CN109240322B - A realization method of satellite formation for ultra-wide-width imaging on the ground - Google Patents

Abstract

The invention discloses a method for realizing satellite formation for super-width imaging on the ground, relates to formation technology for stable satellite imaging, and belongs to the technical field of control and adjustment. This method studies the distributed ultra-wide imaging problem, breaking the single sub-satellite point imaging method of traditional satellite imaging. By carrying high-precision imaging payloads and combining with distributed satellite control technology, satellites can achieve high-resolution imaging in the form of formation. High-precision ultra-wide imaging greatly improves the efficiency of satellite search and imaging. This method proposes a distributed satellite formation ultra-wide imaging mode based on J2 stability, which solves the problems of small satellite staring range, narrow imaging width, and the rotation of the earth, which makes the satellite unable to achieve continuous imaging of adjacent areas on the ground.

Description

A realization method of satellite formation for ultra-wide-width imaging on the ground

technical field

The invention discloses a method for realizing satellite formation for super-width imaging on the ground, relates to formation technology for stable satellite imaging, and belongs to the technical field of control and adjustment.

Background technique

With the rapid development of space technology, satellite remote sensing imaging technology has increasingly highlighted its advantages of speed, convenience and high precision in agriculture, economy, climate, search and rescue, etc. The distributed micro-nano satellites composed of agile satellites have the characteristics of low cost and flexible configuration. Compared with traditional large satellites, micro-nano satellites have short research and development cycles, relatively low technical indicators, and lower launch costs due to their lower quality. Satellite technology can achieve rapid launch and deployment, and low-orbit micro-nano satellites can be launched into orbit by modified missiles, which can flexibly respond to emergencies and meet the needs of rapid response, with technical advantages that large satellites cannot match.

However, at present, satellite imaging technology generally adopts the method of image splicing after single-star imaging to complete the imaging of the large map. Due to the influence of the earth's rotation, the satellite cannot achieve continuous imaging of the adjacent areas on the ground, and it takes a long time to pass the last time. Imaging adjacent areas, so that the imaging quality of adjacent areas is affected by lighting conditions, cloud and fog occlusion and other conditions. At the same time, when a large-scale search is performed for dynamic targets (such as: search and rescue of lost targets at sea, high dynamic target search) , the target is very easy to move to the imaged area in this time gap, resulting in missed inspection. The use of distributed satellite ultra-wide imaging technology can greatly improve the efficiency and accuracy of large-scale investigations, and shorten the imaging delay of adjacent imaging areas.

Based on ultra-wide imaging missions, the formation of micro-nano satellites should be stable for a long time to meet the imaging needs. However, the size of micro-nano satellites is limited and the fuel they carry to maintain the formation is limited, so it is necessary to design so that the satellites do not use or use A small amount of fuel can satisfy the stable formation formation and the number of orbits.

SUMMARY OF THE INVENTION

The purpose of the present invention is to address the deficiencies of the above-mentioned background technology, and provide a method for realizing satellite formation for super-width imaging on the ground, which realizes the formation design and satellite attitude planning of distributed satellite super-width imaging, and further realizes the Ultra-wide imaging solves the technical problems that satellites cannot achieve continuous imaging of adjacent areas on the ground due to the small staring range of satellites, the narrow imaging width, and the rotation of the earth.

The present invention adopts following technical scheme for realizing above-mentioned purpose of invention:

A satellite formation implementation method for ground-based ultra-wide imaging, comprising the following steps:

1. Obtain imaging requirements: determine the dimensional information of the required imaging area, which is used to determine the orbital inclination of distributed satellites. If global imaging is required, polar orbits must be used to determine the required imaging width, and combined with satellite imaging parameters to determine the required the number of satellites;

2. Determine the imaging parameters of the satellite remote sensing camera: mainly the width of the imaging area, the optimal imaging height, and the maximum side-swing capability of the camera imaging;

3. Combine the above two steps to basically determine the number of satellites to be imaged. The number should be greater than or equal to the imaging width/single satellite field of view. Determine the orbital inclination of the formation based on the imaging area. In order to maintain the stability of imaging, the formation adopts a circular orbital level. Eccentricity is 0;

4. Take the reference star as the origin, the speed direction of the reference star as the Y direction, and the horizontal plane as the two-dimensional coordinate plane to set the polar coordinate system, and set the distance and angle between each member star and the reference star according to the imaging width;

5. Based on the stable conditions in the formulas (17) and (18), and according to the design methods in formulas (20)-(27), the analytical solution of the number of satellites in each accompanying flight can be obtained, so as to determine the stable conditions. The number of accompanying satellites below;

6. According to the ephemeris of the reference star, calculate the sub-satellite point of the imaging center of the reference star at each moment in the future and the camera pointing vector of each companion star at this reference position;

7. Combined with the estimated ephemeris of each accompanying flying star and the pointing vector at each future moment to calculate the attitude information of the accompanying flying satellite, so that the satellite formation can stably fly for a long time under the condition of J2 perturbation stability, and realize ultra-wide imaging.

The present invention provides two formation design schemes. The first one aims to eliminate the movement direction of the reference satellite and the offset of the reference satellite orbital plane under the J2 perturbation, and adjust the accompanying flight by combining the distance and phase angle between the reference satellite and the accompanying satellite. The ascending node right ascension and the mean perigee angle of the satellite; the second is to eliminate the offset of the reference satellite's motion direction under the perturbation of J2. For the member stars with the same ascending node right ascension but different orbital inclinations, the first A method to determine the orbital number of the companion satellite, for the member stars with the same orbital inclination but different ascending node right ascension, adjust the companion satellite according to the imaging width of the single star and for the purpose of overlapping the field of view of the companion satellite and the reference satellite. Orbital inclination and anomalies.

σ_b为伴飞卫星的轨道根数，σ_b＝(a_b e_b i_b ω_b Ω_b M_b)，a_b、e_b、i_b、ω_b、Ω_b、M_b分别为伴飞卫星的半长轴、偏心率、轨道倾角、近地点幅角、升交点赤经、平近点角，a_r、e_r、i_r、ω_r、Ω_r、m_r分别为参考卫星的半长轴、偏心率、轨道倾角、近地点幅角、升交点赤经、平近点角，δΩ、δm分别为伴飞卫星和参考卫星的升交点赤经差值和平近点角差值，

O为参考卫星坐标系原点，A为参考卫星轨道面与赤道面的交点，D为伴飞卫星轨道面与赤道面的交点，S为伴飞卫星质点，

为伴飞星轨道面的法向量，

为地轴向量，a为参考卫星的半长轴，

由

确定，R为参考卫星质点，i为参考卫星的轨道倾角，d、phi为参考卫星与伴飞卫星的距离及相角，

S_x、S_z、S_y为

在参考卫星坐标系下的坐标，C_x、C_z、C_y为

在参考卫星坐标系下的坐标。The number of orbits of accompanying satellites determined by the first formation scheme is:

σ _b is the orbital number of the accompanying satellite, σ _b =(a _b e _b i _b ω _b Ω _b M _b ), a _b , e _b , i _b , ω _b , Ω _b , M _b are the accompanying flying Satellite's semi-major axis, eccentricity, orbital inclination, argument of perigee, ascending node right ascension, mean perigee angle, a _r , _{er , i r ,} ω _r , Ω _r , m _r are the half lengths of the reference satellite, respectively axis, eccentricity, orbital inclination, argument of perigee, ascending node right ascension, mean perigee angle, δΩ, δm are the difference between the ascending node right ascension and the mean perigee angle of the accompanying satellite and the reference satellite, respectively,

O is the origin of the reference satellite coordinate system, A is the intersection of the orbital plane of the reference satellite and the equatorial plane, D is the intersection of the orbital plane of the accompanying satellite and the equatorial plane, S is the particle of the accompanying satellite,

is the normal vector of the orbital plane of the companion meteor,

is the terrestrial vector, a is the semi-major axis of the reference satellite,

Depend on

Determine, R is the reference satellite particle, i is the orbital inclination of the reference satellite, d, phi are the distance and phase angle between the reference satellite and the accompanying satellite,

S _x , S _z , S _y are

The coordinates in the reference satellite coordinate system, C _x , C _z , and C _y are

Coordinates in the reference satellite coordinate system.

σ_b为伴飞卫星的轨道根数，σ_b＝(a_b e_b i_b ω_b Ω_b M_b)，a_b、e_b、i_b、ω_b、Ω_b、M_b分别为伴飞卫星的半长轴、偏心率、轨道倾角、近地点幅角、升交点赤经、平近点角，a_r、e_r、i_r、ω_r、Ω_r、m_r分别为参考卫星的半长轴、偏心率、轨道倾角、近地点幅角、升交点赤经、平近点角，δi、δm分别为伴飞卫星和参考卫星的轨道倾角差值和平近点角差值，

a为参考卫星半长轴，sen为单星成像宽度，

R为参考卫星质点，R的坐标为(a0 0)，B为伴飞卫星质点，G为参考卫星的升交点，

为地轴向量，

C_x、C_z、C_y为

在参考卫星坐标系下的坐标，i为参考卫星的轨道倾角，

B_x、B_z、B_y为

在参考卫星坐标系下的坐标，d、phi为参考卫星与伴飞卫星的距离及相角。The number of orbits of accompanying satellites determined by the second formation scheme is:

σ _b is the orbital number of the accompanying satellite, σ _b =(a _b e _b i _b ω _b Ω _b M _b ), a _b , e _b , i _b , ω _b , Ω _b , M _b are the accompanying flying Satellite's semi-major axis, eccentricity, orbital inclination, argument of perigee, ascending node right ascension, mean perigee angle, a _r , _{er , i r ,} ω _r , Ω _r , m _r are the half lengths of the reference satellite, respectively Axis, eccentricity, orbital inclination, argument of perigee, ascending node right ascension, mean perigee angle, δi, δm are the difference between the orbital inclination angle of the accompanying satellite and the reference satellite and the difference between the angle of the mean anomaly and the angle of perigee, respectively,

a is the semi-major axis of the reference satellite, sen is the imaging width of a single satellite,

R is the reference satellite particle, the coordinate of R is (a0 0), B is the companion satellite particle, G is the ascending node of the reference satellite,

is the Earth vector,

C _x , C _z , C _y are

The coordinates in the reference satellite coordinate system, i is the orbital inclination of the reference satellite,

B _x , B _z , _By are

The coordinates in the reference satellite coordinate system, d and phi are the distance and phase angle between the reference satellite and the accompanying satellite.

The present invention adopts the above-mentioned technical scheme, and has the following beneficial effects:

(1) This application considers the high-order small quantities in the precise variational processing of the J2 perturbation model, and obtains a more accurate J2 stability condition through precise variational processing. The formation configuration analysis solution of stable imaging flight is realized for a long time, and the formation design scheme under polar coordinates is established on this basis, which is convenient for the design of stable formation.

(2) This application provides two calculation methods for the analytical solution of the formation configuration. One is to eliminate the movement direction of the reference satellite and the offset of the reference satellite orbital plane under the perturbation of J2. The geometric positional relationship of the satellites maps the geometrical positional relationship of each member star of the formation to the number of satellite orbits. The satellite formation scheme determined according to this analytical method can maintain the overall stability of the formation for a long time, and does not need to consume fuel for orbit. Maintain, save fuel, and overcome the defect that limited fuel is difficult to meet the needs of wide-format imaging; the other only aims to eliminate the offset of the reference satellite's motion direction under the perturbation of J2, and uses the ascending node right ascension to change the orbital plane to compensate for the existence of inclination. The field of vision shrinks caused by the orbit of the difference, the imaging satellite orbit period is short and the imaging width is large, the imaging gap is reduced between adjacent periods, and the situation that the target cannot be captured by the satellite due to the movement between adjacent imaging areas is greatly reduced. Compared with the first formation, it needs more fuel to maintain the formation, but it has very good ultra-wide coverage performance, which realizes the long-term ultra-wide coverage of the satellite formation under perturbation. wide imaging.

(3) The present invention uses high-resolution imaging satellite clusters for imaging. While ensuring the size of the imaging field of view, it solves the problems of insufficient imaging resolution and poor remote sensing image clarity of traditional large-field satellite imaging. The imaging formation involved in the present invention is adopted. The reconstruction scheme has a wide imaging field of view up to 1000KM, which solves the problems of small imaging field of view of high-definition remote sensing satellites, long imaging interval between adjacent remote sensing areas, and inconsistent imaging lighting conditions, which are not conducive to comparative analysis.

Description of drawings

FIG. 1 is a schematic diagram of an orbital coordinate system.

FIG. 2 is a schematic diagram of orbital photographed motion.

FIG. 3 is a schematic diagram of the corresponding relationship between eccentricity and orbital inclination.

Figure 4 is a schematic diagram of calculating the number of orbits of accompanying satellites using the first formation scheme.

FIG. 5 is a schematic diagram of imaging when the imaging width is 700Km and 1000Km.

FIG. 6 is a flowchart of an ultra-wide imaging method.

Figure 7 is a flow chart of a superwide imaging procedure.

Figure 8 shows the simulation results of the distance between the reference satellite and the accompanying satellite when the J2 perturbation condition is satisfied under the J2 perturbation model.

Figure 9 shows the measurement results of the distance between the reference satellite and the accompanying satellite when the J2 perturbation condition is not met under the J2 perturbation model.

Figure 10 shows the simulation results of the distance between the reference satellite and the accompanying satellite when the J2 perturbation stability condition is satisfied under the HPOP model.

Figure 11 shows the simulation results of the distance between the reference satellite and the accompanying satellite when the J2 perturbation stability condition is not satisfied under the HPOP model.

FIG. 12 is a schematic diagram of formation coverage when the coverage width is 700Km and a single viewing angle is 100Km.

Figure 13 is a schematic diagram of the shortened area of the satellite sub-satellite point width when the width is 100KM.

Fig. 14 is a schematic diagram of the variation of satellite coverage width within one orbital period when the width is 100Km.

Figure 15 is a schematic diagram of formation coverage when the coverage width is 1000Km and a single viewing angle is 150Km.

Figure 16 is a schematic diagram of the shortened area of the satellite sub-satellite point width when the width is 150KM.

Fig. 17 is a schematic diagram of the variation of satellite coverage width within one orbital period when the width is 150Km.

Fig. 18 is a schematic diagram of a non-contraction formation.

FIG. 19 is a first group of images in a specific embodiment.

Figure 20 is a schematic diagram of calculating the number of orbits of accompanying satellites using the second formation design scheme.

Figure 21 shows the simulation results of the distance between the reference satellite and the accompanying satellite when the perturbation stability condition of formula (18) is satisfied under the J2 perturbation model.

Figure 22 shows the measurement results of the distance between the reference satellite and the accompanying satellite when the perturbation stability condition of formula (18) is not satisfied under the J2 perturbation model.

Figure 23 shows the simulation results of the distance between the reference satellite and the accompanying satellite when the perturbation stability condition of formula (18) is satisfied under the HPOP model.

Figure 24 shows the simulation results of the distance between the reference satellite and the accompanying satellite when the perturbation stability condition (18) is not satisfied under the HPOP model.

FIG. 25 is a schematic diagram of the satellite coverage width in one orbital period in the second formation in the specific embodiment.

Detailed ways

The technical solutions of the invention will be described in detail below with reference to the accompanying drawings.

Aiming at the distributed satellite ultra-wide imaging technology, the present invention performs variational analysis on the orbital parameters under the J2 perturbation, and further refines the perturbation model, and designs a formation that satisfies long-term stability. The attitude planning of the accompanying satellites is carried out, and long-term stable ultra-wide imaging is realized.

1. The relative motion model of the spacecraft under the perturbation of J2

This part will design the satellite formation required for ultra-wide imaging, mainly based on the imaging requirements of the satellite formation, design the stability conditions of the satellite formation under the long-term perturbation of J2, and design two different formation requirements according to the formation requirements. different imaging formations.

1.1 Coordinate system of relative motion of spacecraft

In the research of spacecraft rendezvous and docking, formation configuration design, etc., the relative distance of the spacecraft is small compared with the semi-major axis of the orbit. The Kepler root number method cannot directly describe the relative positional relationship of the spacecraft, so the spacecraft is set. Relative motion coordinate system. As shown in Figure 1.

In Figure 1, OXYZ is the geocentric inertial coordinate system, and oxyz is the relative motion coordinate system of the spacecraft. The origin of the coordinates in the geocentric inertial system is located at the center of the earth O, the X axis points to the vernal equinox, the Z axis points to the celestial pole, the Y axis and the XOZ plane The right-handed system is formed; the coordinate origin in the spacecraft reference coordinate system (that is, the spacecraft relative motion coordinate system) is located at the satellite mass center o, the x-axis is the direction of the line connecting the earth's center to the spacecraft, the y-axis is the spacecraft motion direction, and the z-axis The right-hand system is perpendicular to the reference spacecraft orbital plane formed by the x- and y-axes.

1.2 The Earth's Aspherical Perturbation Model Based on the Mean Radical Method

When solving the perturbation problem, if the classical perturbation solution method is adopted, then the slowly changing long-period term such as the right ascension of the ascending node and the argument of perigee will become a long-term term, and a Poisson term will appear (the long-period term becomes The power series term of the time interval), the orbital element of this solution structure is not conducive to the analysis of the perturbation term. Therefore, the average number method is introduced, in which the orbital number of the reference spacecraft is σ _r , and the orbital number of the accompanying spacecraft is σ _b . Among them, a _r , _{er , ir , ω r , Ω r , and m r are the semi -} major axis, eccentricity, orbital inclination, argument of perigee, ascending node right ascension, and mean perigee angle of the reference star, respectively. a _b , e _b , i _b , ω _b , Ω _b , and M _b are the semi-major axis, eccentricity, orbital inclination, argument of perigee, ascending node right ascension, and mean perigee angle of the companion star, respectively,

σ _r = (a _r e _r i _r ω _r Ω _r m _r ) (1),

σ _b =(a _b e _b i _b ω _b Ω _b M _b ) (2).

When analyzing the non-spherical perturbation of the earth, since the harmonic term is a third-order infinitesimal with harmonic term, and the magnitude of J3 and J4 in the harmonic term is 10 ^-6 , while the magnitude of J2 is 10 ^-3 , it is ignored. After the high-order infinitesimals are analyzed, the J2 term can be analyzed to obtain the first-order long-term term of the J2 perturbation to the six-root number:

a(tt ₀ )=0 (3),

e(tt ₀ )=0 (4),

i(tt ₀ )=0 (5),

Among them, _Re is the radius of the earth, and μ is the gravitational constant of the earth. It can be seen from the above formula that the perturbation of J2 does not affect the semi-major axis, eccentricity and orbital inclination, but affects the right ascension of the ascending node and the near point. The influence of angle and argument of perigee is a cumulative process over time.

In the design of the orbit, the drift rate of each member star in the formation should be the same due to the perturbation of J2, so as to keep the formation stable for a long time. Therefore, the orbit drift difference between the accompanying spacecraft and the reference spacecraft should be set as :

Among them, since the accompanying spacecraft and the reference spacecraft are jointly affected by the J2 perturbation, and the orbital drift difference between the two spacecraft is a small amount, equations (9) to (11) are varied. Available:

The trajectory of the satellite is no longer a closed ellipse or circle due to the influence of perturbation. Therefore, the position of the subject satellite in the current orbital plane is set as: β=ω+f, ω is the argument of perigee, and f is the true perigee The right ascension of the ascending node will also change, and the parameter changes after the orbital motion is shown in Figure 2.

可得：Since the J2 perturbation does not change the semi-major axis, eccentricity and orbital inclination, the change of β angle relative to the satellite formation is mainly reflected in the change of the y-axis direction of the subject satellite relative to the reference star, that is, the change in the orbital plane, the ascending node is red The change of the warp is mainly reflected in the change of the z-axis direction, that is, the change of the track surface, so as long as the perturbation changes in these two directions are eliminated, stability can be achieved. In order to keep the drift velocity of the accompanying spacecraft relative to the reference spacecraft in the z-axis direction consistent, that is,

Available:

即：In the y-axis direction of the reference star, it should satisfy: Δβ=β ₁ -β ₂ =0, that is: Δβ=ω _r +f _r -ω _b -f _b , since this satellite is a remote sensing satellite, it needs to be kept at the best Imaging height, then set the orbit to be a circular orbit, that is, f=M, M is the near point angle, so there are:

which is:

Therefore, the conditions for the stability of the satellite formation, namely (15) and (16) are satisfied.

1.3 Formation design based on ultra-wide imaging

Based on the specific tasks involved in this paper, it is assumed that all the companion stars and the reference star have the same semi-major axis and use near-circular orbits, and the coefficient term of δa in Eq. (15) is the high-order infinitesimal of the other two, which can be Ignore, then simplify equations (15) and (16) to get:

By analyzing equation (17), the relationship between eccentricity and orbital inclination can be obtained as follows:

为0.01、0.1、1、10、100，偏心率与轨道倾角的对应关系如图3所示。Set separately

are 0.01, 0.1, 1, 10, 100, and the corresponding relationship between eccentricity and orbital inclination is shown in Figure 3.

比值很小时，如果需满足稳定性条件:并且维持较小的偏心率，则参考星的轨道倾角几乎为0，显然无法满足成像编队的覆盖性需求，或，当且仅当偏心率近乎十分大(近乎为1)时，轨道倾角才可以在很大的一个范围内进行选择(如：

)；当且仅当

比值很大时，参考星才可以以一个较小的偏心率在大范围内选择轨道倾角(如：

)。It can be obtained from the relationship in Figure 3: when

If the ratio is small, if the stability condition needs to be met: and a small eccentricity is maintained, the orbital inclination of the reference star is almost 0, which obviously cannot meet the coverage requirements of the imaging formation, or, if and only if the eccentricity is close to very large (nearly 1), the orbital inclination can be selected within a large range (such as:

); if and only if

When the ratio is large, the reference star can select the orbital inclination in a wide range with a small eccentricity (for example:

).

δi的取值应为δe的高阶无穷小，从而参考航天器与伴飞航天器具有几乎相同的轨道倾角。The value range of e itself is between 0 and 1, which is a small amount, and the imaging formation is relatively compact. In order to maintain a relatively ideal imaging formation, the value of δe should be a high-order infinitesimal of the value of e. , while in order to keep the larger

The value of δi should be the high-order infinitesimal of δe, so that the reference spacecraft and the accompanying spacecraft have almost the same orbital inclination.

3 Fuel-saving formation design

Based on the above analysis and satisfying equations (17) and (18) at the same time, it is assumed that the master and slave stars have the same orbital inclination, semi-major axis and eccentricity, that is, δe=0, δi=0, δa=0 and eccentricity is 0. Since the eccentricity is 0, the argument of perigee has no practical significance, and the formation is only controlled by the parallel perigee angle and the ascending node right ascension.

Set the orbital height h=500KM, the number of reference satellites is σ _r =(a _r e _r i _r ω _r Ω _r m _r ), where er _r =0, the coverage area of the camera on the ground is sen*sen, There is an overlapping area of 5KM in the ground coverage area of adjacent satellites.

As shown in Figure 4, in the reference spacecraft coordinate system, the coordinate origin O is located at the center of the earth, the X axis points from the center of the earth to the reference spacecraft, the Y axis is perpendicular to the orbital plane and points to the right of the motion direction of the reference star, and the Z axis constitutes a right-handed system. The distance between the reference star and the companion flying star is d, the phase angle is phi, A is the intersection of the orbital plane of the reference star and the equatorial plane, point D is the intersection of the orbital plane of the companion flying star and the equatorial plane, S is the particle point of the accompanying satellite, and R is the With reference to the satellite particle, OF is the normal vector of the orbital plane of the companion meteor. Therefore, the process of determining the orbital number of accompanying satellites based on equations (17) and (18) is as follows:

The coordinates of the accompanying satellite in the reference spacecraft coordinate system are:

The coordinates of the earth's axis are:

具有如下关系：but,

Has the following relationship:

向量。can be obtained from the above three conditions

vector.

And again,

According to the above can be obtained:

Therefore, the number of available companion flying stars under the condition of J2 perturbation stability is:

According to Equation (27) and combined with the required imaging width, camera roll capability and imaging field size, the distance and phase angle between the master and slave stars can be obtained. Among them, the side-swing maneuverability of the camera is set to 25°, the field of view of the camera is 100Km*100Km and 150Km*150Km, respectively, and the two camera fields of view correspond to the imaging widths of 700Km and 1000Km, respectively. The schematic diagram of the imaging is shown in Figure 5.

In Figure 5, the field of view of a single satellite is set to 100Km or 150Km, corresponding to the imaging target width of 700Km and 1000Km, respectively. The overlapping area between adjacent satellites is 5Km. When the field of view of a single satellite is 100Km, 8 satellites can reach 765Km. When the single-satellite field of view is 150Km, 8 satellites can achieve 1165Km coverage.

As shown in Figure 5, in order to form a stable imaging area, it is necessary to plan the attitude of the satellite during satellite imaging. Among them, 8 member satellites are distributed on both sides of the reference star, and 4 satellites are distributed on the left and right sides of the reference star. The bearing angle is the basis for judging the relative position of the reference star. Since the orbital planes cross each other, after half the orbital period, the positions of the satellites distributed on the left and right sides of the reference star will be interchanged. Set the camera to be installed below the satellite and point to the Z-axis direction of the satellite's own system. Taking the sub-satellite point of the reference star as a reference, each star points to the left and right sides of the reference star's sub-point in turn at equal intervals. When the member star is positioned relative to the reference star After the interchange, the imaging centers are also interchanged left and right, and the distance between the pointing center of each star and the lower point of the reference star is proportional to the distance from the member star to the reference star.

At the same time, considering that if the true perigee angles of each satellite are set to be the same, there is a risk of collision at the intersection of the orbital planes. Therefore, the true perigee angles of two adjacent satellites are alternately arranged to make the formation pass through the orbit in turn. face to face.

When designing this type of orbit, as shown in Figure 6 and Figure 7, first, the initial conditions are set according to the imaging demand index and the maneuverability of the satellite camera's perspective, and the number of reference star orbits is set according to the observation demand. The reference star can be a A virtual satellite is used as a reference point and does not need to exist; on this basis, the satellite formation that satisfies the long-term stability of the J2 perturbation condition is calculated according to formulas (17) and (18) and combined with the satellite formation; on this basis, the satellite imaging center is calculated. The sub-satellite point coordinates are calculated and the sub-satellite point coordinates corresponding to each satellite are calculated in turn, and the pointing vector of each satellite when maintaining the imaging mode is obtained from the satellite's ephemeris, and then the attitude parameters of each member satellite are determined to complete the imaging.

4 Simulation verification

In the simulation, the imaging target widths are set to 700Km and 1000Km, respectively, and the corresponding camera angles of view are 100Km*100Km and 150Km*150Km, respectively. The orbital altitude for satellite imaging is 500Km. Therefore, according to equations (17) and (18), the number of orbits of each satellite when imaging 700Km can be obtained as shown in Table 1.

Table 1 The number of satellite formations

In the simulation within one month, two groups of control satellites were set up according to the stability conditions of equations (17) and (18) to verify their formation stability.

For the first group of perturbation models, J2 perturbation is selected, and the satellites that satisfy and do not satisfy the J2 stability condition are set as comparisons. It can be seen from Figure 8 and Figure 9 that when the J2 perturbation condition is met, the distance between the reference star and the accompanying satellite oscillates stably between 180Km and 205Km, and there is no sign of divergence; when the J2 perturbation condition is not met, the reference star The distance with the companion star will eventually spread to 1200Km, which cannot be stabilized.

The second group is set under the HPOP model, which comprehensively considers three bodies: light pressure, atmospheric resistance, and tidal perturbation. It can be seen from Figure 10 and Figure 11 that due to the influence of various perturbation forces, when the J2 stability condition is met, the distance between the reference star and the companion star will decrease to 80Km after one month, and when the conditions are not met, it will continue to spread. At 700Km, the diffusion under the HPOP model is not as large as that under the J2 model. The main reason is the perturbation of the atmosphere. Since the orbital height of 500Km is obviously affected by the atmospheric perturbation, the height of the satellite orbit decreases, and the size of the formation is reduced in scale. Therefore, the trend of formation diffusion is not as obvious as that under the J2 model.

The above fuel-saving formation is used for super-wide coverage. At the intersection of the orbital planes of the formation satellites, the relative distance between the satellites is relatively close. To ensure the imaging quality, the satellites can sway up to 25°, so there is an arc satellite. In the area of shortened coverage width, the formation coverage when the coverage width is 700Km and a single viewing angle of 100Km are shown in Figure 12 and Figure 13, and the variation trend of satellite coverage width within one orbital period of 100Km width is shown in Figure 14. Figure 15 and Figure 16 show the formation coverage when the coverage width is 1000Km and the single viewing angle is 150Km. Figure 17 shows the variation trend of the satellite coverage width within one orbital period of the 150Km width.

Table 2 The first formation super-wide imaging effect

It can be seen from Table 2 that the designed 700Km coverage formation can meet the coverage requirement of 700Km in 93% of the time and the coverage requirement of 600Km in 98% of the time in the first orbit period (that is, when the formation initialization is completed), and The remaining arcs that cannot be covered are located in high latitude regions such as the North and South Pole, and are not the key areas for imaging. When the J2 perturbation model is set, the formation imaging still maintains 93% of the time of the first cycle to achieve a coverage of 700Km after 320 orbital cycles. It can be seen that the satellite formation can meet the J2 perturbation requirements under the designed orbit. conditions for stable flight. Meanwhile, under the HPOP model, coverage better than 700Km can still be achieved 91.67% of the time after 320 cycles.

The designed 1000Km coverage formation can meet 1000Km coverage in 83% of the time, 700Km coverage in 97% of the time, and 600Km coverage in 100% of the time when initialization is completed. Under the HPOP model, after 320 cycles, the coverage is better than 1000Km 79.17% of the time, better than 700Km 95.83% of the time, and 600Km is achieved 100% of the time.

5-view non-contraction formation design

The above formation can greatly reduce the fuel consumption for maintaining the satellite formation, but it has the disadvantage that the field of view will shrink for a short period of time at the intersection of the orbital planes, and ultra-wide imaging cannot be achieved. Therefore, this paper designs a second ultra-wide imaging formation, which can achieve no shrinkage of the field of view. However, the second formation is more complicated than the first. It not only needs to change the right ascension of the ascending node, but also needs to cooperate with the change of the orbital inclination to construct the formation. However, based on the analysis of eccentricity and orbital inclination, if the orbital inclination is changed, the formula (17) cannot be satisfied, so in this part, the design is only based on the formula (18). Among them, the meaning expressed in equation (17) is the stability of the spacecraft in the z-direction in the relative coordinate system, that is, the offset stability of the orbital plane; while equation (18) is expressed in the orbital plane, that is, the y-direction stability. Therefore, the simplification of (18) can be obtained:

Therefore, set the configuration as shown in Figure 18, 4 satellites in a group, can achieve a full coverage of 385Km wide, by changing the ascending node right ascension of the entire formation (without changing the formation stability) can generate the same Set up satellite formations to achieve full coverage of 765Km wide.

In Figure 19, a single satellite can cover a range of 100Km, the imaging overlap area is 5Km, and the imaging center spacing is 95Km. A group of 4 satellites can achieve 385Km without shrinkage coverage, while the entire 700Km coverage formation uses 2 of the above-mentioned teams. shape to complete.

Since the second formation design uses both the orbital inclination and the ascending node right ascension and the mean perigee angle, Sat1 and Sat2 have the same ascending node right ascension and different orbital inclinations, while Sat3 and Sat4 have the same orbital inclination and Different ascending node right ascension, that is, using the ascending node right ascension to change the orbital plane to compensate for the contraction of the field of view caused by orbits with inclination differences.

Among them, Sat3 and Sat4 have the same orbital inclination, and the design method is the same as the design route of the first formation configuration, but the satellite spacing has changed. That is: d=3·sen-15, using formula (20) to formula (26) to derive the number of the companion star shown in formula (27) under the condition of J2 perturbation stability, in the derivation process, d =3·sen-15.

However, Sat1 and Sat2 have the same ascending node right ascension but different orbital inclinations, which are used to make up for the imaging narrow point of Sat3 and Sat4, and the formation after changing the orbital inclination cannot satisfy (17), so it only satisfies (18), And the difference between the orbital inclinations of the master and slave stars depends on the width of the single star imaging:

As shown in Figure 20, the reference spacecraft particle is R, the companion spacecraft particle is B, the same ascending node is G, the distance between the companion and the reference star is d, and the phase angle is phi. Then according to the relative motion coordinate system of the spacecraft, the coordinates of point R can be obtained as (a 0 0), then the coordinates of the companion flying star are:

The coordinates of the earth's axis are:

Then, the coordinates of the ascending node of the reference star and the companion star are:

Therefore, the difference between the near point angles can be obtained as:

That is:

where sen is the imaging width of a single star.

6 Simulation verification

In the simulation, the imaging target width is set to 700Km, and the corresponding camera angle of view is 100Km*100Km. The orbital altitude for satellite imaging is 500Km. Therefore, according to formula (18), the number of orbits of each satellite when imaging 700Km can be obtained as shown in Table 3.

Table 3 The number of satellite formations

In one month, under the J2 perturbation model and under the HPOP model, the satellites that satisfy and do not satisfy Eq. (18) are set as comparisons. It can be seen from Figure 21 that when the J2 perturbation condition is partially satisfied, the formation cannot oscillate in a stable manner as in Figure 8 when the J2 perturbation condition is fully satisfied, but rather in a state of oscillation and divergence, which can diverge to 1 month later. Above 400Km, as can be seen from Figure 22, the formation that does not satisfy (18) will diverge to above 4000Km after one month.

The second group is set under the HPOP model, which comprehensively considers three bodies: light pressure, atmospheric resistance, and tidal perturbation. It can be seen from Figure 23 and Figure 24 that the perturbation effect under the HPOP model is not very different from that under the J2 perturbation. The main reason is that the design of the second group of formations mainly uses the orbital inclination to form the orbital surface difference. , while the first group is differentiated mainly by the ascending node right ascension.

Under the condition that the coverage target is 700Km, the coverage width of the formation in one circle is shown in Figure 25. It can be seen from the figure that the second formation can achieve 700Km full coverage without shrinkage in the formation design.

Table 4 The second type of formation ultra-wide imaging effect

It can be seen from the above table that the designed second 700Km imaging formation can completely achieve 700Km coverage when the orbit is initially formed. Under the J2 perturbation model, after 336 orbital periods, the coverage of 700Km can still be achieved 94.74% of the time, and the coverage of 600Km can be achieved 100% of the time. Under the HPOP model, 700Km coverage can be achieved in 70.83% of the time and 600Km coverage in 83.33% of the time after 336 cycles.

7 Conclusion

In this application, a formation configuration based on J2 perturbation is designed for the problem of satellite ultra-wide imaging. According to the influence of J2 perturbation on the number of spacecraft orbits, the perturbation is converted into the spacecraft motion relative motion coordinate system for formation. shape design. Through simulation verification, the results show that the satellite formation configuration based on J2 stability has good stability under the action of J2 perturbation, and can achieve long-term stability of the formation configuration under J2 perturbation, and it is less stable under the HPOP model. For formations that satisfy the J2 stability condition, the formation diffusion range is greatly reduced. At the same time, it can be seen from the simulation data that the first designed formation can keep the formation stable for a long time. Although the second formation requires more fuel to maintain the formation than the first formation, it has a very good performance. The ultra-wide coverage performance. The ultra-wide imaging of satellite formations under perturbation for a long time is realized.

Claims (6)

1. a kind of satellite formation realization method oriented to super-width imaging on the ground, it is characterized in that, according to super-width imaging demand and satellite imaging parameter initialization reference satellite orbit root number, it is determined that each member star satisfies the satellite formation under J2 perturbation. For the orbital element under the condition of long-term stability, the sub-satellite point coordinates of the reference satellite imaging center and the pointing vector of each member star’s camera are calculated according to the reference ephemeris, and the ephemeris of each member is updated by the orbital element of each member star. Combined with the pointing vector of each member star's camera, the attitude parameters of each member star in the wide imaging mode are calculated; Among them, there are two schemes to determine the orbital elements of each member star when the satellite formation meets the condition of long-term stability under J2 perturbation: Option 1: The goal is to eliminate the motion direction of the reference satellite and the offset of the reference satellite orbital plane under the perturbation of J2, so that the accompanying satellite has the same semi-major axis, eccentricity, orbital inclination, and argument of perigee as the reference satellite. Combined with the distance and phase angle between the reference satellite and the accompanying satellite, adjust the ascending node right ascension and the mean anomaly angle of the accompanying satellite, Scheme 2: For member stars with the same ascending node right ascension but different orbital inclinations, use scheme one to determine the number of orbital elements, and for member stars with the same orbital inclination but different ascending node right ascension, to eliminate the perturbation of the reference satellite motion direction at J2 The offset below is the target, so that the companion satellite has the same semi-major axis, eccentricity, argument of perigee, ascending node right ascension as the reference satellite, according to the imaging width of a single satellite and the overlap of the field of view of the companion satellite and the reference satellite For the purpose of adjusting the orbital inclination and the perigee angle of the accompanying satellite. 2. a kind of satellite formation realization method oriented to ground super-width imaging according to claim 1, is characterized in that, the orbital root number when each member star satisfies the condition of long-term stability of satellite formation under J2 perturbation is:

σ _b is the orbital number of the accompanying satellite, σ _b =(a _b e _b i _b ω _b Ω _b M _b ), a _b , e _b , i _b , ω _b , Ω _b , M _b are the accompanying flying Satellite's semi-major axis, eccentricity, orbital inclination, argument of perigee, ascending node right ascension, mean perigee angle, a _r , _{er , i r ,} ω _r , Ω _r , m _r are the half lengths of the reference satellite, respectively axis, eccentricity, orbital inclination, argument of perigee, ascending node right ascension, mean perigee angle, δΩ, δm are the difference between the ascending node right ascension and the mean perigee angle of the accompanying satellite and the reference satellite, respectively,

O is the origin of the reference satellite coordinate system, A is the intersection of the orbital plane of the reference satellite and the equatorial plane, D is the intersection of the orbital plane of the accompanying satellite and the equatorial plane, S is the particle of the accompanying satellite,

is the normal vector of the orbital plane of the companion meteor,

is the terrestrial vector, a is the semi-major axis of the reference satellite,

Depend on

Determine, R is the reference satellite particle, i is the orbital inclination of the reference satellite, d, phi are the distance and phase angle between the reference satellite and the accompanying satellite,

S _x , S _z , S _y are

The coordinates in the reference satellite coordinate system, C _x , C _z , and C _y are

Coordinates in the reference satellite coordinate system. 3. a kind of satellite formation realization method oriented to ground super-width imaging according to claim 1, is characterized in that, the orbital root number when each member star satisfies the condition of long-term stability of satellite formation under J2 perturbation is:

σ _b is the orbital number of the accompanying satellite, σ _b =(a _b e _b i _b ω _b Ω _b M _b ), a _b , e _b , i _b , ω _b , Ω _b , M _b are the accompanying flying Satellite's semi-major axis, eccentricity, orbital inclination, argument of perigee, ascending node right ascension, mean perigee angle, a _r , _{er , i r ,} ω _r , Ω _r , m _r are the half lengths of the reference satellite, respectively Axis, eccentricity, orbital inclination, argument of perigee, ascending node right ascension, mean perigee angle, δi, δm are the difference between the orbital inclination angle of the accompanying satellite and the reference satellite and the difference between the angle of the mean anomaly and the angle of perigee, respectively,

a is the semi-major axis of the reference satellite, sen is the imaging width of a single satellite,

R is the reference satellite particle, the coordinate of R is (a 0 0), B is the companion satellite particle, G is the ascending node of the reference satellite,

is the Earth vector,

C _x , C _z , C _y are

The coordinates in the reference satellite coordinate system, i is the orbital inclination of the reference satellite,

B _x , B _z , _By are

The coordinates in the reference satellite coordinate system, d and phi are the distance and phase angle between the reference satellite and the accompanying satellite. 4 . The method for realizing satellite formation for super-wide imaging on the ground according to claim 1 , wherein the super-wide imaging requirements include: dimensional information of a required imaging area and a required imaging width. 5 . 5. A kind of satellite formation realization method for ground-oriented ultra-wide imaging according to claim 1, is characterized in that, described satellite imaging parameter comprises: the width of single-star imaging area, optimum imaging height, camera imaging maximum Swing ability. 6. a kind of satellite formation realization method oriented to super-width imaging to the ground according to claim 1, is characterized in that, described satellite formation is under J2 perturbation this condition of long-term stability by each component in J2 perturbation model In particular, high-order small quantities are obtained by exact variational processing.

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