Atmospheric density dynamic correction-based orbit forecasting method and device

Abstract

The invention provides an orbit forecasting method and device based on atmospheric density dynamic correction. The orbit forecasting method comprises the following steps: determining a plurality of target failure satellites and corresponding TLE orbit data from a failure satellite set; identifying an orbit control time period corresponding to the target failure satellite, so as to determine a real ballistic coefficient corresponding to the target failure satellite based on TLE orbit data of the target failure satellite in a non-orbit control time period; iteratively solving a correction coefficient time series data set according to a real ballistic coefficient corresponding to the target failure satellite and by combining the density-to-position partial derivative equation set; and through a correction coefficient prediction model obtained through pre-training, based on the correction coefficient time sequence data set and the spatial environment index, predicting an atmospheric density dynamic correction coefficient corresponding to the target moment, and carrying out orbit prediction to obtain satellite orbit ephemeris prediction data corresponding to the to-be-predicted satellite. According to the method, the orbit forecasting precision can be improved by using a more accurate atmospheric density dynamic correction coefficient.

Description

Technical Field

[0001] The present invention relates to the technical field of orbit prediction, and in particular to an orbit prediction method and device based on dynamic correction of atmospheric density. Background Art

[0002] The commonly used method for dynamic correction of the current atmospheric density model is to first determine the atmospheric drag coefficient and then obtain the atmospheric density correction coefficient through single-satellite precise orbit solution, and then correct the atmospheric density model.

[0003] The key is to construct a precise single-star solution. However, in actual applications, the single-star solution cannot fully cover the atmospheric density state at all longitudes and latitudes and altitudes, resulting in a relatively large error in the calculated atmospheric density correction coefficient, and the effect is not very obvious in actual applications. Summary of the Invention

[0004] In view of this, the object of the present invention is to provide a method and device for orbit prediction based on dynamic correction of atmospheric density, which can improve the accuracy of orbit prediction by using a more accurate dynamic correction coefficient of atmospheric density.

[0005] In a first aspect, the present invention provides a method for orbit prediction based on dynamic correction of atmospheric density, comprising:

[0006] Determine multiple target failed satellites and their corresponding TLE orbit data from the failed satellite set;

[0007] Identify the orbital control period corresponding to the target inoperative satellite, and determine the true ballistic coefficient corresponding to the target inoperative satellite based on the TLE orbit data of the target inoperative satellite in the non-orbital control period;

[0008] According to the actual ballistic coefficient corresponding to the failed target satellite, combined with the partial derivative equations of density with respect to position, the correction coefficient time series data set is iteratively solved. The correction coefficient time series data set includes the dynamic correction coefficient of atmospheric density in a multi-dimensional time series.

[0009] The correction coefficient prediction model obtained in advance is used to predict the dynamic correction coefficient of atmospheric density corresponding to the target time based on the correction coefficient time series dataset and the space environment index;

[0010] According to the dynamic correction coefficient of atmospheric density corresponding to the target time, the orbit of the satellite to be predicted is predicted, and the satellite orbit ephemeris prediction data corresponding to the satellite to be predicted is obtained.

[0011] In one embodiment, determining a plurality of target failed satellites and their corresponding TLE orbital data from a set of failed satellites includes:

[0012] Selecting a first candidate failed satellite set whose semi-major axis is smaller than a preset semi-major axis threshold from the failed satellite set;

[0013] From the first candidate set of failed satellites, select a second candidate set of failed satellites in ascending order of eccentricity;

[0014] From the second candidate failure satellite set, a target failure satellite set is screened out in descending order of energy dissipation rate. The target failure satellite set includes multiple target failure satellites and their corresponding TLE orbit data.

[0015] In one embodiment, identifying the orbital control period corresponding to the target inoperative satellite, and determining the true ballistic coefficient corresponding to the target inoperative satellite based on TLE orbit data of the target inoperative satellite in the non-orbital control period, includes:

[0016] For any target failed satellite, perform the following operations:

[0017] Determine the satellite ephemeris data corresponding to the target failed satellite according to the TLE orbit data corresponding to the target failed satellite;

[0018] Convert satellite ephemeris data into square root semi-major axis;

[0019] The orbit control period corresponding to the target failed satellite is identified using the flat root semi-major axis, and the TLE orbit data of the target failed satellite in the orbit control period is eliminated to obtain the TLE orbit data of the target failed satellite in the non-orbit control period.

[0020] Based on the TLE orbit data of the target failed satellite during the non-orbit control period, the initial ballistic coefficient of the target failed satellite is determined every day, and the average of the initial ballistic coefficients is taken as the true ballistic coefficient corresponding to the target failed satellite.

[0021] In one embodiment, the correction coefficient time series data set is iteratively solved based on the actual ballistic coefficient corresponding to the target failed satellite and the partial derivative equations of density with respect to position, including:

[0022] The initial atmospheric density value is solved based on the ballistic coefficient, initial position velocity and precision orbit data corresponding to the target failed satellite;

[0023] The initial atmospheric density dynamic correction coefficient is solved based on the initial atmospheric density value through the partial derivative equations of density with respect to position;

[0024] Determining an inflection point temperature correction value according to an initial atmospheric density dynamic correction coefficient, so as to update the atmospheric density value using the inflection point temperature correction value;

[0025] The new atmospheric density dynamic correction coefficient is solved based on the new atmospheric density value through the group of partial derivative equations of density with respect to position, until the preset iteration stop condition is met, and the final atmospheric density dynamic correction coefficient is obtained.

[0026] In one embodiment, updating the atmospheric density value using the inflection point temperature correction value includes:

[0027] Determine the current inflection point temperature and the atmospheric temperature at the target failed satellite altitude, and use the inflection point temperature correction value to correct the current inflection point temperature to obtain a new current inflection point temperature;

[0028] Determine the density values ​​corresponding to the various atmospheric components at the altitude of the target failed satellite based on the new current inflection point temperature and the atmospheric temperature;

[0029] A geomagnetic effect correction coefficient is determined, and a new atmospheric density value is determined based on the geomagnetic effect correction coefficient and the density values ​​corresponding to the atmospheric components at the altitude of the target failed satellite.

[0030] In one embodiment, the iteration stopping condition is that the coefficient deviation value is less than a preset convergence threshold, and the coefficient deviation value is calculated based on the position change matrix of the vector projection of the target failed satellite relative to the center of the earth, the density position partial derivative matrix and the current atmospheric density dynamic correction coefficient.

[0031] In one embodiment, the training step of the correction coefficient prediction model includes:

[0032] The correction coefficient prediction model is used to predict the dynamic correction coefficient of atmospheric density corresponding to a specified time based on the historical correction coefficient time series data set and the historical space environment index.

[0033] According to the dynamic correction coefficient of atmospheric density corresponding to the specified time, the orbit of the target failed satellite is predicted to obtain the satellite orbit ephemeris prediction data of the target failed satellite at the specified time;

[0034] Based on the TLE orbit data corresponding to the target failed satellite, determine the true satellite orbit ephemeris data of the target failed satellite at a specified time;

[0035] Based on the satellite orbit ephemeris prediction data and the satellite orbit ephemeris true value data of the target failed satellite at a specified time, the model parameters of the correction coefficient prediction model are adjusted.

[0036] In a second aspect, the present invention further provides a trajectory prediction device based on dynamic correction of atmospheric density, characterized in that it includes:

[0037] A satellite screening module is used to determine multiple target failed satellites and their corresponding TLE orbit data from the failed satellite set;

[0038] The ballistic coefficient determination module is used to identify the orbital control period corresponding to the target inoperative satellite, so as to determine the actual ballistic coefficient corresponding to the target inoperative satellite based on the TLE orbit data of the target inoperative satellite in the non-orbital control period;

[0039] The correction coefficient solving module is used to iteratively solve the correction coefficient time series data set based on the actual ballistic coefficient corresponding to the target failed satellite and the partial derivative equations of density with respect to position. The correction coefficient time series data set includes the dynamic correction coefficient of atmospheric density in a multi-dimensional time series.

[0040] The correction coefficient prediction module is used to predict the dynamic correction coefficient of atmospheric density corresponding to the target time based on the correction coefficient time series data set and the space environment index using the correction coefficient prediction model obtained in advance;

[0041] The orbit prediction module is used to perform orbit prediction on the satellite to be predicted based on the dynamic correction coefficient of atmospheric density corresponding to the target time, and obtain the satellite orbit ephemeris prediction data corresponding to the satellite to be predicted.

[0042] In a third aspect, the present invention further provides an electronic device comprising a processor and a memory, wherein the memory stores computer-executable instructions that can be executed by the processor, and the processor executes the computer-executable instructions to implement any one of the methods provided in the first aspect.

[0043] In a fourth aspect, the present invention further provides a computer-readable storage medium, which stores computer-executable instructions. When the computer-executable instructions are called and executed by a processor, the computer-executable instructions prompt the processor to implement any one of the methods provided in the first aspect.

[0044] The present invention provides an orbit prediction method and device based on dynamic correction of atmospheric density. The method comprises the following steps: first, determining a plurality of target failed satellites and their corresponding TLE orbit data from a set of failed satellites; then, identifying an orbit control period corresponding to the target failed satellite, and determining a true ballistic coefficient corresponding to the target failed satellite based on the TLE orbit data of the target failed satellite in a non-orbit control period; then, according to the true ballistic coefficient corresponding to the target failed satellite and in combination with a group of partial derivative equations of density with respect to position, iteratively solving a correction coefficient time series data set, the correction coefficient time series data set including a dynamic correction coefficient of atmospheric density of a multidimensional time series; further, using a correction coefficient prediction model obtained by pre-training, based on the correction coefficient time series data set and a space environment index, predicting the dynamic correction coefficient of atmospheric density corresponding to a target time; finally, performing orbit prediction on the satellite to be predicted according to the dynamic correction coefficient of atmospheric density corresponding to the target time, and obtaining satellite orbit ephemeris prediction data corresponding to the satellite to be predicted. The above method determines the corresponding true ballistic coefficient based on the TLE orbit data of the target failed satellite during the non-orbit control period, and then iteratively solves the correction coefficient time series data set according to all the target failed satellites involved in the solution, combined with the partial derivative equations of density with respect to position, and predicts the dynamic correction coefficient of atmospheric density at the target time through the correction coefficient prediction model, thereby using a more accurate dynamic correction coefficient of atmospheric density to improve the orbit prediction accuracy.

[0045] Other features and advantages of the present invention will be described in the following description, and in part will become apparent from the description, or understood by practicing the present invention. The purposes and other advantages of the present invention are realized and obtained by the structures particularly pointed out in the description, claims and drawings.

[0046] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, preferred embodiments are given below and described in detail with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the specific embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0048] Figure 1 A schematic flow chart of a method for orbit prediction based on dynamic correction of atmospheric density provided by an embodiment of the present invention;

[0049] Figure 2 A technical framework diagram of an orbit prediction method based on dynamic correction of atmospheric density provided by an embodiment of the present invention;

[0050] Figure 3 A definition diagram of the solar hour angle α provided in an embodiment of the present invention;

[0051] Figure 4 A flowchart of a correction coefficient prediction model training based on LSTM provided in an embodiment of the present invention;

[0052] Figure 5 A schematic diagram of the principle of an LSTM provided in an embodiment of the present invention;

[0053] Figure 6 A schematic structural diagram of an orbit prediction device based on dynamic correction of atmospheric density provided by an embodiment of the present invention;

[0054] Figure 7 A schematic structural diagram of an electronic device provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0055] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions of the present invention will be clearly and completely described below in conjunction with the embodiments. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of them. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0056] At present, the existing technology has the problem of relatively large errors in the calculated atmospheric density correction coefficient. Based on this, the present invention implements a method and device for orbit prediction based on dynamic correction of atmospheric density, which can use a more accurate dynamic correction coefficient of atmospheric density to improve the accuracy of orbit prediction.

[0057] To facilitate understanding of this embodiment, firstly, a method for orbit prediction based on dynamic correction of atmospheric density disclosed in an embodiment of the present invention is described in detail. Figure 1 The flow chart of a trajectory prediction method based on dynamic correction of atmospheric density is shown, and the method mainly includes the following steps S102 to S110:

[0058] Step S102: determining a plurality of target failed satellites and their corresponding TLE orbit data from the failed satellite set.

[0059] The failed satellite set includes multiple failed satellites (also referred to as calibration satellites or non-operational satellites). In one example, a specified number of target failed satellites and their corresponding TLE (Two-Line Element) orbit data can be selected from the failed satellites based on the semi-major axis, eccentricity, and satellite energy dissipation rate of the failed satellites.

[0060] Step S104: identifying the orbital control period corresponding to the target failed satellite, and determining the true ballistic coefficient corresponding to the target failed satellite based on the TLE orbit data of the target failed satellite in the non-orbital control period.

[0061] Among them, the orbit control period refers to the time window when the satellite performs orbit adjustment or control operations, and the non-orbit control period is the time window when the satellite is in a free flight state; the ballistic coefficient comprehensively reflects the air resistance characteristics of the satellite when it moves in the air.

[0062] In one example, for each target failed satellite, it is possible to identify whether the target failed satellite is in an orbit control period based on its mean root semi-major axis, and then extract the TLE orbit data during the non-orbit control period. The initial ballistic coefficient is solved using the TLE orbit data, and the corresponding true ballistic coefficient is obtained by averaging the initial ballistic coefficients of the target failed satellite over a period of time.

[0063] Step S106 , based on the actual ballistic coefficient corresponding to the failed target satellite and in combination with the density with respect to position partial derivative equations, the correction coefficient time series data set is iteratively solved.

[0064] The density position partial derivative equations can be understood as an equation set consisting of the partial derivatives of the atmospheric density with respect to the position of the target failed satellite; the correction coefficient time series data set includes the dynamic correction coefficients of the atmospheric density of the multidimensional time series.

[0065] In one example, the initial atmospheric density value is first calculated using the actual ballistic coefficients corresponding to multiple target failed satellites. Then, the initial atmospheric density dynamic correction coefficient is solved based on the initial atmospheric density value through the group of partial derivative equations of density with respect to position. The initial atmospheric density is then updated using the initial atmospheric density dynamic correction coefficient. The above process is repeated, and the final atmospheric density dynamic correction coefficient can be obtained when the iteration stops.

[0066] Step S108 , using the pre-trained correction coefficient prediction model, based on the correction coefficient time series data set and the space environment index, predicts the atmospheric density dynamic correction coefficient corresponding to the target time.

[0067] Among them, the correction coefficient prediction model can adopt the LTSM (Long Short-Term Memory) model. The input of the correction coefficient prediction model is the correction coefficient time series data set and the spatial environment index. The spatial environment index includes F10.7 (index solar radio flux index), ap (geomagnetic activity index), and Dst (geomagnetic storm ring current index). The output is the dynamic correction coefficient of atmospheric density corresponding to the target time.

[0068] Step S110 , performing orbit prediction on the satellite to be predicted based on the atmospheric density dynamic correction coefficient corresponding to the target time, and obtaining satellite orbit ephemeris prediction data corresponding to the satellite to be predicted.

[0069] In one example, the process of performing orbit prediction using the atmospheric density dynamic correction coefficient to obtain satellite orbit ephemeris prediction data corresponding to the satellite to be predicted may adopt conventional orbit prediction means, which is not limited in the embodiment of the present invention.

[0070] An orbit prediction method based on dynamic correction of atmospheric density provided by an embodiment of the present invention determines the corresponding true ballistic coefficient based on the TLE orbit data of the target failed satellite during the non-orbit control period. Thus, according to all the target failed satellites involved in the solution, combined with the partial derivative equations of density with respect to position, a correction coefficient time series data set is iteratively solved, and the dynamic correction coefficient of atmospheric density at the target moment is predicted through a correction coefficient prediction model, thereby using a more accurate dynamic correction coefficient of atmospheric density to improve the orbit prediction accuracy.

[0071] For ease of understanding, the embodiment of the present invention provides a specific implementation method of an orbit prediction method based on dynamic correction of atmospheric density, which adopts multi-satellite joint construction of dynamic atmospheric density partial derivative solution equation. During the data period of the satellite's free flight state, the dynamic orbit determination method is used to process the orbit data of all failed satellites at the same time. The parameters to be estimated include the initial position velocity of each satellite involved in the solution, the dynamic correction coefficient of atmospheric density, and the ballistic coefficient. The dynamic correction coefficient of atmospheric density is obtained through iteration, and finally a more accurate atmospheric model is used to improve the orbit prediction accuracy. For details, see Figure 2 The technical framework diagram of an orbit prediction method based on dynamic correction of atmospheric density is shown, which includes: failed satellite orbit data collection, failed satellite orbit data quality assessment, atmospheric density dynamic correction coefficient solution, atmospheric density dynamic correction coefficient prediction, orbit prediction based on the corrected atmospheric density model and other processes.

[0072] (1) Collection of failed satellite orbit data:

[0073] Collect TLE orbital data for all inactive satellites and select at least 20 target inactive satellites that meet the requirements of stable ballistic coefficient, high energy dissipation rate, and good spatial coverage. TLE orbital data for inactive satellites includes historical data and real-time updated data. The historical data covers at least one year and the orbital altitude is below 600 km. The selection process is as follows:

[0074] (1.1) Obtain TLE orbit data of all numbered satellites from the TLE website.

[0075] (1.2) From the set of failed satellites, a first candidate set of failed satellites is selected whose semi-major axes are less than a preset semi-major axis threshold. For example, based on the TLE orbital data, failed satellites with semi-major axes less than 600 km (the atmosphere exists only within 1000 km of the Earth) can be selected to obtain the first candidate set of failed satellites.

[0076] (1.3) From the first candidate set of failed satellites, a second candidate set of failed satellites is selected in ascending order of eccentricity. For example, based on the first candidate set of failed satellites, failed satellites with smaller eccentricities are selected to ensure a relatively stable ballistic coefficient, thereby obtaining the second candidate set of failed satellites.

[0077] (1.4) From the second candidate set of inoperative satellites, select a target inoperative satellite set in descending order of energy dissipation rate. The target inoperative satellite set includes multiple target inoperative satellites and their corresponding TLE orbital data. For example, based on the second candidate set of inoperative satellites, TLE orbital data for each satellite from 2023 to 2025 is collected and the satellite energy dissipation rate is calculated, and the satellites with the largest energy dissipation rate are selected. The calculation formula for the satellite energy dissipation rate is as follows:

[0078]

[0079]

[0080] Among them E DR is the satellite energy dissipation rate, μ is the Earth's gravitational field constant, a(t2) is the orbital semi-major axis at time t2, a(t1) is the orbital semi-major axis at time t1, T is t2-t1, is the mean of the two plane semi-major axes.

[0081] (2) Quality assessment of failed satellite orbit data:

[0082] The TLE orbit data quality assessment of the failed satellite performs preliminary processing on the orbit data and screens the available data for subsequent processing. Due to the large differences in the accuracy and update frequency of the failed satellite data, different strategies are used for quality assessment and data screening to obtain available satellite ephemeris as (pseudo) observations. After the data quality assessment is completed, it is necessary to determine the orbit of each target failed satellite based on high-quality observation data within the historical data arc to obtain the segmented ballistic coefficient within the historical data arc. The long-term ballistic coefficient is processed to offset the error of the atmospheric density model, thereby obtaining the "real" ballistic coefficient of each target failed satellite, which is used for the subsequent calculation of the atmospheric density model correction coefficient. Specifically, the following operations are performed for any target failed satellite:

[0083] (2.1) Determine the satellite ephemeris data corresponding to the target failed satellite based on the TLE orbit data corresponding to the target failed satellite.

[0084] In one example, the satellite ephemeris (time, position, and velocity) data is obtained using the SPG4 prediction model based on the TLE orbit data, and the satellite ephemeris is thinned into one-minute satellite ephemeris data.

[0085] (2.2) Convert satellite ephemeris data into square root semi-major axis.

[0086] In one example, the satellite ephemeris data is converted into six orbital elements, and the six orbital elements are converted into square roots to obtain the square root semi-major axis.

[0087] (2.3) The orbital control period corresponding to the target failed satellite is identified using the flat root semi-major axis, and the TLE orbital data of the target failed satellite in the orbital control period is eliminated to obtain the TLE orbital data of the target failed satellite in the non-orbital control period.

[0088] In one example, due to atmospheric drag and light pressure, the semi-major axis of the flat root mean square (SMA) gradually decays when a satellite is not under orbital control. Calculating the ballistic coefficient requires ephemeris data from the free-flight period, excluding the period of orbital control. Therefore, the period of orbital control is identified based on the change in the SMA. By excluding this period, usable satellite ephemeris is obtained as a (pseudo) observation, i.e., the TLE orbit data of the failed target satellite during the non-orbital control period.

[0089] (2.4) Based on the TLE orbit data of the target failed satellite in the non-orbital control period, the initial ballistic coefficient of the target failed satellite is determined on each day, and the average of the initial ballistic coefficients is used as the true ballistic coefficient corresponding to the target failed satellite.

[0090] In one example, the atmospheric drag coefficient CD is obtained based on (pseudo) observational orbit determination, and then multiplied by the surface-to-mass ratio to obtain the initial ballistic coefficient of the target inoperative satellite on each day. The average of the initial ballistic coefficients for each day from 2001 to 2024 is used as the actual ballistic coefficient corresponding to the target inoperative satellite.

[0091] (3) Calculation of the dynamic correction coefficient for atmospheric density, including:

[0092] To facilitate understanding, we first explain the construction process of the density position partial derivative equations:

[0093] Step 1: Calculate quantities related to the satellite and sun positions, including the satellite's local altitude, the satellite's geodetic latitude φ, and the sun's declination δ. S 、The sun's hour angle α:

[0094] (1a) Local altitude of satellite h:

[0095]

[0096] Where: r is the distance from the satellite to the Earth's center of mass; R E is the equatorial radius of the Earth; f is the flattening of the Earth; e E is the first eccentricity of the Earth; φ′ is the geocentric latitude of the satellite; x o 、y o 、z o is the position component of the satellite in the Earth-fixed coordinate system.

[0097] (1b) Satellite's geodetic latitude φ:

[0098]

[0099] Among them, z b is the coordinate of the satellite altitude direction.

[0100] (1c) The declination of the Sun δ S :

[0101] The unit vector of the sun in the Earth-fixed coordinate system is:

[0102]

[0103] in, is the unit vector of the sun's position, is the sun position unit vector The coordinate component of S is the solar hour angle, r Sb is the actual distance from the sun to the center of the earth.

[0104] (1d) The hour angle of the sun α:

[0105] See also Figure 3 The definition diagram of the solar hour angle α is shown in the figure, where E is the center of the earth, S is the sun, V is the satellite, EA and EB are Projection onto the equatorial plane.

[0106] Step 2: Calculate the nighttime top-of-the-atmosphere temperature when there is no geomagnetic activity:

[0107]

[0108] Here, F 10.7 and are the daily average and 162-day average of the solar 10.7 cm radiation flux, respectively. Since the change of the top atmosphere temperature has a 1-day delay relative to the change of the solar radiation flux, here F 10.7 and The values ​​are taken as the day before time t.

[0109] Step 3: Calculate the diurnal change in the top atmosphere temperature T E :

[0110]

[0111]

[0112] τ=α-37. o 0+6. o 0sin(α+43. o 0)(-π<τ<π);

[0113] Among them: η, θ, τ are intermediate parameters for auxiliary calculations. η and θ are mainly used to describe the relative position relationship between the satellite and the sun, and τ is used to correct the satellite's right ascension.

[0114] Step 4: Calculate the geomagnetic thermal effect to obtain the top atmosphere temperature T ∞ :

[0115] T ∞ =T E +ΔT ∞ ;

[0116] in:

[0117]

[0118] Among them, k p is the geomagnetic activity index. Since the change of the top atmosphere temperature has a 6.7-hour delay relative to the geomagnetic activity, the k p The value should be taken as the value 6.7 hours before time t.

[0119] Step 5: Calculate the atmospheric temperature T at the inflection point (125 km) and the satellite altitude h x 、T:

[0120] 1):

[0121] 2):

[0122] Wherein, equation 1) is the asymptotic form of the temperature distribution for h > 125 km given by Roberts. In order to achieve the best least squares fit between the results given by this expression and those of Jacchia, the parameter l in equation 2) is calculated using the following polynomial:

[0123] 3):

[0124] The coefficient l in the polynomial i for:

[0125] l1=0.1031445×10 5 ,l2=0.2341230;

[0126] l3=0.1579202×10 -2 ,l4=-0.1252487×10 -5 ;

[0127] l5=0.2462708×10 -9 ;

[0128] Step 6, calculate the density of each atmospheric component at 125 kilometers:

[0129] At an altitude of 125 kilometers, the main components of the atmosphere are nitrogen, argon, helium, oxygen, and oxygen atoms. The density of each gas component varies with the temperature at the top of the atmosphere. The number of molecules (or atoms) per unit volume can be expressed as a polynomial of the top-level temperature. The density of each atmospheric component is then:

[0130]

[0131] in:

[0132] δ ij M is the coefficient of the polynomial representing the number of molecules (or atoms) per unit volume of gas component i (i = 1 to 5), i represents the gas component number, and j represents the order of the density polynomial. The coefficients of the polynomial describing the change of atmospheric density with altitude are given in Table 1. i is the molar mass of gas component i. i The values ​​are also given in Table 1. A VR M i =1.660421×10-18, the reciprocal of Avogadro's constant.

[0133] Table 1 Atmospheric composition

[0134]

[0135] Step 7, calculate the density of each atmospheric component at height h:

[0136] Substituting the temperature distribution expression given by formula 2) into the diffusion differential equation and integrating it, the density of each atmospheric component can be obtained.

[0137] 4):

[0138] Where: α i is the thermal diffusivity of gas component i, given in Table 1. r i Used to describe changes in atmospheric composition under specific conditions. o=9.80665 m / s2 is the acceleration of gravity at sea level. a = 6356.766 km. R = 8.31432 × 10-3 Newton km / degree is the gas constant. l is given by equation 3).

[0139] When h>500 km, the atmosphere contains hydrogen in addition to the above five components. Its density is:

[0140]

[0141] in:

[0142]

[0143] T S This is the temperature change function for the area above 125 km modified by Robert.

[0144] When the top-of-the-atmosphere temperature is below 6000 K, the concentration of hydrogen is also quite large below 500 km. However, the resulting density error can be partially compensated by a least squares fit of the Roberts parameter l.

[0145] Step 8, correct for seasonal latitude variations in nitrogen:

[0146] In the density of each atmospheric component calculated in formula (4), the nitrogen density needs to be corrected for seasonal and latitudinal variations. If the nitrogen density calculated in formula (4) is recorded as ρ′3(), the seasonal and latitudinal correction is:

[0147]

[0148] Among them, ε=230.44 is the angle between the ecliptic and the obliquity.

[0149] Step 9, calculate the correction coefficient of the geomagnetic effect on the atmospheric density:

[0150] There is another influence of geomagnetic effect on the standard density of the atmosphere below 200 km altitude (only limited to h < 200 km), which is recorded as geomagnetic correction coefficient Δρ1:

[0151]

[0152] Step 10, correction coefficient Δρ2 for half-year cycle variation:

[0153] Δρ2=10 f(h)g(t) ;

[0154] f(h)=(5.876×10 -72.331 +0.06328)e -0.002868 ;

[0155] g(t)=0.02835+[0.3817+0.17829sin(τ S +4.137)]sin(2τ S +4.259);

[0156]

[0157] JD1958=tMJD-36204 is the Julian day number from January 0, 1958. f(h) is used to describe the change characteristics of atmospheric density with height, g(t) is used to describe the periodic change of atmospheric density with time, τ S Describes the periodic change of atmospheric density over time, and Φ is used to describe the position of a certain time point relative to a reference time point.

[0158] Step 11, calculate the seasonal latitude change correction coefficient of the lower thermal atmosphere:

[0159] When h < 200 km, the standard density of the lower thermal atmosphere needs to be corrected for seasonal latitude. Seasonal latitude correction coefficient Δρ3:

[0160]

[0161] Step 12: Calculate the standard atmospheric density ρ at height h S and atmospheric density ρ:

[0162]

[0163] ρ=ρ S Δρ;

[0164] Among them, Δρ=Δρ1+Δρ2+Δρ3.

[0165] Step 13, partial derivative of atmospheric density with respect to satellite position vector:

[0166] From the above calculation formula of atmospheric density ρ, we can get:

[0167] 5):

[0168] in:

[0169]

[0170] f′(h)=-0.002868f(h)+2.331(5.876×10 -7 )h 1.331 e -0.002868h ;

[0171]

[0172]

[0173]

[0174]

[0175]

[0176]

[0177]

[0178]

[0179]

[0180]

[0181] in, is the sun position unit vector The coordinate component in the horizontal direction, is the satellite position unit vector The coordinate component in the horizontal direction.

[0182] Based on the above-mentioned set of partial derivative equations of density with respect to position, an embodiment of the present invention provides a specific implementation method for solving the dynamic correction coefficient of atmospheric density, including:

[0183] (3.1) Based on the ballistic coefficient, initial position velocity, and precision orbit data corresponding to the target inoperative satellite, the initial atmospheric density value is solved. In one example, the process of solving the initial atmospheric density value ρ can adopt existing methods, which will not be further described in this embodiment of the present invention.

[0184] (3.2) The initial atmospheric density dynamic correction coefficient is solved based on the initial atmospheric density value through the group of partial derivative equations of density with respect to position.

[0185] Optionally, the dynamic correction coefficient of atmospheric density can be solved based on the Newton-Gauss iterative algorithm for density solution.

[0186] After the spherical harmonic expansion of Tc, the atmospheric density is only a function of the spherical harmonic coefficients when the spatial position and spatial environment index are given:

[0187]

[0188] Given the initial value of the spherical harmonic coefficient (that is, the initial atmospheric density dynamic correction coefficient) And perform Taylor expansion on the above formula, ignoring high-order infinitesimals, we have:

[0189]

[0190] in:

[0191]

[0192] The left side of the equation is recorded as the observed value ρ obs , the right side of the equation is the dynamic correction model simulation value ρ model , then for n observation data, we have:

[0193]

[0194] Written in matrix form, we have:

[0195]

[0196] Combined with formula 5), ​​we can get:

[0197]

[0198] The left side of the above formula is denoted as b, the partial derivative matrix on the right side is denoted as A, and the spherical harmonic coefficient (that is, the dynamic correction coefficient of atmospheric density) is denoted as x. The coefficient deviation value Δx can be expressed as:

[0199] Δx=(A T A) -1 ·A T b;

[0200] After obtaining the coefficient deviation value Δx, the new spherical harmonic coefficient (ie, the atmospheric density dynamic correction coefficient) x is obtained.

[0201] (3.3) Determine the inflection point temperature correction value ΔT based on the initial atmospheric density dynamic correction coefficient x , to use the inflection point temperature correction value ΔT x Update the atmospheric density value.

[0202] Among them, the inflection point temperature correction value ΔT x The determination process is as follows:

[0203]

[0204]

[0205]

[0206]

[0207]

[0208] Among them, αi is the thermal diffusion coefficient, such as g0, R p0le 、M i are the average gravitational acceleration on the surface, polar radius, and molecular molar mass, respectively. T0 is the base temperature of 183K, l is the parameter defined by Jacchia, and T corr is the corrected exosphere temperature, and R is the ideal gas constant.

[0209] The process of updating the atmospheric density value is as follows: Determine the current inflection point temperature T x and the atmospheric temperature at the altitude of the target failed satellite, using the inflection point temperature correction value ΔT x For the current inflection point temperature T x Correction is performed to obtain the new current inflection point temperature T x Based on the new current inflection point temperature and the atmospheric temperature, the density values ​​corresponding to the atmospheric components at the target inoperative satellite altitude are determined; the geomagnetic effect correction coefficient is determined, and based on the geomagnetic effect correction coefficient and the density values ​​corresponding to the atmospheric components at the target inoperative satellite altitude, the new atmospheric density value is determined. Specifically, given the new current inflection point temperature T x The process of determining the atmospheric density value can be referred to the aforementioned embodiment, and will not be described in detail in the embodiment of the present invention.

[0210] (3.4) Using the density-with-position partial derivative equations, a new atmospheric density dynamic correction coefficient is solved based on the new atmospheric density value until a preset iteration stop condition is satisfied, resulting in the final atmospheric density dynamic correction coefficient. The iteration stop condition is that the coefficient deviation Δx is less than a preset convergence threshold. The coefficient deviation Δx is calculated based on the position change matrix b of the vector projection of the target failed satellite relative to the center of the Earth, the density-with-position partial derivative matrix A, and the current atmospheric density dynamic correction coefficient x.

[0211] Repeat the above steps (3.2) to (3.3) and stop when Δx is less than the convergence threshold set by the algorithm to obtain the final atmospheric density dynamic correction coefficient x.

[0212] (IV) Forecast of dynamic correction coefficient of atmospheric density:

[0213] The dynamic correction coefficient of atmospheric density is predicted by using a deep learning model (LSTM) with a multi-layer structure that can automatically learn complex data features, optimize and adjust machine learning parameters, and combine the spatial environment index and correction coefficient time series data set to accurately customize and determine the optimal network model structure, thereby achieving accurate prediction in complex systems.

[0214] The dynamic correction coefficient for atmospheric density is closely related to the solar radiation index (F10.7) and the geomagnetic index (ap, Dst). Experiments have demonstrated a nonlinear correlation between these three parameters and the dynamic correction coefficient. However, due to its complex and irregular curve shape, traditional model construction methods are complex, highly dependent on human intervention, and lack robustness, making them unsuitable for engineering applications. Based on the relatively clear regularity exhibited by the correction coefficient time series dataset, an LSTM model based on the dynamic correction coefficient for atmospheric density was constructed. The historical correction coefficient time series dataset and the historical spatial environment index were used as inputs to the LSTM model to obtain the dynamic correction coefficient for atmospheric density at a given moment. The loss value was calculated, and the model weights and biases were calculated through backpropagation. This optimized LSTM model was then used to predict the changing trend of the dynamic correction coefficient for atmospheric density based on the correction coefficient time series dataset. This approach overcomes the limitations of existing atmospheric correction coefficient prediction methods, which suffer from a single model and low accuracy, and addresses the need for iterative optimization of the prediction model based on continuously updated data to improve prediction accuracy.

[0215] See also Figure 4 The training flowchart of the LSTM-based correction coefficient prediction model is shown, which is divided into the input layer, the network layer and the prediction layer.

[0216] (I) Input Layer: Model training data includes spatial environment indices and atmospheric correction coefficients. Spatial environment indices include F10.7, ap, and Dst data. Atmospheric density dynamic correction coefficients include C00, C10, C11, C20, C21, C22, S11, S21, and S22. The training and test datasets have a length ratio of 8:2, and the time range can be flexibly adjusted based on project needs.

[0217] Data standardization includes data alignment and outlier detection. The 3σ principle is used for data outlier detection, which is expressed as follows:

[0218]

[0219] Where, Refers to the data mean, n refers to the number of data. i When it is greater than 3σ, Lagrange polynomial interpolation is performed at that moment:

[0220]

[0221] Where y i Refers to the function value at a known point, l i (x) is an n-degree polynomial that satisfies:

[0222]

[0223] The F10.7 data step size is 24 hours, the AP data step size is 3 hours, the DST data step size is 1 hour, and the atmospheric correction factor step size changes dynamically. Data alignment generates new data based on the atmospheric correction factor and performs Lagrange polynomial interpolation on the F10.7, AP, and DST data to generate new data.

[0224] (II) Network Layer: The network layer structure consists of two LSTM layers, two DropOut layers, and one Dense layer. The LSTM layer has an input time series length of 81 or 27 days, depending on the space weather activity cycle. The number of hidden layers is 16, and the activation function is tanh. A Dropout layer with a deactivation probability of 0.2 is added after the LSTM layer to reduce inter-neuron dependencies, shorten gradient descent time, enhance model generalization, and reduce training time. The final layer is a fully connected layer that outputs the predicted value of the atmospheric density dynamic correction coefficient.

[0225] The information flow of LSTM is a bidirectional parallel propagation of memory elements and hidden states, which carry long-term and short-term information respectively, and are appropriately crossed at each time step through the gating mechanism. Figure 5 The schematic diagram of the principle of LSTM is shown in the figure. The input gate I t 、Forget Gate F t , output gate O t , candidate memory G t The calculation is as follows:

[0226] I t =σ(X t W xi +H t-1 W hi +b i );

[0227] F t =σ(X t W xf +H t-1 W hf +b f );

[0228] O t =σ(X t W xo +H t-1 W ho +b o );

[0229] G t =tanh(X t W xg +H t-1 W hg +b g );

[0230] It can be seen that I t 、F t , O t , G t The calculation method is the same, the difference is the activation function, the weight matrix W (also known as W xi 、W hi 、W xf 、W hf 、W xo 、W ho 、W xg 、W hg ), bias matrix b (also known as b i 、b f 、b o 、b g ). σ is the sigmoid function, I t Determines the current information X t The strength, F t Determined past memory C t-1 The strength of the two together constitutes the current memory C t , O t This determines the current memory C t For the current hidden state H t The degree of influence of the current memory C t The expression is as follows:

[0231] C t =F t ·C t-1 +I t ·G t ;

[0232] In the above formula, C t Indicates the cell memory output at the current moment, represented by I t 、F t To control. t Determine how much information comes from the candidate memory, F t Determine how much information comes from past memory C t-1 The current hidden state H t The expression is as follows:

[0233] H t =O t tanh(C t );

[0234] In the above formula, all the information in the memory element is transferred to the current hidden state H t , update the current historical information and pass the information to the next time step.

[0235] The space environment has both long-term evolution laws and short-term fluctuations. tConvenient for capturing short-term data trend memory of spatial environment, F t It is convenient to capture the long-term data trend memory of the space environment by adjusting O t Suppress unimportant or noisy signals to prevent them from affecting subsequent calculations. t During inhibition, important information is stored in memory cells and is not exposed to the next time step through the hidden state too early, which helps alleviate the problem of gradient disappearance or explosion, allowing the model to have a stronger ability to process long sequences.

[0236] The model backpropagation uses the adaptive optimization algorithm Adam. The training process introduces a cost function to calculate the average loss of all samples and adjust the parameters w and b to obtain the minimum cost function. The cost function is calculated as follows:

[0237]

[0238] In the above formula, m is the length of the data involved in the calculation, y (i) is the theoretical value, x (i) is the calculated value.

[0239] When the cost function is less than the accuracy threshold, stop training and save the model.

[0240] (III) Prediction Layer: By training and comparing models for different time periods for each correction, a highly accurate prediction model is obtained. By inputting data that meets the model input requirements into the model, the dynamic atmospheric density correction coefficient corresponding to the target time is obtained.

[0241] For the above LSTM model, the embodiment of the present invention provides a specific training process:

[0242] (4.1) Using the correction coefficient prediction model, the dynamic atmospheric density correction coefficient corresponding to a given moment is predicted based on a historical correction coefficient time series dataset and a historical spatial environment index. In one example, the correction coefficient time series dataset and the spatial environment index at a given moment are input into the aforementioned LSTM model to obtain the dynamic atmospheric density correction coefficient corresponding to a given moment.

[0243] (4.2) Based on the atmospheric density dynamic correction coefficient corresponding to the specified time, the orbit of the target failed satellite is predicted to obtain satellite orbit ephemeris prediction data for the target failed satellite at the specified time; and based on the TLE orbit data corresponding to the target failed satellite, the true satellite orbit ephemeris data of the target failed satellite at the specified time is determined. In one example, the process of using the atmospheric density dynamic correction coefficient to perform orbit prediction to obtain satellite orbit ephemeris prediction data for the target failed satellite at the specified time can adopt conventional orbit prediction methods, which is not limited by the embodiment of the present invention. Similarly, the process of using the TLE orbit data to solve the satellite orbit ephemeris of the target failed satellite at the specified time and using it as the true satellite orbit ephemeris data can also adopt conventional technical means, which is not further described in the embodiment of the present invention.

[0244] (4.3) Based on the predicted satellite orbit ephemeris data and the true satellite orbit ephemeris data of the target failed satellite at the specified time, the model parameters of the correction coefficient prediction model are adjusted. In one example, the loss value is determined based on the predicted satellite orbit ephemeris data and the true satellite orbit ephemeris data, and the model parameters of the LTSM model are adjusted through backpropagation to achieve model training.

[0245] Finally, the trained LSTM can be used to predict the dynamic correction coefficient of atmospheric density corresponding to the target time based on the correction coefficient time series dataset and the spatial environment index.

[0246] (5) Orbit prediction based on the revised atmospheric density model: Based on the revised predicted atmospheric model, high-precision orbit prediction is used to predict the orbit of the satellite to be predicted to obtain satellite orbit ephemeris data.

[0247] In summary, the embodiments of the present invention provide at least the following features: (a) effective correction of the atmospheric density model; (b) all core algorithms are independently controllable and can be used independently or integrated; (c) cross-platform use, such as Windows, Ubuntu, CentOS, and Kylin Linux; and (d) higher computational efficiency and accuracy.

[0248] Based on the above embodiment, the present invention provides a trajectory prediction device based on dynamic correction of atmospheric density. Figure 6 The structure diagram of a trajectory prediction device based on dynamic correction of atmospheric density is shown in FIG. The device includes the following parts:

[0249] The satellite screening module 602 is used to determine a plurality of target failed satellites and their corresponding TLE orbit data from the failed satellite set;

[0250] The ballistic coefficient determination module 604 is configured to identify the orbital control period corresponding to the target inoperative satellite, and determine the true ballistic coefficient corresponding to the target inoperative satellite based on the TLE orbit data of the target inoperative satellite in the non-orbital control period;

[0251] The correction coefficient solving module 606 is used to iteratively solve the correction coefficient time series data set based on the actual ballistic coefficient corresponding to the target failed satellite and the partial derivative equations of density with respect to position. The correction coefficient time series data set includes the dynamic correction coefficient of atmospheric density in a multi-dimensional time series.

[0252] The correction coefficient prediction module 608 is used to predict the atmospheric density dynamic correction coefficient corresponding to the target time based on the correction coefficient time series data set and the space environment index using the correction coefficient prediction model obtained in advance;

[0253] The orbit prediction module 610 is used to perform orbit prediction for the satellite to be predicted based on the dynamic atmospheric density correction coefficient corresponding to the target time, and obtain satellite orbit ephemeris prediction data corresponding to the satellite to be predicted.

[0254] An orbit prediction device based on dynamic correction of atmospheric density provided by an embodiment of the present invention determines the corresponding true ballistic coefficient based on the TLE orbit data of a target failed satellite during a non-orbit control period. Thus, according to all target failed satellites involved in the solution, combined with a group of partial derivative equations of density with respect to position, a correction coefficient time series data set is iteratively solved, and the dynamic correction coefficient of atmospheric density at the target moment is predicted through a correction coefficient prediction model, thereby using a more accurate dynamic correction coefficient of atmospheric density to improve the accuracy of orbit prediction.

[0255] In one embodiment, the satellite screening module 602 is specifically configured to:

[0256] Selecting a first candidate failed satellite set whose semi-major axis is smaller than a preset semi-major axis threshold from the failed satellite set;

[0257] From the first candidate set of failed satellites, select a second candidate set of failed satellites in ascending order of eccentricity;

[0258] From the second candidate failure satellite set, a target failure satellite set is screened out in descending order of energy dissipation rate. The target failure satellite set includes multiple target failure satellites and their corresponding TLE orbit data.

[0259] In one embodiment, the ballistic coefficient determination module 604 is specifically configured to:

[0260] For any target failed satellite, perform the following operations:

[0261] Determine the satellite ephemeris data corresponding to the target failed satellite according to the TLE orbit data corresponding to the target failed satellite;

[0262] Convert satellite ephemeris data into square root semi-major axis;

[0263] The orbit control period corresponding to the target failed satellite is identified using the flat root semi-major axis, and the TLE orbit data of the target failed satellite in the orbit control period is eliminated to obtain the TLE orbit data of the target failed satellite in the non-orbit control period.

[0264] Based on the TLE orbit data of the target failed satellite during the non-orbit control period, the initial ballistic coefficient of the target failed satellite is determined every day, and the average of the initial ballistic coefficients is taken as the true ballistic coefficient corresponding to the target failed satellite.

[0265] In one embodiment, the correction coefficient solving module 606 is specifically configured to:

[0266] The initial atmospheric density value is solved based on the ballistic coefficient, initial position velocity and precision orbit data corresponding to the target failed satellite;

[0267] The initial atmospheric density dynamic correction coefficient is solved based on the initial atmospheric density value through the partial derivative equations of density with respect to position;

[0268] Determining an inflection point temperature correction value according to an initial atmospheric density dynamic correction coefficient, so as to update the atmospheric density value using the inflection point temperature correction value;

[0269] The new atmospheric density dynamic correction coefficient is solved based on the new atmospheric density value through the group of partial derivative equations of density with respect to position, until the preset iteration stop condition is met, and the final atmospheric density dynamic correction coefficient is obtained.

[0270] In one embodiment, the correction coefficient solving module 606 is specifically configured to:

[0271] Determine the current inflection point temperature and the atmospheric temperature at the target failed satellite altitude, and use the inflection point temperature correction value to correct the current inflection point temperature to obtain a new current inflection point temperature;

[0272] Determine the density values ​​corresponding to the various atmospheric components at the altitude of the target failed satellite based on the new current inflection point temperature and the atmospheric temperature;

[0273] A geomagnetic effect correction coefficient is determined, and a new atmospheric density value is determined based on the geomagnetic effect correction coefficient and the density values ​​corresponding to the atmospheric components at the altitude of the target failed satellite.

[0274] In one embodiment, the iteration stopping condition is that the coefficient deviation value is less than a preset convergence threshold, and the coefficient deviation value is calculated based on the position change matrix of the vector projection of the target failed satellite relative to the center of the earth, the density position partial derivative matrix and the current atmospheric density dynamic correction coefficient.

[0275] In one embodiment, a model training module is further included for:

[0276] The correction coefficient prediction model is used to predict the dynamic correction coefficient of atmospheric density corresponding to a specified time based on the historical correction coefficient time series data set and the historical space environment index.

[0277] According to the dynamic correction coefficient of atmospheric density corresponding to the specified time, the orbit of the target failed satellite is predicted to obtain the satellite orbit ephemeris prediction data of the target failed satellite at the specified time;

[0278] Based on the TLE orbit data corresponding to the target failed satellite, determine the true satellite orbit ephemeris data of the target failed satellite at a specified time;

[0279] Based on the satellite orbit ephemeris prediction data and the satellite orbit ephemeris true value data of the target failed satellite at a specified time, the model parameters of the correction coefficient prediction model are adjusted.

[0280] The device provided in the embodiment of the present invention has the same implementation principle and technical effects as those in the aforementioned method embodiment. For the sake of brief description, for matters not mentioned in the device embodiment, reference can be made to the corresponding content in the aforementioned method embodiment.

[0281] An embodiment of the present invention provides an electronic device. Specifically, the electronic device includes a processor and a storage device. The storage device stores a computer program, and when the computer program is executed by the processor, it executes the method described in any one of the above-mentioned embodiments.

[0282] Figure 7 A structural diagram of an electronic device provided in an embodiment of the present invention, the electronic device 100 includes: a processor 70, a memory 71, a bus 72 and a communication interface 73, wherein the processor 70, the communication interface 73 and the memory 71 are connected via the bus 72; the processor 70 is used to execute an executable module stored in the memory 71, such as a computer program.

[0283] The memory 71 may include high-speed random access memory (RAM) and may also include non-volatile memory, such as at least one disk storage. The system network element communicates with at least one other network element via at least one communication interface 73 (which may be wired or wireless), and may utilize the Internet, a wide area network, a local area network, a metropolitan area network, or the like.

[0284] The bus 72 may be an ISA bus, a PCI bus, or an EISA bus. The bus may be divided into an address bus, a data bus, a control bus, and the like. For ease of representation, Figure 7 Only one bidirectional arrow is used in the diagram, but this does not mean that there is only one bus or one type of bus.

[0285] Among them, the memory 71 is used to store programs, and the processor 70 executes the program after receiving the execution instruction. The method executed by the device for flow process definition disclosed in any embodiment of the above-mentioned embodiment of the present invention can be applied to the processor 70 or implemented by the processor 70.

[0286] The processor 70 may be an integrated circuit chip with signal processing capabilities. During implementation, each step of the above method may be completed by hardware integrated logic circuits or software instructions in the processor 70. The processor 70 may be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; it may also be a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. It may implement or execute the various methods, steps, and logic block diagrams disclosed in the embodiments of the present invention. The general-purpose processor may be a microprocessor or any conventional processor. The steps of the method disclosed in conjunction with the embodiments of the present invention may be directly implemented and executed by a hardware decoding processor, or by a combination of hardware and software modules in the decoding processor. The software module may be located in a storage medium well-known in the art, such as random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or the like. The storage medium is located in the memory 71 , and the processor 70 reads the information in the memory 71 and completes the steps of the above method in combination with its hardware.

[0287] The computer program product of the readable storage medium provided in the embodiment of the present invention includes a computer-readable storage medium storing program code. The instructions included in the program code can be used to execute the method described in the previous method embodiment. The specific implementation can be referred to the previous method embodiment and will not be repeated here.

[0288] If the functions are implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for enabling a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes various media that can store program codes, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk.

[0289] Finally, it should be noted that the above-described embodiments are only specific implementation methods of the present invention, which are used to illustrate the technical solutions of the present invention, rather than to limit them. The scope of protection of the present invention is not limited thereto. Although the present invention has been described in detail with reference to the above-described embodiments, those skilled in the art should understand that any person skilled in the art can modify or easily conceive of changes to the technical solutions described in the above-described embodiments within the technical scope disclosed by the present invention, or replace some of the technical features therein with equivalents. Such modifications, changes, or replacements do not deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should be included in the scope of protection of the present invention. Therefore, the scope of protection of the present invention shall be subject to the scope of protection of the claims.

Claims

1. A trajectory prediction method based on dynamic correction of atmospheric density, characterized in that: include: Determine multiple target failed satellites and their corresponding TLE orbit data from the failed satellite set; Identifying an orbital control period corresponding to the target inoperative satellite, and determining a true ballistic coefficient corresponding to the target inoperative satellite based on TLE orbit data of the target inoperative satellite in a non-orbital control period; According to the true ballistic coefficient corresponding to the target failed satellite, combined with the density with respect to the position partial derivative equation group, a correction coefficient time series data set is iteratively solved, wherein the correction coefficient time series data set includes a multi-dimensional time series of atmospheric density dynamic correction coefficients; The correction coefficient prediction model obtained in advance is used to predict the dynamic correction coefficient of atmospheric density corresponding to the target time based on the correction coefficient time series data set and the space environment index; The orbit of the satellite to be predicted is predicted according to the dynamic correction coefficient of the atmospheric density corresponding to the target time, and the satellite orbit ephemeris prediction data corresponding to the satellite to be predicted is obtained.

2. The orbit prediction method based on dynamic correction of atmospheric density according to claim 1, characterized in that: Determine multiple target failed satellites and their corresponding TLE orbit data from the failed satellite set, including: Selecting a first candidate failed satellite set from the failed satellite set whose semi-major axis is smaller than a preset semi-major axis threshold; Selecting a second candidate set of failed satellites from the first candidate set of failed satellites in ascending order of eccentricity; From the second candidate failure satellite set, a target failure satellite set is screened out in descending order of energy dissipation rate, where the target failure satellite set includes multiple target failure satellites and their corresponding TLE orbit data.

3. The orbit prediction method based on dynamic correction of atmospheric density according to claim 1, characterized in that: Identifying the orbital control period corresponding to the target inoperative satellite, and determining the true ballistic coefficient corresponding to the target inoperative satellite based on the TLE orbit data of the target inoperative satellite in the non-orbital control period, includes: For any of the target failed satellites, perform the following operations: Determine the satellite ephemeris data corresponding to the target failed satellite according to the TLE orbit data corresponding to the target failed satellite; Converting the satellite ephemeris data into a square root semi-major axis; Identifying the orbital control period corresponding to the target failed satellite using the flat root semi-major axis, and removing the TLE orbital data of the target failed satellite in the orbital control period to obtain the TLE orbital data of the target failed satellite in the non-orbital control period; Based on the TLE orbit data of the target failed satellite in the non-orbit control period, the initial ballistic coefficient of the target failed satellite is determined on each day, and the average of the initial ballistic coefficients is used as the true ballistic coefficient corresponding to the target failed satellite.

4. The orbit prediction method based on dynamic correction of atmospheric density according to claim 1, characterized in that: According to the actual ballistic coefficient corresponding to the target failed satellite, combined with the density with respect to the position partial derivative equation group, iteratively solving the correction coefficient time series data set includes: Calculating an initial atmospheric density value based on the ballistic coefficient, initial position velocity, and precision orbit data corresponding to the target failed satellite; Solving the initial atmospheric density dynamic correction coefficient based on the initial atmospheric density value through a group of density-position partial derivative equations; determining an inflection point temperature correction value according to the initial atmospheric density dynamic correction coefficient, so as to update the atmospheric density value using the inflection point temperature correction value; The new atmospheric density dynamic correction coefficient is solved based on the new atmospheric density value through the density position partial derivative equation group until the preset iteration stop condition is met to obtain the final atmospheric density dynamic correction coefficient.

5. The orbit prediction method based on dynamic correction of atmospheric density according to claim 4, characterized in that: Updating the atmospheric density value using the inflection point temperature correction value includes: Determining a current inflection point temperature and an atmospheric temperature at the altitude of the target failed satellite, and correcting the current inflection point temperature using the inflection point temperature correction value to obtain a new current inflection point temperature; Determining density values ​​corresponding to various atmospheric components at the altitude of the target failed satellite based on the new current inflection point temperature and the atmospheric temperature; A geomagnetic effect correction coefficient is determined, and a new atmospheric density value is determined based on the geomagnetic effect correction coefficient and the density values ​​corresponding to the atmospheric components at the altitude of the target failed satellite.

6. The orbit prediction method based on dynamic correction of atmospheric density according to claim 4, characterized in that: The iteration stopping condition is that the coefficient deviation value is less than a preset convergence threshold, and the coefficient deviation value is calculated based on the position change matrix of the vector projection of the target failed satellite relative to the center of the earth, the density-to-position partial derivative matrix and the current atmospheric density dynamic correction coefficient.

7. The orbit prediction method based on dynamic correction of atmospheric density according to claim 1, characterized in that: The training step of the correction coefficient prediction model includes: Using a correction coefficient prediction model, based on the historical correction coefficient time series data set and the historical space environment index, the dynamic correction coefficient of atmospheric density corresponding to a specified time is predicted; performing orbit prediction for the target inoperative satellite according to the atmospheric density dynamic correction coefficient corresponding to the designated time, and obtaining satellite orbit ephemeris prediction data of the target inoperative satellite at the designated time; Determining true satellite orbit ephemeris data of the target failed satellite at the specified time based on the TLE orbit data corresponding to the target failed satellite; Based on the satellite orbit ephemeris prediction data and the satellite orbit ephemeris true value data of the target failed satellite at the specified time, the model parameters of the correction coefficient prediction model are adjusted.

8. An orbit prediction device based on dynamic correction of atmospheric density, characterized in that: include: A satellite screening module is used to determine multiple target failed satellites and their corresponding TLE orbit data from the failed satellite set; a ballistic coefficient determination module, configured to identify an orbital control period corresponding to the target inoperative satellite, and determine a true ballistic coefficient corresponding to the target inoperative satellite based on the TLE orbit data of the target inoperative satellite in the non-orbital control period; a correction coefficient solving module, configured to iteratively solve a correction coefficient time series data set based on the true ballistic coefficient corresponding to the target failed satellite and a group of density-position partial derivative equations, wherein the correction coefficient time series data set includes a multidimensional time series of atmospheric density dynamic correction coefficients; A correction coefficient prediction module is used to predict the atmospheric density dynamic correction coefficient corresponding to the target time based on the correction coefficient time series data set and the space environment index using a pre-trained correction coefficient prediction model; The orbit prediction module is used to perform orbit prediction on the satellite to be predicted based on the dynamic correction coefficient of atmospheric density corresponding to the target time, and obtain satellite orbit ephemeris prediction data corresponding to the satellite to be predicted.

9. An electronic device, characterized in that: The method comprises a processor and a memory, wherein the memory stores computer-executable instructions that can be executed by the processor, and the processor executes the computer-executable instructions to implement the method according to any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that The computer-readable storage medium stores computer-executable instructions. When the computer-executable instructions are called and executed by a processor, the computer-executable instructions prompt the processor to implement the method according to any one of claims 1 to 7.

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