CN115687847A

CN115687847A - Common-scan sensing method for GEO space debris by low-orbit observation platform

Info

Publication number: CN115687847A
Application number: CN202211237128.0A
Authority: CN
Inventors: 冯飞; 胡敏; 汉京滨; 霍俞蓉; 徐灿; 田歌; 李翔宇; 宝竞宇
Original assignee: 63921 Troops of PLA
Current assignee: 63921 Troops of PLA
Priority date: 2022-10-11
Filing date: 2022-10-11
Publication date: 2023-02-03
Anticipated expiration: 2042-10-11
Also published as: CN115687847B

Abstract

The invention discloses a common scanning sensing method of a low-orbit observation platform for GEO space debris, which comprises the steps of selecting evenly distributed spacecrafts as observation platforms in the same height interval of a solar synchronous orbit in the morning and evening, setting the pointing directions of optical axes of star sensors on the observation platforms to be consistent, forming a scanning circle which takes any point on 90-i declination as the center of a circle and can cover the boundary of the GEO zone as the radius from the pointing direction of the optical axes of the star sensors on the GEO zone; setting the optical axis direction of a star sensor of the inclined track observation platform to be not collinear with a connecting line vector from the geocenter to the observation platform; the view field of the star sensor with the inclined track intersects with the view field of the star sensor with the sun synchronous track in the morning and evening at the boundary of the scanning circle, and multiple coverage of GEO space fragments in one day is achieved. The invention solves the technical problem that the star sensor cannot observe GEO space debris in multiple time periods and multiple directions, optimizes the observation capability of a low-orbit multiple observation platform on the GEO space debris, and enhances the pre-warning and collision avoidance perception capability of the GEO space debris.

Description

Common-scan sensing method for GEO space debris by low-orbit observation platform

Technical Field

The invention belongs to the technical field of space situation perception, and relates to a common scanning perception method of a low-orbit observation platform for GEO space debris.

Background

Geosynchronous Orbit (GEO) space debris, GEO space debris for short, does not emit light, and the brightness of GEO space debris mainly depends on the reflection of sunlight, so that the GEO space debris can be captured by a star sensor of an observation platform, as shown in fig. 1. However, due to the change of the high-speed relative position relationship between the GEO space debris and the observation platform in the space, the light incident angle and the light emergent angle of the GEO space debris also present dynamic changes, the star sensor is fixedly connected with the spacecraft body and cannot follow up and track, so that the observation efficiency is low, the detection capability of the star sensor of the observation platform is limited, the imaging of the dark and weak GEO space debris cannot be realized, the imaging under the strong sunlight interference condition cannot be realized, and the multi-period and multi-angle observation of the GEO space debris cannot be realized. The observation position needs to be designed.

According to statistics of the nervous scientist alliance, as long as 2019, 6 months and 20 days, 179 active LEO spacecrafts in China are obtained, wherein 132 spacecrafts in the sun synchronous orbit reach 74.3 percent. A large number of sun synchronous orbit spacecrafts provide possibility for realizing the observation conception of GEO space fragments based on the star sensor. The sun synchronous orbit has the characteristic that the precession angular velocity is equal to the annual motion of the flat sun, so that the sun synchronous orbit is always kept at a favorable position for observing the fragments in the GEO space. Compared with the prior art, due to the characteristic that the star sensor is fixedly arranged on the satellite body and cannot rotate, the time period for observation activities of the spacecraft running on other orbits every year is relatively limited along with the annual apparent motion of the sun. The GEO space debris itself does not emit light and relies on reflection of sunlight to form a point image in the sensor. The observation configuration is closely related to the photometric calculation process of the GEO space debris, and the calculation process is as follows:

the bidirectional reflectance distribution function BRDF is a function describing the relationship between incident light and reflected light on the surface of the material. The method is commonly used for constructing scattering characteristic models of different materials and has higher accuracy than diffuse reflection. The BRDF expression is as follows:

wherein l is the incident direction, v is the emergent direction, beta _l Is the angle of incidence, beta _v To the angle of emergence, dL _v dE is the differential radiance of the reflected light in the outgoing direction _l Is the differential irradiance in the incident direction.

The spectrum of the sun is equivalent to black body radiation at a temperature of 5900k, and in deep space, sunlight can be regarded as a parallel light source. Since the brightness of the spacecraft in the penumbra region is negligible, the following analysis only considers the occlusion of the earth's ghost, not the penumbra. For the solar synchronous orbit, the space relationship of the observation platform, the GEO space debris and the sun is shown in FIG. 2 when the earth is viewed from the north pole. The angle between the sun, the GEO space debris and the observation platform is called the phase angle.

The luminance calculation of the GEO space debris is carried out in two steps, firstly, the sun is used as a radiation source, and the irradiance and the reflected radiation emittance of the GEO space debris are calculated; and then, the GEO space debris is used as a radiation source, and the irradiance of the GEO space debris received by the star sensor is calculated. The BRDF from the irradiance of the sun, GEO space debris can be derived as follows:

the radiant flux density is related to the wavelength of light, and the radiant flux density M of the sun can be expressed as:

wherein, c ₁ ＝3.741844×10 ⁴ (W·cm ² ·μm ⁴ ) Is firstA black body radiation constant; c. C ₂ =1.438769 (cm · K) is the second blackbody radiation constant, λ is the wavelength (μm), and T is the thermodynamic temperature (K). Let the mean solar radius be R _sun ＝6.9599×10 ⁵ km, average distance of day and earth R _SE ＝1.4959787×10 ⁸ km, irradiance E of sunlight reaching the outer edge of the earth's atmosphere _sun Can be expressed as:

it can be seen that irradiance is inversely proportional to the square of distance, with greater attenuation of irradiance the further away from the source. Since the GEO radius is much smaller than the distance to the sun, the irradiance may be approximately equal to the irradiance of sunlight when it reaches the GEO space debris. The irradiance E of the sun in the visible band is about 0.38 μm to about 0.76 μm _Vsun Comprises the following steps:

let dA be the unit bin of the surface of the GEO space debris, the radiation intensity of the GEO space debris can be expressed as:

I _v ＝dL _v dAcosβ _v ＝E _Vsun f _v (l,v)cosβ _l cosβ _v dA

let R _TO Distance of GEO space debris to the observation platform, S _o Regarding the optical aperture area of the star sensor, the GEO space debris is regarded as a radiation source, and then the total radiation flux entering the star sensor is:

by the definition of irradiance, the irradiance of the GEO space debris received by the star sensor can be obtained as follows:

the apparent star of the sun is known as m _sun = -26.74, eye stars and the like m of GEO space debris _T Relative to the sun, the apparent star of the GEO space debris, etc. can be further derived to have the following expression in terms of the logarithm of the irradiance of both:

wherein, star is used to describe the brightness of celestial body, and the celestial body is brighter when the star value is smaller. All the stars and the like referred to in the present invention are all visual stars and the like.

Formula (I) wherein _A f _v (l,v)cosθ _l cosθ _v dA is the optical cross-sectional area (OCS) of the GEO space debris, and is only related to the material, shape, size, and outgoing and incident angles of the light rays of the GEO space debris, but not to the specific parameters of the sun and the star sensor.

OCS＝∫ _A f _v (l,v)cosθ _l cosθ _v dA

Based on the calculation model, the following simulation is carried out:

looking down from the north pole of the earth, as shown in fig. 3, beta is a phase angle, and the GEO space debris runs from a west-side initial point to an east-side end point for 12h, so that the sun and the GEO space debris are respectively positioned on two sides of the orbital plane of the platform, and the observation platform is always positioned at a favorable observation position for the GEO space debris.

As the GEO space debris moves from west to east, simulation results of the GEO space debris star, etc. are shown in FIGS. 4a and 4 b. Fig. 4a shows the variation trend of stars and the like in the field of view of the star sensor when the GEOGEO space debris moves from west to east in summer, and fig. 4b shows the corresponding result in spring minutes and days. Firstly, the relative position relationship of the sun, the GEO space debris and the observation platform in the space is considered during the calculation of the OCS, but the earth body shielding is not considered, the time-varying relationship of stars and the like shown in fig. 4a and 4b is drawn, then the shielding of the earth is considered, the section of the earth shielding the sight line between the observation platform and the GEO space debris is marked by a dotted line, and the section of the earth shielding the sunlight of the GEO space debris is marked by a dotted line, namely the GEO space debris enters the local shadow area of the earth.

It can be seen that when the GEO-space debris is located at a position where the phase angle is close to 90 degrees (near the start and end positions), the GEO-space debris is extremely low in brightness, but as the phase angle decreases, the brightness rises quickly and then fluctuates slowly. If 12 stars etc. are used as detectable star threshold value of the star sensor, the detectable arc segment will cover nearly 80% of the simulation period.

On the basis of the calculation of the GEO space debris stars and the like, the inventor provides a common-scan sensing method for the GEO space debris by a low-orbit observation platform.

In order to expand the application range and reduce the threshold, the common scanning perception method highlights the universality, the observation configuration is not limited to a certain observation platform orbit, and the spacecrafts with different orbits are brought into the range of the available observation platform. However, it is clear that the observation efficiency of the inclined orbit observation platform is influenced by the perturbation force for a long time. For example, a spacecraft operating in a near circular orbit at 400km altitude with an inclination of 45 DEG, at J ₂ Under the influence of item perturbation, the precession angular velocity of the orbital plane is-5.15 °/day (the minus sign indicates that the apparent motion direction of the sun is opposite), the relative motion angular velocity of the sun and the orbital plane reaches 6.13 °/day, that is, in a period of about 59 days, two observation windows at most appear on both sides of a rising intersection point and a falling intersection point respectively, the duration of each observation window is about 20 days by taking 12 stars and the like as limits according to the calculation result of luminosity, but the actual observable time can be further reduced by considering the occlusion of the earth body, as shown in fig. 1. Nevertheless, it is still a useful complement to use the inclined orbit spacecraft platform with different ascension points in near earth space as the GEO space debris observation platform.

Disclosure of Invention

On the one hand, the low-orbit spacecraft for observing the GEO space debris is mostly a small amount of special observation platforms, the orbit type is single, and the low-orbit spacecraft has a short capability in the aspects of covering timeliness, observing revisit degree and the like. On the other hand, the star sensor is widely installed on various spacecraft platforms, is a necessary attitude determination sensor for the spacecraft, and determines the space azimuth inertial direction from the shot star map background, thereby providing an attitude measurement reference for the spacecraft. The star sensor also has the observation capability of capturing a space target. However, because the space debris and the observation platform have a relatively fast relative movement speed, and the star sensor is fixedly connected with the spacecraft body, the space debris cannot be tracked with the star sensor in a following way like other special sensors, so that the observation time and the observation angle of the space debris by the star sensor of the observation platform are limited, and the technology of observing the space debris by the star sensor cannot be popularized. In view of the above, the present invention provides a method for sensing GEO space debris by a low-orbit observation platform in a common scan manner, which is a space-based multi-platform natural intersection observation configuration and comprises a scanning circle formed by a plurality of observation platforms running in a morning and evening sun synchronous orbit, and a method for sensing GEO space debris by a low-orbit observation platform supplemented by an inclined orbit observation platform in a common scan manner. A certain number of observation platforms on the scanning circle can ensure quick full coverage of the GEO band in one day, and the star sensor on the inclined track observation platform can point to the boundary area of the scanning circle from a plurality of positions in the space to form space three-dimensional coverage.

In order to achieve the purpose of multi-time-period and multi-angle observation of GEO space debris, the invention is concretely realized by the following technical scheme:

a low-orbit observation platform is used for sensing GEO space debris in a common scanning mode, wherein the low orbit comprises a morning and evening sun synchronous orbit and an inclined orbit; the method comprises the following steps:

firstly, selecting evenly distributed spacecrafts as an observation platform in the same height interval of the sun synchronous orbit in the morning and evening, setting the optical axis directions of star sensors on the observation platform to be consistent, forming a scanning circle which takes any point on 90-i declination as the center of a circle and can cover the boundary of a GEO zone as the radius from the optical axis directions of the star sensors; the scanning tracks of a plurality of spacecrafts on the GEO belt are overlapped to realize the general scanning foundation coverage of the GEO space debris; wherein i is the track inclination angle of the synchronous track of the morning and evening sun where the observation platform is;

setting the optical axis direction of the star sensor on the inclined track observation platform to be not collinear with a connecting line vector from the geocenter to the observation platform; and the field of view of the star sensor with the inclined track and the field of view of the star sensor with the sun synchronous track at the morning and evening are in an arc section intersected at the boundary of the scanning circle, so that the ordinary scanning basic coverage of the GEO space fragments is supplemented, and the multiple coverage of the GEO space fragments in one day is realized.

In the first step, the distance difference of the observation platform where the adjacent star sensors are located is smaller than or equal to a distance threshold. The observation platforms are distributed at equal intervals or approximately distributed at equal intervals.

In the first step, the optical axis direction of the star sensor on the observation platform comprises an elevation angle and an azimuth angle;

in the orbit coordinate system O of the observation platform _s X _o Y _o Z _o Optical axis L of middle and star sensor _obs And observation platform orbit sub-coordinate system Z _o O _s Y _o The included angle of the plane is an azimuth angle A _z In the orbital coordinate system Z of the observation platform _o O _s Y _o Projection of plane and Y _o The included angle of the negative direction of the shaft is an elevation angle E _l Near to Z _o The positive direction of the shaft is negative, otherwise, the positive direction is positive;

the optical axis pointing optimal elevation angle of the star sensor is the elevation angle of the critical value with the shortest full coverage time of the star sensor to the GEO band; the optimal azimuth angle is the azimuth angle of the critical value with the shortest full coverage time of the star sensor to the GEO band;

the elevation angle and the azimuth angle in the pointing direction of the optical axis of the star sensor jointly influence the radius of a scanning circle, and the influence of the elevation angle is more obvious than that of the azimuth angle.

In the first step, the elevation angle E in the optical axis direction of the star sensor _l And azimuth angle A _z All are not 0 degree, from elevation angle E _l And azimuth angle A _z Calculated radius of the scan circle R _s Comprises the following steps:

wherein,

for the elevation angle E in the optical axis direction of the star sensor _l And azimuth angle A _z All are not 0 degree, from elevation angle E _l And azimuth angle A _z The radius of the calculated scanning circle;

indicating GEO band on E ₂ Point to D ₂ The distance of the points; wherein D is ₂ Is the intersection point of the X axis and the equator in the celestial coordinate system, E ₂ For the optical axis of the star sensor at XO _E The intersection point of the projection on the Y plane and the equator; o is _E Is the earth's centroid; r _s1 Is the azimuth angle A in the optical axis direction of the star sensor _z Angle of elevation E when =0 DEG _l The radius of the calculated scanning circle; alpha (alpha) ("alpha") _s A long half shaft of a track of the observation platform; alpha (alpha) ("alpha") _t The GEO is provided with a long half shaft.

In the first step, the azimuth angle A in the optical axis direction of the star sensor _z Angle of elevation E when =0 DEG _l Calculated radius of the scan circle R _s1 Comprises the following steps:

wherein, angle A ₁ O _E C ₁ Is an azimuth angle A _z Angle of elevation E when =0 ° _l The calculated radius of the scanning circle; alpha (alpha) ("alpha") _s A long half shaft of a track of the observation platform; alpha is alpha _t A GEO with a long half shaft; ejection method of small arc A ₁ O _E B ₁ Represented by the earth's centroid O _E Is a vertex, A ₁ O _E And O _E B ₁ Angle of (A) ₁ Is the intersection point of the star sensor optical axis and the GEO band, B ₁ Is O _s Y _o The intersection of the reverse extension line with the GEO band.

In the first step, the elevation angle E in the optical axis direction of the star sensor _l Angle of orientation A when = 0% _z Calculated radius of the scan circle R _s2 Comprises the following steps:

wherein,

elevation angle E for pointing of optical axis of star sensor _l Angle of orientation A when = 0% _z The radius of the scanning circle is calculated;

indicating GEO band at E ₂ Point to D ₂ The distance of the points;

indicating GEO band on E ₂ Point to C ₂ The distance of the points; d ₂ Is the intersection point of the X axis and the equator in the celestial coordinate system; e ₂ For the optical axis of the star sensor at XO _E The intersection point of the projection on the Y plane and the equator; o is _E Is the earth's centroid; c ₂ Is elevation angle E _l When the angle is 0 degrees, the optical axis of the star sensor points to the intersection point of the GEO band; alpha is alpha _t A GEO with a long half shaft; alpha (alpha) ("alpha") _s The long half shaft of the orbit of the observation platform.

In the first step, when the number of observation platforms on the scan circle is even, the minimum number of observation platforms for ensuring that the GEO space debris is detected in one day is:

wherein,

when the number of the observation platforms on the scanning circle is even, the minimum number of the observation platforms for ensuring the GEO space debris to be detected in one day is ensured; n' represents the number of the view fields of the star sensors rotating on the scanning circle in the process that GEO space debris runs from west to east; omega _t Is the GEO space debris angular velocity; r _s Is the radius of the scanning circle; omega _s To observeA platform angular velocity; the size of the view field of the star sensor is n multiplied by n, n is any numerical value taking an angle as a unit, the view fields of different star sensors are different in size and are determined by the design of an optical system;

when the number of the observation platforms on the scanning circle is odd, the minimum number of the observation platforms which ensure that the GEO space debris is detected in one day is as follows:

wherein,

when the number of observation platforms on the scanning circle is odd, the minimum number of observation platforms for ensuring the detection of GEO space debris in one day is ensured; n' represents the number of the view fields of the star sensors rotating on the scanning circle in the process that GEO space debris runs from west to east; omega _t The angular velocity of the GEO space debris; r _s Is the radius of the scanning circle; omega _s The angular velocity of the observation platform; the size of the view field of the star sensor is n multiplied by n, n is an arbitrary numerical value taking an angle as a unit, the view fields of different star sensors are different in size, and the view field is determined by the design of an optical system.

Preferably, in a field of view of 2 degrees multiplied by 2 degrees, when the number of uniformly distributed platforms of the sun synchronization orbit is 5 in the morning and evening, the coverage of the GEO-strip in one day is 99.9%, and the requirement of full coverage is approximately met.

In the first step, the sun synchronous track in the morning and evening is in a height interval of 300km to 2000km, the variation range of the track inclination angle i is 96.67 degrees to 104.89 degrees, and the value of declination of the center of a scanning circle of a GEO belt is-14.89 degrees to-6.67 degrees; the GEO zone is a spherical annular section which takes the earth center as the sphere center, has the orbit height of 36000km and the declination covered by minus 15 degrees to plus 15 degrees.

In the first step, the track swept by the star sensor on the GEO spherical annular tangent plane is spiral.

In the second step, the track inclination angle of the inclined track is between 0 and 90 degrees; the installation direction limit range of the star sensor is 30-80 degrees.

The sun synchronous orbit is an orbit in which the precession angular velocity of the orbit surface is equal to the annual apparent motion velocity of the sun under the condition that the spacecraft is shot. The morning and evening sun synchronous orbit is an orbit of which the sun synchronous orbit is positioned on the earth morning and evening line.

The beneficial effects of the invention are:

the invention discloses a common-sweep sensing method of a low-orbit observation platform for GEO space debris, which is characterized in that a common-sweep sensing configuration of the low-orbit observation platform for the GEO space debris, which is mainly based on the morning-evening sun synchronous orbit observation platform and supplemented by an inclined orbit observation platform, is constructed for the observation scene of the spacecraft platform of the low-orbit morning-evening sun synchronous orbit and the inclined orbit for the space debris of the high-orbit GEO orbit;

selecting spacecrafts which are uniformly distributed as an observation platform in the same height interval of the sun synchronous orbit in the morning and evening, setting the optical axis directions of star sensors on the observation platform to be consistent, forming a scanning circle which takes any point on 90-i declination as the center of a circle and can cover the boundary of the GEO band as the radius from the optical axis directions of the star sensors on the GEO band; overlapping scanning tracks of a plurality of spacecrafts on the GEO belt to realize common scanning foundation coverage of GEO space fragments; wherein i is the track inclination angle of the synchronous track of the morning and evening sun where the observation platform is;

setting the optical axis direction of a star sensor on the inclined track observation platform to be not collinear with a connecting line vector from the geocenter to the observation platform; and the field of view of the star sensor with the inclined track and the field of view of the star sensor with the sun synchronous track in the morning and evening are in arc sections intersected at the boundary of the scanning circle, so that the coverage of the ordinary scanning foundation of the GEO space debris is supplemented, and the multiple coverage of the GEO space debris in one day is realized.

The observation platform of the morning and evening sun synchronous track is used for realizing full coverage of the GEO belt, and the observation platform of the inclined track is used as a supplement, and the field of view of the inclined track star sensor and the field of view of the morning and evening sun synchronous track star sensor in the first step point to the boundary area of the scanning circle from a plurality of positions in space in an intersecting arc section at the boundary of the scanning circle to form spatial three-dimensional common scanning full coverage; the star sensor can detect and extract the GEO space debris measurement information from the shot star map while completing the inherent attitude determination task, so that the ubiquitous sensing efficiency of the star sensor on the GEO space debris is remarkably improved, and the ubiquitous sensing of the GEO space debris is realized.

In engineering, a spacecraft with a similar rail position as that in the step one can be selected as an observation platform to form a scanning circle observation configuration formed by a morning and evening sun synchronous orbit observation platform, even if the observation platform is possibly distributed uniformly in an unequal phase on the morning and evening sun synchronous orbit, the neutral position caused by unequal phase intervals can be filled by using the quantity advantage and a larger star sensor field angle, and the requirement of full coverage of GEO space fragments within 24 hours is approximately met. And then, respectively adding the inclined rails as auxiliary observation platforms according to the step two. The observation platform of the morning-and-evening sun synchronous track is used for realizing rapid multiple full coverage of a GEO (geosynchronous orbit) belt, and the observation platform of the inclined track can be used for setting the initial installation direction of a proper star sensor, so that the view field of the inclined track star sensor and the view field of the morning-and-evening sun synchronous track star sensor can form three-dimensional observation on GEO space debris around a scanning circle in an arc section intersected with the boundary of the scanning circle, the revisit degree of observation is increased, and good observation data are provided for subsequent track determination. In conclusion, a common scanning perception configuration of the low-rail observation platform, which is mainly based on the morning and evening sun synchronous orbit observation platform and is supplemented by the inclined orbit, on the GEO space debris can be constructed.

In the operation process, each platform can download observation data (right ascension, declination and observation time of the space debris) to a ground data processing center through an inter-satellite link and an inter-satellite link, and can also perform independent analysis and processing on the satellite to complete the track determination and cataloguing work of the space debris, so that the observation capability of the space debris is greatly improved.

The star sensor is used as a necessary attitude sensor for most spacecrafts, if the star sensor is regarded as a 'dual-purpose' space situation perception sensor, the advantage of large resource quantity of on-orbit spacecrafts in China can be fully exerted, the installation angle of the star sensor is adjusted on the basis of a disclosed model, the observation configuration of a sun synchronous orbit to a GEO orbit is constructed, the residual value of a large number of on-orbit spacecrafts in China can be further excavated, particularly, the low-orbit spacecrafts with large quantity are provided, the spacecrafts with the star sensors as many as possible are used as observation platforms, the advantage of a space-based observation system is further expanded, special spacecrafts do not need to be additionally launched, the space situation perception capability of China is greatly improved, the space debris early warning and collision avoidance capability is remarkably enhanced, and suggestions with operability and compatibility are provided for the planning and design of space missions in the future.

Drawings

The invention is explained in more detail below with reference to the figures and examples.

FIG. 1 is a schematic view of a non-sun-synchronous orbit observable window.

Fig. 2 is a schematic view of the spatial viewing geometry (north pole top view).

Fig. 3 is a schematic diagram of a simulation scenario (north pole top view).

Fig. 4a is a diagram of the time-varying curves of the GEO space debris stars and the like on the summer solstice.

FIG. 4b is a graph showing the time-dependent change curves of the GEO space debris stars and the like in the spring minute day.

Fig. 5 is a schematic view of the optical axis orientation of the star sensor on the observation platform.

Fig. 6 is a schematic view of the geometry of the scanning circle for the combined action of elevation and azimuth.

Fig. 7 is a schematic view of the geometry of the scanning circle corresponding to only the elevation angle.

Fig. 8 is a schematic view of the geometry of the scan circle for only azimuth correspondence.

Fig. 9 is an oblique view of a scan circle viewing configuration.

FIG. 10 is a schematic diagram of the relative motion of the GEO space debris and the scan circle.

FIG. 11 is a schematic diagram of the relative motion trajectory of the star sensor and the GEO strip.

FIG. 12 is a schematic view of 12 observation platforms located at different inclination angles of inclined tracks.

Fig. 13 is a schematic view of a general scanning sensing configuration composed of 12 inclined rails with different inclination angles and 12 observation platforms of a morning and evening sun synchronous rail.

FIG. 14 is a plot of coverage time for different latitudes of the GEO zone during a day for a common sweep sensing configuration.

Fig. 15 is a time of day coverage for GEO areas with different longitudes for a common sweep sensing configuration.

FIG. 16 is a graph of coverage ratio simulation results for GEO bands over a day for a common scan perception configuration.

FIG. 17 is a graph of multiple coverage simulations of GEO bands at different latitudes over a day for a common scan perception configuration.

FIG. 18 is a graph of multiple coverage simulations for a general sweep sensing configuration with different longitudes of the GEO band during a day.

Detailed Description

The embodiment of the invention discloses a common-scanning sensing method of a low-orbit observation platform for GEO space debris, wherein a star sensor is arranged on the observation platform; the low rail comprises a morning and evening sun synchronous rail and an inclined rail; the method comprises the following steps:

firstly, selecting evenly distributed spacecrafts as an observation platform in the same height interval of the sun synchronous orbit in the morning and evening, setting the optical axis directions of star sensors on the observation platform to be consistent, forming a scanning circle which takes any point on 90-i declination as the center of a circle and can cover the boundary of a GEO zone as the radius from the optical axis directions of the star sensors; overlapping scanning tracks of a plurality of spacecrafts on the GEO belt to realize common scanning foundation coverage of GEO space fragments; wherein i is the track inclination angle of the synchronous track of the morning and evening sun where the observation platform is;

According to the technical scheme, for the same number of observation platforms, the observation platforms which are uniformly distributed can enable the whole scanning circle to observe fragments in the GEO space uniformly, and the nonuniform distribution can cause a gap between two observation platforms to be larger and certain fragments to be missed.

In the scheme, the distance difference of the observation platforms where the adjacent star sensors are located is smaller than or equal to the distance threshold, so that the technical scheme can be implemented when the plurality of observation platforms which are uniformly distributed are distributed at equal intervals or approximately at equal intervals.

In engineering, a spacecraft with a similar orbit position as that in the step one can be selected as an observation platform to form a scanning circle observation configuration formed by a morning and evening sun synchronous orbit observation platform, even if the observation platform is possibly distributed on the morning and evening sun synchronous orbit in an unequal phase and uniform manner, the neutral position caused by unequal phase can be filled by using the quantity advantage and a larger star sensor view angle, and the requirement of full coverage of GEO space debris within 24 hours is approximately met. And then, respectively adding the inclined tracks as auxiliary observation platforms according to the step two. The observation platform of the morning-and-evening sun synchronous track is used for realizing rapid multiple full coverage of a GEO (geosynchronous orbit) belt, and the observation platform of the inclined track can be used for setting the initial installation direction of a proper star sensor, so that the view field of the inclined track star sensor and the view field of the morning-and-evening sun synchronous track star sensor can form three-dimensional observation on GEO space debris around a scanning circle in an arc section intersected with the boundary of the scanning circle, the revisit degree of observation is increased, and good observation data are provided for subsequent track determination. In conclusion, a common scanning perception configuration of the low-rail observation platform, which is mainly based on the morning and evening sun synchronous orbit observation platform and is supplemented by the inclined orbit, on the GEO space debris can be constructed.

In the first step, the solar synchronous track is within a height interval of 300 km-2000 km in the morning and evening; the variation range of the track inclination angle i is 96.67-104.89 degrees; the GEO zone is a spherical annular section which takes the earth center as the sphere center, has the orbit height of 36000km and the declination covered by minus 15 degrees to plus 15 degrees; the value of the declination of the center of the scanning circle of the GEO belt is between 14 degrees below zero and 6.67 degrees below zero.

As shown in fig. 5, in the first step, the optical axis of the star sensor on the observation platform points to include an elevation angle and an azimuth angle;

in the observation platform orbit coordinate system O _s X _o Y _o Z _o Optical axis L of middle and star sensor _obs And observation platform orbit sub-coordinate system Z _o O _s Y _o The included angle of the planes being azimuth A _z In the orbital coordinate system Z of the observation platform _o O _s Y _o Projection of plane and Y _o The included angle of the negative direction of the shaft is an elevation angle E _l Near to Z _o The positive axis is negative and the opposite is positive.

The optimal elevation angle is the elevation angle of the critical value with the shortest full coverage time of the star sensor to the GEO band; and the optimal azimuth angle is the azimuth angle of the critical value with the shortest full coverage time of the star sensor to the GEO band.

In step one, as shown in FIG. 6,

corresponding to that in FIG. 7

In a spherical triangle

And

middle and elevation angle E _l And azimuth angle A _z All are not 0 degree, from elevation angle E _l And azimuth angle A _z Calculated radius of the scan circle R _s Comprises the following steps:

wherein,

is elevation angle E _l And azimuth angle A _z When they are not 0 deg., the user should lean upwardAngle E _l And azimuth angle A _z The calculated radius of the scanning circle;

for GEO with E ₂ Point to D ₂ Distance of points, wherein D ₂ Is the intersection point of the X axis and the equator in the celestial coordinate system, E ₂ For the star sensor optical axis at XO _E Intersection point of projection on Y plane and sky equator; o is _E Is the earth's centroid; r _s1 Is an azimuth angle A _z Angle of elevation E when =0 DEG _l The calculated radius of the scanning circle; alpha (alpha) ("alpha") _s A long semi-axis of a track of an observation platform; alpha is alpha _t The GEO is provided with a long half shaft.

As shown in fig. 7, the azimuth angle a _z Angle of elevation E when =0 DEG _l Calculated radius of the scan circle R _s1 Comprises the following steps:

then at Δ A ₁ O _s O _E In the middle, easy to obtain:

in a similar manner, at Δ B ₁ O _s O _E In the method, the following steps are included:

combined upper to obtain a radius R _s1 Comprises the following steps:

wherein < A > ₁ O _E C ₁ Is an azimuth angle A _z Angle of elevation E when =0 ° _l The calculated radius of the scanning circle; alpha is alpha _s A long semi-axis of a track of an observation platform; alpha is alpha _t A GEO with a long half shaft; angle A ₁ O _E B ₁ Expressed in terms of the earth's centroid O _E Is a vertex, A ₁ O _E And O _E B ₁ Angle of (A) ₁ Is the intersection point of the optical axis of the star sensor and the GEO band; b is ₁ Is O _s Y _o The intersection point of the reverse extension line and the GEO belt; o is _E Is the center of mass of the earth, O _s Is the center of mass of the observation platform;

is a GEO band; o is _s A ₁ Pointing to the optical axis of the star sensor.

As shown in FIG. 8, O _s C ₂ For the optical axis direction of the star sensor, Z _o O _s Y _o Is a plane in the orbital coordinate system,

for scanning the radius of the circle, the triangle Δ C on the sphere ₂ E ₂ D ₂ Performing the following steps; elevation angle E _l Angle of orientation A when = 0% _z Calculated radius of the scan circle R _s2 Comprises the following steps:

wherein,

is the radius of the scanning circle;

indicating GEO band on E ₂ Point to D ₂ The distance of the points;

indicating GEO band on E ₂ Point to C ₂ The distance of the points; d ₂ Is the intersection point of the X axis and the equator in the celestial coordinate system; e ₂ For the optical axis of the star sensor at XO _E Intersection point of projection on Y plane and sky equator; c ₂ Is E _l When the angle is 0 degrees, the optical axis of the star sensor points to the intersection point of the GEO band; alpha is alpha _t A GEO with a long half shaft; alpha is alpha _s The long half shaft of the orbit of the observation platform.

As shown in fig. 9, taking 12 observation platforms with equal phase difference distribution on the scanning circle as an example, the phase difference between the observation platforms is distributed at equal intervals of 30 °, and the number of the rest tracks is the same except that the true proximal angles of the observation platforms are distributed at equal intervals. The method is an ideal assumed condition, can be customized according to task requirements in engineering practice, and does not require that observation platforms are uniformly distributed at equal intervals. The annular strip is a GEO strip formed within the declination range of +/-15 degrees.

The GEO space debris on the GEO zone naturally moves around the earth from west to east, and the mathematical problem of a minimum number of observation platforms exists in order to enable the GEO space debris to be observed by the sensors distributed on the scanning circle at equal intervals at least once in one orbit period.

The following modeling calculations were made:

and supposing that a plurality of observation platforms running on the same orbit height are distributed at equal intervals, and the star sensors on each platform have consistent optical axis directions, the scanning tracks of the star sensors on the GEO belt are overlapped. The more the number of the observation platforms is, the faster the observation platforms cover the GEO zone is, and the shorter the revisit time is. If the GEO zone is to realize full coverage in one day, the minimum value of the number of observation platforms is set as

The method is not only related to the orbit characteristic of an observation platform, but also related to the field size of the star sensor and the radius of a scanning circle.

The size of the view field of the star sensor is n multiplied by n, and the angular speed of the observation platform is omega _s Angular velocity of GEO space debris is omega _t The star sensor has a pointing elevation angle E _l Azimuth angle is A _z Radius of the scanning circle being R _s (angular separation). The following analyses were performed: the GEO space debris crosses the scan circle twice a day from west to east as shown by the dashed middle line in fig. 10, the critical condition being that the GEO space debris has a field of view N in fig. 10 ₁ The next time after the passage and in the field of view N ₂ The gap that has not yet arrived enters the scan circle, at which point the field of view N ₂ Space apart from GEOAngular distance of the sheets being beta ₂ . In the classification discussion, when the number of observation platforms is even, N is the same as the moment ₂ Symmetrical field of view N _j When the GEO space debris travels to the east boundary of the circle, the corresponding field of view N _k And N _k+1 ，β _k 、β _k+1 Is the angular separation of the two. To ensure that GEO space debris is detected, the following relationship exists:

on the west side of the scan circle, angular separation β ₂ Can be expressed as:

the operation process of GEO space debris from west to east to the beginning of entering the scanning circle and entering the east side scanning view field satisfies the following relation:

wherein N' represents the number of fields of view that the scan circle has rotated during the course of GEO space debris moving from west to east. On the east side of the scan circle, the following relationships exist:

wherein the inequality constrains GEO space fragments to enter N _k+1 Angular distance beta to be satisfied by field of view _k+1 The upper bound of (c). In summary, it can be determined that when the number of observation platforms on the scan circle is even, the minimum number of observation platforms that ensure that GEO space debris is detected during a day is:

wherein,

when scanning the view on the circleWhen the number of the measuring platforms is even, the minimum number of the measuring platforms for detecting the GEO space debris in one day is ensured; n' represents the number of the view fields of the star sensors rotating on the scanning circle in the process that GEO space debris runs from west to east; omega _t Is the GEO space debris angular velocity; r _s Is the radius of the scanning circle; omega _s The angular velocity of the observation platform; the size of the field of view of the star sensor is n multiplied by n, n is an arbitrary numerical value taking an angle as a unit, the field of view of different star sensors is different in size and is determined by the design of an optical system;

when the number of the observation platforms is odd, the observation platforms and the field of view N ₂ Symmetric is the field of view N _i And N _i+1 Becomes the following equation (2-51):

wherein,

when the number of observation platforms on the scanning circle is odd, ensuring the minimum number of observation platforms for detecting GEO space debris in one day; n' represents the number of the view fields of the star sensors rotating on the scanning circle in the process that GEO space debris runs from west to east; omega _t Is the GEO space debris angular velocity; r _s Is the radius of the scanning circle; omega _s To observe the angular velocity of the platform; the size of the view field of the star sensor is n multiplied by n, n is an arbitrary numerical value taking an angle as a unit, the view fields of different star sensors are different in size, and the size is determined by the design of an optical system.

Preferably, in a 2 ° × 2 ° field of view, when the number of uniformly distributed platforms of the sun synchronization orbit is 5 in the morning and evening, the coverage of the GEO-belt in one day is 99.9%, and the requirement of full coverage is approximately met.

The above model determines the minimum number of observation platforms on a scan circle that will achieve full coverage of the GEO-belt in a day. The above formula provides theoretical values for reference, the modeling process is based on certain assumptions, namely the heights of the tracks of the observation platforms are consistent and have the same phase difference, in the engineering, the tracks of the observation platforms are determined according to the task requirements of the observation platforms and cannot be completely consistent, but in the common track height range, the track inclination angle change of the sun synchronous track is very small, namely the circle center of the scanning circle does not have large fluctuation.

The track swept by the star sensor in the GEO spherical annular tangent plane is spiral.

In practice, as shown in fig. 11, the trajectory swept by the star sensor in the plane of the GEO-strip is helical due to the relative movement between the GEO-strip itself and the plane of the observation trajectory. The coverage of the GEO zone by the view field of the star sensor is realized through the spiral relative motion relation, the orbit height of the observation platform and the installation direction of the star sensor can be reasonably designed, and the spiral scans of a plurality of circles are not overlapped repeatedly as much as possible, so that the quick full coverage of the GEO zone GEO space debris is realized in a short time.

In the past, the space-based sensing system mostly adopts a follow-up tracking observation mode, namely, a sensor is controlled by a two-dimensional turntable to observe along with GEO space debris, and the observation arc section is long; however, the star sensor as a dual-purpose sensor has no possibility of follow-up tracking, and can only perform general scanning on the GEO zone in a natural intersection mode. At the moment, the platform of which tracks is selected to be used as an observation platform, and how to obtain good observation efficiency by adjusting the installation direction under the condition of not influencing the normal work of the star sensor is very important. The scanning circle observation model designed by the scheme can fully utilize good illumination observation conditions, forms a spiral observation form along with the movement of the GEO zone, and establishes the corresponding relation between the star sensor installation direction, the observation platform track height and the observation coverage percentage.

In the second step, the so-called inclined orbit is an orbit with an orbit inclination angle of 0-90 degrees, and the spacecraft running on the orbit is distributed in the near-ground space. The invention has no special requirements on the number of the track such as the track inclination angle, the track height, the ascension point right ascension, the argument of the near place and the like of the inclined track, and only limits the installation direction of the star sensor to a certain degree, namely the direction of the optical axis of the star sensor of the inclined track is not collinear (generally 30-80 degrees) with the connecting line vector of the geocentric and the observation platform. Fig. 12 shows a case with 12 observation platforms on different inclination inclined tracks.

Simulation analysis of the embodiment:

as shown in fig. 13, the simulation start time is set to be 2024, 3 month, and 21 days, 12 morning and evening sun synchronous tracks and 12 inclined track observation platforms (the track inclination angles are randomly designed to be 10 °, 15 °, 20 °, 25 °, 30 °, 40 °, 45 °, 50 °, 55 °, 65 °, 70 °, and 75 °) are selected to form a common scanning sensing observation configuration of the low-track observation platform for the GEO space debris. Wherein, the heights of the sun synchronous rails in the morning and the evening are respectively 500 km-700 km. For the observation configuration, the observation efficiency is evaluated from two aspects, namely the coverage time and the full coverage time of the observation configuration on different latitude and longitude day domains of the GEO band, and the multiple coverage degree of the observation configuration on different latitude and longitude day domains of the GEO band.

The simulation results are as follows: see fig. 14, 15, 16, 17 and 18.

Fig. 14 and 15 show the maximum, minimum and average coverage time of the general-scan sensing observation configuration for different latitude and longitude areas on the GEO band, respectively. It can be seen that the average 24-hour coverage duration for different latitudinal strips is between 700 seconds and 2000 seconds, the maximum coverage duration is about 2200 seconds (about 36 minutes), the minimum coverage duration is about 500 seconds (about 8 minutes), the coverage durations for different latitudinal strips exhibit different characteristics, longer north-south latitude and shorter middle latitude. The coverage time characteristics of different longitude zones are different from those of the latitude zones greatly, the local part of the longitude zone is more jittering, but the whole longitude zone is more stable, the average coverage time is about 1000 seconds, the minimum coverage time is about 700 seconds, and the maximum coverage time exceeds 2000 seconds.

Fig. 16 shows the percentage of GEO-band coverage in 24 hours, showing that the early-stage coverage increased faster, and the coverage reached 100% after about 23 hours, which was a common-sweep observation configuration that achieved full GEO-band coverage in one day.

Fig. 17 and 18 show the maximum, minimum and average coverage of different latitude and longitude regions on the GEO-band by the normal-scan perceived viewing configuration. It can be seen that the maximum 2-fold coverage is basically maintained in different latitude bands, and only the coverage around 0 degree is 1-fold, because the inclined track observation window is basically intersected with the observation window in the north-south latitude direction of the scanning circle, so that 2-fold coverage is generated, the intersection chance with the coverage around 0 degree is less, and the average multiple coverage is between 1 and 1.5. In terms of longitude, the maximum coverage repeatedly jumps between 1 and 2, the distribution of the maximum coverage along with the longitude is relatively even, and the average coverage is about 1.2.

In conclusion, simulation results show that the response time of the observation configuration to the full coverage of the GEO zone is displayed during coverage, and the normal-scanning sensing configuration can realize the full coverage of the GEO zone in one day and has longer coverage time in different latitudes and longitudes. The multiple coverage is used for showing the condition that the same area is captured by a plurality of star sensors at the same time, which is one of important characteristics that the common scanning perception of the star sensors is different from that of a common space-based observation system, although the maximum coverage weight of a common scanning perception observation configuration is 2, the coverage weight of a plurality of observation platforms cannot be realized, the multiple coverage is still better than the common condition that the existing observation configuration only has a single coverage weight, the single target is ensured to be simultaneously observed by at least 2 observation platforms, and the possibility is provided for the precise orbit determination of space debris.

The embodiment of the invention has the beneficial effects that:

the embodiment of the invention discloses a common-sweep sensing method of a low-orbit observation platform for GEO space debris, which is characterized in that a common-sweep sensing configuration of the low-orbit observation platform for the GEO space debris is established by taking a morning-evening sun synchronous orbit observation platform as a main part and taking an inclined orbit observation platform as a supplement aiming at an observation scene of a low-orbit spacecraft platform star sensor for high-orbit GEO space debris;

selecting spacecrafts which are uniformly distributed as an observation platform in the same altitude interval of the sun synchronous orbit in the morning and evening, and setting the optical axis directions of the star sensors on the observation platform to be consistent so that the star sensors form a scanning circle which takes any point on 90-i declination as the center of a circle and can cover the boundary of the GEO zone as the radius from the optical axis directions of the star sensors; overlapping scanning tracks of a plurality of spacecrafts on the GEO belt to realize common scanning foundation coverage of GEO space fragments; wherein i is the track inclination angle of the synchronous track of the morning and evening sun where the observation platform is;

setting the optical axis direction of a star sensor on the inclined track observation platform to be not collinear with a connecting line vector from the geocenter to the observation platform; and the field of view of the star sensor with the inclined track and the field of view of the star sensor with the sun synchronous track at the morning and evening are in an arc section intersected at the boundary of the scanning circle, so that the coverage of the ordinary scanning foundation of the GEO space fragments is supplemented, and the multiple coverage of the GEO space fragments is realized.

The observation platform of the morning and evening sun synchronous track is used for realizing full coverage of a GEO (geosynchronous orbit), and the observation platform of the inclined track is used as a supplement, and the view field of the inclined track star sensor and the view field of the morning and evening sun synchronous track star sensor point to the boundary area of a scanning circle from a plurality of positions in space in an arc section intersected at the boundary of the scanning circle to form a multi-coverage three-dimensional common scan; the star sensor is used as a dual-purpose sensor, the inherent attitude determination task is completed, and simultaneously, the measurement information of the GEO space debris is detected and extracted from the shot star map, so that the observation efficiency of the star sensor on the GEO space debris is obviously improved, and the ubiquitous perception of the GEO space debris is realized.

In engineering, a spacecraft with a similar rail position as that in the step one can be selected as an observation platform to form a scanning circle observation configuration formed by a morning and evening sun synchronous orbit observation platform, even if the observation platform is possibly distributed uniformly in an unequal phase on the morning and evening sun synchronous orbit, the neutral position caused by unequal phase intervals can be filled by using the quantity advantage and a larger star sensor field angle, and the requirement of full coverage of GEO space fragments within 24 hours is approximately met. And then, respectively adding the inclined tracks as auxiliary observation platforms according to the step two. The observation platform of the morning-and-evening sun synchronous track is used for realizing rapid multiple full coverage of a GEO (geosynchronous orbit) belt, and the observation platform of the inclined track can be used for setting the initial installation direction of a proper star sensor, so that the view field of the inclined track star sensor and the view field of the morning-and-evening sun synchronous track star sensor can form three-dimensional observation on GEO space debris around a scanning circle in an arc section intersected with the boundary of the scanning circle, the revisit degree of observation is increased, and good observation data are provided for subsequent track determination. In conclusion, a common scanning perception configuration of the low-rail observation platform, which is mainly based on the morning and evening sun synchronous orbit observation platform and is supplemented by the inclined orbit, on the GEO space debris can be constructed.

The above description is only for the specific embodiments of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can easily conceive of the changes or substitutions within the technical scope of the present invention, and all the changes or substitutions should be covered within the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the appended claims.

Claims

1. A general scanning sensing method of a low-orbit observation platform for GEO space debris is disclosed, wherein the low orbit comprises a morning and evening sun synchronous orbit and an inclined orbit; the method is characterized by comprising the following steps:

step one, selecting evenly distributed spacecrafts as an observation platform in an interval with the same height of a sun synchronous orbit in the morning and evening, and setting the optical axis directions of star sensors on the observation platform to be consistent so that the star sensors form a scanning circle which takes any point on 90-i declination as a circle center and can cover the boundary of a GEO zone as a radius from the optical axis directions of the star sensors; the scanning tracks of a plurality of spacecrafts on the GEO belt are overlapped to realize the general scanning foundation coverage of the GEO space debris; wherein i is the track inclination angle of the synchronous track of the morning and evening sun where the observation platform is;

setting the optical axis direction of the star sensor on the inclined track observation platform to be not collinear with a connecting line vector from the geocenter to the observation platform; and the field of view of the star sensor with the inclined track and the field of view of the star sensor with the sun synchronous track in the morning and evening are in arc sections intersected at the boundary of the scanning circle, so that the coverage of the ordinary scanning foundation of the GEO space debris is supplemented, and the multiple coverage of the GEO space debris in one day is realized.

2. The method of claim 1, wherein in the first step, the distance difference between the observation platforms of the adjacent star sensors is smaller than or equal to a distance threshold.

3. The method of claim 1, wherein in the first step, the optical axis of the star sensor on the observation platform is pointed to include an elevation angle and an azimuth angle;

in the observation platform orbit coordinate system O _s X _o Y _o Z _o Optical axis L of middle and star sensor _obs And observation platform orbit sub-coordinate system Z _o O _s Y _o The included angle of the plane is an azimuth angle A _z In the orbital coordinate system Z of the observation platform _o O _s Y _o Projection of plane and Y _o The included angle of the axis negative direction is an elevation angle E _l Near to Z _o The positive direction of the shaft is negative, otherwise, the positive direction is positive;

the optical axis pointing optimal elevation angle of the star sensor is the elevation angle of the critical value with the shortest full coverage time of the star sensor to the GEO band; the optimal azimuth angle is the azimuth angle of a critical value with the shortest full coverage time of the star sensor on the GEO belt;

4. The method according to any one of claims 1-3, wherein in step one, the star sensor is pointed at an elevation angle E in the optical axis direction _l And azimuth angle A _z All are not 0 degree, from elevation angle E _l And azimuth angle A _z Calculated radius of the scan circle R _s Comprises the following steps:

wherein,

elevation angle E for pointing of optical axis of star sensor _l And azimuth angle A _z All are not 0 degree, from elevation angle E _l And azimuth angle A _z The radius of the calculated scanning circle;

indicating GEO band on E ₂ Point to D ₂ The distance of the points; wherein D is ₂ Is the intersection point of the X axis and the equator in the celestial coordinate system, E ₂ For the optical axis of the star sensor at XO _E The intersection point of the projection on the Y plane and the equator; o is _E Is the earth's centroid; r is _s1 Is the azimuth angle A in the optical axis direction of the star sensor _z Angle of elevation E when =0 ° _l The radius of the calculated scanning circle; alpha (alpha) ("alpha") _s A long half shaft of a track of the observation platform; alpha is alpha _t The GEO is provided with a long half shaft.

5. The method according to any of claims 1-4, wherein in step one, the star sensor has an azimuth angle A in the optical axis direction _z Angle of elevation E when =0 DEG _l Calculated radius of the scan circle R _s1 Comprises the following steps:

wherein < A > ₁ O _E C ₁ Is an azimuth angle A _z Angle of elevation E when =0 ° _l The calculated radius of the scanning circle; alpha is alpha _s A long semi-axis of a track of an observation platform; alpha (alpha) ("alpha") _t A GEO with a long half shaft; angle A ₁ O _E B ₁ Expressed in terms of the earth's centroid O _E Is a vertex, A ₁ O _E And O _E B ₁ Angle of (A) ₁ Is the intersection point of the star sensor optical axis and the GEO band, B ₁ Is O _s Y _o The intersection of the reverse extension line with the GEO band.

6. The method according to one of claims 1-3, characterized in that in step one, the star sensor optical axis points at an elevation angle E _l When =0 °, measured by azimuth angle a _z Calculated radius of the scan circle R _s2 Comprises the following steps:

wherein,

elevation angle E for pointing of optical axis of star sensor _l Angle of orientation A when = 0% _z The radius of the calculated scanning circle;

indicating GEO band at E ₂ Point to D ₂ The distance of the points;

indicating GEO band on E ₂ Point to C ₂ The distance of the points; d ₂ Is the intersection point of the X axis and the equator in the celestial coordinate system; e ₂ For the optical axis of the star sensor at XO _E The intersection point of the projection on the Y plane and the equator; o is _E Is the earth's centroid; c ₂ Is elevation angle E _l When the angle is 0 degrees, the optical axis of the star sensor points to the intersection point of the GEO band; alpha is alpha _t A GEO with a long half shaft; alpha is alpha _s For observing the long half shaft of the platform track.

7. The method of claim 1, wherein in the first step, when the number of observation platforms on the scan circle is even, the minimum number of observation platforms that ensure that a GEO space debris is detected during a day is:

wherein,

when the number of observation platforms on the scanning circle is even, the minimum number of observation platforms for ensuring the GEO space debris to be detected in one day is ensured; n' represents the number of the view fields of the star sensors rotating on the scanning circle in the process that GEO space debris runs from west to east; omega _t Is the GEO space debris angular velocity; r is _s Is the radius of the scanning circle; omega _s The angular velocity of the observation platform; the size of the field of view of the star sensor is n multiplied by n, n is an arbitrary numerical value taking an angle as a unit, the field of view of different star sensors is different in size and is determined by the design of an optical system;

wherein,

8. The method according to claim 1, wherein in the first step, the sun-synchronous track in the morning and evening has a variation range of the track inclination angle i of 96.67-104.89 ° within a height interval of 300 km-2000 km, and the value of the declination of the center of the scanning circle of the GEO zone is-14.89 ° -6.67 °; the GEO zone is a spherical annular section which takes the earth center as the sphere center, has the orbit height of 36000km and the declination covered by minus 15 degrees to plus 15 degrees.

9. The method of claim 1, wherein in the first step, the locus swept by the star sensor in the GEO spherical toroidal tangent plane is helical.

10. The method according to claim 1, wherein in the second step, the track inclination angle of the inclined track is between 0 ° and 90 °; the installation direction limit range of the star sensor is 30-80 degrees.