CN109240322A - A kind of satellites formation implementation method towards super breadth imaging over the ground - Google Patents
A kind of satellites formation implementation method towards super breadth imaging over the ground Download PDFInfo
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Abstract
The invention discloses a kind of satellites formation implementation methods towards super breadth imaging over the ground, are related to the Formation Technology that satellite stablizes imaging, belong to the technical field of control, adjusting.This method is studied for distributed super breadth imaging problem, break the single substar imaging mode of conventional satellite imaging, by carrying high-precision imaging load and combining distributed satellites control technology, satellite can be made to realize the super breadth imaging of high-precision in the form of imaging of forming into columns, satellite acquisition imaging efficiency is substantially improved.Method proposes the super breadth imaging patterns of Distributed Satellite Formation based on J2 stability, solve satellite and stare the problems such as range is small, imaging breadth is narrow, earth rotation makes satellite that can not realize continuous imaging to ground adjacent area.
Description
Technical field
The invention discloses a kind of satellites formation implementation methods towards super breadth imaging over the ground, are related to satellite and stablize imaging
Formation Technology, belong to the technical field of control, adjusting.
Background technique
With the fast development of space technology, satellite remote sensing imaging technique is in the side such as agricultural, economy, weather, searching rescue
Face it is increasingly prominent go out the advantages such as its is quick, convenient, precision is high.And there is cost by the distributed micro-nano satellite that quick satellite forms
It is low, configuration it is flexible the features such as.For the relatively traditional large satellite of micro-nano satellite, the R&D cycle is short, and technical indicator is relatively low, transmitting
Cost is also reduced because of its lower quality, and middle-size and small-size country and colleges and universities of scientific research institution can undertake it and develop launching costs, knot
Closing several satellite in a rocket technology can realize that rapid fire is disposed, and the micro-nano satellite of low orbit can be entered the orbit by the MISSILE LAUNCHING after reequiping, energy
Enough flexibly reply emergency situations, meet the needs of quick response, with the incomparable technical advantage of large satellite.
However, the mode that satellite imagery technology generallys use progress image mosaic after single star is imaged at present completes big map
Imaging, due to the influence of earth rotation, satellite can not realize continuous imaging to ground adjacent area, need to undergo longer time
The adjacent area of last time imaging could be passed through, to cause to be illuminated by the light condition to the image quality of adjacent area, cloud and mist blocks
The influence of condition, meanwhile, (such as: marine lost contact target is searched and rescued, high dynamic target is searched when carrying out extensive search for dynamic object
Rope), target is easily moved in the region being imaged in the time slot, to cause under-enumeration.And it is defended using distribution
The super breadth imaging technique of star can the significant increase efficiency and accuracy checked on a large scale, the imaging for shortening adj acent imaging area domain prolongs
When.
Based on super breadth imaging task, micro-nano satellite flight pattern answers stable for extended periods of time to meet imaging demand, and micro-
Nano satellite own vol it is limited and entrained for maintains form into columns fuel it is limited, so need design make satellite do not use or
Form into columns stable flight pattern and orbital tracking can be met using a small amount of fuel.
Summary of the invention
Goal of the invention of the invention is the deficiency for above-mentioned background technique, is provided a kind of towards super breadth imaging over the ground
Satellites formation implementation method, realize the formation design and attitude of satellite planning of distributed satellites super breadth imaging, in turn
The imaging of super breadth is realized, satellite is solved and stares that range is small, imaging breadth is narrow, earth rotation makes satellite can not be to ground phase
Realize the technical issues of continuous imaging in neighbouring region.
The present invention adopts the following technical scheme that for achieving the above object
A kind of satellites formation implementation method towards super breadth imaging over the ground, includes the following steps:
1, imaging demand is obtained: the dimensional information of imaging region needed for determining, for determining that the track of distributed satellites inclines
Angle then needs the width being imaged needed for determining using SSO (Sun Synchronous Orbit) if you need to global range imaging, required for determining in conjunction with satellite imagery parameter
Number of satellite；
2, the imaging parameters of satellite remote sensing camera are determined: predominantly the wide cut of imaging region, optimal imaging height, camera at
As maximum side-sway ability；
3, the number of satellite being imaged needed for determining substantially in conjunction with above two step, quantity should be greater than being equal to imaging wide cut/single
Satellite field of view determines the orbit inclination angle formed into columns based on imaging region, for the stability for keeping imaging, forms into columns and uses circuit orbit
Grade, eccentricity 0；
4, using reference star as origin, reference star directional velocity is Y-direction, and place horizontal plane is two-dimensional coordinate plane sets pole
Coordinate system sets each member's star at a distance from reference star and angle according to imaging wide cut；
5, it based on the stable condition in (17) (18) two formula, according to the design method in (20)-(27) formula, can obtain
The analytic solutions for obtaining each accompanying flying satellite radical, so that it is determined that the radical of the accompanying flying satellite under stable condition；
6, the imaging center substar according to the following each moment reference star of the ephemeris computation of reference star and each accompanying flying star
Camera pointing vector under this reference position；
7, calculate that ephemeris and the pointing vector at following each moment resolve the posture of accompanying flying satellite in conjunction with each accompanying flying star
Information enables satellites formation to fly steadily in the long term in the case where meeting J2 perturbation stable condition, realizes ultra-wide imaging.
The present invention gives two kinds of formation design schemes, the first is to eliminate the reference satellite direction of motion and reference satellite rail
Offset of the road face under J2 perturbation is target combination reference satellite at a distance from accompanying flying satellite and phase angle adjusts the liter of accompanying flying satellite
Intersection point right ascension and mean anomaly；Be for second to eliminate offset of the reference satellite direction of motion under J2 perturbation as target, for
With identical right ascension of ascending node but the different member's star of orbit inclination angle, accompanying flying star orbital tracking is determined using first method, it is right
In with same rail inclination angle but the different member's star of right ascension of ascending node, according to single star imaging width and with accompanying flying satellite and reference
There are the orbit inclination angle and mean anomaly of adjustment accompanying flying satellite for the purpose of overlapping in the visual field of satellite.
The accompanying flying orbit elements of satellite that the first formation scheme determines are as follows:σbFor accompanying flying satellite
Orbital tracking, σb=(ab eb ib ωb Ωb Mb), ab、eb、ib、ωb、Ωb、MbThe respectively semi-major axis of accompanying flying satellite, bias
Rate, orbit inclination angle, argument of perigee, right ascension of ascending node, mean anomaly, ar、er、ir、ωr、Ωr、MrRespectively the half of reference satellite
Long axis, eccentricity, orbit inclination angle, argument of perigee, right ascension of ascending node, mean anomaly, δ Ω, δ m are respectively accompanying flying satellite and reference
The right ascension of ascending node difference and mean anomaly difference of satellite, O
For reference satellite coordinate origin, A is the intersection point of reference satellite orbital plane and the equatorial plane, and D is accompanying flying satellite orbit face and equator
The intersection point in face, S are accompanying flying satellite particle,
For the normal vector of accompanying flying star orbital plane,For ground axial vector, a is the semi-major axis of reference satellite,ByReally
Fixed, R is reference satellite particle, and i is the orbit inclination angle of reference satellite, and d, phi are reference satellite at a distance from accompanying flying satellite and phase
Angle,Sx、Sz、SyForCoordinate under reference satellite coordinate system, Cx、Cz、CyForJoining
Examine the coordinate under co-ordinates of satellite system.
The accompanying flying orbit elements of satellite that second of formation scheme determines are as follows:σbFor accompanying flying satellite
Orbital tracking, σb=(ab eb ib ωb Ωb Mb), ab、eb、ib、ωb、Ωb、MbThe respectively semi-major axis of accompanying flying satellite, bias
Rate, orbit inclination angle, argument of perigee, right ascension of ascending node, mean anomaly, ar、er、ir、ωr、Ωr、MrRespectively reference satellite
Semi-major axis, eccentricity, orbit inclination angle, argument of perigee, right ascension of ascending node, mean anomaly, δ i, δ m are respectively accompanying flying satellite and ginseng
The orbit inclination angle difference and mean anomaly difference of satellite are examined,A is reference satellite semi-major axis, and sen is single
Star imaging width,R is reference satellite particle, and the coordinate of R is (a 0
0), B is accompanying flying satellite particle, and G is the ascending node of reference satellite, For ground axial vector,Cx、Cz、CyForCoordinate under reference satellite coordinate system, i are that the track of reference satellite inclines
Angle,Bx、Bz、ByForCoordinate under reference satellite coordinate system, d, phi be reference satellite with
The distance and phase angle of accompanying flying satellite.
The present invention by adopting the above technical scheme, has the advantages that
(1) it present application contemplates the high-order in the accurate variation processing of J2 perturbation model is a small amount of, is handled by accurate variation
More accurate J2 stability condition is obtained, stable imaging can be realized for a long time by having determined on the basis of the J2 stability condition
The formation configuration analytic solutions of flight, then the configuration design scheme under polar coordinates is established on this basis, it forms into columns convenient for stable type
Design.
(2) the application gives the calculation method of two kinds of formation configuration analytic solutions, and one kind is to eliminate reference satellite movement side
To and reference satellite orbital plane J2 perturbation under offset be target, pass through parsing accompanying flying satellite and reference satellite geometric position
The geometry site for each member's star of forming into columns is mapped to orbit elements of satellite by relationship, is defended according to what this kind of analytic method determined
Star formation scheme is able to maintain that the monolithic stability formed into columns in a long time, does not need consumption fuel and carries out track maintenance, saves
Fuel overcomes limited fuel to be difficult to meet the defect of wide cut imaging demand；Another kind is only existed with eliminating the reference satellite direction of motion
Offset under J2 perturbation is target, and changing orbital plane using right ascension of ascending node, there are views caused by the track of inclination angle difference to make up
Open country is shunk, and the imaging satellite orbital period is big compared with short and imaging wide cut, and imaging gap is reduced between adjacent periods, target is greatly decreased
Can not be by satellite capture due to moving between the domain of adj acent imaging area the case where, solves high dynamic target extensive search under-enumeration
Problem, the first opposite formation needs more fuel to keep rank, but has very good super breadth covering performance, realizes
The satellites formation super breadth imaging under perturbation for a long time.
(3) present invention is imaged using high-resolution imaging satellite cluster, while guaranteeing imaging field of view,
Solve the problems, such as that traditional big visual field satellite imagery lack of resolution, remote sensing images clarity are poor, using it is of the present invention at
As formation reconfiguration scheme, visual field wide cut solves that high definition remote sensing satellite visual field is small, adjacent remote sensing area up to 1000KM
Domain imaging interval time is long, illumination condition inconsistent the problem of being unfavorable for comparative analysis is imaged.
Detailed description of the invention
Fig. 1 is the schematic diagram of orbital coordinate system.
Fig. 2 is the schematic diagram of track disturbed motion.
Fig. 3 is the schematic diagram of eccentricity and orbit inclination angle corresponding relationship.
Fig. 4 is the schematic diagram that accompanying flying orbit elements of satellite is calculated using the first formation scheme.
Fig. 5 is the imaging schematic diagram being imaged when wide cut is 700Km and 1000Km.
Fig. 6 is the flow chart of ultra-wide imaging method.
Fig. 7 is the flow chart of super breadth image forming program.
Fig. 8 is the simulation result of reference star and accompanying flying satellite distance when meeting J2 perturbation conditions under J2 perturbation model.
Fig. 9 is the range measurements that reference star and accompanying flying satellite when J2 perturbation conditions are unsatisfactory under J2 perturbation model.
Figure 10 is the simulation result of reference star and accompanying flying satellite distance when meeting J2 perturbation stable condition under HPOP model.
Figure 11 is the emulation knot of reference star and accompanying flying satellite distance when being unsatisfactory for J2 perturbation stable condition under HPOP model
Fruit.
Figure 12 is the schematic diagram of formation coverage condition when covering breadth 700Km, single visual angle 100Km.
Sub-satellite point breadth shortens the schematic diagram in region when Figure 13 is 100KM breadth.
Satellite covers the schematic diagram of wide cut variation in one orbital period when Figure 14 is 100Km breadth.
Figure 15 is the schematic diagram of formation coverage condition when covering breadth 1000Km, single visual angle 150Km.
Sub-satellite point breadth shortens the schematic diagram in region when Figure 16 is 150KM breadth.
Satellite covers the schematic diagram of wide cut variation in one orbital period when Figure 17 is 150Km breadth.
Figure 18 is the schematic diagram that ungauged regions type in the visual field is formed into columns.
Figure 19 is first group of imaging in specific embodiment.
Figure 20 is the schematic diagram that accompanying flying orbit elements of satellite is calculated using second of formation design scheme.
Figure 21 is that reference star is imitated at a distance from accompanying flying satellite when meeting (18) formula perturbation stable condition under J2 perturbation model
True result.
Reference star is at a distance from accompanying flying satellite when Figure 22 is is unsatisfactory for (18) formula perturbation stable condition under J2 perturbation model
Measurement result.
Figure 23 is that reference star emulates at a distance from accompanying flying satellite when meeting (18) formula perturbation stable condition under HPOP model
As a result.
Figure 24 is that reference star is imitated at a distance from accompanying flying satellite when being unsatisfactory for (18) formula perturbation stable condition under HPOP model
True result.
Satellite covers the schematic diagram of wide cut in one orbital period when Figure 25 is second of formation in specific embodiment.
Specific embodiment
The technical solution of invention is described in detail with reference to the accompanying drawing.
The present invention be directed to the super breadth imaging technique of distributed satellites, to J2 perturbation under orbit parameter progress variation analysis into
And perturbation model has been refined, design meets flight pattern steady in a long-term, and carries out accompanying flying according to the substar coordinate of reference star
The posture of satellite is planned, super breadth imaging steady in a long-term is realized.
Spacecraft Relative Motion model under 1.J2 perturbation
Satellites formation required for this part will be imaged for super breadth is designed, the main imaging according to satellites formation
Demand is designed the stability condition of satellites formation under J2 secular perturbation, and the different designs required according to formation
Two different imagings are formed into columns.
1.1 Spacecraft Relative Motion coordinate systems
In the researchs such as Spacecraft Rendezvous docking, the design of formation configuration, spacecraft relative distance is compared to semi-major axis of orbit
In a small amount, using Kepler's elements method can not directviewing description spacecraft relative positional relationship, then set Spacecraft Relative Motion
Coordinate system.As shown in Figure 1.
In Fig. 1, OXYZ is geocentric inertial coordinate system, and oxyz is Spacecraft Relative Motion coordinate system, wherein Earth central inertial system
Middle coordinate origin is located at the earth's core O, and X-axis is directed toward the first point of Aries, and Z axis is directed toward celestial pole, and Y-axis and the face XOZ constitute right-handed system；Spacecraft reference
Coordinate origin is located at centroid of satellite o in coordinate system (as Spacecraft Relative Motion coordinate system), and x-axis is the earth's core to spacecraft line
Direction, y-axis is the spacecraft direction of motion, the reference spacecraft orbit face that z-axis right-handed system is constituted perpendicular to x-axis and y-axis.
The 1.2 perturbation of earths gravitational field models based on method of average elements
When solving perturbed problem, if using classical Perturbation Solution, right ascension of ascending node is this with argument of perigee
Slowly varying long period term will become secular term, and Poisson item will occur (long period term becomes the power series of time interval
), the orbital tracking of such solution structure is unfavorable for the analysis of perturbing term.Then, method of average elements is introduced, wherein refer to space flight
The orbital tracking of device is σr, the orbital tracking of accompanying flying spacecraft is σb.Wherein, ar、er、ir、ωr、Ωr、MrRespectively reference star
Semi-major axis, eccentricity, orbit inclination angle, argument of perigee, right ascension of ascending node, mean anomaly.ab、eb、ib、ωb、Ωb、MbRespectively
The semi-major axis of accompanying flying star, eccentricity, orbit inclination angle, argument of perigee, right ascension of ascending node, mean anomaly,
σr=(ar er ir ωr Ωr Mr) (1),
σb=(ab eb ib ωb Ωb Mb) (2)。
When carrying out the analysis of perturbation of earths gravitational field, since the humorous item in field is the three ranks infinitesimal with humorous item, and with humorous
The order of magnitude of J3, J4 are 10 in-6, and the order of magnitude of J2 is 10-3, therefore after ignoring higher order indefinite small, J2 are analyzed
Single order secular term of the available J2 perturbation to six roots of sensation number are as follows:
a(t-t0)=0 (3),
e(t-t0)=0 (4),
i(t-t0)=0 (5),
Wherein, ReFor earth radius, μ is Gravitational coefficient of the Earth, by above formula it is known that J2 perturbation can't be half-and-half long
Axis, eccentricity and orbit inclination angle have an impact, and the influence to right ascension of ascending node, mean anomaly, argument of perigee is one
The process accumulated at any time.
In the design of track, the rate that each member's star is perturbed by J2 and drifted about in forming into columns should be made identical to long-term as far as possible
Keep rank stabilization, therefore, sets accompanying flying spacecraft and with reference to the orbital drift difference between spacecraft are as follows:
Wherein, it is influenced jointly by J2 perturbation due to accompanying flying spacecraft and with reference to space flight, and the rail between two spacecrafts
Road drift difference is a small amount of, so, variation is carried out for formula (9) to formula (11).It can obtain:
The track of satellite is because of ellipse or circle that Perturbation Effect is no longer a closure, and then, setting is kept fit star and worked as
Position in preceding orbital plane are as follows: β=ω+f, ω are argument of perigee, and f is true anomaly, and right ascension of ascending node can also change, rail
Parameters variation after road disturbed motion is as shown in Figure 2.
Since J2 perturbation does not change semi-major axis, eccentricity and orbit inclination angle, the main body of transformation relative satellite formation at the angle β
Now by the variation for keeping fit the opposite reference star y-axis direction of star, the as variation in orbital plane, the main body of the variation of right ascension of ascending node
The variation in present z-axis direction, the as variation of orbital plane, as long as so eliminating the perturbation variation in the two directions can reach surely
It is fixed.To keep drift velocity of the accompanying flying spacecraft relative to reference spacecraft in z-axis direction consistent, i.e.,It can obtain:
And it should meet in the y-axis direction of reference star: Δ β=β1-β2=0, i.e., are as follows: Δ β=ωr+fr-ωb-fb, due to this
Satellite is remote sensing satellite, need to be maintained at optimal imaging height, then sets track as circuit orbit, that is, f=M, M are flat near point
Angle then has:That is:
Then meet the stable condition of satellite formation i.e. (15) (16) two formula.
The 1.3 formation designs based on the imaging of super breadth
Based on specific tasks involved in this paper, all accompanying flying stars and reference star semi-major axis having the same and are set
Using near-circular orbit, the coefficient entry of δ a is remaining two higher-order shear deformation in same up-to-date style (15), can be ignored, then to (15)
(16) formula, which carries out simplification, to obtain:
(17) formula is analyzed, the relationship that can obtain eccentricity and orbit inclination angle is as follows:
It is set separatelyIt is 0.01,0.1,1,10,100, the corresponding relationship of eccentricity and orbit inclination angle is as shown in Figure 3.
It can be obtained by the relationship in Fig. 3: whenWhen ratio very little, if stability condition need to be met: and remain lesser
Eccentricity, then the orbit inclination angle of reference star is almost 0, it is clear that the spreadability demand that imaging is formed into columns is unable to satisfy, or, and if only if inclined
Heart rate almost very big (being almost 1) when, orbit inclination angle can just be selected within the scope of very big one (such as:)；
And if only ifWhen ratio is very big, reference star just can with a lesser eccentricity in a wide range of selection orbit inclination angle (such as:)。
And the value range of e itself is between 0-1, as one is a small amount of, and it is more compact to be imaged flight pattern, in order to protect
Ideal imaging formation is held, the value of δ e should be the higher-order shear deformation of e value, and in order to keep biggishδ i's takes
Value should be the higher-order shear deformation of δ e, to have almost the same orbit inclination angle with accompanying flying spacecraft with reference to spacecraft.
3 conservation of fuel types, which are formed into columns, to be designed
Based on above-mentioned analysis and at the same time meeting (17) and (18) formula, then set principal and subordinate's star orbit inclination angle having the same,
Semi-major axis and eccentricity, that is, δ e=0, δ i=0, δ a=0 and eccentricity are 0.Since eccentricity is 0, argument of perigee is had no
Practical significance only controls formation by mean anomaly and right ascension of ascending node.
Orbit altitude h=500KM is set, the radical of reference satellite is σr=(ar er ir ωr Ωr Mr), wherein er=
0, area coverage is sen*sen to camera over the ground, and adjacent satellite has the overlapping region of 5KM in area coverage over the ground.
As shown in figure 4, coordinate origin O is located at the earth's core with reference in space vehicle coordinates system, X-axis is directed toward by the earth's core and refers to space flight
Device, Y-axis are directed toward on the right side of the reference star direction of motion perpendicular to orbital plane, and Z axis constitutes right-handed system.Reference star and accompanying flying star distance are d,
Phase angle is phi, and A is the intersection point of reference star orbital plane and the equatorial plane, and D point is the intersection point of accompanying flying star orbital plane and the equatorial plane, and S is companion
Fly satellite particle, R is reference satellite particle, and OF is accompanying flying star orbital plane normal vector.Then, accompanying flying is determined based on (17) (18) formula
The process of orbit elements of satellite is as follows:
Coordinate of the accompanying flying satellite under reference space vehicle coordinates system are as follows:
The coordinate of the earth's axis are as follows:
Then,With following relationship:
It can get by three above conditionVector.
Have again,
Foundation can obtain above:
Then, radical of the accompanying flying star in the case where meeting J2 perturbation stable condition can be obtained are as follows:
Size according to the width of formula (27) and the required imaging of combination, camera side-sway ability and visual field can get master
From the distance between star and phase angle.Wherein, the side-sway automotive ability of camera is set as 25 °, and camera fields of view size is respectively
100Km*100Km and 150Km*150Km, two kinds of camera fields of view respectively correspond the imaging wide cut of 700Km and 1000Km, and imaging is shown
It is intended to as shown in Figure 5.
In Fig. 5, single satellite field range be set as 100Km the or 150Km time respectively correspond 700Km and 1000Km at
As target width, the overlapping region between adjacent satellite is 5Km, be can reach when single star visual field is 100Km using 8 satellites
The covering of 765Km, 8 satellites can realize the covering of 1165Km when single star visual field is 150Km.
As shown in figure 5, needing to advise the posture of satellite in satellite imagery to form stable imaging region
It draws, wherein each 4 of left and right is distributed in reference star two sides to 8 member's stars respectively, and is sentenced with itself to the deflection of reference star
The foundation in itself opposite reference star orientation of breaking.Since orbital plane intersects, after half of orbital period, it is distributed in reference star
The satellite position of the left and right sides can exchange.Setting camera is mounted on the Z-direction for below satellite and being directed toward satellite body system, with ginseng
The substar of star is examined as reference, each star is successively equally spacedly directed toward at left and right sides of reference star substar respectively, when member's star is opposite
After reference star location swap, imaging center also corresponds to right and left mutually changing, distance of the direction center away from reference star substar of each star
It is directly proportional at a distance from member's star to reference star.
Simultaneously, it is contemplated that if the true anomaly of every satellite of setting is all the same, have collision wind in orbital plane point of intersection
Danger, then, the true anomaly of adjacent two satellites is alternately arranged, and making to form into columns passes sequentially through orbital plane intersection point.
When designing the type track, as shown in Figure 6, Figure 7, firstly, according to imaging demand index and Satellite Camera visual angle
Maneuverability set primary condition, set reference star orbital tracking according to observation requirements, reference star can be one it is virtual
Satellite is not necessarily to necessary being as a reference point；Foundation (17) (18) formula and combination satellite formation calculate full on this basis
Sufficient J2 perturbation conditions satellites formation steady in a long-term；The substar coordinate and successively at satellite imagery center is calculated on this basis
The corresponding substar coordinate of every satellite is calculated, director of the every satellite when keeping imaging pattern is obtained by the ephemeris of satellite
Amount, and then determine the attitude parameter of each member's star, to complete to be imaged.
4 simulating, verifyings
It is 700Km and 1000Km that imaging target width is set separately in simulations, and corresponding camera perspective is respectively
100Km*100Km and 150Km*150Km.The orbit altitude of satellite imagery is 500Km.Then it can get into according to (17) (18) formula
Each orbit elements of satellite is as shown in table 1 when as 700Km.
1 satellites formation radical table of table
Emulation sets two groups of control satellites according to (17) (18) formula stable condition respectively and verifies its volume within one month
Team's stability.
The selection J2 perturbation of first group of perturbation model, be set separately meet be unsatisfactory for the satellite of J2 stable condition as pair
According to.It can be seen that, when meeting J2 perturbation conditions, reference star is at a distance from accompanying flying satellite in 180Km to 205Km by Fig. 8, Fig. 9
Between stablize concussion, divergence-free sign；And when being unsatisfactory for J2 perturbation, the distance between reference star and accompanying flying star finally will diffusions
To 1200Km, can not stablize.
Second group is set under HPOP model, comprehensively considers three-body: optical pressure, atmospheric drag, tidal perturbation.By Figure 10, figure
Known to 11: due to the influence of a variety of perturbative forces, when meeting J2 stable condition, the distance between reference star and accompanying flying star are at one
When will be reduced to 80Km after month, and being unsatisfactory for condition, it will be persistently diffused into 700Km, the diffusion under HPOP model does not have J2 mould
The main reason for big under type is the perturbation of atmosphere, since the orbit altitude of 500Km is by atmospheric perturbation obvious effect, satellite rail
Road height reduces, and the size of formation is reduced on scale, so showing formation diffusion tendency does not have under J2 model obviously.
Super breadth covering is carried out using above-mentioned conservation of fuel type flight pattern, in Satellite Formation Flying orbital plane point of intersection, satellite
Between relative distance it is closer, for guarantee image quality, most 25 ° of satellite side-sway automotive, so there are a segmental arc satellites to cover
Lid breadth shortens region, wherein and formation coverage condition is as shown in Figure 12 and Figure 13 when covering breadth 700Km, single visual angle 100Km,
Satellite covering wide cut variation tendency is as shown in figure 14 in one orbital period of 100Km breadth.Cover breadth 1000Km, single visual angle
Formation coverage condition is as shown in Figure 15, Figure 16 when 150Km, and satellite covering wide cut variation becomes in one orbital period of 150Km breadth
Gesture is as shown in figure 17.
The super breadth imaging effect of the first formation of table 2
It can be obtained by table 2, the 700Km covering of design is formed into columns can in first orbital period (that is, when initialization of forming into columns is completed)
The covering demand for meeting 700Km within 93% time meets the covering demand of 600Km in 98% time, and residue can not
The segmental arc of covering is located at the high latitude areas such as south poles, is not the key area of imaging.When being set as J2 perturbation model, 320
Imaging of forming into columns after a orbital period still keeps the covering of 93% time realization 700Km with a cycle, it can be seen that satellite
It forms into columns and can be achieved to meet the stabilized flight of J2 perturbation conditions under the track of design.Meanwhile under HPOP model, in 320 week
It can still realize that 91.67% time is better than the covering of 700Km after phase.
And the covering of the 1000Km designed is formed into columns, and can meet covering for 1000Km within 83% time when initializing and completing
Lid and the covering for meeting 700Km within 97% time, 100% realizes the covering of 600Km.Under HPOP model, 320 periods
Afterwards, 79.17% covering of the time better than 1000Km can still be met, 95.83% time is better than the covering of 700Km, and 100% is real
The covering of existing 600Km.
5 visual field ungauged regions types, which are formed into columns, to be designed
The above fuel consumption that can largely reduce for keeping satellite formation of forming into columns, but its there are one
Disadvantage, that is, the visual field can be shunk within a bit of time of orbital plane intersection, cannot achieve super breadth imaging.Then it sets herein
It has counted and second has surpassed breadth imaging formation, it can be achieved that visual field whole process ungauged regions.But second of formation is more multiple compared to the first
It is miscellaneous, it not only needs to change right ascension of ascending node, it is also necessary to which the change at matching track inclination angle constructs formation.But based on eccentricity with
The analysis of orbit inclination angle is unable to satisfy (17) formula if changing orbit inclination angle, then if the part only in accordance with (18) formula into
Row design.Wherein, the stability for being meant that spacecraft direction z in relative coordinate system, i.e. orbital plane are stated in (17) formula
Bias stability；And (18) formula is expressed in orbital plane, i.e. the stability in the direction y.Then letter is carried out for (18) formula
Change can obtain:
Then, configuration as shown in figure 18 is set, 4 satellites are for one group, it can be achieved that all standing of 385Km wide cut, passes through
Change the right ascension of ascending node (not changing formation stability) entirely formed into columns and produce same one group of satellites formation, to realize
The all standing of 765Km wide cut.
In Figure 19, single star can cover 100Km range, and imaging overlay region is 5Km, and imaging center spacing is 95Km, and 4 one group
Satellite can realize 385Km, ungauged regions covering, and the formation of entire 700Km covering then can be completed using 2 above-mentioned formations.
Since second of formation designs while having used orbit inclination angle and right ascension of ascending node and mean anomaly, wherein
Sat1 and Sat2 right ascension of ascending node having the same and different orbit inclination angles, and Sat3 and Sat4 orbit inclination angle having the same
With different right ascension of ascending node, that is, changing orbital plane using right ascension of ascending node, there are caused by the track of inclination angle difference to make up
Visual field constriction.
Wherein, Sat3 and Sat4 orbit inclination angle having the same, design method and the first formation configuration design route
It is identical, but intersatellite spacing is changed, and the straight line spacing of Sat3 and Sat4 should meet the spacing of three single star imaging wide cuts,
That is: d=3sen-15 is derived by accompanying flying star shown in formula (27) using formula (20) to formula (26) and is meeting J2 perturbation stabilization
Under the conditions of radical, during derivation, d=3sen-15.
And Sat1 is different from Sat2 right ascension of ascending node having the same but orbit inclination angle, for make up Sat3 and Sat4 at
As narrow point, and change the formation after orbit inclination angle due to being unable to satisfy (17) formula, so only meeting (18) formula, and principal and subordinate's star orbital
The difference of road inclination depends on the wide cut of single star imaging:
It as shown in figure 20, is R with reference to spacecraft particle, accompanying flying spacecraft particle is B, and identical ascending node is G, accompanying flying
Star and reference star distance are d, phase angle phi.The coordinate that R point then can be obtained according to Spacecraft Relative Motion coordinate system is (a 0 0),
Then there is accompanying flying star coordinate are as follows:
The coordinate of the earth's axis are as follows:
Then, reference star and accompanying flying star ascending node coordinate are as follows:
Then the difference of its mean anomaly can be obtained are as follows:
I.e. are as follows:
In formula, sen is single star imaging width.
6 simulating, verifyings
It is 700Km that imaging target width is set separately in simulations, and corresponding camera perspective is respectively 100Km*
100Km.The orbit altitude of satellite imagery is 500Km.Then it can get each orbit elements of satellite when 700Km is imaged according to (18) formula
As shown in table 3.
3 satellites formation radical table of table
Within one month respectively under J2 perturbation model and under HPOP model, setting meets and is unsatisfactory for (18) formula
Satellite as control.By Figure 21, it can be seen that, when partially meeting J2 perturbation conditions, formation is without fully meeting J2 in image of Buddha Fig. 8
In stable concussion when perturbation conditions, but in concussion divergent state, 400Km or more can be dissipated into after 1 month, it can by Figure 22
Know, and the formation for being unsatisfactory for (18) formula can then diffuse to 4000Km or more after one month.
Second group is set under HPOP model, comprehensively considers three-body: optical pressure, atmospheric drag, tidal perturbation.By Figure 23, figure
24 it is found that existing distinguish not is very greatly, the main reason is that second under the Perturbation Effect and J2 perturbation under HPOP model
It is poor that orbital plane mainly is formed with orbit inclination angle in the design of grouping formation, and first group is mainly formed by right ascension of ascending node
Difference.
Under conditions of coverage goal is 700Km, covering breadth of the formation in a circle is as shown in figure 25.It can by figure
See, all standing of 700Km ungauged regions can be achieved in second of formation on configuration design.
The super breadth imaging effect of second of the formation of table 4
It can be obtained by above table, second of 700Km imaging of design is formed into columns can be completely achieved when track initializes to be formed
The covering of 700Km.It can still keep realizing that 700Km covers in 94.74% time under J2 perturbation model, after 336 orbital periods
Lid, 100% realizes the covering of 600Km.Under HPOP model, 700Km can be realized within 70.83% time after 336 periods
600Km covering is realized in covering in 83.33% time.
7 conclusions
The application devises a kind of formation configuration based on J2 perturbation for the super breadth imaging problem of satellite, perturbs according to J2
The perturbation is transformed into the design that spacecraft movement relative motion coordinate system carries out formation by the influence to spacecraft orbit radical.
Pass through simulating, verifying, the results showed that, the satellites formation configuration based on J2 stability has good stabilization under J2 perturbation effect
Property, it can be achieved that keep the formation stable configuration under J2 perturbation for a long time, and J2 stable condition is relatively unsatisfactory under HPOP model
It forms into columns, formation range of scatter substantially reduces.Meanwhile it can be seen that the first formation of design can be in a long time by emulation data
Keep rank stabilization, though second of formation has very well with respect to the fuel that the first formation needs more formations to keep
Super breadth covering performance.Realize super breadth imaging of the satellites formation for a long time under perturbation.
Claims (8)
1. a kind of satellites formation implementation method towards super breadth imaging over the ground, which is characterized in that according to super breadth imaging demand
And satellite imagery parameter initialization reference satellite orbital tracking, it is long-term under J2 perturbation to determine that each member's star meets satellites formation
Stablize orbital tracking when this condition, calculates that the substar of future time instance reference satellite imaging center is sat according to reference star ephemeris
Mark and each member's stellar camera pointing vector update each member's star by the orbital tracking of each member's star and go through, in conjunction with each member's star
Camera pointing vector resolves attitude parameter of each member's star in the case where keeping wide cut imaging pattern.
2. a kind of satellites formation implementation method towards super breadth imaging over the ground according to claim 1, which is characterized in that really
Fixed each member's star meets the method for orbital tracking of the satellites formation under J2 perturbation when this condition steady in a long-term are as follows: to eliminate ginseng
Examining the offset of satellite motion direction and reference satellite orbital plane under J2 perturbation is target, possesses accompanying flying satellite and reference satellite
Identical semi-major axis, eccentricity, orbit inclination angle, in conjunction with reference satellite at a distance from accompanying flying satellite and phase angle adjust accompanying flying satellite
Right ascension of ascending node and mean anomaly.
3. a kind of satellites formation implementation method towards super breadth imaging over the ground according to claim 1, which is characterized in that really
Fixed each member's star meets the method for orbital tracking of the satellites formation under J2 perturbation when this condition steady in a long-term are as follows:
For being taken the photograph with eliminating the reference satellite direction of motion in J2 with identical right ascension of ascending node but the different member's star of orbit inclination angle
Offset under dynamic is target, and accompanying flying satellite is made to possess semi-major axis identical with reference satellite, eccentricity, orbit inclination angle, perigee
Argument, in conjunction with reference satellite at a distance from accompanying flying satellite and phase angle adjustment accompanying flying satellite right ascension of ascending node and mean anomaly,
For being taken the photograph with eliminating the reference satellite direction of motion in J2 with same rail inclination angle but the different member's star of right ascension of ascending node
Offset under dynamic is target, and accompanying flying satellite is made to possess semi-major axis identical with reference satellite, eccentricity, argument of perigee, rise and hand over
Point right ascension has according to single star imaging width and by the visual field of accompanying flying satellite and reference satellite and adjusts accompanying flying satellite for the purpose of being overlapped
Orbit inclination angle and mean anomaly.
4. a kind of satellites formation implementation method towards super breadth imaging over the ground according to claim 2, which is characterized in that each
Member's star meets orbital tracking of the satellites formation under J2 perturbation when this condition steady in a long-term are as follows:
σbFor the orbital tracking of accompanying flying satellite, σb=(ab eb ib ωb Ωb Mb), ab、eb、ib、ωb、Ωb、MbRespectively accompanying flying satellite
Semi-major axis, eccentricity, orbit inclination angle, argument of perigee, right ascension of ascending node, mean anomaly, ar、er、ir、ωr、Ωr、MrRespectively
For the semi-major axis of reference satellite, eccentricity, orbit inclination angle, argument of perigee, right ascension of ascending node, mean anomaly, δ Ω, δ m difference
For the right ascension of ascending node difference and mean anomaly difference of accompanying flying satellite and reference satellite,O is reference satellite coordinate origin, and A is reference satellite rail
The intersection point in road face and the equatorial plane, D are the intersection point in accompanying flying satellite orbit face and the equatorial plane, and S is accompanying flying satellite particle, For the normal vector of accompanying flying star orbital plane,For ground axial vector, a is the semi-major axis of reference satellite,ByIt determines, R is reference satellite particle, and i is
The orbit inclination angle of reference satellite, d, phi are reference satellite at a distance from accompanying flying satellite and phase angle,
Sx、Sz、SyForCoordinate under reference satellite coordinate system, Cx、Cz、CyForCoordinate under reference satellite coordinate system.
5. a kind of satellites formation implementation method towards super breadth imaging over the ground according to claim 3, which is characterized in that each
Member's star meets orbital tracking of the satellites formation under J2 perturbation when this condition steady in a long-term are as follows:
σbFor the orbital tracking of accompanying flying satellite, σb=(ab eb ib ωb Ωb Mb), ab、eb、ib、ωb、Ωb、MbRespectively accompanying flying satellite
Semi-major axis, eccentricity, orbit inclination angle, argument of perigee, right ascension of ascending node, mean anomaly, ar、er、ir、ωr、Ωr、MrRespectively
For the semi-major axis of reference satellite, eccentricity, orbit inclination angle, argument of perigee, right ascension of ascending node, mean anomaly, δ i, δ m are respectively
The orbit inclination angle difference and mean anomaly difference of accompanying flying satellite and reference satellite,A is reference satellite half
Long axis, sen are single star imaging width,R is reference satellite particle, R
Coordinate be (a 0 0), B be accompanying flying satellite particle, G be reference satellite ascending node, For ground
Axial vector,Cx、Cz、CyForCoordinate under reference satellite coordinate system, i are reference satellite
Orbit inclination angle,Bx、Bz、ByForCoordinate under reference satellite coordinate system, d, phi are ginseng
Satellite is examined at a distance from accompanying flying satellite and phase angle.
6. a kind of satellites formation implementation method towards super breadth imaging over the ground according to claim 1, which is characterized in that institute
State the width that super breadth imaging demand includes: the dimensional information of required imaging region, required imaging.
7. a kind of satellites formation implementation method towards super breadth imaging over the ground according to claim 1, which is characterized in that institute
State the wide cut that satellite imagery parameter includes: single star imaging region, optimal imaging height, camera imaging maximum side-sway ability.
8. a kind of satellites formation implementation method towards super breadth imaging over the ground according to claim 1, which is characterized in that institute
State satellites formation under J2 perturbation steady in a long-term this condition by each component especially high-order in J2 perturbation model in a small amount into
The accurate variation of row handles to obtain.
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