Space-based Observation Constellation Orbit Design Method, Equipment, Medium and Product for Low-Earth Orbit Satellite Targets

Abstract

A method, device, medium and product for the orbital design of a space-based observation constellation for low-Earth orbit satellite targets belong to the technical field of space target detection, and solve the problem of low applicability of existing observation constellations. The method of the present invention includes: conducting orbital analysis based on on-orbit low-Earth orbit space targets, establishing the coverage rate of key performance indicators for multi-star observation for the low-Earth orbit observation constellation, proposing an optimized idea for the orbital design of the observation star cluster, determining to use the sun-synchronous dawn-dusk orbit as the observation orbit for optimization, and performing orbital design optimization with an optimization method combining stratified random sampling and adaptive genetic algorithm. The present invention relates to an orbital design and optimization technology and a feasible solution for a space-based observation constellation for low-Earth orbit satellite targets, and is applicable to space target detection.

Description

Technical Field

[0001] This application relates to the technical field of space target detection, and particularly to the orbital design of a space-based observation constellation for low-Earth orbit satellite targets. Background Art

[0002] Currently, the United States and Canada are the countries that have launched the most long-distance optical observation satellites for space targets. Most of the observation satellites they launched are low-Earth orbit satellites, and most of them are in sun-synchronous orbits, followed by polar orbits and general inclined orbits. Among them, the United States Space-Based Space Surveillance System is a constellation composed of more than 4 optical observation satellites, and the first satellite SBSS-1 was put into orbit in 2010. The United States Space-Based Infrared System is expected to launch a constellation composed of 20-40 low-Earth orbit satellites, and three precursor satellites have been launched in 2009. Generally speaking, at present, the foreign long-distance optical observation of space targets has experienced the payload test stage and the single-satellite in-orbit stage. The future development direction is multi-satellite networking, and the orbital types of these observation satellites are mainly sun-synchronous orbits and low-Earth orbit general inclined orbits.

[0003] For the visible light observation of low-Earth orbit satellite targets, the observation distance is generally several hundred kilometers. Due to the high speed of low-Earth orbit targets, which are distributed in the entire spherical space at different altitudes, it is very challenging to observe and revisit all low-Earth orbit targets. Summary of the Invention

[0004] The purpose of the present invention is to solve the problem of low applicability of existing observation constellations, especially the difficulty of observing and revisiting all low-Earth orbit targets, and provide a method, device, medium and product for the orbital design of a space-based observation constellation for low-Earth orbit satellite targets.

[0005] The present invention is achieved through the following technical solutions. On the one hand, the present invention provides a method for the orbital design of a space-based observation constellation for low-Earth orbit satellite targets, and the method includes:

[0006] Step 1: Stratified sampling is used to select sample low-Earth orbit satellite targets;

[0007] Step 2: Use the multi-variable adaptive genetic algorithm to obtain the constellation orbit with the maximum target coverage rate, specifically including:

[0008] Step 2.1: The orbit of the observation satellite is selected as the sun-synchronous dawn-dusk orbit, and the optimization variables are determined;

[0009] Step 2.2: Determine the optimization constraint conditions of the genetic algorithm;

[0010] Step 2.3: Determine the objective function, and the objective function is to maximize the target coverage ratio, specifically:

[0011] max J = P cov

[0012] P cov is the coverage rate, which refers to the ratio of the number of space targets N that can be observed by the observation satellite (group) within a specified time period obs to the total number of targets N all ;

[0013] Step 2.4: Obtain the optimal solution using the multi-mutation-site adaptive genetic algorithm;

[0014] Step 3: Determine the six orbital elements of each satellite in the constellation through the optimal solution, and complete the orbital design that meets the maximum target coverage rate.

[0015] Furthermore, Step 1 specifically includes:

[0016] Step 1.1: Conduct stratification based on orbital characteristics, including:

[0017] Classify according to the orbital inclination, determine that the sun-synchronous orbit layer is the first layer, the polar orbit layer is the second layer, the general orbit with an orbital inclination between 50 and 55 degrees is the third layer, and the remaining other orbits are the fourth layer, and determine the total sample quantity of each layer;

[0018] Step 1.2: Determine the sample size of each layer, including: determining the sample size of each layer according to the ratio between the total sample quantities of each sample layer.

[0019] Furthermore, the optimization variables in Step 2.1 include: the orbital inclination, true anomaly, right ascension of the ascending node, number of orbits, and number of satellites in each orbit of a satellite on the jth orbital plane.

[0020] Furthermore, the optimization variables in Step 2.1 include: the orbital inclination, true anomaly, and right ascension of the ascending node of a satellite on the jth orbital plane.

[0021] Furthermore, Step 2.2 specifically includes:

[0022] The constraint for the target observation time is

[0023] t0 ≤ t ≤ t f

[0024] where t0 is the start time of observation, t f is the end time of observation, and t is the target observation time;

[0025] The constraints of orbital elements and the number of satellites are

[0026]

[0027] where i o , f o , Ω oare the orbital inclination, true anomaly, and right ascension of the ascending node of the satellite to be optimized, f o min , are the minimum orbital inclination, true anomaly, and right ascension of the ascending node during optimization; f o max , are the maximum orbital inclination, true anomaly, and right ascension of the ascending node during optimization; is the maximum total number of satellites during optimization, k is the orbital elements, and n is the number of satellites in each orbit.

[0028] Furthermore, step 2.4 specifically includes:

[0029] Step 2.4.1, population initialization, including: generating a specific number of variable populations that meet the requirements in a random manner according to the optimization variables and the genetic algorithm optimization constraints;

[0030] Step 2.4.2, fitness calculation, including: calculating the fitness of all individuals in the population using the objective function;

[0031] Step 2.4.3, genetic operations, including: replication, crossover, and mutation, to obtain new individuals for the next generation population;

[0032] Step 2.4.4, through continuous iteration of the processes in step 2.4.2 and step 2.4.3, recalculate the fitness of the next generation individuals. After iterating to the set maximum number of generations, the iteration ends, and the individual with the maximum fitness is the optimal solution of the genetic algorithm.

[0033] Furthermore, step 3 specifically includes:

[0034] According to the uniform distribution of satellites on the same orbital plane, determine that the true anomalies of the n satellites on each orbit differ by (360 / n)°;

[0035] Based on the true anomaly of one satellite, obtain the true anomalies of all satellites on the same orbit;

[0036] According to the constellation orbit selection of the sun-synchronous dawn-dusk orbit, determine that the eccentricity e of all satellite orbits is 0, the argument of perigee ω is also 0, and the determination relationship between the semi-major axis a of the orbit and the orbital inclination i;

[0037] Through the optimal solution, determine the six orbital elements of each satellite in the constellation, obtain the orbital data of all observation satellites in the observation constellation, and complete the orbital design that meets the target maximum coverage rate.

[0038] In a second aspect, the present invention provides a computer device, including a memory and a processor. A computer program is stored in the memory. When the processor runs the computer program stored in the memory, the steps of a method for designing an orbit of a space-based observation constellation for low-Earth orbit satellite targets as described above are executed.

[0039] In a third aspect, the present invention provides a computer-readable storage medium. Multiple computer instructions are stored in the computer-readable storage medium. The multiple computer instructions are used to cause a computer to execute a method for designing an orbit of a space-based observation constellation for low-Earth orbit satellite targets as described above.

[0040] In a fourth aspect, the present invention provides a computer program product. When the computer program is executed by a processor, a method for designing an orbit of a space-based observation constellation for low-Earth orbit satellite targets as described above is implemented.

[0041] Advantages of the present invention:

[0042] To enhance the applicability of the observation constellation, the present invention focuses on improving the coverage rate of all space targets, and researches and designs a design technology and a feasible solution for an observation constellation that further considers improving the observable rate of key targets.

[0043] Space-based observation of low-Earth orbit targets can perform target orbit determination by only measuring angles. Compared with ground-based detection, space-based target observation has advantages such as a wide coverage range and no geographical restrictions. At the same time, the revisit characteristics can be improved by adjusting the orbits of the observation satellites.

[0044] Based on the orbit analysis of on-orbit low-Earth orbit space targets, the present invention establishes a key performance index coverage rate for multi-star observation for a low-Earth orbit observation constellation, proposes an optimization idea for the orbit design of an observation satellite group, determines to use a sun-synchronous dawn-dusk orbit as the observation orbit for optimization, and uses an optimization method combining stratified random sampling and an adaptive genetic algorithm for orbit design optimization.

[0045] In the process of orbit design optimization, it is possible to achieve an orbit design with a high coverage rate for targets with a small computational burden and prove the effectiveness of the algorithm. Two design schemes for the distribution of orbital planes are obtained. The scheme with two orbital planes is suitable for single-star observation and is more conducive to the convergence of single-star observation; the three-orbital-plane scheme is more suitable for multi-star observation and can provide a higher double coverage rate.

[0046] The present invention relates to an orbit design and optimization technology and a feasible solution for a space-based observation constellation for low-Earth orbit satellite targets, and is applicable to the technical field of space target detection. Description of the Drawings

[0047] To more clearly illustrate the technical solutions of this application, the following will briefly introduce the attached drawings required in the embodiments. Obviously, for those of ordinary skill in the art, without creative efforts, other attached drawings can also be obtained based on these drawings.

[0048] Figure 1 Schematic diagram of the calculation process of the two-orbit surface genetic algorithm of the present invention;

[0049] Figure 2 Schematic diagram of the calculation process of the three-orbit surface genetic algorithm of the present invention. Specific embodiments

[0050] The following details the embodiments of the present invention. The examples of the embodiments are shown in the attached drawings, where the same or similar reference numerals represent the same or similar elements or elements with the same or similar functions throughout. The embodiments described below with reference to the attached drawings are exemplary and are intended to explain the present invention, and should not be construed as limiting the present invention.

[0051] Specific embodiment 1. A method for designing the orbit of a space-based observation constellation for low-earth orbit satellite targets, the method comprising:

[0052] Step 1. Select sample low-earth orbit satellite targets by stratified sampling;

[0053] Step 2. Use the multi-mutation-site adaptive genetic algorithm to obtain the constellation orbit with the maximum target coverage rate, specifically including:

[0054] Step 2.1. Select the sun-synchronous dawn-dusk orbit for the observation satellite orbit and determine the optimization variables;

[0055] Step 2.2. Determine the optimization constraint conditions of the genetic algorithm;

[0056] Step 2.3. Determine the objective function, where the objective function is to maximize the target coverage ratio, specifically:

[0057] max J = P cov

[0058] P cov is the coverage rate, which refers to the ratio of the number of space targets N obs that can be observed by the observation satellite (group) within a specified time period all to the total number of targets N;

[0059] Step 2.4. Use the multi-mutation-site adaptive genetic algorithm to obtain the optimal solution;

[0060] Step 3. Through the optimal solution, determine the six orbital elements of each satellite in the constellation to complete the orbit design that meets the maximum target coverage rate.

[0061] In this embodiment, orbital analysis is carried out based on low-earth-orbit space targets in orbit. For a low-earth-orbit observation constellation, the coverage rate of key performance indicators for multi-star observation is established. An optimized idea for the orbital design of the observation star cluster is proposed. It is determined to use a sun-synchronous dawn-dusk orbit as the observation orbit for optimization, and an optimization method combining stratified random sampling and adaptive genetic algorithm is used for orbital design optimization.

[0062] Embodiment 2: This embodiment further limits a method for orbital design of a low-earth-orbit satellite target space-based observation constellation described in Embodiment 1. In this embodiment, Step 1 is further limited, specifically including:

[0063] Step 1 specifically includes:

[0064] Step 1.1: Stratify based on orbital characteristics, including:

[0065] Classify according to the orbital inclination. Determine that the sun-synchronous orbit layer is the first layer, the polar orbit layer is the second layer, the general orbit with an orbital inclination between 50 and 55 degrees is the third layer, and the remaining other orbits are the fourth layer, and determine the total sample size of each layer.

[0066] In this embodiment, Step 1.1 can effectively suppress the uneven distribution of parameters in the sampling population, thereby reducing the differences between units, and can improve the accuracy of sampling through independent random sampling.

[0067] Step 1.2: Determine the sample size of each layer, including: Determine the sample size of each layer according to the ratio between the total sample sizes of each sample layer.

[0068] In this embodiment, in Step 1.2, according to the characteristics of the low-earth target orbit, it is more appropriate to use the relative error limit for estimating the accuracy requirement and the proportional allocation for the allocation strategy.

[0069] Embodiment 3: This embodiment further limits a method for orbital design of a low-earth-orbit satellite target space-based observation constellation described in Embodiment 1. In this embodiment, the optimization variables in Step 2.1 are further limited, specifically including:

[0070] The optimization variables in Step 2.1 include: the orbital inclination, true anomaly, right ascension of the ascending node, number of orbits, and number of satellites in each orbit of a satellite on the jth orbital plane.

[0071] In this embodiment, in order to ensure that during the entire mission period, the observation of the target can meet the solar angle constraint conditions and maintain the same solar illumination conditions as much as possible, the best candidate orbit for the observation star is the sun-synchronous dawn-dusk orbit. These special orbits utilize the influence of the earth's oblateness (i.e., the J2 effect) so that the orbital precession is synchronized with the rotation of the sun direction on the equator throughout the year.

[0072] Using a sun-synchronous dawn-dusk orbit has actually determined the eccentricity. Therefore, for each satellite, the optimization variables are the satellite orbit inclination and the true anomaly. For the entire satellite constellation, referring to the design method of the Walker constellation, the satellites are evenly distributed on each orbital plane and the number of satellites is the same. Therefore, the optimization variables are the number of satellites per orbit and the number of orbits.

[0073] Specific Embodiment 4: This embodiment further limits the method for designing the orbit of a low-earth orbit satellite target space-based observation constellation described in Embodiment 1. In this embodiment, the optimization variables in Step 2.1 are further limited, specifically including:

[0074] The optimization variables in Step 2.1 include: the orbit inclination, the true anomaly, and the right ascension of the ascending node of a satellite on the j-th orbital plane.

[0075] In this embodiment, when using the genetic algorithm, the dimension of the optimization variables needs to be determined, so the number of orbits needs to be determined. After determining the number of orbits and the total number of satellites, the optimization variables are finally simplified and determined as the orbit inclination per orbit, the right ascension of the ascending node, and the initial phase distribution of the satellites. Usually, when designing the constellation, the number of orbits k and the number of satellites per orbit n are determined in advance. It can ensure that during the entire mission period, the observation of the target can meet the solar angle constraint conditions and maintain the same solar illumination conditions as much as possible.

[0076] Specific Embodiment 5: This embodiment further limits the method for designing the orbit of a low-earth orbit satellite target space-based observation constellation described in Embodiment 4. In this embodiment, Step 2.2 is further limited, specifically including:

[0077] Step 2.2 specifically includes:

[0078] The constraint for the target observation time is

[0079] t0 ≤ t ≤ t f

[0080] where t0 is the start time of the observation, t f is the end time of the observation, and t is the target observation time;

[0081] The orbital element constraints and the satellite number constraints are

[0082]

[0083] where i o , f o , Ω o are the orbit inclination, the true anomaly, and the right ascension of the ascending node of the satellite to be optimized, f omin , are the minimum orbital inclination, true anomaly, and right ascension of the ascending node at the time of optimization; f o max , are the maximum orbital inclination, true anomaly, and right ascension of the ascending node at the time of optimization; is the maximum total number of satellites at the time of optimization, k is the orbital elements, and n is the number of satellites in each orbit.

[0084] Specific Embodiment Six, this embodiment further limits the method for designing the orbit of a low-earth orbit satellite target space-based observation constellation described in Embodiment One. In this embodiment, Step 2.4 is further limited, specifically including:

[0085] Step 2.4 specifically includes:

[0086] Step 2.4.1, population initialization, including: generating a variable population of a specific quantity and scale that meets the requirements in a random generation manner according to the optimization variables and the genetic algorithm optimization constraints;

[0087] Step 2.4.2, fitness calculation, including: calculating the fitness of all individuals in the population using the objective function;

[0088] Step 2.4.3, genetic operations, including: replication, crossover, and mutation to obtain new individuals of the next generation population;

[0089] Step 2.4.4, through continuous iteration of the processes in Step 2.4.2 and Step 2.4.3, recalculate the fitness of the next generation individuals. After iterating to the set maximum number of evolutionary generations, the iteration ends, and the individual with the maximum fitness is the optimal solution of the genetic algorithm.

[0090] In this embodiment, when using the genetic algorithm, it is necessary to determine the dimension of the optimization variables, so it is necessary to determine the number of orbits. For example, two optimization schemes can be designed. One optimization scheme is a two-orbit plane, and the other scheme is a three-orbit plane; at the same time, determine the maximum number of observation stars. The maximum number of satellites in both schemes is 12. The most significant advantage of using the genetic algorithm is global optimality, which means that the genetic algorithm can avoid the limitation that the optimal solution obtained by other optimization algorithms is only a local optimum as much as possible. Using a set of candidate solutions, that is, the population, and maintaining the diversity of the population through means such as crossover and mutation can avoid the entire population from "converging" prematurely and is more likely to reach the global optimum.

[0091] Specific Embodiment Seven, this embodiment further limits the method for designing the orbit of a low-earth orbit satellite target space-based observation constellation described in Embodiment One. In this embodiment, Step 3 is further limited, specifically including:

[0092] Step 3 specifically includes:

[0093] According to the uniform distribution of satellites on the same orbital plane, determine that the true anomaly of the n satellites on each orbit differs by (360 / n)°.

[0094] Based on the true anomaly of one satellite, obtain the true anomalies of all satellites on the same orbit.

[0095] Select a sun-synchronous dawn-dusk orbit according to the constellation orbit, determine that the eccentricity e of all satellite orbits is 0, the argument of perigee ω is also 0, and the determination relationship between the semi-major axis a of the orbit and the orbital inclination i.

[0096] Through the optimal solution, determine the six orbital elements of each satellite in the constellation, obtain the orbital data of all observed satellites in the observed constellation, and complete the orbital design that meets the target maximum coverage rate.

[0097] In this embodiment, after obtaining the optimal solution, according to the relationship between the orbital elements of the satellites in the sun-synchronous dawn-dusk orbit and the characteristics of the uniform distribution of satellites on the same orbital plane, obtain the orbits of all observed satellites in the observed constellation.

[0098] Specific Embodiment 8. This embodiment is an embodiment 1 of a method for designing the orbit of a low-earth orbit satellite target space-based observation constellation as described above, specifically including:

[0099] 1. Stratified sampling to select sample low-earth orbit satellite targets

[0100] Stratified sampling can obtain a stratified sampling sample with a quantity much smaller than the total sample, and can effectively suppress the uneven distribution of parameters in the sampling population, thereby reducing the differences between units, and can improve the accuracy of sampling through independent random sampling. Design and optimize the observation satellite constellation based on the sample low-earth orbit satellite targets obtained by stratified sampling.

[0101] Stratify based on orbital characteristics:

[0102] Based on the known orbital characteristics of low-earth targets, stratify the space targets. In the present invention, classification is carried out according to the orbital inclination, and it is divided into a sun-synchronous orbit layer (Layer 1), a polar orbit layer (Layer 2), a general orbit with an orbital inclination between 50 and 55 degrees (Layer 3), and the remaining other orbits (Layer 4).

[0103] Determine the sample size of each layer;

[0104] According to the characteristics of the low-earth target orbit, it is more appropriate to use the relative error limit for the estimation accuracy requirement and the proportional allocation for the allocation strategy, that is, determine the sample size of each layer according to the ratio between the total amounts of each sample layer.

[0105] 2. Multi-Mutation Adaptive Genetic Algorithm

[0106] Determination of optimization variables:

[0107] To ensure that during the entire mission, the observation of the target can meet the solar angle constraint conditions and maintain the same solar illumination conditions as much as possible, the best candidate orbit for the observation satellite is the sun-synchronous dawn-dusk orbit. These special orbits utilize the influence of the Earth's oblateness (i.e., the J2 effect) so that the orbital precession is synchronized with the rotation of the sun's direction on the equator throughout the year.

[0108] Using the sun-synchronous dawn-dusk orbit has actually determined the eccentricity. Therefore, for each satellite, the optimization variables are the satellite's orbital inclination and true anomaly. For the entire satellite constellation, referring to the design method of the Walker constellation, the satellites are evenly distributed on each orbital plane and the number of satellites is the same. Thus, the optimization variables are the number of satellites per orbit and the number of orbits.

[0109] When using the genetic algorithm, the dimension of the optimization variables needs to be determined, so the number of orbits needs to be determined. After determining the number of orbits and the total number of satellites, the optimization variables are finally simplified and determined as the orbital inclination per orbit, the right ascension of the ascending node, and the initial phase distribution of the satellites.

[0110] Genetic algorithm calculation:

[0111] Use the multi-mutation adaptive genetic algorithm for calculation to obtain the optimal solution of the optimization variables. According to the optimal solution, the orbital parameters of the optimal constellation can be solved, that is, the orbital design and optimization of the constellation are completed.

[0112] For single-satellite observation and multi-satellite observation, two types of constellation orbits are designed and optimized respectively. The number of observation satellites for both constellations is 12, which are distributed on two orbital planes and three orbital planes respectively.

[0113] Specific implementation method IX. This implementation method is an embodiment 2 of the method for designing the orbit of a low-earth orbit satellite target space-based observation constellation described above, specifically including:

[0114] Step 1: Stratify based on orbital characteristics

[0115] Based on the known orbital characteristics of low-earth orbit targets, the space targets are stratified. In the present invention, they are classified according to the orbital inclination into the sun-synchronous orbit layer (Layer 1), the polar orbit layer (Layer 2), the general orbit with an orbital inclination between 50 and 55 degrees (Layer 3), and the remaining other orbits (Layer 4), and the total sample quantity of each layer is determined. As shown in the following target stratification table:

[0116] Target Stratification Table

[0117] Layer serial number (h) Orbit type <![CDATA[Total number of samples in the h-th layer (N h )]]> 1 Sun-synchronous orbit 1790 2 Polar orbit 717 3 General orbit with 50 < i < 55 (deg) 3146 4 Other general orbits 1117

[0118] Step 2: Determine the sample size of each layer

[0119] According to the characteristics of the low-earth target orbit, it is more appropriate to use the relative error limit for the estimation accuracy requirement and the proportional allocation for the allocation strategy, that is, to determine the sample size of each layer according to the ratio between the total amounts of each sample layer.

[0120] Perform stratified sampling on the target, determine that the total sample size is 100, and use the proportional allocation method to determine the sample size of each layer. Then, according to the total sample size in Table 3, the sample sizes of the targets in each layer are 26, 11, 46, and 17 respectively. The random sampling method is used to determine the orbit of the target in each layer.

[0121] Step 3: Determine the optimization variables

[0122] To ensure that during the entire mission period, the observation of the target can meet the solar angle constraint conditions and maintain the same solar illumination conditions as much as possible, the orbit of the observation satellite is selected as the sun-synchronous dawn-dusk orbit. There is a certain relationship between the six orbital elements of this orbit::

[0123]

[0124]

[0125] e = 0

[0126] In the formula, H is the orbital altitude, is the rotational angular velocity of the sun relative to the ECI coordinate system( The value of is -1.99×10 -7 rad / s), μ e is the earth's gravitational constant (μ e takes 398600.4415 km 3 / s 2 ), a, e, and i are the orbital semi-major axis, eccentricity, and orbital inclination respectively, R e is the earth's radius, and J2 is the second-order zonal harmonic coefficient.

[0127] According to the relationship between the six orbital elements in the sun-synchronous dawn-dusk orbit, the orbital semi-major axis a can be obtained from the orbital inclination i, and the orbital eccentricity e is a constant 0. Therefore, the argument of perigee ω is also 0. Thus, for each satellite orbit, only the satellite orbital inclination i, the true anomaly f, and the right ascension of the ascending node Ω need to be determined to determine the satellite's orbit. For the entire satellite constellation, in addition to optimizing the orbital variables of each satellite, the number of satellites n in each orbit and the number of orbits k also need to be optimized. However, since the satellites on each orbital plane are evenly distributed, only the orbit of one satellite on each orbital plane needs to be determined to determine the orbits of all the other satellites on that orbital plane.

[0128] Therefore, the optimization vector of the entire constellation can be expressed as where j = k. are the orbital inclination, true anomaly, and right ascension of the ascending node of a satellite on the j-th orbital plane respectively. Usually, the number of orbits k and the number of satellites n per orbit are predetermined during constellation design. Therefore, the optimization vector can be simplified to Step 4: Determine the optimization constraints of the genetic algorithm

[0129] The constraint for the target observation time is

[0130] t0 ≤ t ≤ t f

[0131] where t0 is the start time of observation, and t f is the end time of observation;

[0132] The orbital element constraints and satellite number constraints are

[0133]

[0134] where f o min , are the minimum orbital inclination, true anomaly, and right ascension of the ascending node during optimization; f o max , are the maximum orbital inclination, true anomaly, and right ascension of the ascending node during optimization; is the maximum total number of satellites during optimization.

[0135] Step 5: Determine the objective function

[0136] The objective function is to maximize all possible target coverage ratios.

[0137] max J = P cov

[0138] P cov : Coverage rate, which refers to the ratio of the number of space targets N obs that can be observed by the observing satellite(s) during a specified time period to the total number of targets N all .

[0139] Step 6: Calculate the optimal solution using the multi-mutation position adaptive genetic algorithm

[0140] When using the genetic algorithm, the dimension of the optimization variables needs to be determined. Therefore, the number of orbits needs to be determined. Two optimization schemes are designed. One optimization scheme is a two-orbital-plane scheme, and the other is a three-orbital-plane scheme. At the same time, the maximum number of observing satellites is determined. The maximum number of satellites in both schemes is 12.

[0141] After setting the constraint conditions, use the genetic algorithm for calculation.

[0142] The calculation process of the genetic algorithm is briefly introduced as follows:

[0143] 1) Population initialization. According to the optimization variables and the optimization constraint conditions of the genetic algorithm, a variable population of a specific quantity and scale that meets the requirements is generated by means of random generation.

[0144] 2) Fitness calculation. Use the objective function maxJ to calculate the fitness of all individuals in the population.

[0145] 3) Genetic operations. Include replication, crossover, and mutation. Replication is to select individuals with high fitness from the current population and directly inherit them to the next generation of individuals; crossover is to control the generation of new crossover individuals with a certain set crossover constant; and mutation is to reverse the original gene of the mutation point according to the mutation constant for the randomly generated mutation point to obtain a new individual. Through the above three operations, the individuals of the new next-generation population are obtained.

[0146] Recalculate the fitness of the next-generation individuals, that is, the processes of 2) and 3) are continuously iterated. After iterating to the set maximum number of evolutionary generations, the iteration ends. The individual with the maximum fitness obtained is the optimal solution of the genetic algorithm, that is, the constellation orbit with the largest target coverage rate.

[0147] Step 7: Obtain the observation constellation that meets the conditions through the optimal solution

[0148] After obtaining the optimal solution, according to the relationship between the orbital elements of the satellites in the sun-synchronous dawn-dusk orbit and the characteristic of uniform distribution of the satellites on the same orbital plane, the orbits of all the observation satellites in the observation constellation are obtained.

[0149] The optimal solution obtained by the genetic algorithm is presented in the form of optimization variables , that is, the orbital inclination, true anomaly, and right ascension of the ascending node of a satellite on each orbital plane of the constellation with the largest target coverage rate. Since the satellites on the same orbital plane are evenly distributed, the true anomalies of the n satellites on each orbit differ by (360 / n)°. Knowing the true anomaly of one satellite, the true anomalies of all the satellites on the same orbit can be known; and since the constellation orbit selects the sun-synchronous dawn-dusk orbit, the eccentricity e of all the satellite orbits is 0, the argument of perigee ω is also 0, and the semi-major axis a of the orbit has a definite relationship with the orbital inclination i (see the steps for determining the optimization variables). Therefore, through the optimal solution, the six orbital elements of each satellite in the constellation can be determined, that is, the orbital design optimization to meet the maximum target coverage rate is completed.

[0150] (1), Embodiment of two orbital planes:

[0151] Under the condition of two orbital planes, Take 12, with 6 observation stars on each orbital plane, and the optimization variables are The remaining constraint conditions are as shown in Table 1 below:

[0152] Table 1 Constraint parameter settings for two orbital planes

[0153]

[0154] Use the multi-mutation position adaptive genetic algorithm, and the algorithm parameter settings are as shown in Table 2 below:

[0155] Table 2 Genetic algorithm parameter settings

[0156] Parameter Value Coding type Real number Population size 30 Maximum number of generations for evolution 30 Hybridization constant 1 0.6 Hybridization constant 2 0.9 Mutation constant 1 0.01 Mutation constant 2 0.06 Variable discretization precision 0.1

[0157] The calculation process of the genetic algorithm is as Figure 1 , and the optimal solution obtained is:

[0158] x = [97.27, 0.25, 101.152401499558, 97.08, 45.51, 93.52]

[0159] The target coverage rate for the sampling target is 88%. According to the optimal solution, the orbital parameters of all satellites in the two-orbital-plane constellation are as shown in Table 3 below.

[0160] Table 3: Orbits of the two-orbital-plane observation constellation

[0161]

[0162] (2) Example of three orbital planes:

[0163] Adopt the design scheme of observation satellites with three orbital planes, Take 12, with 4 observation stars on each orbital plane, and still adopt the uniform distribution method. Optimize the orbital inclination, right ascension of the ascending node, and true anomaly of the satellite for each orbit, that is The constant values of the remaining constraint conditions are selected as shown in Table 4 below:

[0164] Table 4 Constraint parameter settings for the three-orbital-plane constellation

[0165]

[0166] Under the above constraint conditions, use the multi-mutation position adaptive genetic algorithm, and the algorithm parameter settings are as shown in Table 2. The calculation process is as Figure 2 , and the optimal solution obtained is:

[0167] x = [97.63, 51.09, 36.06, 98.53, 9.12, 108.23, 97.20, 56.98, 253.27]

[0168] The target coverage rate corresponding to the optimal solution is 88%. According to the optimal solution, the orbital parameters of all satellites in the three-orbit-plane constellation are shown in Table 5.

[0169] Table 5: Orbits of the three-orbit-plane observation constellation

[0170]

Claims

1. A method for designing the orbit of a space-based observation constellation for low-Earth orbit satellite targets, characterized in that, The method includes: Step 1: Select sample low-orbit satellite targets by stratified sampling; Step 2: Use the multi-variable adaptive genetic algorithm to obtain the constellation orbit with the maximum coverage of the targets, specifically including: Step 2.1: Select the sun-synchronous dawn-dusk orbit for the observation satellite orbit and determine the optimization variables; Step 2.2: Determine the optimization constraints of the genetic algorithm; Step 2.3: Determine the objective function, and the objective function is to achieve the maximum coverage of the targets, specifically: max J = P cov P cov is the coverage rate, which refers to the ratio of the number of space targets N obs that can be observed by an observation satellite or a satellite constellation within a specified time period all to the total number of targets N; Step 2.4: Obtain the optimal solution by the multi-variable adaptive genetic algorithm; Step 3: Determine the six orbital elements of each satellite in the constellation through the optimal solution, and complete the orbital design that meets the maximum coverage of the targets; Step 1 specifically includes: Step 1.1: Stratify based on orbital characteristics, including: Classify according to the orbital inclination, determine that the sun-synchronous orbit layer is the first layer, the polar orbit layer is the second layer, the general orbit with an orbital inclination between 50 and 55 degrees is the third layer, and the remaining other orbits are the fourth layer, and determine the total sample volume of each layer; Step 1.2: Determine the sample size of each layer, including: Determine the sample size of each layer according to the ratio between the total sample volumes of each layer; Step 2.4 specifically includes: Step 2.4.1: Initialize the population, including: Generate a variable population of a specific quantity and size that meets the requirements in a random generation manner according to the optimization variables and the optimization constraints of the genetic algorithm; Step 2.4.2: Calculate the fitness, including: Calculate the fitness of all individuals in the population using the objective function; Step 2.4.3: Genetic operations, including: Replication, crossover, and mutation, to obtain new individuals of the next generation population; Step 2.4.4: Continuously iterate through the processes of Step 2.4.2 and Step 2.4.3, recalculate the fitness of the next-generation individuals, and end the iteration after iterating to the set maximum number of evolutionary generations. The individual with the maximum fitness is the optimal solution of the genetic algorithm.

2. The method for designing the orbit of a space-based observation constellation for low-Earth orbit satellite targets according to claim 1, characterized in that, The optimization variables in Step 2.1 include: the orbital inclination, true anomaly, right ascension of the ascending node, number of orbits, and number of satellites in each orbit of a satellite on the j-th orbital plane.

3. The method for designing the orbit of a space-based observation constellation for low-Earth orbit satellite targets according to claim 1, characterized in that, The optimization variables in Step 2.1 include: the orbital inclination, true anomaly, and right ascension of the ascending node of a satellite on the j-th orbital plane.

4. The method for designing the orbit of a space-based observation constellation for low-Earth orbit satellite targets according to claim 3, characterized in that, Step 2.2 specifically includes: The constraint for the target observation time is t0≤t≤t f where t0 is the start time of the observation, t f is the end time of the observation, and t is the target observation time; The orbital element constraint and the satellite number constraint are where \(i\) o , \(f\) o , \(\Omega\) o are the orbital inclination, true anomaly, and right ascension of the ascending node of the satellite to be optimized, are the minimum orbital inclination, true anomaly, and right ascension of the ascending node during optimization; are the maximum orbital inclination, true anomaly, and right ascension of the ascending node during optimization; is the maximum total number of satellites during optimization, \(k\) is the orbital elements, and \(n\) is the number of satellites in each orbit.

5. The method for designing the orbit of a space-based observation constellation for low-Earth orbit satellite targets according to any one of claims 1-4, characterized in that, Step 3 specifically includes: According to the uniform distribution of satellites on the same orbital plane, determine that the true anomalies of the n satellites on each orbit differ by (360 / n)°; Obtain the true anomalies of all satellites on the same orbit according to the true anomaly of one satellite; Select the sun-synchronous dawn-dusk orbit according to the constellation orbit, determine that the eccentricity e of all satellite orbits is 0, the argument of perigee ω is also 0, and the determination relationship between the semi-major axis a of the orbit and the orbital inclination i; Determine the six orbital elements of each satellite in the constellation through the optimal solution, obtain the orbital data of all observation satellites in the observation constellation, and complete the orbital design that meets the maximum coverage of the targets.

6. A computer device, comprising a memory and a processor, wherein a computer program is stored in the memory, characterized in that, When the processor runs the computer program stored in the memory, it executes the steps of the method according to any one of claims 1 to 5.

7. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores multiple computer instructions for causing a computer to execute the method according to any one of claims 1 to 5.

8. A computer program product, characterized in that, When the computer program is executed by a processor, it implements the method according to any one of claims 1 to 5.

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