A hybrid multi-layer constellation design method with synchronous and regressive orbital precession

Abstract

The present invention relates to the technical field of satellite constellation design, and specifically discloses a hybrid multi-layer constellation design method for orbital precession synchronization and regression. Step S01: Obtain an orbital precession rate according to an orbital altitude and an orbital inclination, and construct an orbital precession synchronization hybrid multi-layer constellation according to the orbital precession rate; Step S02: Obtain a change curve of orbital altitude and orbital inclination and a regression coefficient curve according to a regression orbit, and use them to determine the orbital altitude and orbital inclination according to the regression coefficient; Step S03: Determine each layer of sub-constellation according to the change curve of orbital altitude and orbital inclination and the orbital precession rate, and obtain a hybrid multi-layer constellation with orbital precession synchronization and regression; Step S04: Construct a multi-objective optimization model, determine the optimization target and constraint conditions, and optimize the hybrid multi-layer constellation with orbital precession synchronization and regression.

Description

Technical Field

[0001] The invention relates to the technical field of satellite constellation design, and specifically discloses a hybrid multi-layer constellation design method for orbital precession synchronization and regression. Background Art

[0002] In order to fairly and efficiently meet the service quality requirements of ground users in different regions, constellation design is the key to building a low-orbit satellite network. At present, many scholars have studied the design of single-layer low-orbit constellations, but as the number of satellites in a single-layer constellation increases, satellite redundancy problems will arise. For example, although the single-layer Walker-Star constellation can achieve global coverage, considering the global population distribution, the population density in high-latitude areas is low but the satellite coverage rate is too high, resulting in a serious waste of satellite resources and limited optimization space; while the single-layer Walker-δ constellation has better coverage performance in low and medium latitudes, but it is difficult to achieve better global coverage. In addition, deploying a large number of satellites at the same altitude will increase the risk of collisions between satellites. Summary of the invention

[0003] In view of the above problems, the purpose of the present invention is to provide a hybrid multi-layer constellation design method with synchronous and regressive orbital precession. The long-term configuration maintenance and orbit prediction of the hybrid multi-layer constellation are comprehensively considered to ensure the stability of the constellation configuration.

[0004] The technical solution adopted by the present invention is: a hybrid multi-layer constellation design method for orbital precession synchronization and regression, comprising:

[0005] Step S01: obtaining an orbital precession rate according to an orbital altitude and an orbital inclination, and constructing an orbital precession synchronous hybrid multi-layer constellation according to the orbital precession rate;

[0006] Step S02: obtaining a change curve of orbit height and orbit inclination and a regression coefficient curve according to the regression orbit, so as to determine the orbit height and orbit inclination according to the regression coefficient;

[0007] Step S03: determining each layer of sub-constellation according to the change curve of the orbital height and orbital inclination and the orbital precession rate, and obtaining a hybrid multi-layer constellation with synchronous and regressive orbital precession;

[0008] Step S04: construct a multi-objective optimization model, determine optimization objectives and constraints, and optimize the orbit precession synchronous and regressive hybrid multi-layer constellation.

[0009] Furthermore, the method for determining the orbital precession rate is:

[0010] ;

[0011] ;

[0012] ;

[0013] in, is the right ascension of the ascending node of the orbital plane, is the rate of change of right ascension of the ascending node, is the average radius of the Earth, is the Earth's gravitational constant, is the semi-major axis of the orbit, is the average angular velocity of the satellite, is the orbital inclination, is the orbital altitude, J2 is a constant representing the second harmonic coefficient of the Earth’s gravity field.

[0014] Preferably, the orbital precession rates of the sub-constellations of each layer in the orbital precession synchronous hybrid multi-layer constellation are the same.

[0015] Furthermore, the regression trajectory satisfies:

[0016] ;

[0017] in, is the node period of the circular orbit satellite, is the node day, is a fixed time interval, D and N are the minimum number of days and circles required to achieve subsatellite point trajectory repetition, respectively;

[0018] The regression coefficient is: ;

[0019] in, is the regression coefficient, D and N are the minimum number of days and circles required to achieve sub-satellite point trajectory repetition, respectively.

[0020] Preferably, the variation curve of the track height and track inclination is:

[0021] ;

[0022] ;

[0023] ;

[0024] in, is the semi-major axis of the orbit, is the Earth's gravitational constant, is the regression coefficient, is the Earth's rotation angular velocity, is the second-order band harmonic coefficient in the Earth's gravitational field, is the radius of the Earth, is the orbit height, is the orbital inclination.

[0025] Preferably, the orbital precession rates and regression coefficients of the sub-constellations at each layer in step S03 are the same.

[0026] Preferably, the method further comprises: estimating a minimum orbital inclination according to a latitude range expected to be covered by a hybrid multi-layer constellation that is synchronous with orbital precession and regressive, wherein the minimum orbital inclination satisfies:

[0027] ;

[0028] in, is the minimum orbital inclination, is the highest latitude expected to be covered, is the half geocentric angle of the satellite's coverage of the earth, is the margin degree estimate, is the minimum elevation angle, is the radius of the Earth, is the track height.

[0029] Preferably, the optimization indicators of the multi-objective optimization model include average coverage multiplicity, coverage uniformity within the mission latitude area, and the total number of satellites in the hybrid constellation;

[0030] The average coverage weight is:

[0031] ;

[0032] ;

[0033] ;

[0034] ;

[0035] The coverage uniformity within the mission latitude area is:

[0036] ;

[0037] The total number of satellites in the hybrid constellation is:

[0038] ;

[0039] in, is the total number of grids in the i-th latitude band, To solve the function of satellite coverage multiplicity, is the satellite coverage multiplicity of the sth grid, T is the constellation simulation period, is the latitude of the grid point user, is the longitude of the grid point user, is the number of sub-constellation orbital planes, is the number of satellites in the orbital plane of the sub-constellation, is the average coverage weight of the i-th latitude band, t represents the simulation time step, is the i-th latitude band, is the maximum longitude range, and are the resolutions in latitude and longitude respectively, is the uniformity of coverage of the hybrid constellation on the i-th latitude band on the ground, is the total number of satellites in the hybrid constellation, K is the number of orbital layers in the constellation, is the number of track surfaces in the j-th track layer, is the number of satellites in the orbital plane of the jth orbital layer.

[0040] Furthermore, the optimization goal is: to simultaneously satisfy the maximum average coverage multiplicity and the maximum uniformity of coverage in the mission latitude area, and to minimize the total number of satellites in the hybrid constellation.

[0041] Furthermore, the constraint condition is:

[0042] ;

[0043] ;

[0044] in, They represent the three objective functions of average coverage weight, uniformity of coverage in the mission latitude area, and the total number of satellites in the hybrid constellation. is the coverage multiplicity of any grid in the i-th latitude band, is the minimum coverage required by the mission in the i-th latitude band, is the maximum value of the total number of satellites in the hybrid constellation, and are the minimum and maximum values ​​of the number of orbital planes to be optimized for the j-th sub-constellation, and are the minimum and maximum values ​​of the number of satellites to be optimized in the orbital plane of the j-th sub-constellation, is the phase factor of the j-th sub-constellation, is an integer, Is a positive integer.

[0045] Beneficial effects of the above technical solution:

[0046] The present invention provides a hybrid multi-layer constellation design method with synchronous and regressive orbital precession, which divides the satellite constellation into multiple layers and deploys more satellites on orbits with different altitudes and inclinations, thereby improving the coverage performance of the constellation; at the same time, deploying satellites at different altitudes can reduce the risk of space collisions, significantly improve the performance and flexibility of the constellation, and meet the needs of future communications and other space missions; on the other hand, for a multi-layer hybrid constellation, the differences in orbital altitudes and inclinations of each layer in the constellation will lead to inconsistent precession rates of the orbital planes of each layer. The present invention takes into account the long-term configuration maintenance and orbit prediction of the hybrid multi-layer constellation, thereby ensuring the stability of the constellation configuration. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 A flow chart of the orbital precession synchronization and regression hybrid multi-layer constellation design method of the present invention;

[0048] Figure 2 A graph showing the change of orbital plane precession rate with orbital inclination at different orbital altitudes provided by one embodiment of the present invention;

[0049] Figure 3 A regression curve diagram formed by the change of the regression coefficient corresponding to the orbit height with the inclination angle provided in one embodiment of the present invention;

[0050] Figure 4 A schematic diagram of the change of orbital altitude with inclination of the regression coefficient and the right ascension rate of ascending node provided by one embodiment of the present invention;

[0051] Figure 5 A schematic diagram of the variation of the half-angle of the earth's center covered by a satellite with respect to the earth as a function of the orbital altitude provided in one embodiment of the present invention;

[0052] Figure 6 This is a schematic diagram of the world's population distribution at intervals of 1 degree in 2020. DETAILED DESCRIPTION

[0053] The following is a further detailed description of the implementation methods of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than an exhaustive list of all the embodiments. It should be noted that the embodiments and features in the embodiments of the present application can be combined with each other without conflict.

[0054] The terms "first", "second", etc. (if any) in the specification and claims are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that the terms used in this way are interchangeable where appropriate so that the embodiments described herein can be implemented in an order other than that illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions, for example, a process, method, system, product, or device that includes a series of steps or units is not necessarily limited to those steps or units that are clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products, or devices.

[0055] It should be understood that the term "and / or" used in this article is only a description of the association relationship of associated objects, indicating that there can be three relationships. For example, A and / or B can represent: A exists alone, A and B exist at the same time, and B exists alone. In addition, the character " / " in this article generally indicates that the associated objects before and after are in an "or" relationship.

[0056] Embodiment 1

[0057] like Figure 1 The flowchart of the hybrid multi-layer constellation design method for orbital precession synchronization and regression of the present invention is shown, which specifically includes the following steps:

[0058] (I): Hybrid multi-layer giant star constellation configuration design A hybrid multi-layer constellation is composed of multiple sub-constellations with different altitudes and inclinations. Considering the stability of the constellation configuration, the satellites in the sub-constellation generally use the same orbital altitude and inclination. The hybrid multi-layer constellation of the present invention is a uniform constellation of circular orbits. The configuration of the sub-constellation can be various Walker constellation configurations such as Walker-Star and Walker-δ, Flower constellation configuration, sun-synchronous orbit constellation, pearl chain constellation and other constellation configurations. In order to ensure the stability of the overall configuration of the constellation, the configuration of each sub-constellation is designed to be the same configuration, combined into a hybrid multi-layer constellation.

[0059] (II): Design of orbital precession synchronous hybrid multi-layer constellation under the action of J2 perturbation

[0060] Since the satellites of the hybrid constellation are deployed at different altitudes and inclinations, the non-spherical J2 perturbation of the earth will cause differences in the precession of the satellite orbital plane, affecting the overall stability of the constellation, and then changing the basic configuration of the constellation as a whole, making it impossible for the constellation to operate accurately according to the established plan. In order to maintain the stability of the overall configuration of the hybrid constellation, it is necessary to reasonably select the orbits of the sub-constellation, and use the appropriate orbital altitude and inclination to adjust the precession rate of the orbital plane, that is, orbits with different orbital radii and inclinations but the same node precession speed, and use these orbits to form a hybrid constellation.

[0061] If only the J2 perturbation is considered, the orbital precession rate is calculated using equation (1), and the change of the orbital plane precession rate with the orbital inclination at different orbital altitudes is obtained, as follows: Figure 2 The change of orbital plane precession rate with orbital inclination at different orbital altitudes is shown in the figure.

[0062] (1)

[0063] In the formula, is the right ascension of the ascending node of the orbital plane, is the rate of change of the right ascension of the ascending node (i.e. the rate of precession of the orbital plane), is the average radius of the Earth, is the Earth's gravitational constant, is the semi-major axis of the orbit, is the average angular velocity of the satellite, and , is the orbit inclination, if the orbit height is , then .

[0064] When designing a hybrid constellation with orbital precession synchronization, first determine a Walker sub-constellation with a basic orbital precession rate, preferably a Walker sub-constellation. The orbital inclination can be determined by the highest latitude area covered, and the corresponding orbital altitude is selected; then other sub-constellations with the same orbital precession rate are selected according to the coverage (orbital altitude and inclination correspond one to one); finally, the entire hybrid constellation with precession synchronization is determined while meeting the performance requirements. Therefore, for a multi-layer hybrid constellation with orbital precession synchronization, the circular orbit precession rate (i.e., the rate of change of the satellite's ascending node right ascension) of different constellation layers should meet the following conditions:

[0065] (2)

[0066] In the formula, is the orbital precession rate of the first-layer constellation, C is a constant, indicating a fixed orbital precession rate, and K is a hybrid constellation with K layers of sub-constellations.

[0067] (III): Design of regression orbit under the action of J2 perturbation

[0068] Adjusting the height and inclination of the satellite orbit can not only achieve the precession synchronization of the orbital plane, but also meet the conditions of the regression orbit when the orbital height and inclination are appropriate, and achieve the repetition of the satellite's ground track. The regression orbit under the action of the J2 perturbation should meet the following conditions:

[0069] (3)

[0070] In the formula, is the node (node) period of the circular orbit satellite, is the node (node) day (the time interval between two passages of a fixed equatorial point on the ascending node of the satellite orbit, in sidereal days), is a fixed time interval, i.e., the regression (or repetition) period. The positive integers D and N are mutually prime, and are the minimum number of days and circles required to achieve the repetition of the subsatellite point trajectory. is the regression coefficient.

[0071] If the Earth's gravitational constant is , the angular velocity of the Earth's rotation is Assume that the semi-major axis of the satellite's orbit is , the orbit height is , the inclination angle is The average angular velocity is ,but Assume that the rate of change of the right ascension and latitude of the ascending node is and , then the cycle and It can be expressed as:

[0072] (4)

[0073] The corresponding rate of change and It can be expressed as:

[0074] ;

[0075] (5)

[0076] In the formula, is the radius of the earth, and J2 is the second-order band harmonic coefficient in the earth's gravitational field.

[0077] Therefore, when the regression coefficient is given and orbital inclination When the semi-major axis of the orbit for:

[0078] (6)

[0079] (7)

[0080] For the radius , the inclination angle is For any circular orbit with an inclination ,radius Any close to The repetitive ground track trajectory can be used to find the regression coefficients with any pre-specified accuracy. When assigning and Then, the orbital semi-major axis can be obtained by solving equations (6) and (7): (or height , ). Therefore, for each regression coefficient , all have The value corresponds to the regression curve formed by the change of orbital height with inclination. That is, when the regression coefficient is When the orbit semi-major axis (or orbit height) changes with the orbit inclination, the orbit semi-major axis (or orbit height) at different inclinations can be obtained according to equations (6) and (7).

[0081] The Newton iteration method is used to solve the problem. The specific algorithm is as follows:

[0082] First, according to formula (6), let:

[0083] (8)

[0084] Secondly, based on:

[0085] (9)

[0086] And taking the first-order derivative, we have:

[0087] (10)

[0088] Finally, you need to select the initial value of the iteration , and determine the convergence condition Medium convergence criterion The size of the semi-major axis If the size is in the order of kilometers, the accuracy of centimeters is sufficient to meet the requirements, so we take .

[0089] Based on the above method, for low earth orbit, Figure 3 The regression curve formed by the regression coefficient corresponding to the orbit height changing with the inclination angle shows the relationship between the orbit height and the inclination angle obtained by using equations (6) and (7) after the regression coefficient Q is given, where D takes the values ​​of 1 and 2.

[0090] 4. Hybrid multi-layer constellation design with synchronous and regressive orbital precession

[0091] When the regression coefficient is given When the orbital semi-major axis (or altitude) and the inclination angle are in one-to-one correspondence, the altitude usually increases gradually with the increase of the inclination angle. When is a constant, there is also a one-to-one correspondence between orbital altitude and inclination. Therefore, by combining the curve of orbital altitude versus inclination when the regression coefficient and the right ascension rate of the ascending node are given, the orbital altitude and inclination of the corresponding Walker sub-constellation can be determined.

[0092] Figure 4 Schematic diagram of the orbital altitude variation with inclination, showing the regression coefficient and the rate of change of the right ascension of the ascending node. The regression coefficients are -4.8, -4.3 and When the orbital altitude is 13, 13.5, 14, and 14.5, the relationship between the orbital altitude and the inclination angle. The intersection of the ascending node right ascension rate curve and the regression coefficient curve is the only determined orbital altitude and inclination angle, and these intersection points simultaneously meet the conditions for regression orbit and orbital precession synchronization. Therefore, for a precession-synchronized hybrid multi-layer regression orbit constellation, the regression orbits of each layer of sub-constellation are required to have the same node precession rate. First, determine the orbital precession rate of the hybrid constellation, and then determine the regression coefficient of the sub-constellation according to the specific requirements of the constellation. For Walker sub-constellations with symmetrical configurations, the precession rates and regression coefficients of satellites in the same sub-constellation are the same. Therefore, as long as the orbital altitude and inclination of a certain satellite in the constellation meet precession synchronization and are a regression orbit, the orbit of this layer of sub-constellation is a precession-synchronized regression orbit constellation.

[0093] Assume that there are K layers of Walker sub-constellations in the hybrid constellation. , , , Respectively The total number of satellites, regression coefficients, orbital semi-major axes and inclinations of the Walker sub-constellation. ,express In intervals of 1 from 1 to K The precession rate of a given hybrid constellation is After that, set the Regression coefficients for layer constellations , we can uniquely determine the satellites in the sub-constellation and , because for Walker constellations we have , , where superscript 1 and Respectively represent The first and satellites, the corresponding orbital altitude .

[0094] The relationship between satellites in a hybrid constellation:

[0095] (11)

[0096] The specific design steps are as follows:

[0097] Step 1: Determine the latitude range you want to cover based on mission requirements And estimate the minimum orbital inclination , refer to formula (10):

[0098] (12)

[0099] Where: is the half geocentric angle of the satellite's coverage of the earth, is the minimum elevation angle, is the radius of the Earth, For margin estimation, it is generally taken between 1° and 3° to achieve the purpose of completely covering the edge of the latitude band. Since the orbital inclination has the greatest impact on the latitude range covered by the satellite, and the orbital height is second. Similarly, the inclination has a great impact on the coverage capability of the constellation. The larger the inclination, the fewer satellites are needed to cover the high latitudes. Therefore, for the constellation network coverage, by weighing the continuity and uniformity of the coverage of the high-latitude edge area, the orbital inclination is A certain threshold value needs to be added. After simulation analysis, the present invention selects a threshold value of 2°.

[0100] From formula (12), we can get the variation of the half-coverage angle of the Earth's center with the orbit altitude in the low-orbit range of 500-2000km at an elevation angle of 10°, as follows: Figure 5 The satellite's half-angle of coverage of the earth's center changes with the orbital altitude. According to formula (12), in step 1, the satellite orbital altitude is used to determine , using the orbit regression characteristics to preliminarily determine the regression coefficient according to the mission requirements, and give the possible minimum orbit height. It can be seen that the orbit height and the orbit semi-major axis correspond one to one.

[0101] Step 2: According to Divide the coverage latitude area. According to the needs, select several latitudes as the reference points for stratification (orbital stratification requirements of the mission), and divide them into multiple latitude intervals, that is, as different mission areas (such as observation, communication, etc.), so as to preliminarily determine the orbital inclination of each layer.

[0102] Step 3: Preliminary determination of the baseline precession rate of the hybrid constellation First, according to Figure 4 and inclination A preliminary qualitative analysis of the precession rate is performed, and the range of orbital altitude is obtained. Then, according to the orbital layering requirements of the mission, the inclination of each layer of sub-constellation is preliminarily determined. Since the regression coefficient is greatly affected by the orbital altitude (semi-major axis), the appropriate orbital semi-major axis is then determined based on the regression orbit conditions and equations (6)-(10) combined with the inclination. (i.e. orbit height ); Finally, quantitative calculation is performed and the required value is fine-tuned to meet the inclination requirements, thereby determining the final reference precession rate .

[0103] Step 4: Using the data from Steps 2 and 3 , ( ), and determine the number of satellites and spatial distribution of the Walker sub-constellation according to the mission needs and requirements, that is, to obtain the spatial configuration of the sub-constellation. This step can be solved by an optimization algorithm to ensure that the constellation that meets the mission requirements has excellent performance and low cost. The spatial configuration of the Walker sub-constellation includes the parameters P / S / F, which are the number of sub-constellation orbital planes, the number of orbital satellites and the phase factor. The total number of sub-constellation satellites is .

[0104] Step 5: Each layer of track needs to meet the requirements of the ground repeat track, that is, set the Regression coefficients for layer constellations , then in the design , Need to consider , ( , ) value pair Finally, the intersection of the ascending node right ascension rate curve and the regression coefficient curve is used to determine the inclination and semi-major axis (or height) of each layer, such as Figure 4 The horizontal and vertical coordinates of the intersection shown in the figure correspond to the orbital inclination and orbital altitude.

[0105] Step 6: Obtain the inclination of each sub-constellation orbital layer according to the methods of steps 1, 2 and 3 , assuming there are K layers of sub-constellations), using equation (11) we can preliminarily obtain the orbital semi-major axis of each layer: (or track height ), and then solve the spatial configuration of each layer of Walker sub-constellation according to step 4.

[0106] because and There is coupling between and ( ) influence each other, and it is necessary to perform iterative selection and adjustment optimization during calculation.

[0107] Multi-layer constellation comprehensive optimization solution:

[0108] Since the designed multi-layer hybrid constellation can achieve orbital precession synchronization and regression, the constellation configuration can remain stable for a period of time, and the disadvantages of simultaneous optimization design of multi-layer hybrid constellations in the prior art can be ignored. This step can combine steps 4, 5, and 6 to simultaneously design and optimize the sub-constellation configuration of each layer. The specific method is as follows:

[0109] (1) Determine the parameters to be optimized when optimizing the design of multi-layer hybrid constellations:

[0110] Assume that there is a hybrid constellation with orbital precession synchronous regression ( ) Walker sub-constellations, the configuration parameters of the j-th sub-constellation are: , are the number of satellite orbital planes of the sub-constellation, the number of satellites in each plane, the phase factor, and the orbital altitude and inclination.

[0111] According to the orbital precession rate and the regression orbit constraint, the unique orbital semi-major axis and inclination of each layer can be determined, that is, the constellation parameters can be determined. , then the parameters to be optimized for the sub-constellation configuration are simplified to The parameter set to be optimized for the multi-layer hybrid constellation is the sum of the parameters to be optimized for the K sub-constellations, which can be expressed as: .

[0112] (2) According to the mission requirements, determine the constraints and the optimization range of parameters, and use the optimization algorithm to optimize the constellation configuration parameters. The specific process of multi-layer constellation configuration comprehensive optimization is as follows:

[0113] The world's population is mainly distributed between 65° north and south latitude. It is assumed that the mission requirement is to use the average coverage density, the uniformity of coverage in the mission latitude area, and the total number of satellites in the hybrid constellation to achieve the best trade-off between regional coverage performance and cost efficiency between 65° north and south latitude.

[0114] First, we divide the service area into latitude zones for the 65° north and south latitude regions according to the distribution pattern of the world population along latitude. We then build a user model based on latitude distribution with reference to the population distribution data in 2020. Figure 6 This is a diagram showing the world population distribution at 1 degree intervals in 2020. According to the population distribution, the area between 65° north and south latitude is divided into : Between 0° and 20° north / south latitude, : Between 20° and 50° north and south latitudes and : Three latitude bands between 50°~65° north / south latitude.

[0115] Secondly, a multi-objective optimization model is established, including:

[0116] ①Average coverage weight

[0117] definition Solve the function of satellite coverage multiplicity, For the s The satellite coverage multiplicity of a grid is T The average coverage weight is:

[0118] (13)

[0119] In the formula, is the latitude of the grid point user, is the grid accuracy in latitude, is the i-th latitude band, i=1,2,3, let is the latitude value 0; similarly is the longitude of the grid point user, is the grid accuracy of longitude; t is the simulation time, is the simulation time step, then within a simulation period T, the time series corresponding to all simulation epochs is , then through statistics, the average coverage weight in each communication latitude band within a simulation cycle can be obtained as:

[0120] (14)

[0121] In the formula, i is the number of the latitude zone. is the total number of grids in the i-th latitude band.

[0122] ② Coverage uniformity within the mission latitude area

[0123] Within each latitude band, the higher the uniformity of latitude distribution, the smaller the difference between the number of coverage repetitions at each latitude and the overall average number of coverage repetitions, that is, the better the uniformity of coverage, which can effectively reduce satellite redundancy. The uniformity of coverage repetitions according to latitude distribution can be expressed by the standard deviation of user coverage in the statistical grid points, and the uniformity of coverage repetitions in each communication latitude band area is:

[0124] (15)

[0125] In the formula, It is the uniformity of the coverage of the i-th latitude band on the ground by the hybrid constellation. The smaller the value, the more uniform it is.

[0126] ③Total number of satellites in hybrid constellation

[0127] Assume that the configuration parameters of the j-th sub-constellation are: , are the number of satellite orbital planes of the sub-constellation, the number of satellites in each plane, the phase factor, and the orbital height and inclination. The total number of satellites in the sub-constellation is: . Assuming a hybrid constellation with K Layer sub-constellation number (the number of layers of the sub-constellation K Determined according to mission requirements), the total number of satellites in the hybrid constellation is:

[0128] (16)

[0129] Due to the deployment, management and operating costs of satellite constellations, it is preferred to complete the mission with the least number of satellites. One of the focuses of analyzing and designing satellite constellations is to minimize the number of satellites required to provide communication services.

[0130] Determine the objective function and constraints

[0131] The constraints are:

[0132] (17)

[0133] The objective function is:

[0134] (18)

[0135] in, They represent the three objective functions of average coverage weight, uniformity of coverage in the mission latitude area, and the total number of satellites in the hybrid constellation. is the coverage multiplicity of any grid in the i-th latitude band, is the minimum coverage required by the mission in the i-th latitude band, is the maximum value of the total number of satellites in the hybrid constellation, and are the minimum and maximum values ​​of the number of orbital planes to be optimized for the j-th sub-constellation, and are the minimum and maximum values ​​of the number of satellites to be optimized in the orbital plane of the j-th sub-constellation, is the phase factor of the j-th sub-constellation, is an integer, Is a positive integer.

[0136] According to the above mission requirements, the goal of multi-layer constellation design is to achieve the best trade-off between coverage performance and cost between 65° north and south latitude, that is, to determine the optimal hybrid constellation configuration to maximize the average coverage multiplicity and the uniformity of coverage in each latitude band, while minimizing the total number of satellites in the hybrid constellation.

[0137] If the coverage multiplicity and coverage uniformity of the three latitude bands are set as the objectives respectively, the complexity of problem solving will increase. We can combine the same type of objective functions by setting appropriate weight factors. According to the population distribution by latitude, the weight factors of the three latitude bands are set to 0.4, 0.5 and 0.1 respectively. Then the average coverage multiplicity and coverage uniformity of the latitude distribution are:

[0138] (19)

[0139] Convert the optimization index into the objective function:

[0140] (20)

[0141] Using the minimization optimization method, the optimization objectives and constraints are as follows:

[0142] (twenty one)

[0143] In the formula, , , They are the minimum coverage multiplicity required by the tasks in three dimensions respectively. It is the maximum value of the total number of satellites in the hybrid constellation.

[0144] Finally, the optimization solution is obtained. According to the above objective function and constraints, the NSGA-III algorithm is used to optimize the problem and determine the final spatial configuration of the hybrid multi-layer constellation.

[0145] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not limitations on the implementation methods of the present invention. For ordinary technicians in the relevant field, other different forms of changes or modifications can be made on the basis of 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 protection scope of the present invention.

Claims

1. A hybrid multi-layer constellation design method for orbital precession synchronization and regression, characterized in that: include: Step S01: obtaining an orbital precession rate according to an orbital altitude and an orbital inclination, and constructing an orbital precession synchronous hybrid multi-layer constellation according to the orbital precession rate; Step S02: obtaining a change curve of orbit height and orbit inclination and a regression coefficient curve according to the regression orbit, so as to determine the orbit height and orbit inclination according to the regression coefficient; Step S03: determining each layer of sub-constellation according to the change curve of the orbital height and orbital inclination and the orbital precession rate, and obtaining a hybrid multi-layer constellation with synchronous and regressive orbital precession; Step S04: construct a multi-objective optimization model, determine optimization objectives and constraints, and optimize the orbital precession synchronous and regressive hybrid multi-layer constellation; The optimization indicators of the multi-objective optimization model include average coverage multiplicity, coverage uniformity in the mission latitude area, and the total number of satellites in the hybrid constellation; The average coverage weight is: Lat=[Lati,Lati+△Lat,…,Lat(i+1)-△Lat,Lat(i+1)] Lon=[0,△Lon,…,mLon-△Lon,mLon]; The coverage uniformity within the mission latitude area is: The total number of satellites in the hybrid constellation is: Among them, S i is the total number of grids in the i-th latitude band, To solve the function of satellite coverage multiplicity, is the satellite coverage multiplicity of the sth grid, T is the constellation simulation period, Lat is the latitude of the grid point user, Lon is the longitude of the grid point user, P j is the number of sub-constellation orbital planes, S j is the number of satellites in the orbital plane of the sub-constellation, Cov i is the average coverage of the ith latitude band, t represents the simulation time step, Lati is the ith latitude band, mLon is the maximum longitude range, △Lat and △Lon are the resolutions of latitude and longitude respectively, Std i is the uniformity of coverage of the ground i-th latitude band by the hybrid constellation, N total is the total number of satellites in the hybrid constellation, K is the number of orbital layers in the constellation, and P j is the number of track surfaces in the jth track layer, S j is the number of satellites in the orbital plane of the jth orbital layer.

2. The orbital precession synchronous and regressive hybrid multi-layer constellation design method according to claim 1, characterized in that: The method for determining the orbital precession rate is: a=R E +h; Where Ω is the right ascension of the ascending node of the orbital plane, R is the rate of change of right ascension of ascending node, E is the average radius of the Earth, μ is the Earth's gravitational constant, a is the semi-major axis of the orbit, and n s is the average angular velocity of the satellite, i is the orbital inclination, h is the orbital altitude, and J2 is a constant representing the second-band harmonic coefficient of the Earth’s gravity field.

3. The orbit precession synchronous and regressive hybrid multi-layer constellation design method according to claim 1, characterized in that: The orbital precession rates of the sub-constellations of each layer in the orbital precession synchronous hybrid multi-layer constellation are the same.

4. The orbit precession synchronous and regressive hybrid multi-layer constellation design method according to claim 2, characterized in that: The regression trajectory satisfies: T r =NT Ω =DT E ; Among them, T Ω is the node period of the circular orbit satellite, T E is the node days, T r is a fixed time interval, D and N are the minimum number of days and circles required to achieve subsatellite point trajectory repetition, respectively; The regression coefficient is: Q = N / D; Where Q is the regression coefficient, D and N are the minimum number of days and circles required to achieve sub-satellite point trajectory repetition, respectively.

5. The orbital precession synchronous and regressive hybrid multi-layer constellation design method according to claim 1, characterized in that: The variation curve of orbit height and orbit inclination: a 3.5 +b1a 2 +b2=0 a=R E +h; Where a is the semi-major axis of the orbit, μ is the Earth's gravitational constant, Q is the regression coefficient, ω E is the angular velocity of the earth's rotation, J2 is the second-order harmonic coefficient in the earth's gravitational field, R E is the radius of the earth, h is the orbital altitude, and i is the orbital inclination.

6. The orbit precession synchronous and regressive hybrid multi-layer constellation design method according to claim 1, characterized in that: In step S03, the orbital precession rates and regression coefficients of the sub-constellations of each layer are the same.

7. The orbit precession synchronous and regressive hybrid multi-layer constellation design method according to claim 1, characterized in that: Also includes: The minimum orbital inclination is estimated based on the latitude range expected to be covered by the orbit precession synchronous and regressive hybrid multi-layer constellation, and the minimum orbital inclination satisfies: Where i0 is the minimum orbital inclination, is the highest latitude expected to be covered, α is the half-geocentric angle of the satellite to the ground, ξ is the margin degree estimate, ε is the minimum elevation angle, R E is the radius of the earth and h is the orbital altitude.

8. The orbit precession synchronous and regressive hybrid multi-layer constellation design method according to claim 1, characterized in that: The optimization goal is: to simultaneously meet the average coverage multiplicity and the maximum coverage uniformity in the mission latitude area, and to minimize the total number of satellites in the hybrid constellation.

9. The orbit precession synchronous and regressive hybrid multi-layer constellation design method according to claim 1, characterized in that: The constraints are: Among them, f1, f2, and f3 represent the three objective functions of average coverage multiplicity, coverage uniformity in the mission latitude area, and the total number of satellites in the hybrid constellation, respectively. is the coverage multiplicity of any grid in the i-th latitude band, is the minimum coverage required by the mission in the i-th latitude band, N max is the maximum value of the total number of satellites in the hybrid constellation, and are the minimum and maximum values ​​of the number of orbital planes to be optimized for the j-th sub-constellation, and are the minimum and maximum numbers of satellites to be optimized in the orbital plane of the j-th sub-constellation, respectively. j is the phase factor of the j-th sub-constellation, is an integer, Is a positive integer.

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