to the long-term trend at different times. Calculate the error between the theoretical value and the long-term trend data based on the least squares method; The parameters of the long-term kinetic model are adjusted to minimize the error.

4. The high-precision low-orbit satellite prediction method according to claim 1 or 2, characterized in that: The steps to construct a medium-term dynamic model based on observational data combined with the Earth's central gravity, non-spherical gravitational perturbations and dynamic change factors include: Obtain the changes in atmospheric density at different altitudes and seasons; Calculate the acceleration of atmospheric drag based on the change in atmospheric density: in, is the drag coefficient of the satellite, A is the cross-sectional area of ​​the satellite, is the satellite mass, is the atmospheric density, v is the satellite velocity vector; The acceleration based on atmospheric drag combined with the long-term dynamics model gives the medium-term dynamics model: + 。 5. The high-precision low-orbit satellite prediction method according to claim 1, characterized in that: The steps of constructing a short-term dynamics model based on observed data combined with the local weighted regression method include: Use the local weighted regression method to fit short-term fluctuations: in, is the local regression function, is the fitting parameter vector, is to find the value of the parameter vector a so that the objective function reaches the minimum value, For all data points To sum, yes The weight value at the moment, The short-term volatility data is measured in The position vector at time, is the basis function at time The value of The second-order derivative of the fitted local regression function is calculated to obtain the short-term dynamic model: in, is the k-th fitting parameter vector, is the kth basis function.

6. The high-precision low-orbit satellite prediction method according to claim 5, characterized in that: In step S3, fitting the short-term variation data with the short-term dynamics model to obtain a short-term fitting result specifically includes: Obtain short-term satellite orbit theoretical values ​​based on short-term dynamics model; Calculate the mean square error between the short-term variation data and the short-term satellite orbit theoretical value; Adjust the parameters of the short-term satellite orbit theoretical value to minimize the mean square error.

7. The high-precision low-orbit satellite prediction method according to claim 1, characterized in that: Step S2 specifically includes: S2-1, obtaining all local maximum points and local minimum points in the observation data sequence based on the observation data; S2-2, the upper envelope and the lower envelope are fitted by cubic spline interpolation method, and the average of the two envelopes is taken as the average envelope; S2-3, subtract the mean envelope from the observed data to obtain a new data series; S2-4, returning to step S2-1 to repeatedly obtain a new data sequence, and obtaining a plurality of decomposed intrinsic mode functions and a residual term; S2-5, based on the frequencies of multiple intrinsic mode functions, the observed data are divided into long-term trend data, medium-term fluctuation data and short-term change data.

8. The high-precision low-orbit satellite prediction method according to claim 1, characterized in that: In S4, the error value of the satellite orbit state fitting result is obtained based on the law of conservation of energy. When the error value is determined to be beyond a reasonable error range, the fitting result is incorrect, and each dynamic model is checked.

9. The high-precision low-orbit satellite prediction method according to claim 1, characterized in that: Step S5 specifically includes: Re-evaluate the Earth's center gravity and non-spherical gravity perturbation factors based on the current satellite orbit state fitting results, and update the relevant parameters in the long-term dynamic model; Based on the current atmospheric density and the actual state of the satellite orbit, the atmospheric drag related parameters in the medium-term dynamic model are updated; Based on the current satellite orbit state fitting results, the current orbit change characteristics and data distribution are obtained, and the relevant parameters in the short-term dynamics model are updated; Taking the current satellite orbital state as the initial condition, the theoretical orbital position and velocity after a preset time step are calculated based on the long-term dynamic model. The theoretical orbital position and velocity after the preset time step are further adjusted based on the medium-term dynamic model to obtain the adjustment result. The adjustment result is finally adjusted based on the short-term dynamic model to obtain the orbital prediction information of the low-orbit satellite after the preset time step.

10. A high-precision low-orbit satellite prediction system, wherein the system executes the high-precision low-orbit satellite prediction method according to any one of claims 1 to 9 when implemented, characterized in that: include: The data acquisition module acquires the observation data of low-orbit satellites based on satellite monitoring equipment, and acquires the parameter data and dynamic change factor data of the earth's center gravity and non-spherical gravitational perturbation; The scale decomposition module decomposes the observation data of low-orbit satellites into long-term trend data, medium-term fluctuation data and short-term change data based on empirical mode decomposition; The dynamic model building and fitting module builds a long-term dynamic model based on the observation data combined with the gravity of the Earth's center and non-spherical gravitational perturbations, and fits the long-term trend data with the long-term dynamic model to obtain the long-term fitting results; Based on the observation data, a medium-term dynamic model is constructed by combining the gravity of the Earth's center, non-spherical gravitational perturbations and dynamic change factors, and the medium-term fluctuation data is fitted with the long-term dynamic model to obtain the medium-term fitting results; A short-term dynamics model is constructed based on the observed data combined with the local weighted regression method, and the short-term variation data is fitted with the short-term dynamics model to obtain the short-term fitting results. The multi-scale fusion module uses a weighted summation method to fuse the long-term fitting results, the mid-term fitting results, and the short-term fitting results to obtain the satellite orbit state fitting results; The orbit prediction module updates the parameters of all the dynamic models constructed in step S3 based on the fitting results of the satellite orbit state at the current moment, and calculates the orbit prediction information of the low-orbit satellite based on the updated dynamic models combined with the numerical calculation method.

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