A low-orbit ultra-dense constellation optimization method based on NSGA-II algorithm

Abstract

A low-orbit ultra-dense constellation optimization method based on the NSGA-II algorithm belongs to the field of satellite communications. The present invention solves the problem that in the scenario of low-orbit ultra-dense constellation configuration optimization, the existing optimization method has high time complexity, cannot guarantee constellation coverage performance, and cannot meet the requirements of inter-satellite link richness. The present invention first simulates the constellation and establishes an objective function according to the goal of constellation optimization; then, the parameters of the constellation are used as input, and the established objective function value is used as output to establish a multi-objective optimization model; then, the NSGA-II algorithm is used to solve the established multi-objective optimization model to obtain a pareto frontier point set and an optimal solution set; finally, K pareto frontier points are selected from the obtained pareto frontier point set, and a low-orbit ultra-dense constellation is designed based on the constellation parameters corresponding to the selected pareto frontier points in the optimal solution set. The method of the present invention can be applied to the optimization of low-orbit ultra-dense constellations.

Description

Technical Field

[0001] The present invention belongs to the field of satellite communications, and in particular relates to a low-orbit ultra-dense constellation optimization method based on the NSGA-II algorithm. Background Art

[0002] In integrated space-ground communications scenarios, the spatial layout of satellite constellations directly determines the quality of communications. In recent years, satellite manufacturing and launch technologies have advanced rapidly, with significant progress in antenna gain and integration. Satellite anti-radiation interference technology has also significantly improved, minimizing the impact of the atmosphere on satellite operations. This allows constellations to be built in lower orbits, making satellite launches more economically viable. The number of satellites in constellations is also increasing, and the pursuit of low-latency, high-quality satellite communications is growing. Typically, constellations with hundreds, thousands, or even tens of thousands of satellites are considered ultra-dense constellations. The most representative example of ultra-dense constellation research internationally is Starlink. Starlink is a hybrid constellation composed of multiple Walker constellations, featuring extensive laser intersatellite links. With a planned launch of 42,000 satellites, it is currently the largest ultra-dense constellation in low-orbit orbit. In addition, the Iridium, Globalstar, Oneweb, and Kuiper constellations are all relatively mature. my country is also actively developing constellations such as Hongyun, Hongyan, China Star Network, and Qianfan.

[0003] To maximize the low latency and wide coverage advantages of ultra-dense low-orbit constellations while reducing costs and preventing coverage failures due to satellite damage, lifespan expiration, and other factors during constellation operation, it is crucial to conduct research on the satellite orbital parameters and spatial distribution at the outset of constellation design. This research should be conducted through constellation simulation and optimization to reduce trial-and-error and construction costs. Existing constellation design methods primarily include geometric analysis, design methods based on modern optimization algorithms, and comparative evaluation methods based on simulation calculations. To optimize ultra-dense constellations, design methods based on modern optimization algorithms are often employed. Common constellation optimization methods include particle swarm optimization, simulated annealing wolf pack algorithms, and genetic algorithms. These methods abstract the constellation's orbital parameters and performance indicators as inputs and outputs, applying multi-objective optimization theory for optimization.

[0004] The direction of constellation optimization and the selection of objective functions are also crucial. To ensure uninterrupted communication services and stable and reliable communication quality, it is necessary to analyze and improve constellation coverage performance and communication links, thereby achieving better constellation coverage and a richer selection of intersatellite links. However, current constellation optimization methods mainly focus on detailed optimizations such as multi-objective satellite access optimization and QoS optimization, or on small-scale constellations of dozens of satellites. For the simulation and performance calculation of ultra-dense constellations of hundreds or thousands of satellites, existing optimization methods have high time complexity, cannot guarantee constellation coverage performance, and cannot meet the requirements for rich intersatellite links. There is also limited research on the optimization of ultra-dense constellations of hundreds or thousands of satellites in low-orbit orbits, and optimization strategies are scarce. Summary of the Invention

[0005] The purpose of the present invention is to solve the problems in the scenario of low-orbit ultra-dense constellation configuration optimization, such as the high time complexity of existing optimization methods, the inability to guarantee constellation coverage performance and the inability to meet the requirements of inter-satellite link richness. A low-orbit ultra-dense constellation optimization method based on the NSGA-II algorithm is proposed.

[0006] The technical solution adopted by the present invention to solve the above technical problems is:

[0007] According to one aspect of the present invention, a low-orbit ultra-dense constellation optimization method based on the NSGA-II algorithm specifically comprises the following steps:

[0008] Step 1: Simulate a single-layer constellation and determine the optimization goal of the single-layer constellation; then establish an objective function based on each optimization goal;

[0009] Step 2: After selecting the latitude band where satellite communication needs to be established, a multi-objective optimization model is established using the constellation parameters as input and the objective function value in step 1 as output;

[0010] Step 3: Use the NSGA-II algorithm to solve the multi-objective optimization model established in step 2 to obtain the Pareto frontier point set and the optimal solution set;

[0011] Each pareto frontier point in the pareto frontier point set includes various objective function values, and the optimal solution set includes the constellation parameters corresponding to each pareto frontier point;

[0012] Step 4: Select K Pareto frontier points from the Pareto frontier point set obtained in Step 3, and perform low-orbit ultra-dense constellation design based on the constellation parameters corresponding to the selected Pareto frontier points in the optimal solution set;

[0013] The K Pareto frontier points are selected from the Pareto frontier points obtained in step 3, specifically:

[0014] Calculate the mean A1 of the average coverage rate of each Pareto frontier point in the Pareto frontier point set, calculate the mean A2 of the average coverage multiplicity of each Pareto frontier point in the Pareto frontier point set, and calculate the mean A3 of the average revisit time of each Pareto frontier point in the Pareto frontier point set;

[0015] Then select the Pareto frontier point that satisfies conditions (1) to (3) at the same time:

[0016] Condition (1), average coverage is greater than A1;

[0017] Condition (2), the average coverage weight is greater than A2;

[0018] Condition (3): The average revisit time is less than A3.

[0019] According to another aspect of the present invention, a low-orbit ultra-dense constellation optimization method based on the NSGA-II algorithm specifically comprises the following steps:

[0020] Step 1: Simulate the hybrid configuration constellation and determine the optimization goal of the hybrid configuration constellation; then establish the objective function according to each optimization goal;

[0021] Step 2: After selecting the latitude band where satellite communication needs to be established, a multi-objective optimization model is established using the constellation parameters as input and the objective function value in step 1 as output;

[0022] Step 3: Use the NSGA-II algorithm to solve the multi-objective optimization model established in step 2 to obtain the Pareto frontier point set and the optimal solution set;

[0023] Each pareto frontier point in the pareto frontier point set includes various objective function values, and the optimal solution set includes the constellation parameters corresponding to each pareto frontier point;

[0024] Step 4: Select K Pareto frontier points from the Pareto frontier point set obtained in Step 3, and perform low-orbit ultra-dense constellation design based on the constellation parameters corresponding to the selected Pareto frontier points in the optimal solution set;

[0025] The K Pareto frontier points are selected from the Pareto frontier points obtained in step 3, specifically:

[0026] First, roughly select the Pareto frontier points that meet both conditions (1) and (2) from the Pareto frontier point set obtained in step 3:

[0027] Condition (1), the proportion of total connection time in the whole day is greater than the threshold A1;

[0028] Condition (2): The average connection time is greater than the threshold A2. The calculation method of threshold A2 is as follows: the average value of the average connection time corresponding to all Pareto frontier points is recorded as a, and then the average value a is compared with 30s. If a is greater than 30s, a is used as threshold A2; otherwise, 30s is used as threshold A2.

[0029] Secondly, the roughly selected Pareto frontier points are screened, and the screening rules are as follows:

[0030] Let a roughly selected Pareto frontier point be recorded as x1, the total connection time of Pareto frontier point x1 be recorded as T1, and the system construction cost of Pareto frontier point x1 be recorded as Q1. Let any roughly selected Pareto frontier point other than x1 be recorded as x2, the total connection time of Pareto frontier point x2 be recorded as T2, and the system construction cost of Pareto frontier point x2 be recorded as Q2.

[0031] If T1≤T2 and Q1≥Q2, filter out the Pareto frontier point x1;

[0032] If 90%×T2≤T1≤T2 and Q1≤70%×Q2, the Pareto frontier point x2 is filtered out.

[0033] The beneficial effects of the present invention are:

[0034] The present invention designs a low-orbit ultra-dense constellation optimization method based on the NSGA-II algorithm. The single-layer low-orbit ultra-dense satellite constellation optimization problem aims to maximize the average coverage rate, average coverage multiplicity, and minimize the average revisit time and system cost within a specific latitude band, and obtains an ideal optimal solution set and Pareto frontier point set, proving the effectiveness of the NSGA-II algorithm in the optimization of low-orbit ultra-dense constellations. The multi-layer heterogeneous constellation optimization problem aims to enrich the inter-satellite links between two ground stations within a specific latitude band and establish short-hop links. A four-hop link of "ground station A-walker constellation-polar orbit constellation-Walker constellation-polar orbit constellation-ground station B" is established, and the existence time is guaranteed to be more than 11 hours per day. At the same time, by selecting the optimal solution, the constellation can reduce the system cost under the condition of similar link performance. The method of the present invention can ensure the constellation coverage performance and meet the requirements of inter-satellite link richness. At the same time, compared with the existing optimization method, the method of the present invention effectively reduces the time complexity. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 This is a schematic diagram of the single-layer Walker configuration low-orbit ultra-dense constellation model in Example 1;

[0036] Figure 2Schematic diagram of satellite orbit parameters in Example 1;

[0037] Figure 3 Schematic diagram of a multi-layer heterogeneous constellation model in Example 2;

[0038] Figure 4 This is a schematic diagram of the four-hop link of "ground station A-walker constellation-polar orbit constellation-Walker constellation-polar orbit constellation-ground station B" in Example 2;

[0039] FIG5(a) is a Pareto frontier diagram of the single-layer Walker configuration constellation after optimization in Example 1, focusing on coverage, coverage multiplicity, and revisit time;

[0040] FIG5( b ) is a Pareto frontier diagram of the single-layer Walker configuration constellation after optimization in Example 1, focusing on coverage multiplicity, revisit time, and system cost;

[0041] Figure 6 This is the Pareto frontier graph after the hybrid configuration constellation optimization in Example 2. DETAILED DESCRIPTION

[0042] Specific embodiment 1: This embodiment describes a low-orbit ultra-dense constellation optimization method based on the NSGA-II algorithm. The low-orbit in the present invention refers to an artificial earth satellite orbit with an orbital altitude of less than 2000 kilometers. The method specifically includes the following steps:

[0043] Step 1: Simulate a single-layer constellation and determine the optimization goal of the single-layer constellation; then establish an objective function based on each optimization goal;

[0044] Step 2: After selecting the latitude band where satellite communication needs to be established, a multi-objective optimization model is established using the constellation parameters as input and the objective function value in step 1 as output;

[0045] Step 3: Use the NSGA-II algorithm to solve the multi-objective optimization model established in step 2 to obtain the Pareto frontier point set and the optimal solution set;

[0046] Each pareto frontier point in the pareto frontier point set includes various objective function values, and the optimal solution set includes the constellation parameters corresponding to each pareto frontier point;

[0047] That is, each Pareto frontier point represents a set of objective function values, which include average coverage, average coverage multiplicity, average revisit time, and system construction cost. The optimal solution set contains the constellation parameters corresponding to this set of objective function values.

[0048] Step 4: Select K Pareto frontier points from the Pareto frontier point set obtained in Step 3, and perform low-orbit ultra-dense constellation design based on the constellation parameters corresponding to the selected Pareto frontier points in the optimal solution set;

[0049] The K Pareto frontier points are selected from the Pareto frontier points obtained in step 3, specifically:

[0050] Calculate the mean A1 of the average coverage rate of each Pareto frontier point in the Pareto frontier point set, calculate the mean A2 of the average coverage multiplicity of each Pareto frontier point in the Pareto frontier point set, and calculate the mean A3 of the average revisit time of each Pareto frontier point in the Pareto frontier point set;

[0051] Then select the Pareto frontier point that satisfies conditions (1) to (3) at the same time:

[0052] Condition (1), average coverage is greater than A1;

[0053] Condition (2), the average coverage weight is greater than A2;

[0054] Condition (3): The average revisit time is less than A3.

[0055] Specific embodiment 2: This embodiment differs from specific embodiment 1 in that the objectives of the single-layer constellation optimization include constellation coverage performance and system construction cost; wherein the constellation coverage performance includes the average coverage rate, average coverage multiplicity, and average revisit time of the constellation;

[0056] The established objective functions are maximizing the average coverage, maximizing the average coverage multiplicity, minimizing the average revisit time and minimizing the system construction cost.

[0057] Other steps and parameters are the same as those in the first embodiment.

[0058] The coverage rate reflects the temporal statistical average of the ratio of the constellation's coverage area to a specific latitude band;

[0059] The coverage density indicates the number of visible satellites above the ground station;

[0060] Revisit time is the time it takes to reconnect to the satellite network after being disconnected from the ground;

[0061] The system cost is how much it would cost to build such a constellation.

[0062] Specific embodiment 3: This embodiment differs from specific embodiment 1 or 2 in that the system construction cost is calculated as follows:

[0063] Q=(P / P0)2 +(i / i0) 2 +(n / n0) 2 +(h / h0) 2

[0064] Among them, Q is the system construction cost, P is the number of orbital planes, i is the orbital inclination, n is the number of satellites on a single orbital plane, h is the orbital altitude, P0 is the lower limit of the number of orbital planes, i0 is the lower limit of the orbital inclination, n0 is the lower limit of the number of satellites on a single orbital plane, and h0 is the lower limit of the orbital altitude.

[0065] Other steps and parameters are the same as those in the first or second embodiment.

[0066] Specific embodiment four: This embodiment differs from any one of specific embodiments one to three in that the constellation parameters in step two include the number of orbital planes of the constellation, the number of satellites on a single orbital plane, the satellite altitude (also called orbital altitude) and the satellite inclination (also called orbital inclination).

[0067] The other steps and parameters are the same as those in the first to third embodiments.

[0068] The number of orbital planes P is the number of orbital planes in the constellation;

[0069] The number of satellites in a single orbital plane, n, is the number of satellites evenly distributed on a single orbit of the constellation;

[0070] Satellite height h is the height above the Earth of the satellites in the constellation;

[0071] The satellite inclination angle i is the angle between the satellite orbital plane and the equatorial plane in the constellation;

[0072] Among them, each orbital plane is evenly distributed, and the satellites in each orbital plane are also evenly distributed. According to the above parameters, a constellation can be uniquely determined.

[0073] Specific embodiment 5: This embodiment differs from specific embodiments 1 to 4 in that, in the NSGA-II algorithm, the congestion degree calculation method is as follows:

[0074]

[0075] Among them, d i is the crowding degree of the i-th individual, n is the number of objective functions, is the value of the i+1th individual on the kth objective function, is the value of the i-1th individual on the kth objective function, and |·| represents the absolute value.

[0076] The other steps and parameters are the same as those in the first to fourth embodiments.

[0077] Specific embodiment 6: This embodiment describes a low-orbit ultra-dense constellation optimization method based on the NSGA-II algorithm, the method specifically comprising the following steps:

[0078] Step 1: Simulate the hybrid configuration constellation and determine the optimization goal of the hybrid configuration constellation; then establish the objective function according to each optimization goal;

[0079] Step 2: After selecting the latitude band where satellite communication needs to be established, a multi-objective optimization model is established using the constellation parameters as input and the objective function value in step 1 as output;

[0080] Step 3: Use the NSGA-II algorithm to solve the multi-objective optimization model established in step 2 to obtain the Pareto frontier point set and the optimal solution set;

[0081] Each pareto frontier point in the pareto frontier point set includes various objective function values, and the optimal solution set includes the constellation parameters corresponding to each pareto frontier point;

[0082] Step 4: Select K Pareto frontier points from the Pareto frontier point set obtained in Step 3, and perform low-orbit ultra-dense constellation design based on the constellation parameters corresponding to the selected Pareto frontier points in the optimal solution set;

[0083] The K Pareto frontier points are selected from the Pareto frontier points obtained in step 3, specifically:

[0084] First, roughly select the Pareto frontier points that meet both conditions (1) and (2) from the Pareto frontier point set obtained in step 3:

[0085] Condition (1): The proportion of total connection time in the whole day is greater than the threshold A1 (the threshold is set to 45% in the present invention);

[0086] Condition (2): The average connection time is greater than the threshold A2. The calculation method of threshold A2 is as follows: the average value of the average connection time corresponding to all Pareto frontier points is recorded as a, and then the average value a is compared with 30s. If a is greater than 30s, a is used as threshold A2; otherwise, 30s is used as threshold A2.

[0087] Secondly, the roughly selected Pareto frontier points are screened, and the screening rules are as follows:

[0088] Let a roughly selected Pareto frontier point be recorded as x1, the total connection time of Pareto frontier point x1 be recorded as T1, and the system construction cost of Pareto frontier point x1 be recorded as Q1. Let any roughly selected Pareto frontier point other than x1 be recorded as x2, the total connection time of Pareto frontier point x2 be recorded as T2, and the system construction cost of Pareto frontier point x2 be recorded as Q2.

[0089] If T1≤T2 and Q1≥Q2, filter out the Pareto frontier point x1;

[0090] If 90%×T2≤T1≤T2 and Q1≤70%×Q2, the Pareto frontier point x2 is filtered out.

[0091] The present invention uses the Pareto frontier point x1 as an example to illustrate screening. Even if the Pareto frontier point x1 is filtered out, it is necessary to continue comparing other Pareto frontier points with the Pareto frontier point x1 to filter out the Pareto frontier point x2 that meets the conditions. Then, the next Pareto frontier point is used as x1, and the comparison continues until every Pareto frontier point has been compared as x1, and the entire comparison process ends. During the entire comparison process, some Pareto frontier points may be filtered out in more than one comparison. The purpose of the present invention is to filter out Pareto frontier points that have not been filtered out at all.

[0092] Specific embodiment 7: This embodiment differs from specific embodiment 6 in that the objectives of hybrid configuration constellation optimization include communication connection performance and system construction cost; wherein: communication connection performance includes total connection time and average connection time;

[0093] The established objective functions are maximizing the total connection time, maximizing the average connection time and minimizing the system construction cost.

[0094] Other steps and parameters are the same as those in the sixth embodiment.

[0095] Specific embodiment eight: This embodiment differs from specific embodiment six or seven in that the system construction cost is calculated as follows:

[0096] Q=(P / P0) 2 +(n / n0) 2

[0097] Among them, Q is the system construction cost, P is the number of orbital planes, n is the number of satellites on a single orbital plane, P0 is the lower limit of the number of orbital planes, and n0 is the lower limit of the number of satellites on a single orbital plane.

[0098] Other steps and parameters are the same as those in specific implementation manner six or seven.

[0099] Specific embodiment nine: This embodiment differs from any one of specific embodiments six to eight in that the constellation parameters in step two include the number of orbital planes of the constellation, the number of satellites on a single orbital plane, the satellite altitude (also called orbital altitude) and the satellite inclination (also called orbital inclination).

[0100] The other steps and parameters are the same as those in any one of the sixth to eighth embodiments.

[0101] Among them, the satellite altitude and satellite inclination are fixed.

[0102] Specific embodiment 10: This embodiment differs from any one of specific embodiments 6 to 9 in that, in the NSGA-II algorithm, the congestion degree calculation method is as follows:

[0103]

[0104] Among them, d i is the crowding degree of the i-th individual, n is the number of objective functions, is the value of the i+1th individual on the kth objective function, is the value of the i-1th individual on the kth objective function, and |·| represents the absolute value.

[0105] The other steps and parameters are the same as those in any one of the sixth to ninth embodiments.

[0106] Example 1

[0107] Step 1: Simulate a single-layer Walker constellation. Simulate the primary model of the Walker constellation and analyze its coverage and link performance. Optimize the single-layer Walker constellation to determine its coverage performance and system construction cost. Coverage performance specifically includes average coverage ratio, average coverage multiplicity, and average revisit time. Optimize the single-layer Walker constellation toward high coverage ratio and coverage multiplicity, while minimizing revisit time and system construction cost.

[0108] like Figure 1 The figure shows a typical single-layer Walker configuration low-orbit ultra-dense constellation. Each point in the figure represents a satellite, and each line represents an orbital plane. Figure 2 Shown are diagrams of orbital parameters for a single satellite;

[0109] Step 2: After selecting the latitude band where satellite communication needs to be established, the constellation parameters are used as input and the objective function value corresponding to the optimization goal determined in step 1 is used as output to establish a multi-objective optimization model;

[0110] For a single-layer Walker configuration constellation, four constellation parameters are determined as input, namely the number of orbital planes P, orbital inclination i, the number of satellites on a single orbital plane n, and orbital height h. The four objective functions are:

[0111]

[0112] A higher average coverage rate indicates a larger constellation coverage area, while a higher average coverage repetition rate indicates a greater number of visible satellites above the ground station, meaning more optional satellite nodes for communication and a more stable system. A shorter average revisit time means a faster reconnection time after a ground station loses connection, making the communication system more reliable. Lower system construction costs also translate into lower capital expenditures and savings.

[0113] Step 3: Use the NSGA-II algorithm to solve the multi-objective optimization model established in step 2 to obtain the Pareto frontier and the optimal solution set; each Pareto frontier point in the Pareto frontier includes each objective function value, and the optimal solution set includes the constellation parameters corresponding to each Pareto frontier point;

[0114] If the multi-objective optimization problem established in step 3 is converted to a single-objective optimization problem using weighting or other methods, it often maximizes only one objective function while leaving the others unsatisfactory, thus losing its systematicity. Because constellation simulation and computational performance are time-consuming, this paper employs the NSGA-II optimization algorithm, which has higher spatial complexity and lower time complexity, to iteratively solve the Pareto frontier and optimal solution set.

[0115] When using the NSGA-II algorithm to optimize the constellation of a single-layer Walker configuration, the constellation parameter range is shown in Table 1:

[0116] Table 1 Setting the constellation parameter range for a single-layer Walker configuration

[0117]

[0118] The NSGA-II optimization algorithm introduces congestion and congestion comparison operators to select individuals with the same priority. Here, individuals are constellations corresponding to a set of input parameters. The congestion is calculated as follows:

[0119]

[0120] Among them, d i is the crowding distance of the i-th individual, n is the number of objective functions, is the value of individual i+1 on the kth objective function, is the value of individual i-1 on the kth objective function. The sum of the distances across all objective functions is the crowding degree of the i-th individual. More dispersed individuals have a greater chance of being selected, making the Pareto front more uniform, maintaining population diversity, and avoiding falling into local optima.

[0121] Step 4: Based on the Pareto frontier obtained in Step 3 and the actual requirements, select several Pareto frontier points with better communication coverage performance for the single-layer Walker constellation. Based on the constellation parameters corresponding to the selected Pareto frontier points in the optimal solution set, perform low-orbit ultra-dense constellation design.

[0122] The specific process of step 4 is as follows:

[0123] Calculate the mean A1 of the average coverage rate of each Pareto frontier point in the Pareto frontier point set, calculate the mean A2 of the average coverage multiplicity of each Pareto frontier point in the Pareto frontier point set, and calculate the mean A3 of the average revisit time of each Pareto frontier point in the Pareto frontier point set;

[0124] Then select the Pareto frontier point that satisfies conditions (1) to (3) at the same time:

[0125] Condition (1), average coverage is greater than A1;

[0126] Condition (2), the average coverage weight is greater than A2;

[0127] Condition (3): The average revisit time is less than A3.

[0128] The optimization results for the single-layer Walker constellation are shown in Figures 5(a) and 5(b). The average coverage multiplicity ranges from 1.74 to 2.95. When selecting a constellation, we can further select points with an average coverage multiplicity above 2 to enhance communication reliability. The average coverage rate ranges from 71% to 91%. The average revisit time ranges from 69.13s to 5915s, with the average revisit time concentrated between 69s and 157s and 5800s and 5915s. Shorter revisit times indicate lower latency for terminals to reconnect to the network and higher communication reliability. The average revisit time ranges from 69s to 7.1s, with the average revisit time around 69s, is selected. The system construction costs vary slightly, ranging from 4 to 7.1. If system construction costs are the final consideration, points with good coverage performance are prioritized, namely points 4, 5, and 7 in Figure 5(a). These three points have an average coverage rate of over 90% within the latitude range of 0°-60°N, an average coverage repetition rate of over 2.5, and an average revisit time of under 75 seconds.

[0129] According to step 4, the Pareto frontier point with excellent coverage performance can be obtained, and then practical individuals can be selected based on the emphasis of different performance indicators and the consideration of system construction cost, which reflects the practical reference value of the method of the present invention.

[0130] Example 2

[0131] Step 1: Simulate a hybrid constellation consisting of a Walker constellation and a polar orbit constellation, analyze coverage performance and link performance, and determine the optimization objectives of the hybrid constellation, including communication connection time and system construction cost.

[0132] Although the single-layer Walker configuration ultra-dense constellation already has abundant inter-satellite links and good coverage performance, establishing a communication connection between two ground stations that are far apart on Earth requires multi-hop inter-satellite links. This places higher demands on the routing selection and information processing capabilities of the onboard payload. At the same time, a high number of communication hops means multiple reception and transmission of signals, resulting in higher communication latency. To solve this problem, taking advantage of the high coverage rate of polar orbit constellations, this embodiment establishes a hybrid configuration constellation of Walker constellations and polar orbit constellations. The multi-layer heterogeneous constellation model is as follows: Figure 3 shown.

[0133] like Figure 4 As shown in FIG, a four-hop link of “ground station A-walker constellation-polar orbit constellation-Walker constellation-polar orbit constellation-ground station B” is established as a supplement to the single-layer Walker constellation inter-satellite link.

[0134] Step 2: After selecting the latitude band where satellite communication needs to be established, the constellation parameters are used as input and the objective function value corresponding to the optimization goal determined in step 1 is used as output to establish a multi-objective optimization model;

[0135] For multi-layer heterogeneous constellations, the orbital altitude of the polar orbit constellation is selected and the orbital inclination is set to 90°. In this case, the constellation input parameters of the multi-optimization model are the number of orbital planes P of each constellation layer and the number of satellites on a single orbital plane n. The three objective functions are:

[0136]

[0137] The connection duration indicates the duration of establishing a four-hop link: ground station A - Walker constellation - polar orbiting constellation - Walker constellation - polar orbiting constellation - ground station B. Intersatellite links using a single-layer Walker constellation require more than four hops to establish communication, resulting in significant latency. Establishing a four-hop link avoids the need for more intersatellite links, reducing latency and improving communication performance.

[0138] Step 3: Use the NSGA-II algorithm to solve the multi-objective optimization model established in step 2 to obtain a Pareto frontier point set and an optimal solution set; each Pareto frontier point in the Pareto frontier point set includes various objective function values, and the optimal solution set includes the constellation parameters corresponding to each Pareto frontier point;

[0139] If the multi-objective optimization problem established in step 3 is converted to a single-objective optimization problem using weighting or other methods, it often maximizes only one objective function while leaving the others unsatisfactory, resulting in a loss of systematicity. Because constellation simulation and computational performance are time-consuming, this paper employs the NSGA-II optimization algorithm, which has higher spatial complexity and lower time complexity, to iteratively solve the Pareto frontier point set and the optimal solution set.

[0140] When setting up a multi-layer heterogeneous constellation, the primary model of the Starlink constellation is set to the first-layer Walker configuration constellation, and the polar orbit constellation with an orbital altitude of 600km is used as the second-layer constellation. The constellation parameter ranges are shown in Table 2:

[0141] Table 2

[0142]

[0143] During multi-objective optimization, constellation parameters are used as input to obtain different objective function values. The NSGA-II algorithm is then iterated to obtain the Pareto frontier point set and the corresponding optimal solution set. The NSGA-II optimization algorithm introduces congestion and a congestion comparison operator to select individuals with the same priority. Here, an individual is a constellation corresponding to a set of input parameters. Congestion is calculated as follows:

[0144]

[0145] Among them, d i is the crowding distance of the i-th individual, n is the number of objective functions, f k i+1 is the value of individual i+1 on the kth objective function, f k i-1 is the value of individual i-1 on the kth objective function. The sum of the distances across all objective functions is the crowding degree of the i-th individual. More dispersed individuals have a greater chance of being selected, making the Pareto front more uniform, maintaining population diversity, and avoiding falling into local optima.

[0146] Step 4: Based on the Pareto frontier point set obtained in Step 3 and the actual requirements, select several Pareto frontier points with better communication connection performance for the multi-layer heterogeneous constellation, and perform low-orbit ultra-dense constellation design based on the constellation parameters corresponding to the selected Pareto frontier points in the optimal solution set;

[0147] The specific process of step four is:

[0148] First, roughly select the Pareto frontier points that meet both conditions (1) and (2) from the Pareto frontier point set obtained in step 3:

[0149] Condition (1): The proportion of total connection time in the whole day is greater than the threshold A1 (the threshold is set to 45% in the present invention);

[0150] Condition (2): The average connection time is greater than the threshold A2. The calculation method of threshold A2 is as follows: the average value of the average connection time corresponding to all Pareto frontier points is recorded as a, and then the average value a is compared with 30s. If a is greater than 30s, a is used as threshold A2; otherwise, 30s is used as threshold A2.

[0151] Secondly, the roughly selected Pareto frontier points are screened, and the screening rules are as follows:

[0152] Let a roughly selected Pareto frontier point be recorded as x1, the total connection time of Pareto frontier point x1 be recorded as T1, and the system construction cost of Pareto frontier point x1 be recorded as Q1. Let any roughly selected Pareto frontier point other than x1 be recorded as x2, the total connection time of Pareto frontier point x2 be recorded as T2, and the system construction cost of Pareto frontier point x2 be recorded as Q2.

[0153] If T1≤T2 and Q1≥Q2, filter out the Pareto frontier point x1;

[0154] If 90%×T2≤T1≤T2 and Q1≤70%×Q2, the Pareto frontier point x2 is filtered out.

[0155] The optimization results obtained by multi-layer heterogeneous constellation are as follows Figure 6 As shown in FIG, the processing method of the data obtained after the constellation optimization using the NSGA-II algorithm in step 4 is as follows:

[0156] Obtained through step three Figure 6 The optimization results show that total connection times range from 7328s to 45671s, with the maximum total connection time accounting for 52.86% of the total day. The average connection time ranges from 22.97s to 36.89s, indicating discontinuous access. Each four-hop communication in this mode is relatively short, and the system construction cost ranges from 1.25 to 54.62. In actual projects, the most appropriate solution can be selected based on the level of emphasis on the indicators.

[0157] Table 3

[0158]

[0159] As shown in Table 3, if system construction costs are considered last and link performance is prioritized, then individuals 2, 4, and 6 perform the best, with a total connection time of over 42,718 seconds, accounting for 49.4% of the entire day, and an average connection time of over 33.88 seconds. The heterogeneous constellation optimization in this embodiment establishes a four-hop link ("New York Station-Starlink-polarsats-Starlink-China Beijing Station") for long-term communication. Furthermore, communication can be achieved through multi-hop intersatellite links established within Starlink. Using polar-orbiting constellations as intermediate communication nodes for satellite communications reduces the number of communication hops, lowers latency, and makes intersatellite links relatively simple to establish.

[0160] The chart data from step 4 shows that point 2, with a very low system construction cost, achieves link performance close to that of points 4 and 6, which have higher system construction costs. The total connection time at point 2 is 6.47% lower than that of point 4, but the system construction cost is 54.98% lower. The total connection time at point 2 is 2.95% lower than that of point 6, but the system construction cost is 32.74% lower. Expanding to other examples, we can select individuals with communication performance reductions of less than 10% and system construction costs reductions of more than 30% to achieve the goal of reducing system costs.

[0161] The present invention can effectively reduce system costs while maintaining similar link performance by adjusting constellation parameters, demonstrating the advantages of multi-objective optimization in ultra-dense constellation optimization.

[0162] The parameters in the present invention can be adjusted to simulate and optimize constellations in different latitude bands and different constellation parameter ranges, and calculate coverage performance and link performance to complete optimization for different goals, which can reduce system costs while meeting good communication performance.

[0163] The above examples are merely illustrative of the calculation model and process of the present invention and are not intended to limit the embodiments of the present invention. Persons skilled in the art will readily appreciate that other variations or modifications based on the above description are possible. This list of embodiments is not exhaustive; however, any obvious variations or modifications derived from the technical solution of the present invention remain within the scope of protection of the present invention.

Claims

1. A low-orbit ultra-dense constellation optimization method based on the NSGA-II algorithm, characterized in that: The method specifically comprises the following steps: Step 1: Simulate a single-layer constellation and determine the optimization goal of the single-layer constellation; then establish an objective function based on each optimization goal; Step 2: After selecting the latitude band where satellite communication needs to be established, a multi-objective optimization model is established using the constellation parameters as input and the objective function value in step 1 as output; Step 3: Use the NSGA-II algorithm to solve the multi-objective optimization model established in step 2 to obtain the Pareto frontier point set and the optimal solution set; Each pareto frontier point in the pareto frontier point set includes various objective function values, and the optimal solution set includes constellation parameters corresponding to each pareto frontier point; Step 4: Select K Pareto frontier points from the Pareto frontier point set obtained in Step 3, and perform low-orbit ultra-dense constellation design based on the constellation parameters corresponding to the selected Pareto frontier points in the optimal solution set; The K Pareto frontier points are selected from the Pareto frontier points obtained in step 3, specifically: Calculate the mean A1 of the average coverage rate of each Pareto frontier point in the Pareto frontier point set, calculate the mean A2 of the average coverage multiplicity of each Pareto frontier point in the Pareto frontier point set, and calculate the mean A3 of the average revisit time of each Pareto frontier point in the Pareto frontier point set; Then select the Pareto frontier point that satisfies conditions (1) to (3) at the same time: Condition (1), average coverage is greater than A1; Condition (2), the average coverage weight is greater than A2; Condition (3): The average revisit time is less than A3.

2. The method for optimizing low-orbit ultra-dense constellations based on the NSGA-II algorithm according to claim 1, wherein: The objectives of the single-layer constellation optimization include constellation coverage performance and system construction cost; wherein the constellation coverage performance includes the average coverage rate, average coverage multiplicity and average revisit time of the constellation; The established objective functions are maximizing the average coverage, maximizing the average coverage multiplicity, minimizing the average revisit time and minimizing the system construction cost.

3. The method for optimizing low-orbit ultra-dense constellations based on the NSGA-II algorithm according to claim 2, wherein: The calculation method of the system construction cost is: Q=(P / P0) 2 +(i / i0) 2 +(n / n0) 2 +(h / h0) 2 Among them, Q is the system construction cost, P is the number of orbital planes, i is the orbital inclination, n is the number of satellites on a single orbital plane, h is the orbital altitude, P0 is the lower limit of the number of orbital planes, i0 is the lower limit of the orbital inclination, n0 is the lower limit of the number of satellites on a single orbital plane, and h0 is the lower limit of the orbital altitude.

4. The method for optimizing low-orbit ultra-dense constellations based on the NSGA-II algorithm according to claim 3, wherein: The constellation parameters in step 2 include the number of orbital planes of the constellation, the number of satellites on a single orbital plane, satellite altitude, and satellite inclination.

5. The method for optimizing low-orbit ultra-dense constellations based on the NSGA-II algorithm according to claim 4, wherein: In the NSGA-II algorithm, the congestion degree is calculated as follows: Among them, d i is the crowding degree of the ith individual, n is the number of objective functions, is the value of the i+1th individual on the kth objective function, is the value of the i-1th individual on the kth objective function, and |·| represents the absolute value.

6. A low-orbit ultra-dense constellation optimization method based on the NSGA-II algorithm, characterized in that: The method specifically comprises the following steps: Step 1: Simulate the hybrid configuration constellation and determine the optimization goal of the hybrid configuration constellation; then establish the objective function according to each optimization goal; Step 2: After selecting the latitude band where satellite communication needs to be established, a multi-objective optimization model is established using the constellation parameters as input and the objective function value in step 1 as output; Step 3: Use the NSGA-II algorithm to solve the multi-objective optimization model established in step 2 to obtain the Pareto frontier point set and the optimal solution set; Each pareto frontier point in the pareto frontier point set includes various objective function values, and the optimal solution set includes constellation parameters corresponding to each pareto frontier point; Step 4: Select K Pareto frontier points from the Pareto frontier point set obtained in Step 3, and perform low-orbit ultra-dense constellation design based on the constellation parameters corresponding to the selected Pareto frontier points in the optimal solution set; The K Pareto frontier points are selected from the Pareto frontier points obtained in step 3, specifically: First, roughly select the Pareto frontier points that meet both conditions (1) and (2) from the Pareto frontier point set obtained in step 3: Condition (1), the proportion of total connection time in the whole day is greater than the threshold A1; Condition (2): The average connection time is greater than the threshold A2. The calculation method of threshold A2 is as follows: the average value of the average connection time corresponding to all Pareto frontier points is recorded as a, and then the average value a is compared with 30s. If a is greater than 30s, a is used as threshold A2; otherwise, 30s is used as threshold A2. Secondly, the roughly selected Pareto frontier points are screened, and the screening rules are as follows: Let a roughly selected Pareto frontier point be recorded as x1, the total connection time of Pareto frontier point x1 be recorded as T1, and the system construction cost of Pareto frontier point x1 be recorded as Q1. Let any roughly selected Pareto frontier point other than x1 be recorded as x2, the total connection time of Pareto frontier point x2 be recorded as T2, and the system construction cost of Pareto frontier point x2 be recorded as Q2. If T1≤T2 and Q1≥Q2, filter out the Pareto frontier point x1; If 90%×T2≤T1≤T2 and Q1≤70%×Q2, the Pareto frontier point x2 is filtered out.

7. The method for optimizing low-orbit ultra-dense constellations based on the NSGA-II algorithm according to claim 6, wherein: The objectives of hybrid configuration constellation optimization include communication connection performance and system construction cost; wherein: communication connection performance includes total connection time and average connection time; The established objective functions are maximizing the total connection time, maximizing the average connection time and minimizing the system construction cost.

8. The method for optimizing low-orbit ultra-dense constellations based on the NSGA-II algorithm according to claim 7, wherein: The calculation method of the system construction cost is: Q=(P / P0) 2 +(n / n0) 2 Among them, Q is the system construction cost, P is the number of orbital planes, n is the number of satellites on a single orbital plane, P0 is the lower limit of the number of orbital planes, and n0 is the lower limit of the number of satellites on a single orbital plane.

9. The method for optimizing low-orbit ultra-dense constellations based on the NSGA-II algorithm according to claim 8, wherein: The constellation parameters in step 2 include the number of orbital planes of the constellation, the number of satellites on a single orbital plane, satellite altitude, and satellite inclination.

10. The method for optimizing low-orbit ultra-dense constellations based on the NSGA-II algorithm according to claim 9, wherein: In the NSGA-II algorithm, the congestion degree is calculated as follows: Among them, d i is the crowding degree of the ith individual, n is the number of objective functions, is the value of the i+1th individual on the kth objective function, is the value of the i-1th individual on the kth objective function, and |·| represents the absolute value.

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