CN117521260A - Discrete distribution-oriented satellite constellation design method for multi-target area coverage - Google Patents
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Abstract
The invention discloses a satellite constellation design method for multi-target area coverage oriented to discrete distribution, which relates to the field of orbit dynamics and comprises the following steps of S1: analyzing a periodical movement rule of the right ascent and descent of a return period of a low-altitude return orbit under a two-body model, and determining a satellite sensor coverage mode; s2: constructing an inner layer optimization algorithm, and referring to a satellite lower point track optimization algorithm, giving coverage loss definition and analyzing; s3: analyzing distribution characteristics of the target sites and orbit regression characteristics of the reference satellites, and giving a grouping scheme of the target sites and a reference satellite distribution scheme; s4: and constructing an outer layer optimization algorithm by taking the undersea point track provided by the reference satellite as a constellation design basis. The satellite constellation design method for the multi-target area coverage oriented to the discrete distribution is adopted, the coverage targets can be selected randomly, the single-star utilization rate is high, the method applicability is high, and the communication and remote sensing requirements of important areas in the global scope can be met.
Description
Technical Field
The invention relates to the field of orbit dynamics, in particular to a satellite constellation design method for multi-target area coverage oriented to discrete distribution.
Background
Low Earth Orbit (LEO) satellites have the advantages of low latency, low path loss, high resolution, etc. in the fields of communications and remote sensing. LEO satellites may be limited in terms of service time, satellite communications, global coverage, etc., due to limited coverage capabilities. Thus, ensuring stable communication or achieving space-time continuous coverage requires priority in LEO constellation design. Heuristic algorithms have become effective tools for solving such problems in the optimization design of constellation configurations. In this context, the choice of decision variables in the algorithm is consistent, and the key is the design of the performance index and objective function. These factors have an important guiding role in the optimization process of the constellation design. In the design of space symmetric distribution constellation configuration, factors such as the number of visible satellites, revisiting time intervals, constellation construction cost and the like are indispensable optimization indexes. As can be seen, constellation configuration design is a complex task, often taking into account multiple metrics. However, using a single objective optimization algorithm requires integrating multiple performance metrics into a single objective function, which tends to produce a very complex objective function that further affects the quality of the optimization results. To break this limitation, multi-objective optimization algorithms gradually replace single-objective optimization algorithms. Specifically, aiming at the quick revisit problem, schemes such as a multi-island genetic algorithm, a multi-target particle swarm optimization algorithm and the like can be used for generating an optimal constellation configuration under the specific problem. These algorithms allow multiple targets to be optimized simultaneously, giving a more efficient, stable constellation design approach. The structure of the symmetrically distributed constellation is relatively simple, and the single-satellite utilization rate of satellites in the constellation is not obviously improved, so that the constellation cannot give an efficient solution when facing a specific coverage task.
Therefore, it is necessary to provide a satellite constellation design method for multi-target area coverage of discrete distribution to solve the above-mentioned problems.
Disclosure of Invention
The invention aims to provide a satellite constellation design method for multi-target area coverage oriented to discrete distribution, which solves the communication and remote sensing requirements of important areas in the global scope.
In order to achieve the above object, the present invention provides a satellite constellation design method for multi-target area coverage oriented to discrete distribution, the constellation design method comprising the following steps:
s1: analyzing a periodical movement rule of the right ascent and descent of a return period of a low-altitude return orbit under a two-body model, and determining a satellite sensor coverage mode;
s2: constructing an inner layer optimization algorithm, and referring to a satellite lower point track optimization algorithm, giving coverage loss definition and analyzing;
s3: analyzing distribution characteristics of the target sites and orbit regression characteristics of the reference satellites, and giving a grouping scheme of the target sites and a reference satellite distribution scheme;
s4: and constructing an outer layer optimization algorithm by taking the undersea point track provided by the reference satellite as a constellation design basis.
Preferably, in step S1, the return orbit refers to the orbit return period T of the satellite S Is sun day T G The satellite-borne point tracks of the reference satellites are overlapped periodically, initial orbit parameters of a plurality of satellites are designed, and a common ground track RGT constellation is constructed;
wherein T is S Is an orbital regression period, T G Is the sun day, N E And N S The number of sun days of the earth star and the number of reference satellite orbit running cycles are respectively;
from equation (1), T is derived G For a constant, determine T G And T is S After the ratio of (2), the orbit period and the orbit half-major axis a of the satellite are determined by the formula (2) sat ；
Wherein mu is e Is the gravitational constant;
calculating elevation angle alpha according to formula (3) r ，
In the equatorial inertial coordinate system of the earth, the position vector of the target region is denoted as r tar The normal vector of the target point level is denoted as n tar The satellite position vector is denoted r sat 。
Preferably, in step S2, the inner layer optimization algorithm is a reference satellite lower point trajectory optimization algorithm, wherein n places are considered in total, and the coverage of each area is independently optimized by using NSGA-II, so as to ensure that the coverage of each area is regarded as an independent target in trade-off analysis;
by T S /T G Ratio of =12/1, solve for a using equation (2) sat Will i sat And omega sat As decision variables, chromosomes are encoded as real numbers and the decision variables are normalized, in intervals [0,1]Internal optimization;
wherein y is q To optimize any value of the variable within its interval ρ 1 And ρ 2 For optimizing the upper and lower edge values of the variables, G is the code value, q=1, 2 respectively represents i sat And omega sat The range of values of the decision variables is as follows:
coverage f of each position in the n target areas by the reference satellite ci As a performance index, an objective function F i Expressed as:
wherein the objective function is a forward optimization index, the algorithm generates a group of Pareto non-dominant solutions with 1 level, the entropy weight method is adopted to calculate the comprehensive score of all individuals, the optimal individual is selected from the Pareto solutions, and the chromosome is decoded by the inverse formula (5) to obtain y q Is the optimal solution for the reference satellite.
Preferably, in step S3, the grouping optimization scheme is regarded as an optimization scheme corresponding to Case III, the K-means algorithm is adopted to group the regions, and the right ascension of the initial satellite point trajectory of the reference satellite is changed to ΔΩ after each orbital period r The declination and the declination of the target area are treated as follows:
in the method, in the process of the invention,sum phi l For declination and declination of the target site, < ->And [ phi ] l ]Is a parameter, ω, used by the K-means clustering algorithm to group target sites E Is the rotational angular velocity of the earth.
Preferably, in step S4, the outer layer optimization algorithm is a constellation configuration overall optimization design algorithm, and in Case of Case III, a plurality of target areas have a plurality of sub-constellations, and in order to construct a secondary integer programming algorithm, the following formula is introduced:
wherein V is 0,j (z) (J E J, Z E Z) is a coverage time matrix, x (Z) is a constellation configuration vector, the coverage of each satellite in the RGT constellation to the target position is the same, the time of participation in the coverage is different, and x (Z) is set as a 01 vector;
wherein a satellite needs to be covered at the specific time, and the time step is marked as 1; otherwise, the symbol is 0, bj is the expected coverage time axis, J is the base number of the target point set J, and Z is the base number of the sub-constellation Z;
grouping the target areas, wherein each group only has one configuration of a reference satellite control sub-constellation, and the formula (11) is rewritten as follows:
wherein P is a coverage time matrix of the target sites in the same group;
wherein S is r (S r =1, 2, …, K) is the reference satellite index, T r For each set of the number of target sites, according to the following equation (14);
and defining a desired coverage time axis B, and solving the optimal x by using a quadratic integer programming algorithm.
Therefore, the satellite constellation design method facing to the discrete distribution multi-target area coverage has the following beneficial effects:
(1) The coverage target can be selected at will, an asymmetric constellation is used as a constellation construction basis, the degree of freedom of constellation space distribution is high, and the configuration design is highly targeted.
(2) The invention has high single star utilization rate, adopts a K-means clustering algorithm in the target packet, deeply analyzes the relation between the track characteristic and the target site distribution, and nests an NSGA-II optimization algorithm with a secondary integer programming algorithm on the constellation design, thereby effectively reducing the coverage loss.
(3) The method has strong applicability, wherein the constellation design method is simultaneously suitable for target site coverage of concentrated distribution and discrete distribution, and the algorithm processing process is flexible.
The technical scheme of the invention is further described in detail through the drawings and the embodiments.
Drawings
FIG. 1 is a flow chart of a method of designing a satellite constellation for discrete distribution-oriented multi-target area coverage in accordance with the present invention;
FIG. 2 is a schematic view of satellite coverage according to the present invention;
FIG. 3 is a graph of sensor elevation versus coverage in accordance with the present invention;
FIG. 4 is a coverage loss schematic of the present invention;
FIG. 5 is a schematic diagram of a reference satellite configuration of the present invention;
FIG. 6 is an illustration of coverage loss for the present invention;
FIG. 7 is a diagram showing the right ascent point of the present invention;
FIG. 8 is a schematic diagram of the destination point grouping results of the present invention;
FIG. 9 is a coverage loss comparison plot of the present invention;
FIG. 10 is a schematic view of the spatial distribution of satellite constellation according to the present invention;
FIG. 11 is a schematic view of a three-dimensional configuration of a satellite constellation according to the present invention;
FIG. 12 is a histogram of the coverage results of the target site of the present invention;
Detailed Description
The technical scheme of the invention is further described below through the attached drawings and the embodiments.
Unless defined otherwise, technical or scientific terms used herein should be given the ordinary meaning as understood by one of ordinary skill in the art to which this invention belongs.
As used herein, the word "comprising" or "comprises" and the like means that elements preceding the word encompass the elements recited after the word, and not exclude the possibility of also encompassing other elements. The terms "inner," "outer," "upper," "lower," and the like are used for convenience in describing and simplifying the description based on the orientation or positional relationship shown in the drawings, and do not denote or imply that the devices or elements referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus should not be construed as limiting the invention, but the relative positional relationship may be changed when the absolute position of the object to be described is changed accordingly. In the present invention, unless explicitly specified and limited otherwise, the term "attached" and the like should be construed broadly, and may be, for example, fixedly attached, detachably attached, or integrally formed; can be directly connected or indirectly connected through an intermediate medium, and can be communicated with the inside of two elements or the interaction relationship of the two elements. The specific meaning of the above terms in the present invention can be understood by those of ordinary skill in the art according to the specific circumstances.
Examples
As shown in fig. 1, the invention provides a satellite constellation design method for multi-target area coverage oriented to discrete distribution, which comprises the following steps:
s1: analyzing a periodical movement rule of the right ascent and descent of a return period of a low-altitude return orbit under a two-body model, and determining a satellite sensor coverage mode;
s2: constructing an inner layer optimization algorithm, and referring to a satellite lower point track optimization algorithm, giving coverage loss definition and analyzing;
s3: analyzing distribution characteristics of the target sites and orbit regression characteristics of the reference satellites, and giving a grouping scheme of the target sites and a reference satellite distribution scheme;
s4: and constructing an outer layer optimization algorithm by taking the undersea point track provided by the reference satellite as a constellation design basis.
In step S1, the return orbit refers to the orbit return period T of the satellite S Is sun day T G The satellite-borne point tracks of the reference satellites are overlapped periodically, initial orbit parameters of a plurality of satellites are designed, and a common ground track RGT constellation is constructed;
wherein T is S Is an orbital regression period, T G Is the sun day, N E And N S The number of sun days of the earth star and the number of reference satellite orbit running cycles are respectively;
from equation (1), T is derived G For a constant, determine T G And T is S After the ratio of (2), the orbit period and the orbit half-major axis a of the satellite are determined by the formula (2) sat ；
Wherein mu is e Is the gravitational constant;
calculating elevation angle alpha according to formula (3) r The geometrical relationship is shown in fig. 2, the simulation duration is set as the track recursion period T, the time step number k=720, and the time step is calculated as T step ＝T/k。
In the equatorial inertial coordinate system of the earth, the position vector of the target region is denoted as r tar The normal vector of the target point level is denoted as n tar The satellite position vector is denoted r sat 。
Assuming n target areas, the coverage is recorded in a binary matrix p 0 In (a) recording the coverage of the ith target area by the reference satellite at the jth time step at p 0 (i, j);
wherein alpha is s For a minimum elevation threshold, for different regions, the required α s The values are different. In a wider area, the signal transmission process has less blockage and smaller alpha s Can meet the requirements. Also, in the area where signal transmission is blocked, a larger α is required s Generally alpha s ∈[5°,50°]. FIG. 3 shows target area coverage C r Following alpha s Is a variation of (2). Wherein the target area position is [116.4 DEG E,39.6 DEG N]The satellite orbit parameters are [9100.5km,0.001,66.4 degrees, 227.4 degrees, 0 degrees and 0 degree]。
In step S2, the inner layer optimization algorithm is a reference satellite point-under-satellite trajectory optimization algorithm, wherein n places are considered in total, the coverage of each area is optimized independently by using NSGA-II, and the coverage of each area is ensured to be regarded as an independent target in trade-off analysis;
by T S /T G Ratio of =12/1, solve for a using equation (2) sat Will i sat And omega sat As decision variables, chromosomes are encoded as real numbers and the decision variables are normalized, in intervals [0,1]Internal optimization;
wherein y is q To optimize any value of the variable within its interval ρ 1 And ρ 2 For optimizing the upper and lower edge values of the variables, G is the code value, q=1, 2 respectively represents i sat And omega sat The range of values of the decision variables is as follows:
coverage f of each position in the n target areas by the reference satellite ci As a performance index, an objective function F i Expressed as:
wherein the objective function is a forward optimization index, the algorithm generates a group of Pareto non-dominant solutions with 1 level, the entropy weight method is adopted to calculate the comprehensive score of all individuals, the optimal individual is selected from the Pareto solutions, and the chromosome is decoded by the inverse formula (5) to obtain y q Is the optimal solution for the reference satellite.
In summary, the solution obtained by the reference satellite orbit element optimization algorithm represents the result of "average advantage and disadvantage" among the multiple targets. The algorithm will seek trade-offs between objective functions during the optimization process, and as new objective regions are added, the coverage of the original objective regions will decrease. This problem can be illustrated by fig. 4. Likewise, the coverage of the reference satellite in the target area 2 in the present case is reduced, also due to the addition of the target area 1.
Assuming that the understar trajectory of each sub-constellation is controlled by an independent reference satellite, the number of reference satellites is equal to the number of sub-constellations. In this case, a simple mathematical formula is used to quantify the extent of coverage loss:
wherein C is l 0 And C b 0 The loss of coverage and the optimal coverage of the satellite to the respective target area are respectively.Is the coverage loss rate. On the basis, the coverage loss is further dividedAnalysis, the following treatments were performed and the results were compared:
case I: n regions-n reference satellites;
case II: n regions-1 reference satellite;
case III: n regions-K reference satellites (K is the number of target site groupings).
Case I to III are shown in fig. 5. Taking coverage of 12 target areas by a reference satellite as an example, using the Red warp ψ l And declination phi l The position of the target area is shown in table 1. In this analysis, first consider the coverage loss of Case I and Case II in a star day. Case III corresponds to a packet optimization scheme (GOS) to be discussed later.
Fig. 6 (a) shows the coverage loss after global optimization, and it can be seen from the figure that the reference satellite has different degrees of coverage loss for each target area with respect to its optimal coverage capability. Fig. 6 (b) shows the coverage loss of the target area.
In step S3, the grouping optimization scheme is regarded as an optimization scheme corresponding to Case III, the K-means algorithm is adopted to group the regions, and the right ascension of the initial satellite point track of the reference satellite is changed into delta omega after each orbit period r As shown in fig. 7, the declination and the declination of the target area are treated as follows:
in the method, in the process of the invention,sum phi l For declination and declination of the target site, < ->And [ phi ] l ]Is a K-means clustering algorithm for grouping target sitesParameters omega E Is the rotational angular velocity of the earth.
The K-means clustering algorithm is a simple method of dividing a dataset into K distinct clusters. In order to perform K-means clustering, the required number of clusters K must be specified first; the K-means algorithm then assigns each observation to an exact cluster. After the coordinates of the target site are processed, two parameters [ phi ] are utilized l ]And [ phi ] l ]The target sites with more dispersed distribution can be concentrated at [ 0], delta omega r]In this interval, the original coverage characteristics are not lost. Grouping results as shown in fig. 8, the positions of the arbitrarily chosen 12 target sites are listed in table one and have been divided into three groups, under which condition NSGA-II can generate reference satellites for all groups.
The orbit parameters of the three reference satellites are τ1= [8061.7km,0.01,72.4 °,10.14 °,0], τ2= [8061.7km,0.01,42.79 °,274.16 °,0], τ3= [8061.7km,0.01,72.36 °,302.29 °,0].
List of target site locations
In connection with the above analysis, the coverage loss of GOS is smaller compared to the Overall Optimization Scheme (OOS), as shown in fig. 9. Therefore, a preliminary conclusion is made that the satellite utilization can be improved by packet optimization, and the total number of satellites in the constellation can be reduced. In this example, the GOS algorithm is effective.
In step S4, the outer layer optimization algorithm is a constellation configuration overall optimization design algorithm, and in Case of Case III, a plurality of target areas have a plurality of sub-constellations, in order to construct a secondary integer programming algorithm, the following formula is introduced:
wherein V is 0,j (z) (J E J, Z E Z) is a coverage time matrix, x (Z) is a constellation configuration vector, RGT constellationEach satellite has the same coverage on the target position and different participation time, and x (z) is set as a 01 vector;
wherein a satellite needs to be covered at the specific time, and the time step is marked as 1; otherwise, the symbol is 0, bj is the expected coverage time axis, J is the base number of the target point set J, and Z is the base number of the sub-constellation Z;
grouping the target areas, wherein each group only has one configuration of a reference satellite control sub-constellation, and the formula (11) is rewritten as follows:
wherein P is a coverage time matrix of the target sites in the same group;
wherein S is r (S r =1, 2, …, K) is the reference satellite index, T r For each set of the number of target sites, according to the following equation (14);
and defining a desired coverage time axis B, and solving the optimal x by using a quadratic integer programming algorithm.
The algorithm is designed as follows:
example two
The validity of the algorithm is verified by a set of examples, the position of the target site is shown in table two, and the constellation design results are shown in fig. 10-12. Fig. 10 shows the spatial distribution of the satellite constellation, fig. 11 is a three-dimensional schematic diagram of the satellite constellation, and fig. 12 is the coverage rate of the selected target sites.
Watch two target site positions
Therefore, the satellite constellation design method for the multi-target area coverage oriented to the discrete distribution solves the communication and remote sensing requirements on key targets in the global scope.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention and not for limiting it, and although the present invention has been described in detail with reference to the preferred embodiments, it will be understood by those skilled in the art that: the technical scheme of the invention can be modified or replaced by the same, and the modified technical scheme cannot deviate from the spirit and scope of the technical scheme of the invention.
Claims (5)
1. A satellite constellation design method for multi-target area coverage oriented to discrete distribution is characterized by comprising the following steps: the constellation design method comprises the following steps:
s1: analyzing a periodical movement rule of the right ascent and descent of a return period of a low-altitude return orbit under a two-body model, and determining a satellite sensor coverage mode;
s2: constructing an inner layer optimization algorithm, and referring to a satellite lower point track optimization algorithm, giving coverage loss definition and analyzing;
s3: analyzing distribution characteristics of the target sites and orbit regression characteristics of the reference satellites, and giving a grouping scheme of the target sites and a reference satellite distribution scheme;
s4: and constructing an outer layer optimization algorithm by taking the undersea point track provided by the reference satellite as a constellation design basis.
2. The method for designing a satellite constellation for multi-target area coverage for discrete distribution according to claim 1, wherein: in step S1, the return orbit refers to the orbit return period T of the satellite S Is constantStar day T G The satellite-borne point tracks of the reference satellites are overlapped periodically, initial orbit parameters of a plurality of satellites are designed, and a common ground track RGT constellation is constructed;
wherein T is S Is an orbital regression period, T G Is the sun day, N E And N S The number of sun days of the earth star and the number of reference satellite orbit running cycles are respectively;
from equation (1), T is derived G For a constant, determine T G And T is S After the ratio of (2), the orbit period and the orbit half-major axis a of the satellite are determined by the formula (2) sat ；
Wherein mu is e Is the gravitational constant;
calculating elevation angle alpha according to formula (3) r ，
In the equatorial inertial coordinate system of the earth, the position vector of the target region is denoted as r tar The normal vector of the target point level is denoted as n tar The satellite position vector is denoted r sat 。
3. A method for designing a satellite constellation for multi-target area coverage for discrete distribution according to claim 2, wherein: in step S2, the inner layer optimization algorithm is a reference satellite point-under-satellite trajectory optimization algorithm, wherein n places are considered in total, the coverage of each area is optimized independently by using NSGA-II, and the coverage of each area is ensured to be regarded as an independent target in trade-off analysis;
by T S /T G Ratio of =12/1, solve for a using equation (2) sat Will i sat And omega sat As decision variables, chromosomes are encoded as real numbers and the decision variables are normalized, in intervals [0,1]Internal optimization;
wherein y is q To optimize any value of the variable within its interval ρ 1 And ρ 2 For optimizing the upper and lower edge values of the variables, G is the code value, q=1, 2 respectively represents i sat And omega sat The range of values of the decision variables is as follows:
coverage f of each position in the n target areas by the reference satellite ci As a performance index, an objective function F i Expressed as:
wherein the objective function is a forward optimization index, the algorithm generates a group of Pareto non-dominant solutions with 1 level, the entropy weight method is adopted to calculate the comprehensive score of all individuals, the optimal individual is selected from the Pareto solutions, and the chromosome is decoded by the inverse formula (5) to obtain y q Is the optimal solution for the reference satellite.
4. A method for designing a satellite constellation for multi-target area coverage for discrete distribution according to claim 3, wherein: in step S3, the grouping optimization scheme is regarded as an optimization scheme corresponding to Case III, the K-means algorithm is adopted to group the regions, and the right ascension of the initial satellite point track of the reference satellite is changed into delta omega after each orbit period r The declination and the declination of the target area are treated as follows:
in the method, in the process of the invention,sum phi l For declination and declination of the target site, < ->And [ phi ] l ]Is a parameter, ω, used by the K-means clustering algorithm to group target sites E Is the rotational angular velocity of the earth.
5. The method for designing a satellite constellation for multi-target area coverage for discrete distribution according to claim 4, wherein: in step S4, the outer layer optimization algorithm is a constellation configuration overall optimization design algorithm, and in Case of Case III, a plurality of target areas have a plurality of sub-constellations, in order to construct a secondary integer programming algorithm, the following formula is introduced:
wherein V is 0,j (z) (J E J, Z E Z) is a coverage time matrix, x (Z) is a constellation configuration vector, the coverage of each satellite in the RGT constellation to the target position is the same, the time of participation in the coverage is different, and x (Z) is set as a 01 vector;
wherein a satellite needs to be covered at the specific time, and the time step is marked as 1; otherwise, the symbol is 0, bj is the expected coverage time axis, J is the base number of the target point set J, and Z is the base number of the sub-constellation Z;
grouping the target areas, wherein each group only has one configuration of a reference satellite control sub-constellation, and the formula (11) is rewritten as follows:
wherein P is a coverage time matrix of the target sites in the same group;
wherein S is r (S r =1, 2, …, K) is the reference satellite index, T r For each set of the number of target sites, according to the following equation (14);
and defining a desired coverage time axis B, and solving the optimal x by using a quadratic integer programming algorithm.
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