CN115563437A - Three-dimensional sensing method for GEO space debris by sun synchronous orbit observation platform - Google Patents
Three-dimensional sensing method for GEO space debris by sun synchronous orbit observation platform Download PDFInfo
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Abstract
The invention discloses a method for three-dimensionally sensing GEO space debris by a sun synchronous orbit observation platform, which comprises the following steps: in the same height interval in the solar synchronous orbit in the morning and evening, different numbers of observation platforms are uniformly distributed, the optical axis directions of the star sensors on the observation platforms are consistent, scanning circles which can cover the boundary of a GEO zone and are used as radii and any point on the GEO zone from 90 degrees to i degrees as the center of a circle are constructed by the optical axis directions of the star sensors, and the tracks of the scanning circles of the different numbers of observation platforms are superposed to realize the three-dimensional sensing basic coverage of GEO space debris; and the observation platform in the non-morning and non-evening sun synchronous track height interval is supplemented by adopting a cross observation mode, so that the full coverage of the stereoscopic perception of the GEO space debris in one day is ensured. The invention solves the design problem of full-time and multi-angle natural intersection observation configuration of the low-orbit observation platform on the GEO space debris, optimizes the observation capability of the low-orbit multi-observation platform on the GEO space debris, and realizes full coverage of the GEO zone in one day.
Description
Technical Field
The invention belongs to the technical field of space situation perception, and relates to a three-dimensional perception method of a solar synchronous 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 the space debris mainly depends on the reflection of sunlight, so that the 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 space debris and the observation platform in the space, the light incident angle and the light emergent angle of the space debris also present dynamic changes, the observation efficiency is low because the star sensor is fixedly connected with the spacecraft body and cannot follow up and track, the detection capability of the star sensor of the observation platform is limited, the imaging of the dark and weak space debris cannot be realized, the imaging under the strong sunlight interference condition cannot be realized, and the full-time and multi-angle observation of the 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 space debris ubiquitous perception conception based on a 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 space debris. 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 space debris itself does not emit light, and forms a point image in the sensor by reflection of sunlight. The ubiquitous sensing observation configuration is closely related to the space debris luminosity calculation process, 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 exit direction, β 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 visible sunlight is a parallel light source in deep space. Since the brightness of the spacecraft in the penumbra region is negligible, the following analysis only considers the occlusion of the ghost of the earth, not the penumbra. For the sun-synchronous orbit, the spatial relationship of the observation platform, the target and the sun is as shown in fig. 2 when viewed from the north pole of the earth. The angle between the sun, the space debris, and the observation platform is called the phase angle.
The luminance calculation of the space debris is carried out in two steps, firstly, the sun is used as a radiation source, and the irradiance and the reflected radiation exitance of the space debris are calculated; and then, calculating the target irradiance received by the star sensor by taking the target as a radiation source. The BRDF from the irradiance of the sun, the target, can be derived as follows:
the radiant flux density is related to the wavelength of the 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 ) A first blackbody radiation constant; c. C 2 =1.438769 (cm · K) as the second blackbody radiation constantλ is the wavelength (. Mu.m) 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 can be approximately equivalent to the irradiance of sunlight when it reaches 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 space debris surface, the radiation intensity of the target can be expressed as:
I v ＝dL v dAcosβ v ＝E Vsun f v (l,v)cosβ l cosβ v dA
let R TO Is the distance of the target from the observation platform, S o Regarding the optical aperture area of the star sensor, and regarding the target as a radiation source, the total radiation flux entering the star sensor is as follows:
by the definition of irradiance, the irradiance of the obtained space debris received by the star sensor is as follows:
known asThe yang sight star is m sun = 26.74, apparent star of space debris, etc. m T Relative to the sun, with respect to the logarithm of irradiance of the two, the apparent star, etc., which can further be targeted, has the following expression:
wherein, star is used to describe the brightness of celestial body, and the smaller the star value, the brighter the celestial body. All the stars and the like in the present invention are all sight stars and the like.
Wherein [ formula (I) ] A f v (l,v)cosθ l cosθ v dA is the optical cross-sectional area (OCS) of the space debris, and is only related to the material, shape, size, and outgoing and incoming angles of the 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, the target runs from a west-side starting point to an east-side end point for 12h, and the sun and the space debris are respectively positioned on two sides of the track surface of the platform, so that the observation platform is always positioned at a favorable observation position for the target.
As the target moves from west to east, the target star, etc. simulation results are shown in fig. 4a and 4 b. Fig. 4a shows the variation trend of the star and the like in the field of view of the star sensor when the GEO target moves from west to east on the summer solstice, and fig. 4b shows the corresponding result in the spring minute. Firstly, the relative position relationship of the sun, the 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 the star and the like shown in the figures 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 target is marked by a dotted line, and the section of the earth shielding the sunlight of the target is marked by a dotted line, namely the target enters the earth ghost area.
It can be seen that when the target is located at a position at a phase angle close to 90 degrees (near the start and end positions), the brightness of the target is extremely low, but as the phase angle decreases, the brightness rises quickly and then fluctuates slowly. If 12 stars are used as the 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 space debris star and the like, the inventor provides a three-dimensional sensing method for GEO space debris by a sun synchronous orbit 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 spatial 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 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 contrast, the invention provides a method for three-dimensionally sensing GEO space debris by a sun synchronous orbit observation platform, which realizes three-dimensional sensing of the GEO space debris by using a plurality of sun synchronous orbit observation platforms in a natural intersection mode. The viewing configuration includes a scan circle made up of a plurality of viewing platforms running on a synchronized track of the morning and evening sun, and a plurality of viewing platforms running on a synchronized track of the non-morning and evening sun. A certain number of observation platforms on the scanning circle can ensure rapid full coverage of the GEO band in one day, and the star sensor of the observation platform of the non-morning and evening sun synchronous orbit 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 observing space debris in full time and at multiple angles, the invention is concretely realized by the following technical scheme:
a three-dimensional sensing method of a solar synchronous orbit observation platform for GEO space debris is disclosed, wherein the solar synchronous orbit comprises a morning and evening solar synchronous orbit and a non-morning and evening solar synchronous orbit; the method comprises the following steps:
step one, in the same height interval in the solar synchronous orbit in the morning and evening, different numbers of observation platforms are uniformly distributed, the optical axis directions of star sensors on the observation platforms are consistent, scanning circles which can cover the boundary of a GEO zone and are used as radii and any point on the 90-i declination of the GEO zone as the circle center are constructed by the optical axis directions of the star sensors, and the tracks of the scanning circles of the different numbers of observation platforms are superposed to realize the three-dimensional sensing basic coverage of 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;
step two, adopting a cross observation mode for an observation platform in the non-morning and evening sun synchronous track height interval to enable the optical axis of the star sensor on the observation platform on the west side track of the non-morning and evening sun synchronous track to point to the east side boundary of the scanning circle, and enabling the optical axis of the star sensor on the observation platform on the east side track of the non-morning and evening sun synchronous track to point to the west side boundary of the scanning circle; and supplementing the three-dimensional perception basic coverage of the GEO space fragments in an arc section where the field of view of the non-morning-and-evening sun synchronous orbit star sensor and the field of view of the morning-and-evening sun synchronous orbit star sensor in the step one intersect at the boundary of the scanning circle, and ensuring the three-dimensional perception full coverage of the GEO space fragments in one day.
In the first step, the distance difference of the observation platforms of the adjacent star sensors is smaller than or equal to a distance threshold value. The observation platforms are distributed at equal intervals or approximately at equal intervals.
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 about 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.
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 observation platform orbit coordinate system O s X o Y o Z o Optical axis L of middle and star sensor obs And an observation platform orbit 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 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 optimal elevation angle is the elevation angle of the critical value with the shortest full coverage time of the star sensor to the GEO belt; the optimal azimuth angle is the azimuth angle of the critical value with the shortest full coverage time of the star sensor on the GEO belt.
In the first step, the star sensor is pointed to the middle elevation angle E of the optical axis l And azimuth angle A z All are not 0 degree, from elevation angle E l And azimuth angle A z Calculated radius R of the sweep circle s Comprises the following steps:
wherein the content of the first and second substances,
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 scanning circle is calculated;
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 Intersection point of projection on Y plane and sky 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 is 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.
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 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 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 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 star sensor is pointed to the middle elevation angle E of the optical axis l Angle of orientation A when = 0% z Calculated radius of the scan circle R s2 Comprises the following steps:
wherein, the first and the second end of the pipe are connected with each other,
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 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; c 2 Is elevation angle E l When the angle is not less than 0 degree, 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.
In the first step, when the number of observation platforms on the scan circle is even, the number of observation platforms detected by GEO space debris in one day is ensured to be the minimum:
wherein the content of the first and second substances,
ensuring the minimum number of observation platforms detected by GEO space debris in one day when the number of observation platforms on the scanning circle is even; n' represents the number of the rotating fields 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 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 on the scanning circle is odd, the minimum number of the observation platforms for ensuring that the GEO space debris is detected in one day is as follows:
wherein, the first and the second end of the pipe are connected with each other,
when the number of observation platforms on the scanning circle is odd, the observation platforms are ensured to be in a normal stateThe minimum number of observation platforms for which GEO space debris is detected in one day is guaranteed; n' represents the number of the view fields rotated 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 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.
In the first step, the track swept by the star sensor on the GEO spherical annular tangent plane is spiral.
The sun synchronous orbit is an orbit in which the precession angular velocity of an orbit surface is equal to the annual apparent motion velocity of the average sun under the shooting condition of the spacecraft. Including morning and evening sun synchronous tracks and non-morning and evening sun synchronous tracks. 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.
In the second step, the pointing direction of the optical axis of the star sensor on the observation platform in the non-morning-and-evening sun synchronous track height interval is specifically as follows:
wherein, beta s Is the pointing angle of the star sensor, a t With the half-axis of length, θ, for GEO E For observing the track surface and O of the platform E Angle of X axis, O E Is the earth's centroid; r s For the radius of the scanning circle when neither the elevation nor the azimuth is 0,
the long half shaft of the orbit of the observation platform.
The invention has the beneficial effects that:
the invention discloses a method for three-dimensional perception of a sun synchronous orbit observation platform on GEO space debris, which is used for constructing a three-dimensional perception configuration which takes a morning and evening sun synchronous orbit observation platform as a main part and takes a non-morning and evening sun synchronous orbit observation platform as a supplement aiming at an observation scene of a low-orbit sun synchronous orbit spacecraft platform on high-orbit GEO space debris;
in the same height interval in the solar synchronous orbit in the morning and evening, different numbers of observation platforms are uniformly distributed, the optical axes of the star sensors on the observation platforms point to be consistent, scanning circles which can cover the boundary of a GEO zone as a radius and take any point on the GEO zone from 90 degrees to i declination as a circle center are constructed by the pointing of the optical axes of the star sensors, and the scanning circle tracks of the different numbers of observation platforms are overlapped to realize the three-dimensional perception foundation coverage of GEO space fragments; wherein i is the track inclination angle of the morning and evening sun synchronous track where the observation platform is located;
the observation platform in the non-morning and evening sun synchronous track height interval adopts a cross observation mode, so that the optical axis of the star sensor on the observation platform on the west side track of the non-morning and evening sun synchronous track points to the east side boundary of the scanning circle, and the optical axis of the star sensor on the observation platform on the east side track of the non-morning and evening sun synchronous track points to the west side boundary of the scanning circle; and supplementing the three-dimensional perception basic coverage of the GEO space fragments in an arc section where the field of view of the non-morning-and-evening sun synchronous orbit star sensor and the field of view of the morning-and-evening sun synchronous orbit star sensor in the step one intersect at the boundary of the scanning circle, and ensuring the three-dimensional perception full coverage of the GEO space fragments in one day.
The observation platform of the morning-and-evening sun synchronous track is used for realizing full coverage of the GEO band, and is supplemented with the observation platform of the non-morning-and-evening sun synchronous track, and in an arc section where the field of view of the non-morning-and-evening sun synchronous track star sensor intersects with the field of view of the morning-and-evening sun synchronous track star sensor at the boundary of the scanning circle in the first step, the field of view points to the boundary area of the scanning circle from a plurality of positions in space to form spatial three-dimensional coverage; the star sensor can detect and extract 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 space debris is remarkably improved, and the ubiquitous sensing of the 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 circular ubiquitous sensing 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 uniform manner, 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, adding an observation platform which takes the non-morning-and-evening sun synchronous track as an auxiliary according to the second step. The observation platform of the synchronous track of morning and evening sun is used for realizing quick multiple full coverage to the GEO area, and the observation platform of the synchronous track of non-morning and evening sun can be pointed through setting up proper star sensor initial installation, so that in the crossing arc segment of the star sensor field of view of the synchronous track of non-morning and evening sun and the star sensor field of view of the synchronous track of morning and evening sun, the object boundary both sides of the scanning circle are formed to observe space debris in a three-dimensional manner, the revisit degree of observation is increased, and good observation data are provided for the follow-up track determination. In conclusion, the three-dimensional sensing configuration of the GEO space debris by the sun synchronous track observation platform mainly based on the morning and evening sun synchronous track observation platform and supplemented by the non-morning and evening sun synchronous track 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 the on-orbit spacecraft 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 the sun synchronous orbit to the GEO orbit is constructed, the residual value of a large number of on-orbit spacecrafts in China can be further excavated, particularly, a large number of low-orbit spacecrafts are provided, the spacecrafts with the star sensor are used as observation platforms as many as possible, 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 the user 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. The invention solves the design problem of full-time and multi-angle natural intersection observation configuration of the low-orbit observation platform on the GEO space debris, expands the orbit types of the observation platform, optimizes the observation capability of the low-orbit multi-observation platform on the GEO space debris, improves the timeliness and realizes the full coverage of the GEO belt in one day.
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 graph showing the time-varying curves of the GEO target stars and the like on the summer solstice.
FIG. 4b is a graph showing the GEO target star etc. in spring minutes and days as a function of time.
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 scan circle in combination with elevation and azimuth.
Fig. 7 is a schematic view of the geometry of the scanning circle for elevation-only correspondence.
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 target 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 top view of a north pole of a non-morning-and-evening sun-synchronous orbit observation configuration.
Fig. 13 is a schematic diagram of the installation orientation of the sun synchronous orbit star sensor in the non-morning and non-evening.
FIG. 14 is a top view of the north pole of a scanning circle and non-morning-and-evening sun synchronous orbit observation configuration.
Fig. 15 is a graph of simulation results of coverage time for GEO-zones of different latitudes within one day of a stereographic configuration.
FIG. 16 is a graph of coverage ratio simulation results for GEO bands for a day for a stereographic configuration.
FIG. 17 is a graph of multiple coverage simulation results for GEO bands at different latitudes within one day for a stereographic configuration.
FIG. 18 is a graph of multiple coverage simulations of a stereo viewing configuration at different longitudes of the GEO band during a day.
Detailed Description
The embodiment of the invention discloses a three-dimensional sensing method for GEO space debris by a sun synchronous orbit observation platform, wherein a star sensor is arranged on the observation platform; the sun synchronous track comprises a morning and evening sun synchronous track and a non-morning and evening sun synchronous track; the method comprises the following steps:
step one, in the same height interval in the solar synchronous orbit in the morning and evening, different numbers of observation platforms are uniformly distributed, the optical axis directions of star sensors on the observation platforms are consistent, scanning circles which can cover the boundary of a GEO zone and are used as radii and any point on the 90-i declination of the GEO zone as the circle center are constructed by the optical axis directions of the star sensors, and the tracks of the scanning circles of the different numbers of observation platforms are superposed to realize the three-dimensional sensing basic coverage of 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;
step two, adopting a cross observation mode for an observation platform in the non-morning and evening sun synchronous track height interval to enable the optical axis of the star sensor on the observation platform on the west side track of the non-morning and evening sun synchronous track to point to the east side boundary of the scanning circle, and enabling the optical axis of the star sensor on the observation platform on the east side track of the non-morning and evening sun synchronous track to point to the west side boundary of the scanning circle; and supplementing the three-dimensional perception basic coverage of the GEO space fragments in an arc section where the field of view of the non-morning-and-evening sun synchronous orbit star sensor and the field of view of the morning-and-evening sun synchronous orbit star sensor in the step one intersect at the boundary of the scanning circle, and ensuring the three-dimensional perception full coverage of the GEO space fragments in one day.
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 space debris uniformly, and the non-uniform distribution can cause a gap between two certain observation platforms to be larger and certain debris 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.
As shown in fig. 14, in the engineering, a spacecraft similar to the orbit position in the step one can be selected as an observation platform to form a scanning circular ubiquitous sensing observation configuration formed by the observation platform of the solar synchronous orbit in the morning and evening, and even though the observation platform may be unevenly distributed in the phase on the solar synchronous orbit in the morning and evening, the observation platform can still fill the neutral position caused by unequal intervals of the phase by using the quantity advantage and the larger field angle of view of the star sensor, and approximately meets the requirement of full coverage of GEO space debris within 24 hours. And then, adding an observation platform which takes the non-morning-and-evening sun synchronous track as an auxiliary according to the second step. The observation platform of the synchronous track of morning and evening sun is used for realizing quick multiple full coverage to the GEO area, and the observation platform of the synchronous track of non-morning and evening sun can be pointed through setting up proper star sensor initial installation, so that in the crossing arc segment of the star sensor field of view of the synchronous track of non-morning and evening sun and the star sensor field of view of the synchronous track of morning and evening sun, the object boundary both sides of the scanning circle are formed to observe space debris in a three-dimensional manner, the revisit degree of observation is increased, and good observation data are provided for the follow-up track determination. In conclusion, the three-dimensional sensing configuration of the GEO space debris by the sun synchronous track observation platform mainly based on the morning and evening sun synchronous track observation platform and supplemented by the non-morning and evening sun synchronous track can be constructed.
In the operation process, each platform can download the observation data (the right ascension, the declination and the observation time of the space debris) to a ground data processing center through inter-satellite and inter-satellite links, and can also perform independent analysis and processing on the satellite to complete the track determination and cataloguing work of the space debris, thereby greatly improving the observation capability of the space debris.
In the first step, the solar synchronous track is in 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 ℃ below zero and 6.67 ℃ 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 an observation platform orbit 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 axis negative direction 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 figure 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, the first and the second end of the pipe are connected with each other,
is elevation angle E l And azimuth angle A z All are not 0 degree, from elevation angle E l And azimuth angle A z The calculated radius of the scanning circle;
bringing E to GEO 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 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 an azimuth angle A z Angle of elevation E when =0 DEG 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 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:
similarly, at Δ B 1 O s O E In the specification, the following are:
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 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 A long half shaft is provided for GEO; 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 the content of the first and second substances,
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 The intersection point of the projection on the Y plane and the 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 long half shaft is provided for GEO; alpha (alpha) ("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.
Space debris on the GEO zone naturally moves around the earth from west to east, and in order to enable the space debris to be observed by sensors distributed on a scanning circle at equal intervals at least once in one orbit period, the mathematical problem of a minimum number of observation platforms exists. 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 band is to realize full coverage in one day, the minimum value of the number of the 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.
Let the view field size of the star sensor be nxn and the angular velocity of the observation platform be omega s GEO targetAngular velocity of 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 target crosses the scan circle twice a day from west to east as shown by the dashed middle line in fig. 10, the critical situation being that the target 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 Angular distance beta from target 2 . Classification discussion, when the number of observation platforms is even, N exists at the moment 2 Symmetrical field of view N j When the target runs 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 an object is detected, the following relationship exists:
on the west side of the scan circle, angular separation β 2 Can be expressed as:
the target is from west to east, and the operation process from entering the scanning circle to entering the east side scanning field of view satisfies the following relation:
where N' represents the number of fields of view rotated over the scan circle during the west-east operation of the target. On the east side of the scan circle, the following relationship holds:
wherein the inequality constrains the target 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 the GEO space debris to be detected in a day is:
wherein the content of the first and second substances,
ensuring the minimum number of observation platforms detected by GEO space debris in one day when the number of observation platforms on the scanning circle is even; n' represents the number of the rotating fields 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 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 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):
when the number of the observation platforms on the scanning circle is odd, the minimum number of the observation platforms for ensuring that the GEO space debris is detected in one day is as follows:
wherein the content of the first and second substances,
when the number of observation platforms on the scanning circle is odd, the minimum number of observation platforms for which GEO space debris is detected in one day is ensured; n' represents the number of the rotating fields 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 To observePlatform angular velocity; 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.
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 section 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 field of view of the star sensor on the GEO zone is realized through the spiral relative motion relationship, 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 repeatedly superposed with each other as far as possible, so that the quick full coverage of space fragments of the GEO zone 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 to observe along with a target through a two-dimensional rotary table, the observation arc section is long, and the efficiency is high; however, the star sensor is used as a 'dual-purpose' sensor, the possibility of follow-up tracking does not exist, and the general scanning of the GEO band can be performed only 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, in order to ensure that the space observation geometry has a longer baseline, which is beneficial to the application of subsequent observation data in the track determination field, on the basis of not influencing the imaging of the star sensor on the sky background, the observation platform on the non-morning-evening sun synchronous track is particularly set to adopt a cross observation mode, as shown in fig. 12, namely, the star sensor of the observation platform on the west side track points to the east area of the scanning circle, and the star sensor of the observation platform on the east side points to the west area of the scanning circle, so that the optical axis of the star sensor on the non-morning-evening sun synchronous track observation platform points to the boundary of the scanning circle in the direction opposite to the direction of the non-morning-evening sun synchronous track observation platform.
And in the second step, the right ascension of the intersection point of the non-morning and non-evening sun synchronous track is not restricted, and the optical axis direction of the star sensor on the observation platform is adjusted only before emission.
Fig. 13 is a top view of the north celestial pole of the earth, which is the same in the opposite direction by taking the east observation platform star sensor as an example of pointing to the boundary region of the west of the scanning circle. The optical axis direction of the star sensor on the observation platform in the non-morning and non-evening sun synchronous track height interval is specifically as follows:
wherein beta is s Is the pointing angle of the star sensor, a t With the half-axis of length, θ, for GEO E For observing the track surface and O of the platform E Angle of X axis, O E Is the earth's centroid; r s For the radius of the scanning circle when neither the elevation nor the azimuth is 0,
for observing the long half shaft of the platform track.
Simulation analysis of the embodiment:
setting simulation starting time to 2024, 3 months and 21 days, and selecting 12 morning and evening sun synchronous tracks and 12 common sun synchronous track observation platforms, wherein the heights of the morning and evening sun synchronous tracks are respectively 500 km-700 km, and the rising points of the other sun synchronous tracks, namely the right ascension points and the track heights are randomly distributed to form a three-dimensional perception observation configuration of the GEO space debris based on the sun synchronous track observation platforms. For the observation configuration, the observation efficiency is evaluated from two aspects, namely the coverage time and the full coverage of the observation configuration on different latitude day domains of the GEO zone, and the multiple coverage of the observation configuration on different latitude and longitude day domains of the GEO zone.
The simulation results are as follows: see fig. 15, 16, 17, 18.
Wherein, fig. 15 shows the maximum, minimum and average coverage duration of the stereo perception observation configuration for different latitudinal regions on the GEO zone. It can be seen that the average observation time of 24 hours of different latitude zones is more than 1000 seconds (about 16 minutes), the maximum observation time exceeds 2500 seconds (about 41 minutes), the minimum observation time exceeds 500 seconds (about 8 minutes), the observation time of different latitude zones presents different characteristics, and the north and south latitude is longer.
Fig. 16 shows the percentage of GEO-strip covered in 24 hours, showing that the percentage of coverage increased faster in the first 2 hours and approached 100% after about 22 hours, which was a stereoscopically observable configuration that achieved full coverage of GEO-strip in one day.
Fig. 17 and 18 show the maximum, minimum and average coverage of the GEO-belts for different latitudinal and longitudinal regions of the stereoscopic viewing configuration. Therefore, the average coverage of different latitudes is about 1.5, and at most 4 star sensors can simultaneously cover the star sensors. The average coverage for different longitudes is also about 1.5, except that it fluctuates more significantly with longitude, with the maximum coverage fluctuating with longitude between 2 and 3.
In conclusion, the simulation result is used for displaying the response time of the observation configuration to the full coverage of the GEO band during coverage, and the multiple coverage is used for displaying the condition that the same area is captured by a plurality of star sensors at the same time, which is one of the important characteristics that the three-dimensional perception of the star sensors is different from that of a common space-based observation system, and the advantage of the number of observation platforms is fully exerted, so that the three-dimensional observation of a single target by a plurality of platforms becomes possible.
It should be noted that all the above analyses are established on the basis of the number of observation platforms stated initially in simulation, and only for evaluating the stereoscopic perception observation efficiency and characteristics of the observation platform based on the solar synchronous orbit on the GEO space debris, which are provided by the present invention, the method of the present invention is not limited to the type and number of the platform orbit, but can be continuously expanded. In engineering, by combining the actual observation platform track and the star sensor direction, the observation efficiency may have slight differences. Considering that the number of star sensors installed on most spacecrafts is more than one, the observation efficiency is further improved if more star sensors and spacecrafts which are possibly launched in the future are brought into the observation configuration.
The embodiment of the invention has the beneficial effects that:
the embodiment of the invention discloses a method for three-dimensional perception of a solar synchronous orbit observation platform on GEO space debris, which is used for constructing a three-dimensional perception configuration mainly comprising a morning-evening solar synchronous orbit observation platform and supplementing a non-morning-evening solar synchronous orbit observation platform aiming at an observation scene of a low-orbit solar synchronous orbit spacecraft platform on high-orbit GEO space debris;
in the same height interval in the solar synchronous orbit in the morning and evening, different numbers of observation platforms are uniformly distributed, the optical axes of the star sensors on the observation platforms point to be consistent, scanning circles which can cover the boundary of a GEO zone as a radius and take any point on the GEO zone from 90 degrees to i declination as a circle center are constructed by the pointing of the optical axes of the star sensors, and the scanning circle tracks of the different numbers of observation platforms are overlapped to realize the three-dimensional perception 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;
an observation platform in the non-morning-and-evening sun synchronous track height interval adopts a cross observation mode, so that the optical axis of the star sensor on the observation platform on the west side track of the non-morning-and-evening sun synchronous track points to the east side boundary of the scanning circle, and the optical axis of the star sensor on the observation platform on the east side track of the non-morning-and-evening sun synchronous track points to the west side boundary of the scanning circle; and supplementing the three-dimensional perception basic coverage of the GEO space fragments in an arc section where the field of view of the non-morning-and-evening sun synchronous orbit star sensor and the field of view of the morning-and-evening sun synchronous orbit star sensor in the step one intersect at the boundary of the scanning circle, and ensuring the three-dimensional perception full coverage of the GEO space fragments in one day.
The observation platform of the morning-and-evening sun synchronous track is used for realizing full coverage of the GEO band, and is supplemented with the observation platform of the non-morning-and-evening sun synchronous track, and in an arc section where the field of view of the non-morning-and-evening sun synchronous track star sensor intersects with the field of view of the morning-and-evening sun synchronous track star sensor at the boundary of the scanning circle in the first step, the field of view points to the boundary area of the scanning circle from a plurality of positions in space to form spatial three-dimensional coverage; the star sensor completes the inherent attitude determination task, and simultaneously detects and extracts space debris measurement information from the shot star map, so that the three-dimensional perception efficiency of the star sensor on the space debris is obviously improved.
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 circular ubiquitous sensing 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 uniform manner, 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, adding an observation platform which takes the non-morning-and-evening sun synchronous track as an auxiliary according to the second step. The synchronous orbital observation platform of morning and evening sun is used for realizing quick multiple full coverage to the GEO area, and non-morning and evening synchronous orbital observation platform of sun can be through setting up proper star sensor initial installation pointing to for in the crossing arc section in the synchronous orbital star sensor field of view of sun sensor field of morning and evening and synchronous orbital star sensor field of view of sun, both formed at scanning circle east-west border both sides department and observed the space piece stereoscopically, increased the revisit degree of observation again, confirm for follow-up track and provide good observation data. In conclusion, the three-dimensional sensing configuration of the GEO space debris by the sun synchronous track observation platform mainly based on the morning and evening sun synchronous track observation platform and supplemented by the non-morning and evening sun synchronous track 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 invention solves the design problem of full-time and multi-angle natural intersection observation configuration of the low-orbit observation platform on the GEO space debris, expands the orbit types of the observation platform, optimizes the observation capability of the low-orbit multi-observation platform on the GEO space debris, improves the timeliness and realizes the full coverage of the GEO belt in one day.
The above description is only for the specific embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in 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 (10)
1. A three-dimensional sensing method of a solar synchronous orbit observation platform for GEO space debris is disclosed, wherein the solar synchronous orbit comprises a morning and evening solar synchronous orbit and a non-morning and evening solar synchronous orbit; the method is characterized by comprising the following steps:
step one, in the same height interval in the solar synchronous orbit in the morning and evening, different numbers of observation platforms are uniformly distributed, the optical axes of star sensors on the observation platforms point to be consistent, scanning circles which can cover the boundary of a GEO zone as a radius and take any point on the 90-i declination of the GEO zone as a circle center are constructed by the pointing of the optical axes of the star sensors, and the scanning circle tracks of the different numbers of observation platforms are overlapped to realize the three-dimensional perception basic 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;
step two, adopting a cross observation mode for an observation platform in the height interval of the non-morning-evening sun synchronous track, so that the optical axis of the star sensor on the observation platform on the west side track of the non-morning-evening sun synchronous track points to the east side boundary of the scanning circle, and the optical axis of the star sensor on the observation platform on the east side track of the non-morning-evening sun synchronous track points to the west side boundary of the scanning circle; and supplementing the three-dimensional perception basic coverage of the GEO space fragments in an arc section where the field of view of the non-morning-and-evening sun synchronous orbit star sensor and the field of view of the morning-and-evening sun synchronous orbit star sensor in the step one intersect at the boundary of the scanning circle, and ensuring the three-dimensional perception full coverage of the GEO space fragments in one day.
2. The method of claim 1, wherein in the first step, the distance difference between the observation platforms of the adjacent star sensors is less than or equal to a distance threshold.
3. The method as claimed in claim 1, wherein in the first step, the solar synchronous orbit is within the range of 300 km-2000 km in height; 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.
4. 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 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 an observation platform orbit 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 optimal elevation angle is the elevation angle of the critical value with the shortest full coverage time of the star sensor to the GEO belt; 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.
5. The method according to any one of claims 1-4, wherein in step one, the star sensor optical axis refers toAngle of elevation E of direction l And azimuth angle A z All are not 0 degree, from elevation angle E l And azimuth angle A z Calculated radius R of the sweep circle s Comprises the following steps:
wherein the content of the first and second substances,
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 is 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.
6. The method according to any one of claims 1-5, 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, angle A 1 O E C 1 Is the azimuth angle A in the optical axis direction of the star sensor z Angle of elevation E when =0 DEG l Calculated scan circleThe radius of (a); alpha is alpha s A long half shaft of a track of the observation platform; alpha is alpha t A GEO with a long half shaft; angle 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.
7. The method according to any one of claims 1-4, wherein in step one, the star sensor is pointed at an elevation angle E in the optical axis direction l When =0 °, measured by azimuth angle a z Calculated radius of the scan circle R s2 Comprises the following steps:
wherein, the first and the second end of the pipe are connected with each other,
for the elevation angle E in the optical axis direction of the star sensor l When =0 °, measured by azimuth angle a 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 star sensor optical axis 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 (alpha) ("alpha") t A GEO with a long half shaft; alpha is alpha s The long half shaft of the orbit of the observation platform.
8. 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 for which a GEO space debris is detected during a day is ensured as follows:
wherein the content of the first and second substances,
when the number of the observation platforms on the scanning circle is even, ensuring the minimum number of the observation platforms for detecting GEO space debris in one day; n' represents the number of the rotating fields 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 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 on the scanning circle is odd, the minimum number of the observation platforms for ensuring that the GEO space debris is detected in one day is as follows:
wherein the content of the first and second substances,
when the number of observation platforms on the scanning circle is odd, the minimum number of observation platforms for detecting GEO space debris in one day is ensured; n' represents the number of the rotating fields 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 star sensor field of view is n multiplied by n, n is an arbitrary number value taking an angle as a unit, and n is notThe size of the field of view of the same star sensor is different and is determined by the design of an optical system.
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 of claim 1, wherein in the second step, the optical axis of the star sensor on the observation platform in the non-morning-and-evening-sun synchronous orbit altitude interval is pointed specifically as follows:
wherein, beta s Is the pointing angle of the star sensor, a t With the semi-axis of length, θ, for GEO E For observing the track surface and O of the platform E Angle of X axis, O E Is the earth's centroid; r s For the radius of the scanning circle when neither the elevation nor the azimuth is 0,
the long half shaft of the orbit of the observation platform.
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