CN115396010B - Optimal phase factor selection method for Walker constellation to avoid internal collision - Google Patents

Optimal phase factor selection method for Walker constellation to avoid internal collision Download PDF

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CN115396010B
CN115396010B CN202211012267.3A CN202211012267A CN115396010B CN 115396010 B CN115396010 B CN 115396010B CN 202211012267 A CN202211012267 A CN 202211012267A CN 115396010 B CN115396010 B CN 115396010B
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苏博
周庆瑞
郑威
王辉
孙昌浩
邵将
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China Academy of Space Technology CAST
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Abstract

The invention discloses a selection method of an optimal phase factor for avoiding internal collision of a Walker constellation, which comprises the steps of designing and obtaining an orbit semi-long axis, an orbit inclination angle and a near-site angular distance of each satellite of the Walker constellation; acquiring the total number of satellites and the track surface number of a Walker constellation; acquiring two closest point angle values at the intersection point of the ith track surface and the first track surface according to the semi-long axis, the eccentricity, the track inclination angle, the total number of satellites and the track surface number of each satellite of the Walker constellation; acquiring a satellite number nearest to the intersection point on the ith track surface according to two closest point angle values at the intersection point of the ith track surface and the first track surface; according to the satellite number nearest to the intersection point on the ith track surface, obtaining the minimum angular distance of each track surface to the 1 st track surface, and obtaining the minimum value to obtain the minimum angular distance of any two satellites in the whole constellation; and traversing F=0, … and P-1, and repeating the process to obtain the optimal phase factor for maximizing the minimum angular distance between any two satellites in the whole constellation.

Description

Optimal phase factor selection method for Walker constellation to avoid internal collision
Technical Field
The invention relates to the technical field of satellite running tracks, in particular to a method for selecting an optimal phase factor for avoiding internal collision of a Walker constellation.
Background
In recent years, a broad-band constellation is formed by networking a large number of microsatellites in a low-orbit space. Compared with the traditional medium-high orbit navigation constellation, the satellite is densely distributed, and the earth coverage performance is greatly enhanced. Therefore, when designing a constellation, a designer often needs to pay more attention to the safe operation condition of the constellation, and if the constellation can safely operate with a smaller collision probability, a large number of satellites can naturally ensure the coverage performance. The Walker constellation is the most common constellation configuration, described using reference codes. The scale of the constellation satellite and the number of track surfaces can be determined in advance by solving optimization problems such as coverage performance, communication quality, emission and deployment cost and the like, and the minimum angular distance of any two satellites in the constellation is directly influenced by the phase factor F. Therefore, the problem of selecting the phase factor that makes the constellation operation safer and minimizes the probability of internal collision is needed to be solved.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide the optimal phase factor selection method for avoiding internal collision of the Walker constellation, the phase factor which enables the satellites in the Walker constellation to be most dispersed and the collision probability to be minimum can be obtained by adopting the traversing method, and the problems that the coverage of the constellation is more concerned than the safety in the selection of the traditional phase factor can be solved by adopting the invention.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
a method for selecting an optimal phase factor for Walker constellations to avoid internal collisions, the method comprising:
designing and obtaining an orbit semi-long axis, an orbit inclination angle and a near-site angular distance of each satellite of the Walker constellation;
designing and obtaining the total number of satellites and the track surface number of a Walker constellation;
acquiring two closest point angle values at the intersection point of the ith track surface and the first track surface according to the semi-long axis, the eccentricity and the track inclination angle of each satellite of the Walker constellation, the total number of satellites and the track surface number;
acquiring a satellite number nearest to the intersection point on the ith track surface according to two closest point angle values at the intersection point of the ith track surface and the first track surface;
according to the satellite number nearest to the intersection point on the ith track surface, obtaining the minimum angular distance of each track surface facing the 1 st track surface, and obtaining the minimum value of the minimum angular distance to obtain the minimum angular distance of any two satellites in the whole constellation;
and traversing F=0, … and P-1, and repeating the process to obtain the optimal phase factor for maximizing the minimum angular distance between any two satellites in the whole constellation.
It should be noted that the Walker constellation is a circular orbit constellation under the action of gravity.
The normal vector of the track surface and the right ascent and descent vector of the ascent point are established under the geocentric inertial coordinate system, and two values of the angle of the closest point at the intersection point of the ith track surface and the first track surface are obtained by using a space analysis geometrical method.
The satellite number closest to this intersection point on the ith track surface is represented by:
Figure BDA0003811045980000031
/>
wherein j is c The number of the satellite closest to the intersection on the i-th track plane,
Figure BDA0003811045980000032
and->
Figure BDA0003811045980000033
Two values of the angle of closest point at the intersection of the ith track surface and the 1 st track surface are shown +>
Figure BDA0003811045980000034
T represents the total number of satellites, P represents the number of orbit planes, and square brackets [ f (x) ]]The function f (x) is rounded, mod is modulo operation, and pi is the circumference ratio.
It should be noted that, the track plane numbers are traversed from 2 to P, and the minimum value is taken to obtain the minimum angular distance between any two satellites in the whole constellation.
It should be noted that all possible values of the phase factor f=0, …, P-1 are traversed to obtain the optimal phase factor F * 。
Compared with the prior art, the invention optimizes the minimum distance of any satellite in the constellation so as to achieve the goal of the safest operation of the constellation and the minimum probability of internal collision.
Drawings
Fig. 1 is a flowchart of a Walker constellation internal collision avoidance phase factor selection method according to the present invention;
fig. 2 is a schematic diagram of minimum angular distances of any two satellites in the Walker constellation according to the present invention.
Detailed Description
The following description of the present invention will further illustrate the present invention, and the following examples are provided on the premise of the present technical solution, and the detailed implementation and the specific operation procedure are given, but the protection scope of the present invention is not limited to the present examples.
The invention relates to a method for selecting an optimal phase factor for avoiding internal collision of a Walker constellation, which comprises the following steps:
designing and obtaining an orbit semi-long axis, an orbit inclination angle and a near-site angular distance of each satellite of the Walker constellation;
designing and obtaining the total number of satellites and the track surface number of a Walker constellation;
acquiring two closest point angle values at the intersection point of the ith track surface and the first track surface according to the semi-long axis, the eccentricity and the track inclination angle of each satellite of the Walker constellation, the total number of satellites and the track surface number;
acquiring a satellite number nearest to the intersection point on the ith track surface according to two closest point angle values at the intersection point of the ith track surface and the first track surface;
according to the satellite number nearest to the intersection point on the ith track surface, obtaining the minimum angular distance of each track surface facing the 1 st track surface, and obtaining the minimum value of the minimum angular distance to obtain the minimum angular distance of any two satellites in the whole constellation;
and traversing F=0, … and P-1, and repeating the process to obtain the optimal phase factor for maximizing the minimum angular distance between any two satellites in the whole constellation.
Further, the Walker constellation of the invention is a circular orbit constellation under the action of gravity.
Furthermore, the invention establishes a track surface normal vector and an ascending intersection point right ascent vector under a geocentric inertial coordinate system, and obtains two closest point angle values at the intersection point of the ith track surface and the first track surface by using a space analytic geometry method.
Further, in the present invention, the satellite number closest to the intersection on the ith track surface is expressed as:
Figure BDA0003811045980000051
wherein j is c The number of the satellite closest to the intersection on the i-th track plane,
Figure BDA0003811045980000052
and->
Figure BDA0003811045980000053
Two values of the angle of closest point at the intersection of the ith track surface and the 1 st track surface are shown +>
Figure BDA0003811045980000054
T represents the total number of satellites, P represents the number of orbit planes, and square brackets [ f (x) ]]The function f (x) is rounded, mod is modulo operation, and pi is the circumference ratio. />
Further, in the present invention, track plane numbers are traversed from 2 to P, and a minimum value is taken to obtain a minimum angular distance of any two satellites in the entire constellation.
Further, in the present invention, all possible values of the phase factor f=0, …, P-1 are traversed to obtain the optimal phase factor F * 。
Example 1
As shown in fig. 1, the optimal phase factor selection method for avoiding internal collision of the Walker constellation of the present invention includes the following steps:
step 1, designing and obtaining the orbit inclination inc and the near-spot angular distance omega of each satellite of the Walker constellation, and setting the near-spot angular distance of each satellite to be the same value.
The satellite involved in this embodiment may be a low-orbit satellite that is orbiting 200-2000 km from the ground. Satellites may refer to satellites launched in space for military target detection, communication services, scientific experiments, and other tasks.
According to the actual task demands, the orbit inclination angle inc and the near-site angular distance omega of each satellite in the Walker constellation can be determined.
Step 2, designing and obtainingTotal number of satellites T, number of orbit planes P, initial value Ω of rising intersection point of Walker constellation 0 And initial value M of short-and-short point angle 0 And sets the initial value of the phase factor F to 0.
Wherein the total number T of satellites represents the total number of satellites contained in the Walker constellation, the number P of track planes represents the total number of track planes contained in the Walker constellation, the phase factor F represents the difference between the even and odd point angles of the different-plane satellites in the Walker constellation, and the rising point has an initial value of Ω 0 Characterizing the right ascent point and the right ascent point of the 1 st satellite on the 1 st track surface, and the initial value M of the closest point angle 0 And representing initial values of the closest point angles of the 1 st satellite on the 1 st track surface.
The total number of satellites T and the number of track surfaces P can be determined according to actual task requirements.
Step 3, according to the orbital tilt inc and near-spot angular distance omega of each satellite of the Walker constellation, the total number T of satellites, the track surface number P, the phase factor F and the initial value omega of the rising intersection point 0 And initial value M of short-and-short point angle 0 Obtaining two values of angle of closest point at intersection of ith track surface and first track surface
Figure BDA0003811045980000064
And->
Figure BDA0003811045980000065
Since the Walker constellation track has rotational symmetry, the ith is selected 1 Track face and i 2 Track surface is calculated, its effect is as follows for the ith 1 +1 track plane and ith 2 The +1 track surface was found to have the same analytical calculation effect. So the 1 st satellite S is selected without losing generality 1,1 And the jth satellite S on the ith track surface i,j Analysis was performed. Suppose S 1,1 Just to the intersection of the 1 st track face and the i-th track face, as shown in fig. 2.
Then, under the geocentric inertial coordinate system, the orbital inclination angle of any one satellite orbit is set as inc, the right ascent point and the right ascent point are set as omega, and the near-place angular distance is set as omega. The satellite orbit surface normal vector and the rising-intersection right ascent vector are respectively:
Figure BDA0003811045980000061
in the method, in the process of the invention,
Figure BDA0003811045980000062
r is the normal vector of the satellite orbit plane z (-Ω)、R x (-inc) and R z (- ω) means counterclockwise rotation about the z-axis by an angle of- Ω, counterclockwise rotation about the x-axis by an angle of-inc, counterclockwise rotation about the z-axis by an angle of- ω, -/-, respectively>
Figure BDA0003811045980000063
Is the right-hand vector of the rising intersection point of the satellite. Wherein, the rotation matrix of anticlockwise rotation theta angle is
Figure BDA0003811045980000071
/>
The right-hand warp of the ascending intersection point of the 1 st track surface and the i-th track surface is omega 1 And omega i Wherein
Ω 1 ＝Ω 0
Figure BDA0003811045980000072
The normal vectors of the 1 st track surface and the i th track surface can be obtained from the expression of the normal vector of the track surface and the right ascent point
Figure BDA0003811045980000073
And->
Figure BDA0003811045980000074
The right-angle vector of the intersection point of the two track surfaces is +.>
Figure BDA0003811045980000075
And->
Figure BDA0003811045980000076
The two track plane intersection vectors are:
Figure BDA0003811045980000077
the straight-on point angles at the intersection of the two track surfaces (considering only the intersection of the z-axis normal hemisphere) are respectively:
Figure BDA0003811045980000078
step 4, according to the two values of the angle of the closest point at the intersection point of the ith track surface and the 1 st track surface
Figure BDA00038110459800000710
And->
Figure BDA00038110459800000711
Acquiring the number j of the satellite closest to the intersection on the ith track plane c 。
The satellite number closest to this intersection on the ith orbital plane is:
Figure BDA0003811045980000079
in the formula, square brackets [ f (x) ] represent rounding the function f (x), and mod represents modulo operation.
Step 5, according to the satellite number j nearest to the intersection point on the ith track surface c Traversing i=2, …, P, obtaining the minimum angular distance of each orbit facing the 1 st orbit surface, and obtaining the minimum value thereof to obtain the minimum angular distance delta phi of any two satellites in the whole constellation min 。
For the 1 st track face and the i th track face, the minimum angular distances of any two satellites are:
Figure BDA0003811045980000081
in the method, in the process of the invention,
Figure BDA0003811045980000082
is the ith track plane j c The angle of the closest point of the satellites is represented by the Walker constellation configuration:
Figure BDA0003811045980000083
and (5) determining. In omega 0 For the right-way reference setting value of the intersection point, M 0 Is a reference setting value of the angle of the closest point.
Traversing i=2, …, P, the minimum angular distance of each orbit facing the 1 st orbit surface can be obtained, and the minimum value is obtained, so that the minimum value in any two satellite angular distances in the whole constellation can be obtained:
Figure BDA0003811045980000084
step 6, traversing F=0, …, P-1, repeating steps 3-5 to obtain delta phi min (F) Maximum phase factor F * 。
Will be delta phi min Form delta phi of function written as pair F min (F) A. The invention relates to a method for producing a fibre-reinforced plastic composite Recording delta phi corresponding to different F values min (F) Value, delta phi min (F) When the maximum value is taken, the corresponding phase factor F is the optimal phase factor F which ensures that the separation degree of each satellite of the Walker constellation is maximum and the collision probability is minimum *
Various modifications and variations of the present invention will be apparent to those skilled in the art in light of the foregoing teachings and are intended to be included within the scope of the following claims.

Claims (3)

1. A method for selecting an optimal phase factor for Walker constellation to avoid internal collisions, the method comprising:
step 1, designing and obtaining an orbit semi-major axis, an orbit inclination angle and a near-site angular distance of each satellite of a Walker constellation;
step 2, designing and obtaining the total number of satellites and the track surface number of the Walker constellation;
step 3, obtaining two closest point angle values at the intersection point of the ith track surface and the first track surface according to the semi-long axis, the eccentricity and the track inclination angle of each satellite of the Walker constellation, the total number of satellites and the track surface number;
step 4, acquiring a satellite number closest to the intersection point on the ith track surface according to two closest point angle values at the intersection point of the ith track surface and the 1 st track surface;
step 5, according to the satellite number closest to the intersection point on the ith track surface, obtaining the minimum angular distance of each track surface facing the 1 st track surface, and obtaining the minimum value of the minimum angular distance to obtain the minimum angular distance of any two satellites in the whole constellation;
step 6, traversing the phase factors F=0, … and P-1, and repeating the processes of the steps 3-5 to obtain an optimal phase factor which enables the minimum angular distance of any two satellites in the whole constellation to be maximum;
the method comprises the steps of establishing a track surface normal vector and an ascending intersection point right ascent vector under a geocentric inertial coordinate system, and obtaining two flat near point angle values at the intersection point of an ith track surface and a 1 st track surface by using a space analysis geometric method, wherein the satellite number nearest to the intersection point on the ith track surface is expressed as:
Figure QLYQS_1
；
wherein j is c A number ℳ indicating the satellite closest to the intersection on the i-th track plane i And ℳ 1 Representing two values of the angle of the closest point at the intersection of the ith and 1 st track surfaces, T representing the total number of satellites, P representing the number of track surfaces, square brackets [ f (x) ]]The function f (x) is rounded, mod is modulo operation, and pi is the circumference ratio.
2. The optimal phase factor selection method for avoiding internal collisions of a Walker constellation according to claim 1, wherein the Walker constellation is a circular orbit constellation under the action of gravity.
3. The optimal phase factor selection method for avoiding internal collisions of a Walker constellation according to claim 1, wherein the track plane numbers are traversed from 2 to P and the minimum angular distance of each track plane to the 1 st track plane is taken, wherein the minimum value is taken and the minimum value is taken to obtain the minimum angular distance of any two satellites in the whole constellation.
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