CN109240322B - Satellite formation implementation method for ground-oriented ultra-wide imaging - Google Patents
Satellite formation implementation method for ground-oriented ultra-wide imaging Download PDFInfo
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Abstract
The invention discloses a method for realizing formation of a satellite facing ground ultra-width imaging, relates to a formation technology of satellite stable imaging, and belongs to the technical field of control and adjustment. The method is researched aiming at the problem of distributed ultra-width imaging, breaks through a single sub-satellite point imaging mode of the traditional satellite imaging, can enable the satellite to realize high-precision ultra-width imaging in a formation imaging mode by carrying a high-precision imaging load and combining a distributed satellite control technology, and greatly improves the satellite search imaging efficiency. The method provides a distributed satellite formation ultra-wide imaging mode based on the stability of J2, and solves the problems that the satellite staring range is small, the imaging width is narrow, and the satellite cannot realize continuous imaging on the ground adjacent area due to earth rotation.
Description
Technical Field
The invention discloses a method for realizing formation of a satellite facing ground ultra-width imaging, relates to a formation technology of satellite stable imaging, and belongs to the technical field of control and adjustment.
Background
With the rapid development of the space technology, the satellite remote sensing imaging technology increasingly shows the advantages of rapidness, convenience, high precision and the like in the aspects of agriculture, economy, climate, search and rescue and the like. And the distributed micro-nano satellite consisting of the agile satellite has the characteristics of low cost, flexible configuration and the like. Compared with the traditional large satellite, the micro-nano satellite has the advantages that the research and development period is short, the technical index is relatively low, the launching cost is reduced due to the low quality, the research and launching expenses can be borne by medium and small countries and colleges of scientific research institutions, the rapid launching deployment can be realized by combining the one-rocket multi-satellite technology, the low-orbit micro-nano satellite can be launched into orbit by the modified missile, the emergency situation can be flexibly met, the requirement on rapid response is met, and the technical advantages which cannot be achieved by the large satellite are achieved.
However, in the existing satellite imaging technology, a single-satellite imaging and image splicing mode is generally adopted to complete imaging of a large map, due to the influence of earth rotation, a satellite cannot realize continuous imaging on adjacent areas on the ground, and the adjacent areas imaged last time can be passed through after a long time, so that the imaging quality of the adjacent areas is influenced by conditions such as illumination conditions, cloud and fog shielding, and meanwhile, when a dynamic target is searched in a large range (such as maritime lost-connection target search and rescue and high-dynamic target search), the target is easy to move into the imaged area in the time gap, and thus the missed search is caused. And the distributed satellite ultra-wide imaging technology can greatly improve the efficiency and accuracy of large-range investigation and shorten the imaging delay of adjacent imaging areas.
Based on the ultra-width imaging task, the formation shape of the micro-nano satellite should be kept stable for a long time to meet the imaging requirement, the volume of the micro-nano satellite is limited, and the fuel carried by the micro-nano satellite for maintaining the formation is limited, so that the formation shape and the number of the orbits which are stable for the formation can be met by designing the satellite without using or using a small amount of fuel.
Disclosure of Invention
The invention aims to provide a method for realizing formation of a satellite facing to ground ultra-wide imaging, which aims to overcome the defects of the background technology, realizes formation design of distributed satellite ultra-wide imaging and satellite attitude planning, further realizes ultra-wide imaging, and solves the technical problems that the satellite cannot realize continuous imaging on ground adjacent areas due to small staring range, narrow imaging width and earth rotation.
The invention adopts the following technical scheme for realizing the aim of the invention:
a satellite formation implementation method for ground-oriented ultra-wide imaging comprises the following steps:
1. acquiring imaging requirements: determining dimension information of a required imaging area, determining an orbital inclination angle of a distributed satellite, determining the width of the required imaging by adopting a polar orbit if the global range imaging is required, and determining the number of the required satellites by combining with satellite imaging parameters;
2. determining imaging parameters of a satellite remote sensing camera: the method mainly comprises the steps of wide width of an imaging area, optimal imaging height and maximum side swing capability of camera imaging;
3. the number of the satellites needing to be imaged is basically determined by combining the two steps, the number is more than or equal to the imaging width/single satellite visual field, the orbital inclination angle of the formation is determined based on the imaging area, in order to keep the imaging stability, the formation adopts a circular orbit grade, and the eccentricity is 0;
4. setting a polar coordinate system for a two-dimensional coordinate plane by taking the reference satellite as an origin, taking the speed direction of the reference satellite as the Y direction and the horizontal plane, and setting the distance and the angle between each member satellite and the reference satellite according to the imaging width;
5. based on the stable conditions in the formulas (17) and (18), according to the design method in the formulas (20) to (27), the analytic solution of the number of each satellite can be obtained, so that the number of the satellites under the stable conditions can be determined;
6. calculating the imaging center sub-satellite point of the reference satellite at each future moment and the camera pointing vector of each satellite-flying satellite at the reference position according to the ephemeris of the reference satellite;
7. the attitude information of the satellite is resolved by combining the ephemeris of each satellite and the pointing vector at each future moment, so that the formation of the satellite can stably fly for a long time under the condition of satisfying J2 perturbation stability, and ultra-wide imaging is realized.
The invention provides two formation design schemes, wherein the first scheme is to eliminate the movement direction of a reference satellite and the offset of the orbital plane of the reference satellite under the perturbation of J2 as a target and adjust the ascension point, the right ascension point and the mean-nearpoint angle of the satellite by combining the distance and the phase angle between the reference satellite and the satellite; the second method is to determine the number of satellite orbits of the satellite by adopting the first method for member satellites with the same ascending point right ascension but different orbit inclinations by eliminating the deviation of the motion direction of the reference satellite under J2 perturbation, and adjust the orbit inclination angle and the paraxial point angle of the satellite according to the single-satellite imaging width and aiming at the purpose of overlapping the visual fields of the satellite and the reference satellite for the member satellites with the same orbit inclination but different ascending point right ascension.
The first formation scheme determines the number of satellite orbits accompanied by flight as follows:
σbnumber of orbits, σ, for satelliteb＝(ab eb ib ωb Ωb Mb)，ab、eb、ib、ωb、Ωb、MbRespectively the semi-major axis, eccentricity, orbit inclination, amplitude angle of perigee, right ascension of ascending intersection point, and average perigee angle of the satelliter、er、ir、ωr、Ωr、mrRespectively a semi-major axis, eccentricity, orbit inclination, amplitude angle of near place, ascension at ascending intersection point, and mean angle of near point of the reference satellite, omega and m respectively represent the difference value of ascension at ascending intersection point and mean angle of near point of the satellite and the reference satellite,
o is the origin of the reference satellite coordinate system, A is the intersection point of the orbit plane of the reference satellite and the equatorial plane, D is the intersection point of the orbit plane of the satellite accompanying the flight and the equatorial plane, S is the mass point of the satellite accompanying the flight,
is a normal vector of the orbit surface of the satellite,
is the earth axis vector, a is the semi-major axis of the reference satellite,
by
Determining that R is reference satellite mass point, i is orbit inclination angle of the reference satellite, d and phi are distance and phase angle between the reference satellite and the satellite,
Sx、Sz、Syis composed of
Coordinates in the reference satellite coordinate system, Cx、Cz、CyIs composed of
Coordinates in a reference satellite coordinate system.
The second formation scheme determines the number of satellite orbits accompanied by flight as follows:
σbnumber of orbits, σ, for satelliteb＝(ab eb ib ωb Ωb Mb)，ab、eb、ib、ωb、Ωb、MbRespectively the semi-major axis, eccentricity, orbit inclination, amplitude angle of perigee, right ascension of ascending intersection point, and average perigee angle of the satelliter、er、ir、ωr、Ωr、mrRespectively is a semi-major axis, eccentricity, orbit inclination, amplitude angle of near place, right ascension of ascending intersection point and mean angle of near point of the reference satellite, i and m are respectively orbit inclination difference and mean angle of near point of the satellite and the reference satellite,
a is the semi-major axis of the reference satellite, sen is the single-star imaging width,
r is the reference satellite mass point, the coordinates of R are (a 00), B is the satellite mass point, G is the intersection point of the reference satellite,
is a vector of the earth's axis,
Cx、Cz、Cyis composed of
Coordinates under the coordinate system of the reference satellite, i is the orbital inclination of the reference satellite,
Bx、Bz、Byis composed of
And d and phi are the distance and phase angle between the reference satellite and the satellite in flight.
By adopting the technical scheme, the invention has the following beneficial effects:
(1) according to the method, high-order small quantity in accurate variation processing of the J2 perturbation model is considered, more accurate J2 stability condition is obtained through accurate variation processing, a formation configuration analytic solution capable of realizing stable imaging flight for a long time is determined on the basis of the J2 stability condition, a formation design scheme under polar coordinates is established on the basis, and design of stable formation is facilitated.
(2) The method comprises the steps that the deviation of a reference satellite motion direction and a reference satellite orbital plane under the perturbation of J2 is eliminated, the geometric position relation of each member satellite in the formation is mapped to the number of satellite orbits by analyzing the geometric position relation of a satellite accompanying the flight and a reference satellite, the overall stability of the formation in a long time can be maintained according to a satellite formation scheme determined by the analysis method, the orbit maintenance is carried out without consuming fuel, the fuel is saved, and the defect that the limited fuel cannot meet the requirement of wide-range imaging easily is overcome; the other method only aims at eliminating the offset of the motion direction of the reference satellite under the perturbation of J2, the elevation point right ascension changes the orbital plane to make up for the visual field shrinkage caused by the orbit with the inclination angle difference, the orbit period of the imaging satellite is short, the imaging width is large, the imaging gaps are reduced in the adjacent period, the situation that the target cannot be captured by the satellite due to the movement between the adjacent imaging areas is greatly reduced, the problem that the high-dynamic target is missed in large-range search is solved, more fuel is needed to maintain the formation compared with the first formation, the formation has very good ultra-width coverage performance, and the ultra-width imaging of the satellite formation under the perturbation for a long time is realized.
(3) The invention uses the imaging satellite cluster with high resolution to carry out imaging, and solves the problems of insufficient imaging resolution and poor remote sensing image definition of the traditional large-view satellite while ensuring the size of an imaging view.
Drawings
Fig. 1 is a schematic diagram of a track coordinate system.
Fig. 2 is a schematic illustration of orbital photographic motion.
FIG. 3 is a diagram illustrating the relationship between eccentricity and track inclination.
Fig. 4 is a diagram illustrating the calculation of the satellite orbital number by the first formation scheme.
FIG. 5 is a schematic diagram of imaging at 700Km and 1000Km widths.
Fig. 6 is a flow chart of an ultra-wide imaging method.
Fig. 7 is a flowchart of an ultra-wide imaging procedure.
Fig. 8 is a simulation result of the distance of the reference satellite from the satellite when the J2 perturbation condition is satisfied under the J2 perturbation model.
Fig. 9 is a distance measurement result of a reference satellite and a satellite in flight when the J2 perturbation condition is not satisfied under the J2 perturbation model.
Fig. 10 is a simulation result of the reference satellite-satellite distance when the J2 perturbation stabilization condition is satisfied under the HPOP model.
Fig. 11 is a simulation result of the reference satellite-satellite distance when the J2 perturbation stabilization condition is not satisfied under the HPOP model.
FIG. 12 is a diagram showing the formation coverage at a single view angle of 100Km covering a width of 700 Km.
Fig. 13 is a schematic diagram showing a region where the width of the satellite intersatellite point is reduced at a width of 100 KM.
Fig. 14 is a diagram showing the variation of satellite coverage width within one orbital period at 100Km width.
FIG. 15 is a diagram showing the formation coverage at a single viewing angle of 150Km, covering a width of 1000 Km.
FIG. 16 is a schematic view showing a region where the width of the satellite intersatellite point is reduced at a width of 150 KM.
Fig. 17 is a diagram showing the variation of satellite coverage width in one orbital period at 150Km width.
Fig. 18 is a schematic view of a visual field non-shrinking type formation.
FIG. 19 is a first set of images in an example embodiment.
Fig. 20 is a diagram illustrating the calculation of the satellite orbits according to the second formation scheme.
Fig. 21 is a result of a simulation of the distance between the reference satellite and the satellite in flight when the equation (18) perturbation stabilization condition is satisfied under the J2 perturbation model.
Fig. 22 is a result of distance measurement of the reference satellite and the satellite in flight when the formula (18) perturbation stabilization condition is not satisfied under the J2 perturbation model.
Fig. 23 is a result of distance simulation of the reference satellite and the satellite in flight when the perturbation stabilization condition of formula (18) is satisfied under the HPOP model.
Fig. 24 is a result of simulation of the distance between the reference satellite and the satellite in flight when the perturbation stabilization condition of formula (18) is not satisfied under the HPOP model.
Fig. 25 is a diagram illustrating satellite coverage in one orbital period for the second formation in accordance with an exemplary embodiment.
Detailed Description
The technical scheme of the invention is explained in detail in the following with reference to the attached drawings.
Aiming at the distributed satellite ultra-wide imaging technology, the variation analysis is carried out on the orbit parameters under the perturbation of J2, the perturbation model is further refined, the formation meeting the long-term stability is designed, the attitude planning of the satellite accompanying flight is carried out according to the sub-satellite point coordinates of the reference satellite, and the long-term stable ultra-wide imaging is realized.
Spacecraft relative motion model under J2 perturbation
The part is designed aiming at the satellite formation required by ultra-wide imaging, the stability condition of the satellite formation is designed under the long-term perturbation of J2 mainly according to the imaging requirement of the satellite formation, and two different imaging formations are designed according to the difference of the formation requirements.
1.1 spacecraft relative motion coordinate System
In the researches of spacecraft rendezvous and docking, formation configuration design and the like, the relative distance of the spacecraft is a small amount compared with the semi-long axis of the orbit, the relative position relation of the spacecraft cannot be visually described by using a Keplerian root number method, and then a relative motion coordinate system of the spacecraft is set. As shown in fig. 1.
In fig. 1, xyz is a geocentric inertial coordinate system, and OXYZ is a relative motion coordinate system of the spacecraft, wherein an origin of coordinates in the geocentric inertial system is located at geocentric O, an X axis points to a spring minute point, a Z axis points to a polar, and a Y axis and an XOZ plane form a right-hand system; in a spacecraft reference coordinate system (namely a relative motion coordinate system of a spacecraft), the origin of coordinates is located at the center of mass o of the satellite, the x axis is the direction from the earth center to the connection line of the spacecraft, the y axis is the motion direction of the spacecraft, and a z-axis right-hand system is perpendicular to a reference spacecraft orbital plane formed by the x axis and the y axis.
1.2 Earth non-spherical perturbation model based on mean root method
In solving the perturbation problem, if classical perturbation solution is adopted, the slowly varying long-period term of the ascension crossing point and the perigee argument will become the long-term, and poise will appearThe number of orbits of the solution structure is not beneficial to the analysis of perturbation terms. Then, an average radical method is introduced, in which the number of orbits of the reference spacecraft is σrThe number of orbits of the accompanying spacecraft is sigmab. Wherein, ar、er、ir、ωr、Ωr、mrRespectively the semi-major axis, eccentricity, orbit inclination, amplitude angle of the near place, right ascension of the ascending intersection point and the horizontal near point angle of the reference star. a isb、eb、ib、ωb、Ωb、MbRespectively a semi-major axis, eccentricity, track inclination, amplitude angle of the near place, right ascension of the ascending intersection point and a horizontal near point angle of the satellite,
σr＝(ar er ir ωr Ωr mr) (1)，
σb＝(ab eb ib ωb Ωb Mb) (2)。
when the analysis of the earth's non-spherical perturbation is carried out, the third order of the harmonic terms is infinitesimal because of the field harmonic terms, and the orders of magnitude of J3 and J4 in the harmonic terms are 10-6And J2 is on the order of 10-3Therefore, after ignoring the high-order infinitesimal quantities, analyzing the J2 terms can obtain that the first-order long-term of the J2 perturbation for six numbers is:
a(t-t0)＝0 (3)，
e(t-t0)＝0 (4)，
i(t-t0)＝0 (5)，
wherein R iseAs the radius of the earth, mu is the gravitational constant of the earth, it can be seen from the above formula that J2 perturbation does not affect the semi-major axis, eccentricity and orbital inclination, and the effects on the ascension point declination, mean anomaly angle and argument of anomaly are accumulated over time.
In the design of the orbit, the drift rate of each member satellite in the formation perturbed by J2 should be as much as possible to keep the formation stable for a long time, so the orbit drift difference between the accompanying spacecraft and the reference spacecraft is set as follows:
wherein, since the accompanying spacecraft and the reference spacecraft are affected by perturbation of J2 together and the orbit drift difference between the two spacecrafts is small, the equations (9) to (11) are varied. The following can be obtained:
the satellite trajectory is no longer a closed ellipse or circle due to perturbation, and then the position of the satellite in the current orbital plane is set as: β is ω + f, ω is the amplitude angle of the perigee, f is the true perigee angle, the ascension of the ascension point also changes, and the parameter change after the orbital panning is shown in fig. 2.
Because the perturbation of J2 does not change the semimajor axis, eccentricity and orbit inclination, the change of beta angle relative to the satellite formation is mainly reflected in the change of the y-axis direction of the satellite relative to the reference satellite, namely the change in the orbit plane, and the change of the right ascension at the intersection point is mainly reflected in the change of the z-axis direction, namely the change in the orbit plane, the stability can be achieved by only eliminating the perturbation change in the two directions. To maintain the uniform drift velocity of the companion spacecraft relative to the reference spacecraft in the z-axis direction, i.e.
The following can be obtained:
and the y-axis direction of the reference star should satisfy: Δ β ═ β1-β2When the value is 0, the result is: Δ β ═ ωr+fr-ωb-fbSince the satellite is a remote sensing satellite and needs to be maintained at the optimal imaging height, the orbit is set to be a circular orbit, that is, f is equal to M, and M is an approximate point angle, so that:
namely:
therefore, the two formulas (15) and (16) are satisfied.
1.3 formation design based on ultra-breadth imaging
Based on the specific tasks involved here, it is assumed that all satellite satellites have the same semi-major axis as the reference satellite and all use a near-circular orbit, while the coefficient term of a in equation (15) is the higher order infinitesimal of the remaining two terms, which can be ignored, so that simplifying equations (15) (16) results:
by analyzing the equation (17), the relationship between the eccentricity and the track inclination can be obtained as follows:
respectively set
0.01, 0.1, 1, 10, 100, and the eccentricity ratio and the track inclination angle are in the corresponding relationship as shown in fig. 3.
From the relationship in fig. 3, one can see: when in use
If the ratio is small, the stability condition is met if the eccentricity is small and maintained, the orbit inclination of the reference star is almost 0, obviously not meeting the coverage requirements of the imaging formation, or if and only if the eccentricity is nearly very large (nearly 1), the orbit inclination can be chosen within a very large range (for example:
) (ii) a If and only if
When the ratio is large, the reference star can select the track inclination angle in a large range with a small eccentricity (such as:
)。
the value range of e is between 0 and 1, namely a small quantity, the imaging formation is compact, in order to keep an ideal imaging formation, the value of e is infinitely small in the high order of the value of e, and in order to keep a larger imaging formation, the value of e is infinitely small in the high order of the value of e
The value of i should be high order infinitesimal of e, so that the reference spacecraft and the accompanying spacecraft have almost the same orbital inclination angle.
3 fuel saving formation design
Based on the above analysis and satisfying equations (17) and (18) at the same time, the master and slave stars are set to have the same orbit inclination, semimajor axis, and eccentricity, that is, e is 0, i is 0, a is 0, and eccentricity is 0. Since the eccentricity ratio is 0, the argument of the perigee has no practical significance, and the formation is controlled only by the mean perigee angle and the ascension crossing right ascension.
The orbit height h is set to 500KM, and the number of reference satellites is sigmar＝(ar er ir ωr Ωr mr) Wherein e isrAt 0, the camera footprint is sen, and there is an overlapping area of 5KM in the neighboring satellite footprint.
As shown in fig. 4, in the reference spacecraft coordinate system, the coordinate origin O is located at the geocentric, the X-axis is directed to the reference spacecraft from the geocentric, the Y-axis is perpendicular to the orbital plane and directed to the right side of the reference satellite in the moving direction, and the Z-axis forms a right-hand system. The distance between the reference satellite and the satellite is D, the phase angle is phi, A is the intersection point OF the orbital plane OF the reference satellite and the equatorial plane, D is the intersection point OF the orbital plane OF the satellite and the equatorial plane, S is a satellite mass point, R is a reference satellite mass point, and OF is a normal vector OF the orbital plane OF the satellite. Then, the procedure for determining the number of orbits of the satellite based on the equations (17) and (18) is as follows:
the coordinates of the satellite in the reference spacecraft coordinate system are as follows:
the coordinates of the earth axis are:
then the process of the first step is carried out,
has the following relationship:
obtained by the above three conditions
And (5) vector quantity.
In addition, the following methods are provided,
according to the above, the following can be obtained:
thus, the number of the companion stars under the condition satisfying the perturbation stability of J2 is given as:
the distance and phase angle between the master and slave stars can be obtained according to equation (27) in combination with the required imaging width, camera yaw capability and imaging field of view size. The lateral swing maneuvering capability of the camera is set to be 25 degrees, the camera view sizes are respectively 100Km × 100Km and 150Km × 150Km, the two camera views respectively correspond to imaging widths of 700Km and 1000Km, and an imaging schematic diagram is shown in fig. 5.
In fig. 5, the field of view of a single satellite is set to 100Km or 150Km for 700Km and 1000Km, respectively, the overlap region between adjacent satellites is 5Km, 765Km coverage can be achieved by using 8 satellites when the field of view of the single satellite is 100Km, and 1165Km coverage can be achieved by using 8 satellites when the field of view of the single satellite is 150 Km.
As shown in fig. 5, in order to form a stable imaging area, the attitude of the satellite needs to be planned during satellite imaging, wherein 8 member satellites are respectively distributed on the left and right sides of a reference satellite, and the direction angle from the satellite to the reference satellite is used as the basis for judging the azimuth of the satellite relative to the reference satellite. Because the orbital planes are intersected with each other, after half an orbital period, the positions of the satellites distributed on the left side and the right side of the reference satellite are interchanged. The camera is arranged below the satellite and points to the Z-axis direction of the satellite body system, the satellite points of the reference satellites are used as reference, the satellites respectively point to the left side and the right side of the reference satellite points at equal intervals in sequence, after the positions of the member satellites relative to the reference satellites are interchanged, the imaging centers of the member satellites are correspondingly interchanged from left to right, and the distance between the pointing center of each satellite and the reference satellite points is in direct proportion to the distance between the member satellites and the reference satellites.
Meanwhile, if the true approach angles of each satellite are set to be the same, the collision risk exists at the intersection of the orbital planes, and then the true approach angles of two adjacent satellites are alternately configured, so that the formation sequentially passes through the intersection of the orbital planes.
When designing the type of orbit, as shown in fig. 6 and 7, firstly, initial conditions are set according to imaging requirement indexes and maneuvering capability of a satellite camera view angle, and the number of orbits of a reference satellite is set according to observation requirements, wherein the reference satellite can be a virtual satellite as a reference point and does not need to exist really; calculating a satellite formation which is stable for a long time and meets the perturbation condition of J2 according to the formulas (17) and (18) and by combining the satellite formation; and calculating the coordinate of the point under the satellite of the imaging center of the satellite on the basis, sequentially calculating the coordinate of the point under the satellite corresponding to each satellite, obtaining the pointing vector of each satellite when the imaging mode is kept by the ephemeris of the satellite, and further determining the attitude parameters of each member satellite so as to finish imaging.
4 simulation verification
In the simulation, the imaging target widths are set to 700Km and 1000Km, respectively, and the corresponding camera viewing angles are set to 100Km × 100Km and 150Km × 150Km, respectively. The orbital height for satellite imaging is 500 Km. The number of orbits of each satellite at 700Km of imaging was obtained according to the expressions (17) and (18) is shown in table 1.
TABLE 1 satellite formation root table
And (4) setting two groups of comparison satellites to verify the formation stability of the control satellites according to the stability conditions of the formulas (17) and (18) in one month.
The first set of perturbation models selected J2 perturbations, with satellites meeting and not meeting the J2 stability conditions set as controls, respectively. As can be seen from fig. 8 and 9: when the perturbation condition of J2 is met, the distance between the reference satellite and the satellite is in stable oscillation between 180Km and 205Km, and no dispersion sign exists; when J2 perturbation is not satisfied, the distance between the reference satellite and the satellite is finally spread to 1200Km, and the satellite cannot be stabilized.
The second set was set under HPOP model, considering three volumes together: light pressure, atmospheric drag, tidal perturbation. As can be seen from fig. 10 and 11: due to the influence of various perturbation forces, when the J2 stable condition is met, the distance between the reference satellite and the satellite is reduced to 80Km after one month, when the condition is not met, the distance is continuously diffused to 700Km, the diffusion under the HPOP model has no big main reason of the J2 model, namely the perturbation of the atmosphere, and the diffusion trend of the formation is not obvious under the J2 model because the orbit height of 500Km is obviously influenced by the perturbation of the atmosphere, the orbit height of the satellite is reduced, and the size of the formation is reduced in scale.
The fuel-saving formation is used for ultra-wide coverage, the relative distance between satellites is short at the intersection of the formation satellite orbit surfaces, the satellite side swing maneuver is at most 25 degrees to ensure the imaging quality, so an arc satellite coverage width shortening area exists, wherein the formation coverage condition when the coverage width is 700Km and a single visual angle is 100Km is shown in figures 12 and 13, and the satellite coverage width change trend in a 100Km width one orbit period is shown in figure 14. The coverage width is 1000Km, the formation coverage at a single view angle of 150Km is shown in fig. 15 and 16, and the variation trend of the satellite coverage width within one orbital period of 150Km width is shown in fig. 17.
TABLE 2 ultra-breadth imaging effect of first formation
As can be seen from table 2, the designed 700Km coverage formation can satisfy the coverage requirement of 700Km in 93% of the time in the first orbital cycle (i.e., when the formation initialization is completed), the coverage requirement of 600Km in 98% of the time, and the remaining uncovered arc segments are located in high-altitude areas such as north and south poles, and are not the key areas for imaging. When set as the J2 perturbation model, 700Km coverage was achieved after 320 orbital cycles with formation imaging remaining 93% of the time with the first cycle, and it can be seen that stable flight meeting the J2 perturbation condition was achieved by the satellite formation in the designed orbit. Meanwhile, under the HPOP model, coverage of 91.67% of the time better than 700Km can still be achieved after 320 cycles.
And the designed coverage formation of 1000Km can meet the coverage of 1000Km in 83% of time and the coverage of 700Km in 97% of time when the initialization is completed, and the coverage of 600Km is realized by 100%. Under the HPOP model, after 320 cycles, 79.17% of the time is better than 1000Km of coverage, 95.83% of the time is better than 700Km of coverage, and 100% of the time realizes 600Km of coverage.
5-view non-shrinking formation design
The above formation can reduce fuel consumption for maintaining the satellite formation to a great extent, but it has a disadvantage that the field of view is contracted for a short period of time at the intersection of the orbital planes, failing to achieve ultra-wide imaging. Thus, a second ultra-wide imaging formation is designed herein to achieve a complete non-shrinking field of view. However, the second formation is more complex than the first one, and not only the ascension point right ascension needs to be changed, but also the formation needs to be constructed in cooperation with the change of the track inclination angle. However, based on the analysis of the eccentricity and the track inclination, the formula (17) cannot be satisfied if the track inclination is changed, and thus the design is performed only according to the formula (18) in this portion. Wherein, the meaning expressed in the formula (17) is the stability of the spacecraft in the z direction in a relative coordinate system, namely the offset stability of the orbital plane; and equation (18) is expressed in terms of stability in the track plane, i.e., in the y-direction. Then, simplification with respect to equation (18) can be obtained:
thus, assuming the configuration shown in fig. 18, a set of 4 satellites can achieve 385Km wide full coverage, and the same set of satellite formations can be generated by changing the rising point right ascension (without changing formation stability) of the entire formation, thereby achieving 765Km wide full coverage.
In fig. 19, a single satellite can cover a 100Km range, the imaging overlap is 5Km, the imaging centers are spaced 95Km apart, 385Km can be achieved for a group of 4 satellites without shrink coverage, and the entire 700Km coverage formation can be completed using 2 formations as described above.
Since the second formation design uses both the orbit inclination angle and the ascent point right ascension and the horizontal approach angle, Sat1 and Sat2 have the same ascension point right ascension and different orbit inclination angles, and Sat3 and Sat4 have the same orbit inclination angle and different ascension point right ascension, that is, the ascent point right ascension changes the orbit plane to compensate for the view field shrinkage caused by the orbit having the inclination angle difference.
Wherein, Sat3 and Sat4 have the same orbit inclination angle, the design method is the same as the first formation configuration design route, but the satellite spacing is changed, and the linear spacing between Sat3 and Sat4 should satisfy the spacing of three single-star imaging broadwidths, namely: and d is 3 · sen-15, and the number of the satellites represented by the formula (27) satisfying the perturbation stability condition of J2 is derived by using the formulae (20) to (26), and in the process of deriving d is 3 · sen-15.
And Sat1 and Sat2 have the same ascending intersection right ascension but different orbit inclination angles and are used for compensating the narrow imaging points of Sat3 and Sat4, the formation after changing the orbit inclination angles can not satisfy the expression (17), so that the expression (18) is only satisfied, and the difference value of the orbit inclination angles of the main satellite and the auxiliary satellite depends on the width of single-satellite imaging:
as shown in fig. 20, the reference spacecraft particle is R, the satellite spacecraft particle is B, the same ascending intersection point is G, the distance between the satellite and the reference satellite is d, and the phase angle is phi. Then, the coordinate of the R point obtained according to the relative motion coordinate system of the spacecraft is (a 00), and then the coordinate of the satellite is:
the coordinates of the earth axis are:
then, the coordinates of the ascending and intersecting point of the reference star and the satellite are:
the difference between the mean and the approximate point angles is then:
namely:
in the formula, sen is the single star imaging width.
6 simulation verification
In the simulation, the imaging target width is set to 700Km, and the corresponding camera view angle is set to 100Km × 100 Km. The orbital height for satellite imaging is 500 Km. The number of orbits of each satellite at 700Km for which an image was obtained according to equation (18) is shown in table 3.
TABLE 3 satellite formation root table
Satellites that satisfy and do not satisfy expression (18) were set as controls under the J2 perturbation model and the HPOP model, respectively, over a one-month period. As can be seen from fig. 21, when the perturbation condition of J2 is partially satisfied, the formation cannot show stable oscillation as in fig. 8 when the perturbation condition of J2 is completely satisfied, but shows an oscillation divergent state, and can be dispersed to 400Km or more after 1 month, as can be seen from fig. 22, while the formation which does not satisfy the formula (18) can be dispersed to 4000Km or more after one month.
The second set was set under HPOP model, considering three volumes together: light pressure, atmospheric drag, tidal perturbation. As can be seen from fig. 23 and 24, the perturbation effect in the HPOP model is not very different from that in the perturbation of J2, and the main reason is that the track inclination is mainly used to form the track surface difference in the design of the second group of formation, while the difference is mainly formed by the rising point and the right ascension of the first group.
Under the condition that the coverage target is 700Km, the coverage width of the formation within one turn is as shown in fig. 25. As can be seen, the second formation can achieve 700Km non-shrink full coverage on formation design.
TABLE 4 ultra-breadth imaging effect of second formation
From the above table, a second 700Km imaging convoy of the design can fully achieve 700Km coverage at initial formation of the track. Under the J2 perturbation model, 700Km coverage can still be achieved 94.74% of the time after 336 orbital periods, and 600Km coverage can be achieved 100%. Under the HPOP model, 700Km coverage can be achieved 70.83% of the time and 600Km coverage 83.33% of the time after 336 cycles.
7 conclusion
The formation configuration based on J2 perturbation is designed for the problem of satellite super-breadth imaging, and the perturbation is converted into a spacecraft motion relative motion coordinate system for formation design according to the influence of the J2 perturbation on the number of orbits of a spacecraft. Through simulation verification, the results show that the satellite formation configuration based on the J2 stability has good stability under the action of J2 perturbation, the formation configuration under the J2 perturbation can be kept stable for a long time, and the formation diffusion range is greatly reduced compared with the formation which does not meet the J2 stable condition under the HPOP model. Meanwhile, simulation data show that the first formation can keep the formation stable for a long time, and the second formation needs more fuel kept by the formation than the first formation, but has very good super-width coverage performance. The ultra-width imaging of the satellite formation under perturbation for a long time is realized.
Claims (6)
1. A satellite formation implementation method facing to ground ultra-width imaging is characterized in that reference satellite orbit number is initialized according to ultra-width imaging requirements and satellite imaging parameters, the orbit number of each member satellite meeting the condition that the satellite formation is stable for a long time under J2 perturbation is determined, the satellite lower point coordinates of a reference satellite imaging center and the pointing vector of each member satellite camera at the future moment are calculated according to a reference satellite ephemeris, the satellite ephemeris of each member satellite is updated according to the orbit number of each member satellite, and the attitude parameters of each member satellite in a wide-width imaging mode are solved by combining the pointing vector of each member satellite camera;
the number of orbits of each member satellite meeting the condition of long-term stability of the satellite formation under the perturbation of J2 is determined by two schemes:
the first scheme is as follows: the method aims at eliminating the deviation of the motion direction of a reference satellite and the orbital plane of the reference satellite under the perturbation of J2, so that the satellite has the same semimajor axis, eccentricity, orbital inclination angle and amplitude angle of the perigee as the reference satellite, and the ascension point and the mean-anomaly point angle of the satellite are adjusted by combining the distance and the phase angle between the reference satellite and the satellite,
scheme II: the method comprises the steps of determining the number of orbits by adopting a first scheme for member satellites with the same elevation point right ascension but different orbit inclination angles, aiming at eliminating the deviation of the motion direction of a reference satellite under the perturbation of J2 for the member satellites with the same orbit inclination angles but different elevation point right ascension, enabling the satellite to have the same semimajor axis, eccentricity, perigee amplitude angles and elevation point right ascension as the reference satellite, and adjusting the orbit inclination angles and the perigee angles of the satellite according to the single-satellite imaging width and with the purpose of overlapping the visual fields of the satellite and the reference satellite.
2. The method for realizing formation of satellite formations oriented to ground ultra-width imaging according to claim 1, wherein the orbit number of each member satellite meeting the condition that the formation of satellite formations are stable for a long time under J2 perturbation is as follows:
σbnumber of orbits, σ, for satelliteb＝(ab eb ib ωb Ωb Mb)，ab、eb、ib、ωb、Ωb、MbRespectively the semi-major axis, eccentricity, orbit inclination, amplitude angle of perigee, right ascension of ascending intersection point, and average perigee angle of the satelliter、er、ir、ωr、Ωr、mrSemi-major axis, eccentricity, orbital inclination of reference satellite respectivelyThe altitude angle at the near place, the ascension at the ascending intersection point and the average angle at the near point, wherein omega and m are the difference value of the ascension at the ascending intersection point and the average angle at the approaching intersection point of the satellite and the reference satellite respectively,
o is the origin of the reference satellite coordinate system, A is the intersection point of the orbit plane of the reference satellite and the equatorial plane, D is the intersection point of the orbit plane of the satellite accompanying the flight and the equatorial plane, S is the mass point of the satellite accompanying the flight,
is a normal vector of the orbit surface of the satellite,
is the earth axis vector, a is the semi-major axis of the reference satellite,
by
Determining that R is reference satellite mass point, i is orbit inclination angle of the reference satellite, d and phi are distance and phase angle between the reference satellite and the satellite,
Sx、Sz、Syis composed of
Coordinates in the reference satellite coordinate system, Cx、Cz、CyIs composed of
Coordinates in a reference satellite coordinate system.
3. The method for realizing formation of satellite formations oriented to ground ultra-width imaging according to claim 1, wherein the orbit number of each member satellite meeting the condition that the formation of satellite formations are stable for a long time under J2 perturbation is as follows:
σbnumber of orbits, σ, for satelliteb＝(ab eb ib ωb Ωb Mb)，ab、eb、ib、ωb、Ωb、MbRespectively the semi-major axis, eccentricity, orbit inclination, amplitude angle of perigee, right ascension of ascending intersection point, and average perigee angle of the satelliter、er、ir、ωr、Ωr、mrRespectively is a semi-major axis, eccentricity, orbit inclination, amplitude angle of near place, right ascension of ascending intersection point and mean angle of near point of the reference satellite, i and m are respectively orbit inclination difference and mean angle of near point of the satellite and the reference satellite,
a is the semi-major axis of the reference satellite, sen is the single-star imaging width,
r is the reference satellite mass point, the coordinates of R are (a 00), B is the satellite mass point, G is the intersection point of the reference satellite,
is a vector of the earth's axis,
Cx、Cz、Cyis composed of
Coordinates under the coordinate system of the reference satellite, i is the orbital inclination of the reference satellite,
Bx、Bz、Byis composed of
And d and phi are the distance and phase angle between the reference satellite and the satellite in flight.
4. The method for realizing formation of satellite facing ground ultra-width imaging according to claim 1, wherein the ultra-width imaging requirement comprises: dimension information of a desired imaging area, a width of a desired imaging.
5. The method for realizing formation of satellite facing to ground ultra-width imaging according to claim 1, wherein the satellite imaging parameters comprise: the wide range of a single-star imaging area, the optimal imaging height and the maximum side swing capability of camera imaging.
6. The method for realizing the formation of the satellite facing the ground ultra-width imaging is characterized in that the condition that the formation of the satellite is stable for a long time under the J2 perturbation is obtained by carrying out precise variation processing on components, particularly high-order small quantities, in a J2 perturbation model.
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