Low-orbit super-dense constellation optimization method based on NSGA-II algorithm

Abstract

The invention discloses a low-orbit super-dense constellation optimization method based on an NSGA-II algorithm, and belongs to the field of satellite communication. According to the method, the problems that in the scene of low-orbit super-dense constellation configuration optimization, an existing optimization method is high in time complexity, the constellation coverage performance cannot be guaranteed, and the inter-satellite link richness requirement cannot be met are solved. The method comprises the following steps: firstly, simulating a constellation, and establishing a target function according to a constellation optimization target; establishing a multi-objective optimization model by taking parameters of the constellation as input and taking the established objective function value as output; then, an NSGA-II algorithm is adopted to solve the established multi-objective optimization model, and a pareto leading edge point set and an optimal solution set are obtained; and finally, K pareto front edge points are selected from the obtained pareto front edge point set, and low-orbit super-dense constellation design is carried out based on constellation parameters corresponding to the selected pareto front edge points in the optimal solution set. The method can be applied to low-orbit super-dense constellation optimization.

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 the integrated space-ground communication scenario, the spatial layout of satellite constellations directly determines the quality of communication. In recent years, satellite manufacturing and launch technology has developed rapidly, antenna gain and integration technology have also made great progress, and satellite anti-radiation interference technology has greatly developed. The impact of the atmosphere on satellite operation can be controlled in a smaller range, so the constellation can be built in a lower orbit, and there is better economic support for satellite launch. The number of satellites in the constellation is also increasing, and people are more pursuing satellite communications with low latency and high communication quality. Usually, constellations with hundreds, thousands, or tens of thousands of satellites are called ultra-dense constellations. The most representative of the current international ultra-dense constellation research is the Starlink constellation. The Starlink constellation is a hybrid constellation composed of multiple walker constellations with rich laser intersatellite links. It is planned to launch a total of 42,000 satellites, which is the largest low-orbit ultra-dense constellation. In addition, the Iridium, Globalstar, Oneweb and Kuiper constellations are all relatively mature. my country is also actively planning the construction of Hongyun, Hongyan, "China Star Network", Qianfan and other constellations.

[0003] In order to maximize the low latency and wide coverage advantages of low-orbit ultra-dense constellations, while reducing costs and avoiding the failure of ground coverage due to satellite damage and expiration of life during the operation of the constellation, it is necessary to study the satellite's orbital parameter design itself and spatial distribution at the beginning of the satellite constellation design, and reduce the trial and error cost and construction cost through constellation simulation and optimization research. The existing constellation design methods mainly include geometric analysis methods, design methods based on modern optimization algorithms, and comparative evaluation design methods based on simulation calculations. In order to achieve the optimization of ultra-dense constellations, design methods based on modern optimization algorithms are often used. At present, common constellation optimization methods include particle swarm optimization, simulated annealing wolf pack algorithm, genetic algorithm, etc., which abstract the orbital parameters and performance indicators of the constellation as input and output, and use multi-objective optimization theory for optimization.

[0004] The direction of constellation optimization and the selection of objective functions are also crucial. In order to ensure uninterrupted communication services and stable and reliable communication quality, it is necessary to analyze and improve the constellation coverage performance and communication links to make the constellation coverage performance better and have more inter-satellite link options. However, the current constellation optimization methods mainly consider the optimization of details such as multi-objective satellite access optimization and QoS optimization, or the optimization of small-scale constellations of dozens of satellites. For the simulation and performance calculation of ultra-dense constellations of hundreds or thousands of satellites, the time complexity of the existing optimization methods is high, and the constellation coverage performance cannot be guaranteed and the requirements for the richness of inter-satellite links cannot be met. There is little research on the optimization of ultra-dense constellation configurations of hundreds or thousands of low-orbit satellites, and there is a lack of optimization strategies. Summary of the invention

[0005] The purpose of the present invention is to solve the problem that in the scenario of low-orbit ultra-dense constellation configuration optimization, the existing optimization methods have high time complexity, cannot guarantee the constellation coverage performance and cannot meet the requirements of inter-satellite link richness, and propose a low-orbit ultra-dense constellation optimization method based on the NSGA-II algorithm.

[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, the method specifically comprises the following steps:

[0008] Step 1: simulate a single-layer constellation and determine the optimization target of the single-layer constellation; then establish the objective function according to each optimization target;

[0009] 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 in step 1 is used as output to establish a multi-objective optimization model;

[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 each objective function value, 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 weight 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), the 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, the method specifically comprises the following steps:

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

[0021] 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 in step 1 is used as output to establish a multi-objective optimization model;

[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 each objective function value, 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 satisfy 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 the 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 the threshold A2. Otherwise, 30s is used as the threshold A2.

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

[0030] A roughly selected Pareto frontier point is recorded as x1, the total connection time of Pareto frontier point x1 is recorded as T1, and the system construction cost of Pareto frontier point x1 is recorded as Q1; any roughly selected Pareto frontier point other than x1 is recorded as x2, the total connection time of Pareto frontier point x2 is recorded as T2, and the system construction cost of Pareto frontier point x2 is 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, minimize the average revisit time and system cost in a specific latitude band, and obtains an ideal optimal solution set and a 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 in a specific latitude band and establish a short-hop link. 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 of more than 11 hours per day is guaranteed. At the same time, the selection of the optimal solution can reduce the system cost of the constellation under the condition of similar link performance. The method of the present invention can ensure the constellation coverage performance and meet the requirements of the richness of inter-satellite links. 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 a 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 This is a schematic diagram of a multi-layer heterogeneous constellation model in Example 2;

[0038] Figure 4 This is a schematic diagram of a 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 front 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 front diagram after the hybrid configuration constellation optimization in Example 2. DETAILED DESCRIPTION

[0042] Specific implementation method 1: This implementation method is 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 target of the single-layer constellation; then establish the objective function according to each optimization target;

[0044] 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 in step 1 is used as output to establish a multi-objective optimization model;

[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 each objective function value, 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 the 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 weight 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), the 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 implementation method 2: This implementation method is different from specific implementation method 1 in that the objectives of the single-layer constellation optimization include constellation coverage performance and system construction cost; wherein: constellation coverage performance includes 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] The 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 implementation method three: This implementation method is different from specific implementation methods one or two in that the calculation method of the system construction cost is:

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

[0066] Specific implementation method four: This implementation method is different from any one of specific implementation methods 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 Specific Embodiments 1 to 3.

[0068] The number of orbital planes P is the number of orbital planes of 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 altitude h is the altitude 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 implementation method 5: This implementation method is different from the specific implementation methods 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 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.

[0076] The other steps and parameters are the same as those in Specific Embodiments 1 to 4.

[0077] Specific implementation method 6: This implementation method is a low-orbit ultra-dense constellation optimization method based on the NSGA-II algorithm, and the method specifically includes the following steps:

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

[0079] 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 in step 1 is used as output to establish a multi-objective optimization model;

[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 each objective function value, 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 satisfy 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 the 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 the threshold A2; otherwise, 30s is used as the threshold A2.

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

[0088] A roughly selected Pareto frontier point is recorded as x1, the total connection time of Pareto frontier point x1 is recorded as T1, and the system construction cost of Pareto frontier point x1 is recorded as Q1; any roughly selected Pareto frontier point other than x1 is recorded as x2, the total connection time of Pareto frontier point x2 is recorded as T2, and the system construction cost of Pareto frontier point x2 is 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 for screening. Even if the pareto frontier point x1 is filtered out, it is necessary to continue to compare other pareto frontier points with the pareto frontier point x1 to filter out the pareto frontier point x2 that meets the conditions; then continue to use the next pareto frontier point as x1, and continue to compare until each pareto frontier point has been compared as x1, and then end the entire comparison process. During the entire comparison process, some pareto frontier points may be filtered out more than once. The purpose of the present invention is to filter out the pareto frontier points that have not been filtered out once.

[0092] Specific implementation example 7: This implementation example is different from specific implementation example 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] The other steps and parameters are the same as those in the sixth embodiment.

[0095] Specific implementation eight: This implementation differs from specific implementation 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] The other steps and parameters are the same as those in the sixth or seventh embodiment.

[0099] Specific implementation nine: This implementation differs from any one of specific implementations 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 implementation method 10: This implementation method is different from any one of specific implementation methods 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 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.

[0105] The other steps and parameters are the same as those in Specific Embodiments 6 to 9.

[0106] Example 1

[0107] Step 1: Simulate a single-layer Walker constellation. Simulate the primary model of the Walker constellation and analyze the coverage performance and link performance. Determine the optimization goals of the single-layer Walker constellation, including coverage performance and system construction cost. The coverage performance specifically includes average coverage rate, average coverage multiplicity and average revisit time. The single-layer Walker constellation is optimized in the direction of large coverage rate and coverage multiplicity, small 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 is a diagram 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 target 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, the orbital inclination i, the number of satellites on a single orbital plane n, and the orbital height h. The four objective functions are:

[0111]

[0112] Among them, the larger the average coverage rate, the larger the constellation's coverage area of ​​the ground, and the larger the average coverage number, the more satellites are visible above the ground station, that is, the more optional satellite nodes for communication, and the more stable the system. The shorter the average revisit time, the shorter the time it takes for the ground station to reconnect to the network after losing contact, and the more reliable the communication system. The lower the system construction cost, the less money is spent and the less money is saved.

[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 into a single-objective optimization problem by weighting or other methods for solution, it often only satisfies one objective function while other objective functions are not ideal, which is not systematic. Since constellation simulation and calculation performance are time-consuming, the present invention adopts the NSGA-II optimization algorithm with higher space complexity and lower time complexity, and obtains the Pareto frontier and the optimal solution set through iterative solution.

[0115] When the NSGA-II algorithm is used 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 interval of 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 ith 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 on all objective functions is the crowding degree of the i-th individual. The more dispersed individuals are, the greater the chance of being selected, making the Pareto front more uniform, maintaining the diversity of the population, and avoiding falling into the local optimum.

[0121] Step 4: According to the Pareto frontier obtained in step 3 and the actual demand focus, several Pareto frontier points with better communication coverage performance are selected for the single-layer Walker constellation, and the low-orbit ultra-dense constellation is designed based on the constellation parameters corresponding to the selected Pareto frontier points in the optimal solution set;

[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 weight 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), the 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 of the single-layer Walker configuration constellation are shown in Figure 5(a) and Figure 5(b). It can be seen that the average coverage multiplicity is distributed between 1.74 and 2.95. When selecting, we can further select points where the objective function value is above the average to increase the communication reliability. Here, we select points where the average coverage multiplicity is above 2. The average coverage rate ranges from 71% to 91%. We select points where the objective function value is above the average. Here, we select points where the average coverage rate is above 80%. The average revisit time is distributed within 69.13s to 5915s, mainly concentrated in the intervals of 69s to 157s and 5800s to 5915s. The shorter the revisit time, the smaller the delay of the terminal re-accessing the network and the stronger the communication reliability. We select points where the objective function value is below the average. Here, we select points where the average revisit time is around 69s. The difference in system construction costs is not large, ranging from 4 to 7.1. If the system construction cost is considered in the end, the points with better coverage performance are preferred, namely the points numbered 4, 5, and 7 in Figure 5(a). The average coverage of these three points in the range of 0°-60°N is above 90%, the average coverage number is above 2.5, and the average revisit time is below 75s.

[0129] According to step 4, the Pareto frontier point with excellent coverage performance can be obtained, and then practical individuals are selected according to 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 the hybrid configuration constellation composed of the Walker constellation and the polar orbit constellation, and analyze the coverage performance and link performance to determine the optimization objectives of the hybrid configuration constellation, including the communication connection time and the system construction cost;

[0132] Since the single-layer Walker configuration ultra-dense constellation already has abundant inter-satellite links and good coverage performance, it requires multi-hop inter-satellite links to establish a communication connection between two ground stations that are far apart on the earth. 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 delays. In order to solve this problem, the present embodiment uses the high coverage of the polar orbit constellation to establish a hybrid configuration constellation of the Walker constellation and the polar orbit constellation. The multi-layer heterogeneous constellation model is as follows: Figure 3 shown.

[0133] like Figure 4 As shown, 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 target determined in step 1 is used as output to establish a multi-objective optimization model;

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

[0136]

[0137] The connection time indicates the time it takes to establish a four-hop link of "ground station A-walker constellation-polar orbit constellation-Walker constellation-polar orbit constellation-ground station B". If the inter-satellite link using a single-layer Walker constellation requires more than four hops to establish communication, the communication delay is large. By establishing this four-hop link, it is possible to avoid using inter-satellite link communications with more hops, thereby reducing the communication delay and achieving better 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 each objective function value, 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 into a single-objective optimization problem by weighting or other methods for solution, it often only satisfies one objective function while other objective functions are not ideal, which is not systematic. Since constellation simulation and calculation performance are time-consuming, the present invention adopts the NSGA-II optimization algorithm with higher space complexity and lower time complexity, and obtains the Pareto frontier point set and the optimal solution set through iterative solution.

[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 range is shown in Table 2:

[0141] Table 2

[0142]

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

[0144]

[0145] Among them, d i is the crowding distance of the ith 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 on all objective functions is the crowding degree of the i-th individual. The more dispersed individuals are, the greater the chance of being selected, making the Pareto front more uniform, maintaining the diversity of the population, and avoiding falling into the local optimum.

[0146] Step 4: According to the Pareto frontier point set obtained in step 3 and the actual demand focus, several Pareto frontier points with better communication connection performance are selected for the multi-layer heterogeneous constellation, and the low-orbit ultra-dense constellation is designed based on the constellation parameters corresponding to the selected Pareto frontier points in the optimal solution set;

[0147] The specific process of step 4 is as follows:

[0148] First, roughly select the Pareto frontier points that satisfy 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 the 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 the threshold A2; otherwise, 30s is used as the threshold A2.

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

[0152] A roughly selected Pareto frontier point is recorded as x1, the total connection time of Pareto frontier point x1 is recorded as T1, and the system construction cost of Pareto frontier point x1 is recorded as Q1; any roughly selected Pareto frontier point other than x1 is recorded as x2, the total connection time of Pareto frontier point x2 is recorded as T2, and the system construction cost of Pareto frontier point x2 is 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, the processing method of the data obtained after the constellation optimization using the NSGA-II algorithm in step 4 is:

[0156] Through step three, Figure 6 From the optimization results, we can see that the total connection time is between 7328s and 45671s, the maximum total connection time accounts for 52.86% of the whole day, and the average connection time ranges from 22.97s to 36.89s. This also shows the discontinuity of access. The four-hop communication time through this mode is relatively short each time, and the system construction cost ranges from 1.25 to 54.62. In actual projects, we can also choose the solution that best suits the current project according to the different emphasis on indicators.

[0157] Table 3

[0158]

[0159] As shown in Table 3, if the system construction cost is considered last and the link performance is given priority, then individuals 2, 4, and 6 are the best performers, with a total connection time of more than 42718s, accounting for 49.4% of the whole day, and an average connection time of more than 33.88s. The heterogeneous constellation optimization in this embodiment is to establish a long-term communication of a four-hop link of "New York Station-Starlink-polarsats-Starlink-China Beijing Station". In addition, communication can be achieved by establishing a multi-hop intersatellite link inside Starlink. Using polar orbit constellations as intermediate communication nodes for satellite communications can reduce the number of communication hops, reduce communication delays, and the intersatellite links established are relatively simple.

[0160] The chart data obtained in step 4 shows that point No. 2 achieves link performance close to that of points 4 and 6 with high system construction costs at a very low system construction cost. The total connection time of point No. 2 is reduced by 6.47% compared to point No. 4, but the system construction cost is reduced by 54.98%. The total connection time of point No. 2 is reduced by 2.95% compared to point No. 6, but the system construction cost is reduced by 32.74%. Expanding to other instances, individuals with a communication performance reduction of less than 10% and a system construction cost reduction of more than 30% can be selected to achieve the purpose of reducing system costs.

[0161] The present invention can effectively reduce system cost when link performance is close by adjusting constellation parameters, which proves the advantage 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 calculation examples of the present invention are only used to explain the calculation model and calculation process of the present invention in detail, and are not intended to limit the implementation methods of the present invention. For ordinary technicians in the relevant field, other different forms of changes or modifications can be made based on the above description. It is impossible to list all the implementation methods here. All obvious changes or modifications derived from the technical solution of the present invention are still 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 target of the single-layer constellation; then establish the objective function according to each optimization target; 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 in step 1 is used as output to establish a multi-objective optimization model; 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 each objective function value, and the optimal solution set includes the 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 weight 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), the 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, characterized in that: The objectives of the single-layer constellation optimization include constellation coverage performance and system construction cost; wherein: constellation coverage performance includes 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, characterized in that: 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, characterized in that: 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, characterized in that: In the NSGA-II algorithm, the congestion degree calculation method is 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 target of the hybrid configuration constellation; then establish the objective function according to each optimization target; 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 in step 1 is used as output to establish a multi-objective optimization model; 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 each objective function value, and the optimal solution set includes the 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 satisfy 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 the 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 the threshold A2. Otherwise, 30s is used as the threshold A2. Secondly, the roughly selected Pareto frontier points are screened, and the screening rules are as follows: A roughly selected Pareto frontier point is recorded as x1, the total connection time of Pareto frontier point x1 is recorded as T1, and the system construction cost of Pareto frontier point x1 is recorded as Q1; any roughly selected Pareto frontier point other than x1 is recorded as x2, the total connection time of Pareto frontier point x2 is recorded as T2, and the system construction cost of Pareto frontier point x2 is 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, characterized in that: The objectives of hybrid 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, characterized in that: 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, characterized in that: 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, characterized in that: In the NSGA-II algorithm, the congestion degree calculation method is 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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