Arbitrary polyhedron spinning space debris space-based observation light variation curve simulation method

Abstract

The invention relates to an arbitrary polyhedron spinning space debris space-based observation light variation curve simulation method. The method comprises the following steps: calculating position vectors of debris and an observation satellite in a geocentric inertial system at the current moment according to orbital elements of the debris and the observation satellite; calculating a sun vector and an observation satellite vector under the debris body system according to the attitude of the debris at the current moment; calculating a sun incident zenith angle and a satellite observation zenith angle of each surface of the debris; calculating the actual effective reflection area of each surface of the fragment; calculating the optical reflectivity of each surface of the fragments based on a BRDF scattering model; calculating the total reflection irradiance of each surface of the fragments; calculating to obtain the apparent magnitude of the fragments at the observation satellite according to an apparent magnitude calculation formula; and on the basis of a preset fragment attitude sequence, repeating the steps to calculate and obtain the light variation curve of the fragments. According to the method, the attitude spinning condition of the debris target is fully considered, and a basis can be provided for designing a space-based debris observation satellite remote sensor and inverting the debris attitude by using the light variation curve.

Description

Technical Field

[0001] The present invention relates to the technical field of space debris space-based observation, and particularly to a simulation method for the light curve of space debris with arbitrary polyhedron spin observed from space-based. Background Art

[0002] With the increasingly frequent space activities of mankind in outer space, the number of space debris has increased sharply, and the space environment is deteriorating day by day. At present, ground-based means cannot effectively monitor small-sized debris, and space-based observation means need to be adopted to make up for the deficiencies of ground-based monitoring capabilities. The difference between space-based platform for debris observation and ground-based observation is that the relative distance between the ground observation station and the space debris is far, and the distance and the change range of the observation phase angle are small and the change speed is slow during the observation. The distance between the space-based platform and the debris is close, and the rendezvous speed of the two is fast, resulting in large amplitude and fast change speed of the distance and the phase angle, and complex change of the debris apparent magnitude. Small-sized space debris has characteristics such as uncontrolled attitude and complex shape. To clarify the design input of space-based debris observation remote sensors, the research on the photometric characteristics of space debris with satellites as space-based observation stations is urgently needed.

[0003] Existing research on the apparent magnitude characteristics of space debris all takes ground observation points as observation stations, and the shape of the debris target is simple, and generally does not consider the attitude spin of the debris target. Summary of the Invention

[0004] In order to solve the technical problems existing in the above-mentioned prior art, the purpose of the present invention is to provide a simulation method for the light curve of space debris with arbitrary polyhedron spin observed from space-based, which fully considers the attitude spin of the debris target and can provide a basis for the design of space-based debris observation satellite remote sensors and the inversion of debris attitude using the light curve.

[0005] To achieve the above-mentioned invention purpose, the present invention provides a simulation method for the light curve of space debris with arbitrary polyhedron spin observed from space-based, including the following steps:

[0006] Step S1: Calculate the position vectors of the debris and the observation satellite in the geocentric inertial system at the current moment according to the orbital elements of the debris and the orbital elements of the observation satellite;

[0007] Step S2: Calculate the position vectors of the sun and the observation satellite in the body coordinate system of the debris according to the attitude of the debris at the current moment;

[0008] Step S3: Establish the normal vectors of the surfaces of the debris in the body coordinate system of the debris according to the surface shape of the debris and its attitude at the current moment;

[0009] Step S4: Obtain the solar incidence zenith angle and the satellite observation zenith angle of each surface of the debris based on the cosine of the angle between the normal vector of each surface of the debris in the debris body coordinate system and the solar vector and the position vector of the observation satellite in the debris body coordinate system;

[0010] Step S5: Calculate the actual effective reflection area of each surface of the debris under the current moment, current attitude, and current position relationship based on the area of each surface of the debris;

[0011] Step S6: Calculate the optical reflectivity of each surface of the debris under the current moment, current attitude, and current position relationship based on the BRDF scattering model;

[0012] Step S7: Calculate the total reflected irradiance received by the observation satellite from each surface of the debris based on the optical reflectivity of each surface of the debris and the distance between the debris and the observation satellite at the current moment;

[0013] Step S8: Calculate the apparent magnitude of the debris at the observation satellite at the current moment according to the apparent magnitude calculation formula;

[0014] Step S9: Based on the preset debris attitude sequence, repeat Steps S1 to S8 at each moment within the specified time period to obtain the light curve of the debris.

[0015] According to a technical solution of the present invention, in Step S1, the position vectors of the debris and the observation satellite in the geocentric inertial system at the current moment are calculated according to the following formula based on the orbital elements of the debris and the orbital elements of the observation satellite, so as to obtain the debris position vector in the geocentric inertial coordinate system at the current moment and the observation satellite position vector I represents that the vector is located in the Earth inertial coordinate system:

[0016]

[0017] where x, y, and z represent the position vectors in the geocentric inertial coordinate system; a is the semi-major axis of the orbit; e is the eccentricity; j is the satellite orbit inclination; ω is the argument of perigee; Ω is the right ascension of the ascending node; f is the true anomaly.

[0018] According to a technical solution of the present invention, in Step S2, calculating the position vectors of the sun and the observation satellite in the debris body coordinate system specifically includes:

[0019] The transformation matrix C from the geocentric inertial coordinate system to the debris centroid orbit coordinate system OI is

[0020]

[0021] The transformation matrix C from the centroid orbit coordinate system of the debris to the body coordinate system of the debris BO where

[0022]

[0023] where φ, θ, and ψ are respectively the roll angle, pitch angle, and yaw angle of the debris at the current moment;

[0024] After the translational attitude matrix is rotated and normalized, the position vectors of the sun and the observation satellite in the body coordinate system of the debris can be obtained and which are expressed as

[0025]

[0026] where B indicates that the vector is located in the body coordinate system of the debris, represents the position vector of the sun in the geocentric inertial coordinate system at the current moment, represents the position vector of the debris in the geocentric inertial coordinate system at the current moment, represents the position vector of the observation satellite in the geocentric inertial coordinate system at the current moment.

[0027] According to a technical solution of the present invention, in the step S3, it specifically includes:

[0028] The outer surface of the debris is composed of n surfaces spliced together, and the normal vector of the i-th debris surface in the body coordinate system of the debris is obtained by converting the normal vector of the i-th debris surface in the geocentric inertial coordinate system, which is expressed as

[0029]

[0030] According to a technical solution of the present invention, in the step S4, the cosine values of the solar incidence zenith angle α(i) and the satellite observation zenith angle β(i) of the i-th debris surface are expressed as

[0031]

[0032]

[0033] According to a technical solution of the present invention, in the step S5, the calculation formula for the actual effective reflection area of each surface of the debris is

[0034]

[0035] where S(i) represents the area of the i-th debris surface.

[0036] According to a technical solution of the present invention, in the step S6, it specifically includes:

[0037] The BRDF model is an ideal Lambertian surface diffuse reflection model, a Phong model, or a Davies model. The BRDF scattering model takes the solar incident zenith angle, the satellite observation zenith angle, and the material surface related characteristic parameters of the surface i of the debris as input parameters to obtain the reflectivity ρ(α(i), β(i)) of the surface i of the debris.

[0038] According to a technical solution of the present invention, in the step S7, it specifically includes:

[0039] The total reflected irradiance E of each surface of the debris received by the observation satellite obs_sum is the sum of the emitted irradiances of each surface of the debris, expressed as

[0040]

[0041] where E sun = 671 W / m 2 , which is the illuminance of the sun at the debris in the visible light band, and R represents the distance between the debris and the observation satellite at the current moment.

[0042] According to a technical solution of the present invention, in the step S8, the apparent magnitude of the debris at the observation satellite at the current moment is

[0043]

[0044] Compared with the prior art, the present invention has the following beneficial effects:

[0045] The present invention proposes a method for simulating the light variation curve of space debris with arbitrary polyhedron spin by space-based observation, fully considering the complexity of the geometric shape of space debris and the time-variability of debris attitude. By defining the debris attitude and the normal vectors of each surface in the body coordinate system, the effective reflection area and reflectivity of each surface of the debris at the current moment and current attitude are calculated respectively. Combining the distance between the debris and the observation satellite, the total irradiance at the observation satellite can be calculated, and thus the apparent magnitude photometric value of the debris can be calculated. The calculation result has high accuracy. By obtaining the light variation curve of space debris with arbitrary polyhedron spin by space-based observation, it can provide a basis for the design of space-based debris observation satellite remote sensors and the inversion of debris attitude using the light variation curve. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following will briefly introduce the drawings required for the embodiments. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0047] Figure 1 Schematic flowchart showing a method for simulating the light curve of space debris observed from space based on an arbitrary polyhedron spin space debris according to an embodiment of the present invention;

[0048] Figure 2 Schematic representation of a reflection model of the surface shape of debris according to an embodiment of the present invention;

[0049] Figure 3 Schematic representation of the shape of debris and the surface normal according to an embodiment of the present invention;

[0050] Figure 4 Schematic representation of the simulation result of the light curve of space debris at the observation satellite according to an embodiment of the present invention. Detailed implementation manners

[0051] The description of the implementation manners of this specification should be combined with the corresponding drawings, and the drawings should be regarded as a part of the complete specification. In the drawings, the shape or thickness of the embodiments may be enlarged and simplified or conveniently marked. Furthermore, each part of the structure in the drawings will be described separately. It should be noted that the elements not shown or described in words in the drawings are in the forms known to those of ordinary skill in the art.

[0052] Any reference to directions and orientations in the description of the embodiments herein is for convenience of description only and should not be construed as any limitation to the scope of protection of the present invention. The following description of the preferred embodiments involves combinations of features, which may exist independently or in combination. The present invention is not particularly limited to the preferred embodiments. The scope of the present invention is defined by the claims.

[0053] As Figure 1 shown, the present invention relates to a method for simulating the light curve of space debris observed from space based on an arbitrary polyhedron spin space debris, specifically including:

[0054] Step S1: Calculate the position vectors of the debris and the observation satellite in the geocentric inertial system at the current moment according to the orbital elements of the debris and the orbital elements of the observation satellite;

[0055] According to the six orbital elements of the satellite, through the following formula, the position vectors of the debris and the observation satellite in the geocentric inertial system at the current moment can be calculated, and the position vector of the debris in the geocentric inertial coordinate system at the current moment and the position vector of the observation satellite I represents that the vector is located in the Earth inertial coordinate system:

[0056]

[0057] Among them, x, y, and z represent the position vectors in the geocentric inertial coordinate system; a is the semi-major axis of the orbit; e is the eccentricity; j is the inclination of the satellite orbit; ω is the argument of perigee; Ω is the right ascension of the ascending node; f is the true anomaly.

[0058] Step S2: Calculate the position vectors of the sun and the observation satellite in the body coordinate system of the debris according to the attitude of the debris at the current moment.

[0059] In step S2, calculating the position vectors of the sun and the observation satellite in the body coordinate system of the debris specifically includes:

[0060] First, convert the position vector from the geocentric inertial coordinate system to the debris centroid orbit coordinate system, and the conversion matrix C OI is

[0061]

[0062] Then, based on the roll angle, pitch angle, and yaw angle of the debris at the current moment, convert the position vector from the debris centroid orbit coordinate system to the debris body coordinate system, and the conversion matrix C BO is

[0063]

[0064] where φ, θ, and ψ are respectively the roll angle, pitch angle, and yaw angle of the debris at the current moment;

[0065] Furthermore, through the rotation normalization of the translation attitude matrix, the position vectors of the sun and the observation satellite in the debris body coordinate system can be obtained and are expressed as

[0066]

[0067] Among them, B represents that the vector is in the debris body coordinate system, represents the sun position vector in the geocentric inertial coordinate system at the current moment, represents the debris position vector in the geocentric inertial coordinate system at the current moment, represents the observation satellite position vector in the geocentric inertial coordinate system at the current moment.

[0068] Step S3: Establish the normal vectors of each surface of the debris in the debris body coordinate system according to the surface shape of the debris and its attitude at the current moment.

[0069] The outer surface of the debris is composed of n surfaces spliced together, as Figure 2 shown. On the debris surface i, is the normal vector of this surface, perpendicular to the surface and pointing outwards, is the unit vector of this debris pointing to the sun, It is the unit vector of the fragment pointing to the observation satellite.

[0070] The normal vector of the i-th fragment surface in the body coordinate system of the fragment It is obtained by converting the normal vector of the i-th fragment surface in the geocentric inertial coordinate system, denoted as

[0071]

[0072] Step S4: According to the cosine of the angle between the normal vector of each surface of the fragment in the body coordinate system of the fragment and the solar vector and the position vector of the observation satellite in the body coordinate system of the fragment, obtain the solar incidence zenith angle and the satellite observation zenith angle of each surface of the fragment;

[0073] In step S4, the cosine values of the solar incidence zenith angle α(i) and the satellite observation zenith angle β(i) of the i-th fragment surface are denoted as

[0074]

[0075] Step S5: According to the area of each surface of the fragment, calculate the actual effective reflection area of each surface of the fragment under the current moment, current attitude and current position relationship;

[0076] For the observation satellite to receive the reflected sunlight from the i-th fragment surface, it is necessary to satisfy that both α(i) and β(i) are in the range of 0 to π / 2. Among all the surfaces of the fragment, only some surfaces meet this condition. If the area of the i-th fragment surface is S(i), then the projection in the direction of the observation satellite.

[0077] Therefore, in step S5, the calculation formula for the actual effective reflection area of each surface of the fragment is

[0078]

[0079] Among them, S(i) represents the area of the i-th fragment surface.

[0080] Step S6: Based on the BRDF scattering model, calculate the optical reflectivity of each surface of the fragment under the current moment, current attitude and current position relationship;

[0081] In step S6, it specifically includes:

[0082] The BRDF model is an ideal Lambertian surface diffuse reflection model, Phong model or Davies model. The BRDF scattering model takes the solar incidence zenith angle, the satellite observation zenith angle and the material surface related characteristic parameters of the i-th fragment surface as input parameters to obtain the reflectivity ρ(α(i), β(i)) of the i-th fragment surface.

[0083] Taking the Davies model as an example, the reflectivity in the observation direction is

[0084]

[0085] Among them, TOA is the total hemispherical reflectance, and δ i is a vector at the azimuth angle on the surface i of the debris, that is, the incident azimuth angle, and δ r is a vector at the azimuth angle on the surface i of the debris, that is, the observation azimuth angle, σ is the root mean square of the surface roughness, and ε is the surface autocorrelation length.

[0086] Step S7: According to the optical reflectance of each surface of the debris and the distance between the debris and the observation satellite at the current moment, calculate the total reflected irradiance of each surface of the debris received by the observation satellite;

[0087] In step S7, it specifically includes:

[0088] The total reflected irradiance E of each surface of the debris received by the observation satellite obs_sum is the sum of the emitted irradiances of each surface of the debris, expressed as

[0089]

[0090] Among them, E sun = 671 W / m 2 , is the illuminance of the sun at the debris in the visible light band, and R represents the distance between the debris and the observation satellite at the current moment.

[0091] Step S8: According to the visual magnitude calculation formula, calculate the visual magnitude of the debris at the observation satellite at the current moment;

[0092] In step S8, the visual magnitude of the debris at the observation satellite at the current moment is

[0093]

[0094] Step S9: Based on the preset debris attitude sequence, repeat steps S1 to S8 at each moment within a specified time period to obtain the light curve of the debris.

[0095] In an embodiment of the present invention, the observation satellite is in a 650 km sun-synchronous dawn-dusk orbit. The space debris is in a 655 km sun-synchronous orbit and is a 10×10×10 cm cube. As Figure 3 shown, the coordinate system O-XYZ is the debris body coordinate system. The debris takes the +Z axis as the spin axis, the spin speed is 6° / s, and the surface is an ideal Lambert scattering surface. When the space debris enters within 100 km of the observation satellite and the included angle between the observation satellite, the space debris, and the sun is within 90°, the simulation of the photometric change curve of the space debris is carried out.

[0096] The simulation results are as Figure 4As shown. The fragment apparent magnitude ranges from 6.5 to 9.5 Mv. Spinning will cause fluctuations in the fragment's luminosity. For example, during the simulation period, the luminosity of the cube-shaped space fragment fluctuates by 0.3 to 2 Mv. Therefore, the optical payload of the observation satellite needs to be adaptively designed for the dynamic range of spinning fragments; the period of luminosity change when the fragment spins is related to the spinning speed and the number of surfaces of the fragment. The period of brightness change is T = 360 / v / s, where v is the spinning speed and s is the number of surfaces of the fragment in the direction parallel to the spin axis. For example, when the cube-shaped fragment spins around the +Z axis, v = 6° / s, s = 4, and the period T = 16 s. This characteristic can be used as a basis for retrieving fragment characteristics from the photometric observation results.

[0097] It should be noted that in this article, the term "including", "comprising" or any other variant thereof is intended to cover non-exclusive inclusion, so that a process, method, article or terminal device including a series of elements not only includes those elements, but also includes other elements not explicitly listed, or further includes elements inherent to such process, method, article or terminal device. Without more limitations, an element defined by the statement "including one..." does not exclude the existence of additional identical elements in the process, method, article or terminal device including the said element.

[0098] Finally, it should be noted that the above description is the preferred embodiment of the present invention. It should be pointed out that although the preferred embodiments of the present invention have been described, for those skilled in the art of this technology, once the basic creative concept of the present invention is known, without departing from the principle described in the present invention, several improvements and refinements can still be made, and these improvements and refinements should also be regarded as the protection scope of the present invention. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications falling within the scope of the embodiments of the present invention.

Claims

1. A simulation method for the light curve of space-based observation of the spin space debris of any polyhedron, characterized in that Including the following steps: Step S1: Calculate the position vectors of the debris and the observation satellite in the geocentric inertial system at the current moment according to the orbital elements of the debris and the orbital elements of the observation satellite; Step S2: Calculate the position vectors of the sun and the observation satellite in the body-fixed coordinate system of the debris according to the attitude of the debris at the current moment; Step S3: Establish the normal vectors of each surface of the debris in the body-fixed coordinate system of the debris according to the surface shape of the debris and its attitude at the current moment; Step S4: Obtain the solar incidence zenith angle and the satellite observation zenith angle of each surface of the debris according to the cosine of the angle between the normal vector of each surface of the debris in the body-fixed coordinate system of the debris and the solar vector and the position vector of the observation satellite in the body-fixed coordinate system of the debris; Step S5: Calculate the actual effective reflection area of each surface of the debris under the current attitude and current position relationship at the current moment according to the area of each surface of the debris; Step S6: Calculate the optical reflectivity of each surface of the debris under the current attitude and current position relationship at the current moment based on the BRDF scattering model; Step S7: According to the optical reflectivity of each surface of the debris and the distance between the debris and the observation satellite at the current moment, calculate the total reflected irradiance received by the observation satellite from each surface of the debris; Step S8: Calculate the apparent magnitude of the debris at the observation satellite at the current moment according to the apparent magnitude calculation formula; Step S9: Based on the preset debris attitude sequence, repeat steps S1 to S8 at each moment within the specified time period to obtain the light curve of the debris.

2. The method for simulating the light curve of the space-based observation of arbitrary polyhedron spin space debris according to claim 1, wherein In step S1, according to the following formula, based on the orbital elements of the debris and the orbital elements of the observation satellite, the position vectors of the debris and the observation satellite in the geocentric inertial system at the current moment are calculated, and the debris position vector in the geocentric inertial coordinate system at the current moment is obtained and the observation satellite position vector I indicates that the vector is in the Earth inertial coordinate system: Wherein, x, y, z represent the position vectors in the geocentric inertial coordinate system; a is the semi-major axis of the orbit; e is the eccentricity; j is the satellite orbit inclination; ω is the argument of perigee; Ω is the right ascension of the ascending node; f is the true anomaly.

3. The method for simulating the light curve of the space-based observation of any polyhedron spin space debris according to claim 2, wherein In step S2, calculating the position vectors of the sun and the observation satellite in the body-fixed coordinate system of the debris specifically includes: The transformation matrix C from the geocentric inertial coordinate system to the debris centroid orbital coordinate system OI is The transformation matrix C from the fragment centroid orbit coordinate system to the fragment body coordinate system BO is Where φ, θ, and ψ are respectively the roll angle, pitch angle, and yaw angle of the debris at the current moment; After rotation normalization of the translation attitude matrix, the position vectors of the sun and the observation satellite in the debris body coordinate system can be obtained and expressed as where B represents the vector in the debris body coordinate system, represents the solar position vector in the geocentric inertial coordinate system at the current moment, represents the debris position vector in the geocentric inertial coordinate system at the current moment, represents the observation satellite position vector in the geocentric inertial coordinate system at the current moment.

4. The method for simulating the light curve of the space-based observation of any polyhedron spin space debris according to claim 3, wherein In step S3, it specifically includes: The outer surface of the fragment is composed of n surfaces spliced together, and the normal vector of the fragment surface i in the fragment's own coordinate system is obtained by converting the normal vector of the fragment surface i in the geocentric inertial coordinate system, denoted as 5. The method for simulating the light curve of the space-based observation of any polyhedron spin space debris according to claim 4, characterized in that, In step S4, the cosine values of the solar incidence zenith angle α(i) and the satellite observation zenith angle β(i) of the debris surface i are expressed as 6. The method for simulating the light curve of the space-based observation of any polyhedron spin space debris according to claim 5, characterized in that In step S5, the calculation formula for the actual effective reflection area of each surface of the debris is Wherein, S(i) represents the area of the debris surface i.

7. The method for simulating the light curve of the space-based observation of any polyhedron spin space debris according to claim 6, wherein In step S6, it specifically includes: The BRDF model is an ideal Lambertian surface diffuse reflection model, a Phong model, or a Davies model. The BRDF scattering model takes the solar incidence zenith angle, the satellite observation zenith angle, and the material surface related characteristic parameters of the debris surface i as input parameters to obtain the reflectivity ρ(α(i), β(i)) of the debris surface i.

8. The method for simulating the light curve of the arbitrary polyhedron spin space debris space-based observation according to claim 7, wherein In step S7, it specifically includes: The total reflected irradiance E of each surface of the debris received by the observation satellite obs_sum is the sum of the emitted irradiances of each surface of the debris, expressed as Among them, E sun = 671 W / m 2 , is the illuminance of the sun in the visible light band at the debris, and R represents the distance between the debris and the observation satellite at the current moment.

9. The method for simulating the light curve of any polyhedron spin space debris space-based observation according to claim 8, wherein In step S8, the apparent magnitude of the debris at the observation satellite at the current moment is

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