阅读说明：本技术 一种同构卫星星座对地覆盖性能分析方法 (Method for analyzing earth coverage performance of isomorphic satellite constellation ) 是由 张世杰 龚宇鹏 彭璇 于 2021-01-07 设计创作，主要内容包括：一种同构卫星星座对地覆盖性能分析方法,涉及轨道分析技术领域,针对现有方法中获取巨型同构星座对地覆盖性能效率低的问题,利用同构星座星间相位关系恒定的特点,在由升交点赤经和纬度辐角构成的二维相空间中表征卫星的空间位置和相位关系,避免了求解周期性变化的星间距离关系；根据同构星座构型判定在二维空间中的覆盖性能分析范围,避免了对覆盖性能相似区域的重复求解和冗余的星地位置关系计算,使所述覆盖分析方法计算量不随卫星数量增加而显著增加,提高了获取巨型同构星座对地覆盖性能的效率。(A isomorphic satellite constellation ground coverage performance analysis method relates to the technical field of orbit analysis, aims at the problem that the efficiency of acquiring giant isomorphic constellation ground coverage performance in the existing method is low, and utilizes the characteristic of constant phase relationship among isomorphic constellation stars to represent the space position and phase relationship of a satellite in a two-dimensional phase space formed by ascension at a rising point and latitude argument, thereby avoiding solving the periodically-changed inter-satellite distance relationship; the coverage performance analysis range in the two-dimensional space is judged according to the isomorphic constellation configuration, repeated solution of coverage performance similar areas and redundant satellite position relation calculation are avoided, the calculated amount of the coverage analysis method is not obviously increased along with the increase of the number of satellites, and the efficiency of obtaining the earth coverage performance of the giant isomorphic constellation is improved.)

1. A method for analyzing the earth coverage performance of a homogeneous satellite constellation is characterized by comprising the following steps:

establishing phase mappings of all satellites in a constellation in a two-dimensional phase space, and determining an analysis range of coverage performance in the two-dimensional phase space according to a distribution rule of the phase mappings of all the satellites, wherein the constellation is an isomorphic constellation, at least an orbit semimajor axis, an orbit inclination angle and an orbit eccentricity ratio in orbit parameters of all the satellites in the isomorphic constellation are equal, and the two-dimensional phase space is a phase space formed by ascension and latitude argument at an ascending point in the orbit parameters of the satellites;

inputting longitude and latitude coordinates corresponding to the ground target needing coverage performance analysis, obtaining phase mapping points according to phase mapping of the longitude and latitude coordinates in a two-dimensional phase space, and finally obtaining a visible satellite phase range of the ground target in the two-dimensional phase space;

step three, screening out satellites required for calculating the coverage performance in the two-dimensional phase space according to the analysis range of the coverage performance in the step one and the phase range of the visible satellites in the step two;

step four, taking the phase mapping point in the step two as a translation reference point of the phase range of the visible satellite, translating the phase range of the visible satellite according to the phase of the satellite required by the coverage performance calculation in the two-dimensional phase space, and keeping the translation result of each time, so that after the phase range of the visible satellite is translated, the reference point of the phase range of the visible satellite coincides with the phase of the satellite required by the coverage performance calculation in the two-dimensional phase space;

step five, calculating the continuous coverage performance of the constellation to the ground target according to the translation result of each time, and the specific steps are as follows:

step five, first: acquiring a superposition area after the phase range of the visible satellite is translated within the coverage performance analysis range;

step five two: acquiring the area of the overlapping area in a two-dimensional phase space and the overlapping weight corresponding to the overlapping area;

step five and step three: obtaining the sum of the areas of the coincident regions with the same coincident numbers, obtaining the ratio of the sum of the areas of the coincident regions with the same coincident numbers to the area of the analysis range of the coverage performance, finally obtaining the continuous coverage performance of the constellation according to the ratio of the areas, and obtaining the analysis result according to the continuous coverage performance of the constellation.

2. The method according to claim 1, wherein the analysis range of the coverage performance in the two-dimensional phase space in the first step satisfies the following condition:

the coverage performance analysis range is a closed area in a two-dimensional phase space;

the coverage performance analysis range realizes the close-spread of the two-dimensional phase space only through translation transformation, and the number of the satellites contained in each unit after close-spread and the phase distribution of the satellites are completely the same.

3. The method according to claim 2, wherein the phase mapping of the latitude and longitude coordinates in the two-dimensional phase space in the second step satisfies the following condition:

Ω₊＝λ-arctan(cosi·tanu)

Ω_-＝2λ_t-π-Ω₊＝λ-arctan(cosi·tanu_-)

wherein omega₊、Ω_-Respectively longitude and latitude coordinatesElevation intersection right ascension mapping, u, at the ascending and descending sections of the track₊、u_-Respectively longitude and latitude coordinatesAnd (3) latitude argument mapping of an orbit ascending section and an orbit descending section, wherein i is the orbit inclination angle of all the orbits in the isomorphic constellation, and sgn (x) represents that the positive sign and the negative sign of a variable x are taken.

4. The method according to claim 3, wherein the visible satellite phase range of the ground target in the two-dimensional phase space in the second step is a range of values of the ascension point and the latitude and longitude phase of the intersection point of the satellite covering the longitude and latitude of the selected ground target.

5. The method for analyzing the earth coverage performance of the isomorphic satellite constellation according to claim 4, wherein the step of specifically obtaining the phase value range of the satellite covering the longitude and latitude of the selected ground target in the two-dimensional phase space comprises the following steps:

firstly, the hemispherical central angle of a satellite coverage cone is made to be alpha, and when the satellite can cover a target, the satellite subsatellite point longitude and latitude are enabledAnd the latitude and longitude of the targetSatisfies the following conditions:

then, the latitude and longitude of the sub-satellite pointThe phase mapping in the two-dimensional phase space is substituted into the formula to obtain the visible satellite phase range of the target in the two-dimensional phase spaceSatisfies the relationship:

in two-dimensional phase space, if a phase belongs toIt is assumed that the satellite can cover the target when it is in that phaseOtherwise, if a certain phase does not belong toThe satellite is considered to be in that phase and not covering the target

6. The method according to claim 5, wherein the step three of selecting the satellites required for calculating the coverage performance in the two-dimensional phase space comprises the following specific steps:

according to the analysis range of the coverage performance in the two-dimensional phase space determined in the step one, a closed area is searched in the two-dimensional phase space, so that the closed area satisfies the following conditions:

the distance between the upper boundary of the closed region and the upper boundary of the coverage performance analysis range is equal to the distance between the ground target phase mapped to the lower boundary of the visible satellite phase range;

the distance between the lower boundary of the closed region and the lower boundary of the coverage performance analysis range is equal to the distance between the ground target phase mapped to the upper boundary of the visible satellite phase range;

the distance between the left boundary of the closed region and the left boundary of the coverage performance analysis range is equal to the distance between the ground target phase and the right boundary of the visible satellite phase range;

the distance between the right boundary of the closed region and the right boundary of the coverage performance analysis range is equal to the distance between the ground target phase and the left boundary of the visible satellite phase range;

the satellite phase in the constellation is the satellite contained in the closed region in the two-dimensional phase space, namely the result of the screened satellite;

and the distance of the ground target phase mapped to the upper boundary of the visible satellite phase range, the distance of the ground target phase mapped to the lower boundary of the visible satellite phase range, the distance of the ground target phase mapped to the right boundary of the visible satellite phase range and the distance of the ground target phase mapped to the left boundary of the visible satellite phase range are obtained according to the phase mapping of the latitude coordinate in the step two in the two-dimensional phase space and the visible satellite phase range of the ground target in the two-dimensional phase space.

7. The method according to claim 6, wherein the step four of translating the phase range of the visible satellite according to the phase of the satellite required for calculating the coverage performance in the two-dimensional phase space comprises the following specific steps:

firstly, respectively calculating distance vectors from a reference point translated in a visible satellite phase range to the phases of all the satellites screened in the third step in a two-dimensional phase space;

and then, respectively translating the phase range of the visible satellite in the two-dimensional phase space by all the distance vectors to obtain a range area as a translation result.

8. The method according to claim 1, wherein the spatial position represented by any phase coordinate in the two-dimensional phase space is the same as all mapping relationships after the phase coordinate is shifted by an integer multiple of a periodic constant along the direction of the coordinate axis of the phase space.

9. The method according to claim 8, wherein the periodic constant has a value of 2 pi.

Technical Field

The invention relates to the technical field of orbit analysis, in particular to a method for analyzing the earth coverage performance of a isomorphic satellite constellation.

Background

With the development of satellite miniaturization technology and diversified launching deployment technology, low-orbit giant constellations of more than thousands of satellite scales become the development trend of future communication constellations. The concept of constructing a global or regional constellation system by using a large number of low-earth orbit satellites is proposed by various domestic and foreign commercial space companies such as SpaceX, Oneweb, Amazon and the like. Compared with the conventional global coverage communication constellation (Iridium, Globalstar, Orbcomm), the low-orbit giant constellation has a higher communication bandwidth and a smaller time delay, and the cost of a single satellite and the carrying cost are relatively low.

In order to balance the influence of the non-spherical gravitational perturbation and the environmental force perturbation of the earth, the giant constellations proposed at present are all designed by adopting isostructural constellations such as Walker and Polar. The isomorphic constellation is a circular orbit constellation with the same orbit height and orbit inclination angle, so that perturbation has the same long-term influence on all satellites in the constellation, and the phase relation among the satellites cannot change along with time. At the same time, the spatial configuration of such an isomorphic constellation can be determined by few design parameters, thus facilitating design and analysis.

For the problem of analysis of the earth coverage of the constellation, the traditional method is mainly to discretize the earth area and the analysis time, and solve the problem by utilizing the distance relationship between the satellite and the target point at different moments instead of the coincidence relationship between the satellite coverage area and the earth target area within a period of time. Therefore, the conventional coverage analysis method needs to calculate the position relationship between each satellite and each ground point target at all times. With the increase of the number of satellites and the reduction of the coverage of a single satellite, the calculation amount and the time consumption of the traditional solving method are obviously increased, and the coverage performance of the giant isomorphic constellation cannot be rapidly and intuitively analyzed. Therefore, how to rapidly and accurately solve and analyze the coverage performance of the giant isomorphic constellation is a problem to be solved at present.

Disclosure of Invention

The purpose of the invention is: aiming at the problem of low efficiency of acquiring the earth coverage performance of the giant isomorphic constellation in the prior art, the earth coverage performance analysis method of the isomorphic satellite constellation is provided.

The technical scheme adopted by the invention to solve the technical problems is as follows:

a method for analyzing the earth coverage performance of a homogeneous satellite constellation comprises the following steps:

establishing phase mappings of all satellites in a constellation in a two-dimensional phase space, and determining an analysis range of coverage performance in the two-dimensional phase space according to a distribution rule of the phase mappings of all the satellites, wherein the constellation is an isomorphic constellation, at least an orbit semimajor axis, an orbit inclination angle and an orbit eccentricity ratio in orbit parameters of all the satellites in the isomorphic constellation are equal, and the two-dimensional phase space is a phase space formed by ascension and latitude argument at an ascending point in the orbit parameters of the satellites;

inputting longitude and latitude coordinates corresponding to the ground target needing coverage performance analysis, obtaining phase mapping points according to phase mapping of the longitude and latitude coordinates in a two-dimensional phase space, and finally obtaining a visible satellite phase range of the ground target in the two-dimensional phase space;

step three, screening out satellites required for calculating the coverage performance in the two-dimensional phase space according to the analysis range of the coverage performance in the step one and the phase range of the visible satellites in the step two;

step four, taking the phase mapping point in the step two as a translation reference point of the phase range of the visible satellite, translating the phase range of the visible satellite according to the phase of the satellite required by the coverage performance calculation in the two-dimensional phase space, and keeping the translation result of each time, so that after the phase range of the visible satellite is translated, the reference point of the phase range of the visible satellite coincides with the phase of the satellite required by the coverage performance calculation in the two-dimensional phase space;

step five, calculating the continuous coverage performance of the constellation to the ground target according to the translation result of each time, and the specific steps are as follows:

step five, first: acquiring a superposition area after the phase range of the visible satellite is translated within the coverage performance analysis range;

step five two: acquiring the area of the overlapping area in a two-dimensional phase space and the overlapping weight corresponding to the overlapping area;

step five and step three: obtaining the sum of the areas of the coincident regions with the same coincident numbers, obtaining the ratio of the sum of the areas of the coincident regions with the same coincident numbers to the area of the analysis range of the coverage performance, finally obtaining the continuous coverage performance of the constellation according to the ratio of the areas, and obtaining the analysis result according to the continuous coverage performance of the constellation.

Further, the analysis range of the coverage performance in the two-dimensional phase space in the first step meets the following condition:

the coverage performance analysis range is a closed area in a two-dimensional phase space;

the coverage performance analysis range realizes the close-spread of the two-dimensional phase space only through translation transformation, and the number of the satellites contained in each unit after close-spread and the phase distribution of the satellites are completely the same.

Further, the phase mapping of the latitude and longitude coordinates in the two-dimensional phase space in the second step satisfies the following condition:

Ω₊＝λ-arctan(cosi·tanu)

Ω_-＝2λ_t-π-Ω₊＝λ-arctan(cosi·tanu_-)

wherein omega₊、Ω_-Respectively longitude and latitude coordinatesElevation intersection right ascension mapping, u, at the ascending and descending sections of the track₊、u_-Respectively longitude and latitude coordinatesAnd (3) latitude argument mapping of an orbit ascending section and an orbit descending section, wherein i is the orbit inclination angle of all the orbits in the isomorphic constellation, and sgn (x) represents that the positive sign and the negative sign of a variable x are taken.

Further, the visible satellite phase range of the ground target in the two-dimensional phase space in the second step is a value range of the elevation intersection declination and the dimension argument phase of the satellite covering the longitude and the latitude of the selected ground target.

Further, the phase value range of the satellite covering the longitude and latitude of the selected ground target in the two-dimensional phase space specifically comprises the following steps:

firstly, let the half-sphere center angle of the satellite coverage cone be alpha whenWhen the satellite can cover the target, the satellite makes the latitude and longitude of the satellite pointAnd the latitude and longitude of the targetSatisfies the following conditions:

then, the latitude and longitude of the sub-satellite pointThe phase mapping in the two-dimensional phase space is substituted into the formula to obtain the visible satellite phase range of the target in the two-dimensional phase spaceSatisfies the relationship:

in two-dimensional phase space, if a phase belongs toIt is assumed that the satellite can cover the target when it is in that phaseOtherwise, if a certain phase does not belong toThe satellite is considered to be in that phase and not covering the target

Further, the specific steps of screening out the satellites required for calculating the coverage performance in the two-dimensional phase space in the third step are as follows:

according to the analysis range of the coverage performance in the two-dimensional phase space determined in the step one, a closed area is searched in the two-dimensional phase space, so that the closed area satisfies the following conditions:

the distance between the upper boundary of the closed region and the upper boundary of the coverage performance analysis range is equal to the distance between the ground target phase mapped to the lower boundary of the visible satellite phase range;

the distance between the lower boundary of the closed region and the lower boundary of the coverage performance analysis range is equal to the distance between the ground target phase mapped to the upper boundary of the visible satellite phase range;

the distance between the left boundary of the closed region and the left boundary of the coverage performance analysis range is equal to the distance between the ground target phase and the right boundary of the visible satellite phase range;

the distance between the right boundary of the closed region and the right boundary of the coverage performance analysis range is equal to the distance between the ground target phase and the left boundary of the visible satellite phase range;

the satellite phase in the constellation is the satellite contained in the closed region in the two-dimensional phase space, namely the result of the screened satellite;

and the distance of the ground target phase mapped to the upper boundary of the visible satellite phase range, the distance of the ground target phase mapped to the lower boundary of the visible satellite phase range, the distance of the ground target phase mapped to the right boundary of the visible satellite phase range and the distance of the ground target phase mapped to the left boundary of the visible satellite phase range are obtained according to the phase mapping of the latitude coordinate in the step two in the two-dimensional phase space and the visible satellite phase range of the ground target in the two-dimensional phase space.

Further, the specific step of translating the phase range of the visible satellite according to the phase of the satellite required for calculating the coverage performance in the two-dimensional phase space in the fourth step is as follows:

firstly, respectively calculating distance vectors from a reference point translated in a visible satellite phase range to the phases of all the satellites screened in the third step in a two-dimensional phase space;

and then, respectively translating the phase range of the visible satellite in the two-dimensional phase space by all the distance vectors to obtain a range area as a translation result.

Furthermore, after the spatial position represented by any phase coordinate in the two-dimensional phase space and all mapping relations are shifted by an integral multiple distance of the periodic constant value along the direction of the coordinate axis of the phase space, the spatial position represented by the obtained coordinate is the same as all mapping relations.

Further, the period constant value is 2 π.

The invention has the beneficial effects that:

the space position and the phase relation of the satellite are characterized in a two-dimensional phase space formed by the right ascension at the intersection point and the latitude argument by utilizing the characteristic that the phase relation among the satellites of the isomorphic constellation is constant, so that the problem of solving the distance relation among the satellites with periodic change is avoided; the coverage performance analysis range in the two-dimensional space is judged according to the isomorphic constellation configuration, repeated solution of coverage performance similar areas and redundant satellite position relation calculation are avoided, the calculated amount of the coverage analysis method is not obviously increased along with the increase of the number of satellites, and the efficiency of obtaining the earth coverage performance of the giant isomorphic constellation is improved.

Drawings

FIG. 1 is a flow chart of an isomorphic constellation coverage performance analysis method of the present invention;

FIG. 2 is a schematic diagram of phase mapping and coverage analysis of constellation satellites

FIG. 3 is a schematic diagram of a phase range of a ground target visible satellite;

FIG. 4 is a schematic diagram of satellite phase filtering;

FIG. 5 is a diagram illustrating phase range shifting of visible satellites;

FIG. 6 is a partial magnified view of the area covered for analysis;

FIG. 7 shows the results of overlay analysis.

Detailed Description

It should be noted that, in the present invention, the embodiments disclosed in the present application may be combined with each other without conflict.

The first embodiment is as follows: specifically describing this embodiment with reference to fig. 1, a method for analyzing a coverage performance of a homogeneous satellite constellation over the ground in this embodiment includes:

establishing phase mappings of all satellites in a constellation in a two-dimensional phase space, and determining an analysis range of coverage performance in the two-dimensional phase space according to a distribution rule of the phase mappings of all the satellites, wherein the constellation is an isomorphic constellation, at least an orbit semimajor axis, an orbit inclination angle and an orbit eccentricity ratio in orbit parameters of all the satellites in the isomorphic constellation are equal, and the two-dimensional phase space is a phase space formed by ascension and latitude argument at an ascending point in the orbit parameters of the satellites;

inputting longitude and latitude coordinates corresponding to the ground target needing coverage performance analysis, obtaining phase mapping points according to phase mapping of the longitude and latitude coordinates in a two-dimensional phase space, and finally obtaining a visible satellite phase range of the ground target in the two-dimensional phase space;

step three, screening out satellites required for calculating the coverage performance in the two-dimensional phase space according to the analysis range of the coverage performance in the step one and the phase range of the visible satellites in the step two;

step four, taking the phase mapping point in the step two as a translation reference point of the phase range of the visible satellite, translating the phase range of the visible satellite according to the phase of the satellite required by the coverage performance calculation in the two-dimensional phase space, and keeping the translation result of each time, so that after the phase range of the visible satellite is translated, the reference point of the phase range of the visible satellite coincides with the phase of the satellite required by the coverage performance calculation in the two-dimensional phase space;

step five, calculating the continuous coverage performance of the constellation to the ground target according to the translation result of each time, and the specific steps are as follows:

step five, first: acquiring a superposition area after the phase range of the visible satellite is translated within the coverage performance analysis range;

step five two: acquiring the area of the overlapping area in a two-dimensional phase space and the overlapping weight corresponding to the overlapping area;

step five and step three: obtaining the sum of the areas of the coincident regions with the same coincident numbers, obtaining the ratio of the sum of the areas of the coincident regions with the same coincident numbers to the area of the analysis range of the coverage performance, finally obtaining the continuous coverage performance of the constellation according to the ratio of the areas, and obtaining the analysis result according to the continuous coverage performance of the constellation.

The method for analyzing the ground coverage performance of the constellation utilizes the characteristic that the phase relationship among the satellites of the constellation is constant, and analyzes the ground coverage performance of the constellation based on the geometric relationship between the satellite phase mapping and the coverage mapping in the two-dimensional phase space, and specifically comprises the following steps:

step one, establishing phase mapping of all satellites in a constellation in a two-dimensional phase space, and determining an analysis range of coverage performance in the two-dimensional phase space according to a distribution rule of all satellite phase mapping, specifically:

establishing a two-dimensional phase space in the following form, wherein the horizontal axis is the ascension channel omega of the satellite at the ascending point in the isomorphic constellation, the vertical axis is the latitude amplitude angle u of the satellite, and any phase (omega, u) in the two-dimensional phase space meets the following conditions:

(Ω,u)＝(Ω+2jπ,u+2kπ)j,k∈Z

because the orbit semimajor axis, the orbit eccentricity and the orbit inclination of all satellites in the isomorphic constellation are completely the same, the (omega, u) phase difference is uniform and fixed, and the relative distance of the satellites in the (omega, u) two-dimensional phase space can not change along with the operation of the constellation. And selecting a coverage analysis area in the two-dimensional phase space by taking the phase mapping of all satellites in the initial time constellation in the two-dimensional phase space as a reference. The selected coverage analysis area needs to satisfy the following conditions:

the selected coverage analysis region may be densely populated with a two-dimensional phase space and at least one type of tiling exists such that the number and location distribution of the phase maps comprising the satellites is the same within each tiling unit.

Selecting the longitude and latitude of the ground target needing coverage analysis, calculating the phase mapping of the longitude and latitude coordinates in a two-dimensional phase space, and calculating the phase range of the visible satellite of the ground target in the two-dimensional phase space, wherein the steps are as follows:

selecting a ground target whose coverage performance has not been analyzed, and recording the longitude and latitude of the selected ground target asThen according to the mapping relation between the longitude and latitude coordinates and the (omega, u) two-dimensional phase space coordinates, the ground target can be obtainedThe phase mapping in the two-dimensional phase space satisfies:

Ω₊＝λ_t-arctan(cosi·tanu₊)

Ω_-＝2λ_t-π-Ω₊＝λ_t-arctan(cosi·tanu_-)

in the formula: omega₊，Ω_-Respectively longitude and latitude coordinatesElevation intersection right ascension mapping, u, at the ascending and descending sections of the track₊，u_-Respectively longitude and latitude coordinatesAnd (3) latitude argument mapping of an orbit ascending section and an orbit descending section, wherein i is the orbit inclination angle of all the orbits in the isomorphic constellation, and sgn x represents the positive sign and the negative sign of a variable x.

In order to solve for the range of possible satellite phase mappings that can cover the selected terrestrial target, it is necessary to first calculate the actual coverage of the satellites in the constellation from the constellation orbital parameters or directly externally input. Assuming that the orbital altitude of the satellite is Hs and the minimum elevation angle at which the ground can communicate with the satellite is Emin, when no other coverage area constraints are considered, the coverage area of the satellite on the ground is considered to be circular, and the central angle α of the covered hemisphere is:

to satisfy the coverage condition, satellite sub-satellite latitude and longitudeTo the target longitude and latitudeShould satisfy:

longitude and latitude of the points under the starThe phase mapping in the two-dimensional phase space, in which the target can be covered, is obtained by substituting the above equationOf satellite phase, i.e. targetVisual phase range ofThe following relationship is satisfied:

step three, screening out the satellites required for calculating the coverage performance in the two-dimensional phase space according to the analysis range of the coverage performance in the step one and the calculation result of the visible phase range in the step two, specifically:

first, the target in two-dimensional phase space is calculatedVisual phase range ofThe phase boundary of (1). Visual phase range for isomorphic constellations with coverage angle α and orbital dip iUpper and lower latitude argument boundaries u_bUAnd u_bDCan be expressed as:

calculating the ascension boundary at the ascending intersection requires first calculating the range of the visible phaseThe latitude argument at the boundary of the right ascension at the intersection point is raised. According to the spherical trigonometric relation, the latitude amplitude angle u when the right and left boundary values of the ascension point right ascension are taken can be obtained_bLAnd u_bRRespectively as follows:

substituting the latitude argument obtained by the above formula into the visual phase rangeThe rising point right ascension boundary can be obtained as:

then, according to the coverage performance analysis range selected in the step one, a closed region is searched in the two-dimensional phase space, so that the region satisfies the following conditions:

the distance between the upper boundary of the region and the upper boundary of the coverage performance analysis range is equal to the distance u of the target mapping to the lower boundary of the visual phase range_bD；

The distance between the lower boundary of the region and the lower boundary of the coverage analysis range is equal to the distance u from the target to the upper boundary of the visible phase range_bU；

The distance between the left boundary of the region and the left boundary of the coverage analysis performance range is equal to the distance omega of the target mapping to the right boundary of the visual phase range_bR；

The distance between the right boundary of the region and the right boundary of the coverage performance analysis range is equal to the distance omega of the target mapping to the left boundary of the visual phase range_bL；

The satellite phase in the constellation is the satellite contained in the closed region in the two-dimensional phase space, namely the result of the screened satellite.

Step four, performing multiple translations on the visual phase range according to the satellite screening results obtained in the step three, and keeping the translation result of each time, so that after all translations of the visual phase range, the reference point of the visual phase range coincides with the phases of all screened satellites, specifically:

the phase set of all the satellites screened out in the third step is recorded as S (omega, u), and the ground targetRespectively, are (omega)₊,u₊) And (omega)_-,u_-) The visual phase range of the target isSelection of (omega)_-,u_-) As a reference point for the translation of the visual phase range, thenComputing a phase map (Ω) of the selected reference point to the satellite_s,u_s) Distance vectors in two-dimensional phase space. ThenThe translation result for the visible phase range is:

step five, calculating the continuous coverage performance of the constellation to the ground target according to the superposition condition of each region range obtained after the translation in the step four in the two-dimensional phase space, specifically:

calculating the overlapping area between each area obtained after the visible satellite phase range is translated in the fourth step within the coverage performance analysis range;

calculating the area of the overlapping area in the two-dimensional phase space and the overlapping weight corresponding to each overlapping area;

calculating the sum of the areas of the overlapping areas with the same overlapping weight number, and calculating the ratio of the sum of the areas of the overlapping areas with the same weight number to the area of the coverage performance analysis range;

and calculating the continuous coverage performance of the constellation according to the area ratio of the overlapping areas and the corresponding overlapping weight.

In the range of coverage performance analysis, when the overlapping areas among the areas are judged after the translation in the fourth step, all the areas are polygons, so that the overlapping areas among the areas can be judged through the topological relation of the plane graph. The judgment of intersection or inclusion of two regions by using a topological relation algorithm belongs to the prior art and is not described in more detail here.

For example, an example of low latitude coverage performance analysis is given in the embodiment of the present invention by taking a Walker isomorphic constellation with a configuration parameter of N/P/F-36/9/4 as an analysis object. The constellation consists of 36 satellites, all the satellites are uniformly distributed on 9 orbits respectively, and the phase difference of the satellites between the adjacent orbits is 2 pi F/N-2 pi/9. Preferably, the orbit inclination of the constellation in the embodiment is set to be 52.25 °, and the hemispherical angle of each satellite coverage area is set to be 26.23 °.

According to the Walker constellation configuration parameters, the right ascension phase omega and the latitude argument phase u of all satellites in the constellation can be calculated to meet the following relation. Suppose that the ascent point right ascension of the reference satellite at the initial time is Ω₀Latitude argumentIs u₀Then, the latitude argument and the ascent point right ascension phase set of all satellites in the constellation can be expressed as:

in the formula: j is 1,2, …,9, k is 1,2, …,4 are the orbit of the Walker constellation and the satellite number of each orbit respectively,is the rate of change of satellite phase over time. For the analysis problem of constellation continuous coverage performance, the method can be approximately considered as Is a constant value that does not change with time.

For convenience, the reference satellite phase (Ω) is hereinafter defaulted₀,u₀) The value is (0, 0). Fig. 2 shows the phase distribution of the satellite at the initial time calculated by the above formula. The ascension phase interval of the ascending intersection point between the selected Walker constellation orbits and the latitude amplitude phase interval of the satellite in the same orbit are respectively (d omega, du) ═ 2 pi/9, pi/2.

According to the phase distribution of the Walker constellation, a parallelogram grid with the width d omega being 2 pi/9 and the height du being pi/2 can be selected as a coverage analysis area in the (omega, u) two-dimensional phase space. As shown in fig. 2, each grid is completely equal to the other grids in shape, and 4 satellites are distributed only at 4 corner points of the parallelogram grid, so that the number and the position distribution of the satellite phase maps contained in the grid are the same. Further, in order to simplify the judgment of the topological relation of the plane graph in the process of coverage analysis, rectangular areas with the same length and width are selected as coverage analysis areas, and the reasonability of the coverage analysis areas is not repeatedly proved.

After the satellite phase in the two-dimensional phase space is converted into the spherical longitude and latitude coordinates, the spherical surface from the satellite to the ground target can be solved according to the spherical geometryDistance. Two-dimensional phase space phase (omega, u) and longitude and latitude coordinatesThe conversion relation of (1) satisfies:

satellite subsatellite point longitude and latitudeTo the target longitude and latitudeThe spherical distance α d is:

defining a two-dimensional phase space in which the target can be coveredIs targeted to the satellite (omega, u) phase rangeA set of visual phases. The boundary of the visual phase set can be solved by substituting the transformation relationship between the phase space coordinates and the longitude and latitude coordinates into the spherical distance relationship of the above formula:

in general, the visual phase sets of ground targets at different latitudes can be classified into 4 types as shown in fig. 3, i.e., non-connected type, connected concave type, connected convex type and strip type. Due to the limitation of the orbit inclination and the coverage, only the first 3 regions can appear when the satellite can not cover the north-south pole. When the north-south pole can be covered, a banding coverage area occurs because the north-south pole includes all longitudes. To illustrate the strip-type visual phase set, the orbit tilt angle was set to 74 ° only in the simulation of fig. 3, which would not affect the calculation of the ground target visual phase set when performing the coverage analysis in this embodiment.

In order to reduce the calculation amount of the graph topological relation, the satellite influencing the calculation result of the coverage performance needs to be screened. Fig. 4 shows a method for screening satellites according to the distance of the target mapping to the boundary of the visual phase range and the coverage analysis range. As shown in fig. 4, to calculate the constellation vs. latitudeFor the coverage performance of an object at 65 °, the visible phase range of the object at that point is calculated first. The distances u that the target maps to the upper, lower, left and right boundaries of the visible phase range are then calculated_bU，u_bD，Ω_bL，Ω_bRThe specific calculation method has been given in the detailed description, and thus is not described in detail.

The upper, lower, left and right boundaries covering the analysis range in the first binding step are u-0, u-pi/2, omega-0 and omega-2 pi/9, respectively. The upper boundary of the up-track phase screening range is 0-u_bDThe lower boundary is-pi/2-u_bUThe left boundary is 0-omega_bRThe right boundary is 2 pi/9-omega_bL. Similarly, the upper boundary of the down-tracking phase screening range is 0+ u_bUThe lower boundary is-pi/2 + u_bDLeft boundary of 0+ omega_bLThe right boundary is 2 pi/9 + omega_bR.. And the satellite with the phase in the ascending orbit or descending orbit phase screening range is the screened satellite with influence on the coverage analysis calculation. Since other satellites have no influence on the calculation result of the coverage performance of the method, subsequent calculation is not carried out on the coverage performance. The method avoids redundant inter-satellite and inter-satellite position relation calculation, and the calculation amount of the coverage analysis method is not obviously increased along with the increase of the number of satellites.

When a satellite is visible to a ground target, the ground target must also be within the coverage area of the satellite. And therefore, the number of satellites in view of the terrestrial target,the coverage multiplicity of the constellation at that location is the same at any time. To solve for the number of visible satellites of interest, the visible phase range may be determinedAs a coverage area map of the satellite to the latitude target. Then, willAnd C, performing phase translation according to the result of the satellite screened in the step three, and converting the number of visible satellites of the target with different phases of the constellation into the equivalent coverage weight of the target at the different phases of the constellation. Due to the fact thatThe shape of (2) is only related to the latitude of the target, so that after translation, the number of visible satellites of the target at different moments can be directly calculated according to the geometric relation without solving the coverage performance of the target on a discrete time domain.

After the satellites influencing the coverage performance analysis are screened out, the results of the satellites need to be screened out according to the third step, and the ground targets are calculated in the second stepPhase mapping (omega) of_-,u_-) As a reference point, the visual phase range of the targetThe process of translation is performed. FIG. 5 shows latitudeThe visual phase range of (a) shifts the result. Assume that the translational target of the current visual phase range is the satellite phase (Ω)_s,u_s) Then shift the pre-target phase map (Ω)_-,u_-) Relative toPosition of (1) andtranslated satellite phase (omega)_s,u_s) Relative to the range obtained after translationAre the same.

Fig. 6 is a partially enlarged schematic view of the overlapping situation between the regions obtained after the four translation steps of the visual phase range in the coverage analysis range. Because the number of coincident times of the translated region at different positions is the same as the number of visible satellites when the satellites are located at the positions, the area of the coincident region represents the time of the ground targets with different longitudes at the same latitude and under the number of the visible satellites, and therefore the constellation coverage performance required to be solved can be obtained quantitatively by analyzing the coincident areas and the number of coincident times of the regions. Specifically, in fig. 6, the sum of the areas of all the regions with the overlapping number of 1 and the sum of the areas of all the regions with the overlapping number of 2 are calculated, and the obtained areas are compared with the area of the coverage analysis range, so that the latitude is obtainedThe ground target, the time with the number of visible satellites being 1 and 2 respectively, is the proportion of the total simulation time.

Taking the distribution of coverage multiplicity at different latitudes over time as an example, fig. 7 shows the results of coverage performance analysis of the adopted embodiments by using the method of the present invention. As can be seen from the results, the results obtainedThe result of the coverage analysis is approximately the same as the area ratio of each coverage weight in fig. 6. Compared with the traditional coverage analysis method based on time and position discretization, the method utilizes the characteristic that the phase relationship among the satellites of the isomorphic constellation is constant, represents the spatial position and the phase relationship of the satellite in a two-dimensional phase space formed by the right ascension at the intersection point and the latitude argument, and avoids solving the periodically-changed inter-satellite distance relationship; the coverage performance analysis range in the two-dimensional space is judged according to the isomorphic constellation configuration, and repeated solving of coverage performance similar areas are avoidedThe redundant satellite position relation is calculated, so that the calculated amount of the coverage analysis method is not obviously increased along with the increase of the number of satellites, and the calculation efficiency of the coverage analysis is improved.

It should be noted that the detailed description is only for explaining and explaining the technical solution of the present invention, and the scope of protection of the claims is not limited thereby. It is intended that all such modifications and variations be included within the scope of the invention as defined in the following claims and the description.