Geo target coverage analysis method based on field of view mapping model

Abstract

This invention discloses a GEO target coverage analysis method based on a field-of-view mapping model, comprising: constructing the payload apparent element equation for the observation of the GEO target by the space-based observation platform based on the geometric relationship between the space-based observation platform and the GEO target; and using the longitude Ω of the ascending node as the basis for the analysis. G Establish a two-dimensional coordinate plane (Ω) with the horizontal axis as the x-axis and the latitude argument u as the y-axis. G ,u), and calculate the analytical solution of the load apparent element equation to obtain the plane (Ω). G The field of view mapping domain of the space-based observation platform to the GEO target; the trajectory of the space-based observation platform is projected onto the plane (Ω). G The invention utilizes the field of view mapping domain and the trajectory of the space-based observation platform to obtain the visibility window of the space-based observation platform for GEO targets. Applied to the field of space-based observation, this invention is applicable to the visibility analysis of GEO and quasi-GEO targets by any type of payload on a space-based observation platform, and is highly efficient, effectively ensuring space safety.

Description

Technical Field

[0001] This invention relates to the field of space-based observation technology, specifically a GEO target coverage analysis method based on a field-of-view mapping model. Background Technology

[0002] Geostationary orbit (GEO) spacecraft are high-value space assets and important targets in space situational awareness. The space situational awareness system includes ground-based surveillance systems and space-based space surveillance systems. Space-based observation-based space target surveillance has characteristics such as on-orbit operation, large field of view, and all-weather capability, which can meet the requirements for continuous monitoring, tracking, and precise orbit determination of space targets. The calculation of the visibility window of space targets by the payloads carried by space-based observation platforms is the basis for orbit determination and mission planning; therefore, it is essential to conduct coverage analysis research on GEO targets by space-based observation platforms.

[0003] While a significant amount of research has been conducted on satellite coverage analysis of ground targets, research on space target coverage analysis remains relatively limited. In existing technologies, Lawton developed a Fast Fourier Transform (FFT) method for calculating satellite-to-satellite observation intervals. Sun et al. studied inter-satellite link communication, considering the Earth's occlusion of the inter-satellite line of sight, and introduced curve fitting to approximate the visibility function to calculate the visibility window. Wang et al. used a surrogate model method to fit the visibility function curve and solve for the inter-satellite visibility window. To address the challenge of large-scale node spatial computation, Li et al. introduced the concept of a global spatial grid and proposed an efficient computational method for constellation spatial interconnection. Yang et al. proposed a method for determining occultation windows between low-Earth orbit (LEO) satellites. This method reduces the sampling steps in adaptive methods and improves the solution efficiency of numerical methods by deriving the position and velocity equations of the occultation tangency point. Similarly, for the problem of occultation orbit design and window calculation between LEO satellites, Li et al. proposed a fast numerical calculation method for occultation events using a linear J2 perturbation model, and further realized orbit design for point target revisits by characterizing the revisit conditions of occultation events for specified targets. The above studies all used numerical methods for calculation. The methods have good versatility, but the solution process still consumes relatively more computational resources and time, and will still face computational difficulties in the context of large-scale constellations and massive observation missions.

[0004] While some studies have proposed analytical calculation methods for ground target coverage problems—for example, Zhang et al. proposed a payload field-of-view mapping method based on geometric analysis, which can be used to calculate the visible window of satellites for ground targets; and Gu et al. proposed an equivalent field-of-view mapping domain considering the influence of ground elevation angle constraints, for analytically analyzing satellite Earth observation payload coverage problems under elevation angle constraints—there is currently no analytical solution for space target coverage analysis. Summary of the Invention

[0005] To address the shortcomings of the existing technologies, this invention provides a GEO target coverage analysis method based on a field-of-view mapping model. This method is applicable to the visibility analysis of GEO and quasi-GEO targets on the field of view of any type of payload on space-based observation platforms, and is highly efficient, effectively ensuring space safety.

[0006] To achieve the above objectives, this invention provides a GEO target coverage analysis method based on a field-of-view mapping model, comprising the following steps:

[0007] Step 1: Based on the geometric relationship between the space-based observation platform and the GEO target, construct the payload apparent equation for the space-based observation platform's observation of the GEO target;

[0008] Step 2, using the longitude Ω of the ascending node G Establish a two-dimensional coordinate plane (Ω) with the horizontal axis as the x-axis and the latitude argument u as the y-axis. G The load apparent element equation is calculated, and the analytical solution is obtained to obtain the two-dimensional coordinate plane (Ω). G ,u) Field of view mapping domain of the space-based observation platform for GEO targets;

[0009] Step 3: Project the trajectory of the space-based observation platform onto the two-dimensional coordinate plane (Ω). G On the plane (Ω), and based on the two-dimensional coordinate plane (Ω). G The intersection of the field of view mapping domain described above and the trajectory of the space-based observation platform is used to obtain the visible window of the space-based observation platform for the GEO target, thus completing the coverage analysis of the space-based observation platform for the GEO target.

[0010] Compared with the prior art, the present invention has the following beneficial technical effects:

[0011] 1. This invention applies the field-of-view mapping domain method to space-based target perception missions, establishes the payload-view element equation for GEO target observation, calculates the analytical solution of the payload-view element equation, and then obtains the field-of-view mapping domain on a two-dimensional plane. This transforms the problem of calculating the observation window of space-based resources for targets into a trajectory intersection problem, enabling rapid coverage analysis and window solving.

[0012] 2. In the preferred embodiment of this invention, for the problem of GEO target coverage at different orbital altitudes, the concept of equivalent rotational angular velocity is proposed, which transforms the translational motion of the field of view mapping domain into the slope change of the satellite trajectory, thereby extending the GEO target coverage analysis method to space targets at different orbital altitudes;

[0013] 3. In the preferred embodiment, this invention proposes a constellation field-of-view mapping domain based on the concept of relative mapping, which can realize coverage analysis of homogeneous satellite constellations, transforming the problem of multi-satellite coverage of space targets into a time-invariant, multi-mapping-domain single-satellite coverage problem, thus accelerating the coverage analysis process. Attached Figure Description

[0014] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.

[0015] Figure 1 This is a flowchart of the GEO target coverage analysis method based on the field-of-view mapping model in an embodiment of the present invention;

[0016] Figure 2 This is a schematic diagram of a space-based situational awareness scenario in an embodiment of the present invention;

[0017] Figure 3 This is a schematic diagram of the payload installation coordinate system of the space-based observation platform in an embodiment of the present invention;

[0018] Figure 4 This is a schematic diagram of the observation of the GEO target by the on-orbit platform payload visual element in an embodiment of the present invention;

[0019] Figure 5 This is a diagram showing the relationship between the operating trajectory of the space-based observation platform and the field of view mapping domain in an embodiment of the present invention;

[0020] Figure 6 This is a schematic diagram showing the relative positional relationship between stars A and B in an embodiment of the present invention;

[0021] Figure 7 This is a schematic diagram illustrating the relationship between the two-dimensional plane motion trajectory of satellites A / B and the field of view mapping domain in an embodiment of the present invention;

[0022] Figure 8 This is a schematic diagram illustrating the relationship between the trajectory of satellite A in a two-dimensional plane and the mapping domain in an embodiment of the present invention;

[0023] Figure 9 This is a schematic diagram of the field of view mapping of the space-based observation platform for different GEO targets in an embodiment of the present invention;

[0024] Figure 10 This is a schematic diagram of the field-of-view mapping domain of the target for different observation payloads in an embodiment of the present invention;

[0025] Figure 11 This is a schematic diagram of the coverage analysis results for a quasi-GEO target with a semi-major axis of 35,000 km in an embodiment of the present invention;

[0026] Figure 12 This is a schematic diagram of the field-of-view mapping domain results of the constellation to the GEO target in an embodiment of the present invention;

[0027] Figure 13 This is a schematic diagram of the field-of-view mapping result of the rectangular payload constellation aligned with the GEO target in an embodiment of the present invention.

[0028] The realization of the objective, functional features and advantages of the present invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0029] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0030] Furthermore, the technical solutions of the various embodiments of the present invention can be combined with each other, but only if they are feasible for those skilled in the art. If the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention.

[0031] This embodiment discloses a GEO target coverage analysis method based on a field-of-view mapping model, primarily addressing the mission requirements of space-based situational awareness. It models and analyzes the coverage problem of high-orbit space targets, employing a viewfinder description method to model the payload viewfinders of the space-based observation platform. Through geometric analysis of the space-based observation platform, the GEO target, and the payload viewfinders, a viewfinder mapping equation is established, yielding the field-of-view mapping domain of the space-based observation platform over the GEO target. Then, on a two-dimensional plane, the visible window for the GEO target is quickly determined using the trajectory intersection method. The GEO target coverage analysis method in this embodiment is applicable to target coverage analysis of any type of payload field of view. Furthermore, by designing the rotation angular velocity of an equivalent virtual Earth, the applicability of this method can be extended to zero-tilt space targets at different orbital altitudes. In addition, this embodiment extends the single-star coverage analysis method to multiple stars and constellations based on the concept of relative mapping, achieving rapid constellation coverage of space targets.

[0032] refer to Figure 1 The GEO target coverage analysis method based on the field-of-view mapping model in this embodiment specifically includes the following steps:

[0033] Step 1: Based on the geometric relationship between the space-based observation platform and the GEO target, construct the payload apparent equation for the space-based observation platform's observation of the GEO target;

[0034] Step 2, using the longitude Ω of the ascending node G Establish a two-dimensional coordinate plane (Ω) with the horizontal axis as the x-axis and the latitude argument u as the y-axis. G The equations for the load apparent elements are calculated, and the analytical solution is obtained to obtain the two-dimensional coordinate plane (Ω). G ,u) Field of view mapping domain of the space-based observation platform for GEO targets;

[0035] Step 3: Project the trajectory of the space-based observation platform onto the two-dimensional coordinate plane (Ω). G On the plane (Ω), and based on the two-dimensional coordinate plane (Ω). G The intersection of the upper field of view mapping domain and the trajectory of the space-based observation platform is used to obtain the visible window of the space-based observation platform on the GEO target, thus completing the coverage analysis of the space-based observation platform on the GEO target.

[0036] Space-based situational awareness refers to the observation of space targets using space-based equipment to obtain corresponding measurement information. Compared with satellite-based Earth observation missions, the relative motion relationship between the observation platform and the target in space target awareness missions is more complex, and target coverage analysis requires separate research. For example... Figure 2 As shown, this embodiment studies the situational awareness scenario of high-orbit space targets. The space-based observation platform is a low-orbit spacecraft, and the imaging payload it carries has a specific field of view. Considering the geometric visibility of the space-based observation platform to GEO targets, when the GEO target is within the payload coverage area of ​​the space-based observation platform, it is considered that a visible window exists.

[0037] The GEO target coverage analysis method in this embodiment mainly targets the geometric coverage characteristics of targets by space-based observation payloads. To highlight the characteristics of the problem, the following assumptions are made for the specific scenario:

[0038] 1) Assuming the imaging payload on the space-based observation platform is installed in the zenith direction, the Earth's obstruction of the line of sight can be avoided;

[0039] 2) Ignoring the backlight interference from sunlight and the ground shadow constraint effect of visible light load, constraint processing can be performed after geometric coverage analysis is completed;

[0040] 3) Considering the large distance between the space-based observation platform and the high-orbit target, the size of the observation target is ignored, and it is regarded as a point target;

[0041] 4) Ignore the detection distance constraint of the observation payload.

[0042] The above assumptions are all constraints for spatial target perception. After obtaining the visible window, the target can be filtered and post-processed according to the constraint discrimination conditions. Therefore, this embodiment will not elaborate on them.

[0043] In this embodiment, the image payload of the space-based observation platform is defined using the image pixel description method. By characterizing the boundary of the image payload through discrete image pixel vectors, the field of view coverage can be represented. Specifically, the payload image pixel vector is denoted as n. s Define it in the load installation coordinate system, which is the load installation coordinate system. Figure 3 Sx in s y s z s Let the azimuth and elevation angles of the load's view vector in the load installation coordinate system be α and β, respectively. When using M discrete view vectors to describe the boundary of the satellite load's field of view, the angle definition of the load's field of view can be written as:

[0044] FOV M ={(α1,β1),(α2,β2),...,(α M ,β M )} (1)

[0045] Among them, FOV M Let α1, ..., α be the angles of the load's field of view. M Let β1, ..., M be the azimuth angles of the view element vectors. M The pitch angles are the first, ..., Mth view vectors.

[0046] It should be noted that space-based observation platforms are generally low-Earth orbit spacecraft, and the imaging payload for observing GEO targets involves an installation matrix transformation between the platform and its own architecture. For ease of subsequent analysis, this embodiment assumes the installation matrix of the imaging payload is as follows: Figure 2 As shown. Where Sx b y b z b Let x be the body coordinate system of the space-based observation platform. s The horizontal axis direction of the load field of view is represented by y. s Let R represent the vertical axis direction of the payload's field of view. Then, the coordinate transformation matrix R between the payload installation matrix and the coordinate system of the space-based observation platform is... bs for:

[0047]

[0048] The payload apparent vector in the body coordinate system of the space-based observation platform is represented as follows:

[0049]

[0050] Where, {n s} b The representation of the payload apparent vector in the body coordinate system of the space-based observation platform, {n s} s This represents the load visual element vector in the load mounting coordinate system.

[0051] In the observation mission of GEO targets by the space-based observation platform, the payload apparent vector n s The pointer is as follows Figure 4 As shown, where r s r represents the position vector of the on-orbit space-based observation platform. g The vector represents the position of the GEO target, and ρ represents the distance between the on-orbit space-based observation platform and the GEO target. When the apparent vector n... s When the projection point on the GEO orbit coincides with the position of the GEO target, the geometric equation between the payload image of the space-based observation platform and the GEO target can be established as follows:

[0052] r s +ρ·n s =r g (4)

[0053] The position vector r of the space-based observation platform s Projecting onto the geocentric inertial coordinate system (ECI), the coordinate transformation relationship is as follows:

[0054]

[0055] Among them, {r s} I For position vector r s In the geocentric inertial coordinate system (ECI), x0 = [1, 0, 0]. T Let be the identity matrix, T be the transpose of the matrix, a be the semi-major axis of the space-based observation platform's orbit, e be the orbital eccentricity, i be the orbital inclination, Ω be the right ascension of the ascending node, ω be the argument of perigee, u be the argument of latitude, and u = ω + θ, where θ is the true anomaly angle, R x R y R z These represent the coordinate transformation matrices for rotating around the x, y, and z axes by the corresponding angles.

[0056] In this embodiment, the transformation relationship between the geocentric inertial coordinate system ECI and the geocentric Earth-fixed coordinate system ECEF can be obtained through Greenwich sidereal time α. G The conversion calculation is performed as follows:

[0057] {r s} e =R z (α G ){r s} I (6)

[0058]

[0059] Among them, {r s} e For position vector r s Representation in the Earth-centered Earth-fixed coordinate system ECEF For Greenwich Mean Time at time t0, ω E The angular velocity of Earth's rotation is represented by t, which is a time parameter.

[0060] Furthermore, the position vector r of the space-based observation platform s The representation in the geocentric-fixed coordinate system ECEF coordinate system is as follows:

[0061]

[0062] Among them, Ω G =Ω-α G The geographical longitude of the ascending node is called the ascending node longitude.

[0063] Assuming the space-based observation platform coincides with the orbital coordinate system, then the payload apparent vector n s The transformation relationship to the ECEF coordinate system is as follows:

[0064] {n s} e =R z (-Ω G )R x (-i)R z (-u)R o′o {n s} b (9)

[0065]

[0066] Where, {n s} e For the load view element vector n s In the Earth-centered Earth-fixed coordinate system ECEF, R is represented as... o′o This is the transformation matrix between the orbital coordinate systems;

[0067] Combining equations (3), (9), and (10), the load apparent vector n can be obtained. s The representation in the geocentric-fixed coordinate system ECEF is:

[0068]

[0069] Next, we need to input the position vector r of the GEO target. g Projected onto the ECEF coordinate system, when the GEO target is stationary relative to the Earth, the latitude and longitude of its projection point on the Earth's surface are denoted as... Therefore, the transformation relationship from the spherical coordinate system to the ECEF coordinate system can be obtained as follows:

[0070]

[0071] Among them, {r g} e For position vector r g In the Earth-centered Earth-fixed coordinate system ECEF, a0 is the semi-major axis of the GEO target's orbit;

[0072] Finally, substituting equations (8), (11), and (12) into equation (4), we can obtain the payload apparent element equation of the space-based observation platform, which is:

[0073]

[0074] The payload visual element equation in this embodiment involves the projection of orbital features and payload visual element parameters onto the ECEF coordinate system. Furthermore, the time parameter t is implicit in this payload visual element equation, which correlates the payload field-of-view parameters of the space-based observation platform, the satellite's orbital features, and the target's visibility window. By solving this payload visual element equation, the visibility window between the space-based observation platform and the GEO target can be calculated.

[0075] When the orbital eccentricity of the celestial observation platform is 0, the load apparent element equation (13) can be simplified to:

[0076]

[0077] Due to the coordinate transformation matrix R z (-Ω G ), R x (-i), R z (-u), R z (-λ), Since all are orthogonal matrices, coordinate transformation does not change the length of the multiplied vector. Therefore, in this embodiment, the intermediate parameter n0 is set as:

[0078] n0=[sin(β)cos(α)cos(β)sin(α)cos(β)] T (15)

[0079] By taking the inner product of both sides of equation (14), all transformation matrices can be removed, and the following result is obtained:

[0080]

[0081] Equation (16) contains only the unknown ρ, and can be rearranged as follows:

[0082]

[0083] Therefore, we can solve for:

[0084]

[0085] Because a0 >> a, therefore This holds true, and it is known that ρ2 > 0 and ρ1 < 0. The physical meaning of ρ1 refers to the intersection point of the opposite direction of the apparent vector of the space-based observation platform and the great circle containing the geosynchronous orbit. Therefore, in this embodiment, ρ2 is selected as the distance from the space-based observation platform to the GEO target, i.e., in this embodiment...

[0086] To further solve equation (14), this embodiment introduces intermediate parameters λ0, The following conditions must be met:

[0087]

[0088] Substituting equations (15) and (18) into equation (19) yields the intermediate variable λ0. The expression is:

[0089]

[0090] Substituting equations (19) and (20) into equation (14), we get:

[0091]

[0092] By rearranging and simplifying, equation (21) can be rearranged as follows:

[0093]

[0094] Let the intermediate parameters γ and Ω λ Satisfying γ=u+λ0、Ω λ =Ω G -λ, we can obtain:

[0095]

[0096] Let the intermediate parameters Ψ and Θ be:

[0097]

[0098] From equation (23), it can be seen that the intermediate parameters γ and Ωλ Both have two sets of solutions γ1 and Ω. λ1 With γ2, Ω λ2 They are respectively:

[0099]

[0100] Where Π is pi. According to equations (25) and (26), the intermediate parameters γ and Ω are... λ There are four possible combinations of values ​​for , but at the same time, its value must simultaneously satisfy the third equation in equation (23). Due to the change in the sign of the trigonometric function, it can be seen that the combination of solutions will degenerate from four groups to two groups. Therefore, in this embodiment, (γ1,Ω) in equations (25) and (26) are first set. λ1 ) and (γ2,Ω λ2 ) represents intermediate parameters γ and Ω λ Find the two correct solutions for Anzu and substitute them into... Perform verification; if the verification passes, directly output (γ1, Ω). λ1 ) and (γ2,Ω λ2 Otherwise, let:

[0101]

[0102] Then output a new (γ1,Ω) λ1 ) and (γ2,Ω λ2 );

[0103] After the above analysis of the intermediate parameters γ and Ω λ By judging and adjusting the solution, we can ensure that equation (23) always holds true, and finally obtain the analytical solution of the load apparent element equation:

[0104]

[0105] Among them, (u1,Ω) G1 ) and (u2,Ω G2 This is the load apparent element equation with respect to the latitude argument u and the ascending node longitude Ω. G The two sets of analytical solutions, corresponding to the two-dimensional coordinate plane (Ω) G The two field-of-view mapping domains of the space-based observation platform for the GEO target.

[0106] According to equations (28) and (29), for a given view element vector (α,β), the view element equation has two sets of real roots (u1,Ω). G1 ) and (u2,Ω G2 Based on this, this embodiment introduces a time-invariant field-of-view mapping domain. A two-dimensional coordinate plane (Ω) is defined. G ,u), where the horizontal axis represents the longitude of the ascending node Ω. GThe vertical axis represents the latitudinal argument u. Given the parameters of the celestial observation platform and the position of the GEO target, two sets of mapping domains (u, Ω) can be obtained regarding the payload field-of-view parameters (α, β). G Furthermore, the result of the field-of-view mapping can be completely determined by (α,β) and the analytical solution of the load element equation, and the resulting field-of-view mapping domain has time-invariant properties. Solving the load element equation yields a two-dimensional coordinate plane (Ω). G If the instantaneous trajectory of the space-based observation platform is within the field of view mapping domain on the ,u), it indicates that the payload of the space-based observation platform can observe the GEO target.

[0107] In this embodiment, when the GEO target is stationary relative to the Earth, the trajectory of the space-based observation platform is projected onto the two-dimensional coordinate plane (Ω). G The process of determining the visible window of GEO targets on the ground and on the space-based observation platform is as follows:

[0108] When considering the J2 orbital perturbation, the latitudinal argument u and the longitude Ω of the ascending node of the circular orbit space-based observation platform... G The average rate of change is:

[0109]

[0110] Among them, K u R is the rate of change of latitude angle, μ is the Earth's gravitational constant, and R is the Earth's gravitational constant. E K is the semi-major axis of the Earth. Ω ω is the rate of change of longitude at the ascending node. E This is the Earth's rotational angular velocity;

[0111] Because of K u K Ω All are parameters, therefore the space-based observation platform is in the two-dimensional coordinate plane (Ω) G The movement on (u) can be represented as a series of equidistant lines with a fixed slope K, as follows:

[0112]

[0113] This allows us to plot the space-based observation platform in a two-dimensional coordinate plane (Ω). G The projection of the motion trajectory onto the field of view (u) can provide the visible time interval of the payload's field of view for the GEO target when the trajectory intersects with the field of view mapping domain. For example... Figure 5 As shown, it is clear which orbital period the platform has a visible window for the GEO target. By calculating the coordinates of the trajectory intersection points and combining them with the orbital period and the slope of the trajectory of the on-orbit space-based observation platform, the visible window of the space-based observation platform for the GEO target can be quickly obtained.

[0114] It is worth noting that the GEO target coverage analysis method in this embodiment is not only applicable to static GEO targets, but also to zero-inclination space orbit targets with different orbital altitudes, i.e., those whose rotational angular velocity is similar to that of the Earth's rotational angular velocity ω. E Different GEO targets are defined as quasi-GEO targets in this embodiment. Compared to GEO targets, the angular velocity of quasi-GEO targets is related to the Earth's rotation angular velocity ω. E The difference is that the sub-satellite point of a space target will move at a constant speed along the equator, in (Ω) G On the plane, the shape of the equivalent field of view mapping domain remains unchanged, but its position changes over time. When performing coverage analysis on space targets at different orbital altitudes, we can assume the existence of a virtual Earth with a rotational angular velocity ω′. E If the rotational angular velocity of the quasi-GEO target is the same, and the parameters such as Earth's perturbation force, semi-minor axis, and gravitational constant are the same as those of the real Earth, then the calculation process of equations (13) to (32) can also be applied. The parameter of Earth's rotational angular velocity only affects K in equation (31). Ω Calculation, and thus affect Figure 5 The slope of the trajectory of the China Space-based observation platform affects the coverage analysis results.

[0115] In this embodiment, when the rotational angular velocity of the GEO target is equal to the rotational angular velocity of the Earth ω... E At the same time, the trajectory of the space-based observation platform is projected onto the two-dimensional coordinate plane (Ω). G The process of determining the visible window of GEO targets on the ground and on the space-based observation platform is as follows:

[0116] Imagine a virtual Earth with a rotational angular velocity ω′. E It has the same rotational angular velocity as the GEO target, making its Earth perturbation force, semi-major axis, semi-minor axis, and Earth gravitational constant the same as the real Earth;

[0117] When considering the J2 orbital perturbation, the latitude argument u and the longitude Ω of the ascending node of the space-based observation platform are obtained. G The average rate of change is:

[0118]

[0119] Because of K u K Ω All are parameters, therefore the space-based observation platform is in the two-dimensional coordinate plane (Ω) G The movement on (u) can be represented as a series of equidistant lines with a fixed slope K, as follows:

[0120]

[0121] This allows us to plot the space-based observation platform in a two-dimensional coordinate plane (Ω). G By projecting the motion trajectory onto the field of view (u), when the trajectory intersects with the field of view mapping domain, the visible time interval of the payload's field of view for the GEO target can be given.

[0122] In the specific implementation process, the rotational angular velocity of the GEO target and the rotational angular velocity ω′ of the virtual Earth are... E The calculation process is as follows:

[0123] Considering the shift of the ascending node Δλ1 caused by the Earth's rotational angular velocity and the shift of the ascending node Δλ2 caused by the Earth's oblateness, the following equation is established:

[0124] Δλ1+Δλ2=-2π (36)

[0125]

[0126] Where, ω S The rotational angular velocity of the GEO target;

[0127] Combining equations (36), (37), and (38), we can obtain the simplified result when the orbital eccentricity of the celestial observation platform is 0, which is:

[0128]

[0129] When the orbital inclination of the celestial observation platform is i = 0, further simplification yields:

[0130]

[0131] Substituting the semi-major axis of the GEO target at different orbital altitudes into formula (40), the rotational angular velocity ω of the GEO target can be obtained. S And the rotational angular velocity ω′ of the virtual Earth E =ω S .

[0132] In practical applications, this embodiment is not only applicable to the coverage analysis of a single satellite over a GEO target, but also to application scenarios involving multiple observation satellites. To provide a unified expression, this embodiment assumes that the payload field of view of each satellite is the same. Based on equation (14), it can be seen that the field of view mapping domain of a satellite depends on the satellite's orbital altitude, inclination, payload field of view, and the position of the target satellite. Therefore, for any satellite in a homogeneous satellite constellation, the field of view mapping domain of each satellite over the same observation target is the same. However, due to the different latitudinal argument and right ascension of the ascending node of each satellite, the orbital trajectories of different satellites differ. For two satellites A and B in the constellation, such as Figure 6 As shown, the relative ascending node right ascension ΔΩ between the two is... BA relative latitude argument ΔuBA for:

[0133]

[0134] Among them, Ω A u A These are the right ascension and latitude argument of the ascending node of star A, Ω. B u B These are the right ascension and latitude argument of the ascending node of star B.

[0135] Since stars A and B have the same orbital altitude and inclination, the relative latitude argument Δu is considered when taking into account the J2 perturbation condition. BA Right ascension ΔΩ of the relative ascending node BA Given that the apparent pixel mapping equations for stars A and B are constant and under the same altitude and inclination angle, their field-of-view mapping domains for the same target point are identical. However, due to the different phases of the two stars, their apparent pixel mapping domains differ in (Ω). G The trajectories in a two-dimensional plane are different, for example... Figure 7 As shown.

[0136] By calculating the intersection points of the trajectories of stars A and B in the two-dimensional plane with the field-of-view mapping domain, the visible time windows of the two stars at the same ground point can be obtained. This embodiment sets... The analytical solution to the apparent mapping equation is given, taking satellite B as the object of analysis. When satellite B is visible to the target, its... Should meet:

[0137]

[0138] Substituting equation (41) into equation (42), we get:

[0139]

[0140] Equation (43) gives the position of satellite A in (Ω) when satellite B is visible to the space target. G Position in a two-dimensional plane From the perspective of field of view mapping, when satellite B is visible to the target, that is, when B is located within the field of view mapping domain Γ, according to equation (43), it can be determined that satellite A must be located within another mapping domain Γ′. Furthermore, Γ′ can be transformed into a relative field of view mapping domain simply by shifting the mapping domain Γ based on the relative positional relationship between the two satellites. Using satellite A in (Ω... G The intersection of the trajectory in the two-dimensional plane and the relative field-of-view mapping domain Γ′ can be used to obtain the visible time window of satellite B on the ground. For example Figure 8As shown, when the trajectory of satellite A is within the relative field of view mapping domain, the payload field of view of satellite B is visible to the space target. Therefore, by calculating the intersection of the trajectory of satellite A and the relative field of view mapping domain, the visible arc segment of satellite B to the target point can be obtained.

[0141] This embodiment introduces the concept of relative field-of-view mapping domain, completely transforming the problem of satellite B's coverage of space targets into the problem of satellite A's coverage of targets. Analysis shows that the right-hand side of equation (43)... With (ΔΩ) G ,Δu), are all parameters that do not change with time. Therefore, the relative field mapping domain Γ′, like the field mapping domain Γ, is also a mapping domain that does not change with time. In equation (43), the relative mapping domain is obtained by adding and subtracting the mapping domains, while (Ω G The two-dimensional representation of u) is a translation transformation of the field of view mapping domain. The specific steps for solving the relative field of view mapping domain of satellite B with respect to satellite A are as follows: 1) The field of view mapping domain is first translated to the left by ΔΩ. BA Units, when ΔΩ BA A value less than 0 indicates a rightward shift; 2) The mapping domain is then shifted downward by Δu. BA Units, when Δu BA A value less than 0 indicates an upward translation.

[0142] In summary, the coverage problem of two observation satellites A and B can be transformed into a geometric intersection problem between the orbital trajectory of satellite A, the field-of-view mapping area of ​​satellite A, and the relative field-of-view mapping area of ​​satellite B through relative field-of-view mapping. In other words, the proposed concept of relative field-of-view mapping effectively transforms the two-satellite coverage problem into a single-satellite coverage problem, thereby reducing the complexity of the original two-satellite coverage problem.

[0143] Based on the aforementioned dual-satellite coverage analysis, this embodiment also discloses a method for coverage analysis of GEO targets by a constellation of multiple space-based observation satellites, the specific implementation process of which is as follows:

[0144] A space-based observation satellite is randomly selected from the constellation as a reference star, and a two-dimensional coordinate plane (Ω) is obtained based on the specific implementation process of steps 1 and 2. G The field of view mapping domain of the reference star on the GEO target;

[0145] The relative ascending node right ascension and relative latitude argument between other space-based observation satellites in the constellation and the reference satellite are calculated as follows:

[0146]

[0147] Where, ΔΩ j , Δu jThese represent the right ascension of the relative ascending node and the relative latitude argument between the j-th base observation satellite and the reference satellite in the constellation, Ω. j u j These are the right ascension and latitude argument of the ascending node of the j-th base observation satellite in the constellation, Ω. f u f These are the right ascension of the ascending node and the argument of latitude of the reference star, respectively.

[0148] Based on the field of view mapping domain of the reference satellite to the GEO target and the relative ascending node right ascension and relative latitude argument of the reference satellite and other space-based observation satellites, a two-dimensional coordinate plane (Ω) is obtained. G By mapping the field of view of the constellation to the GEO target, the problem of multi-star coverage of the GEO target can be transformed into a time-invariant, multi-mapping-domain single-star coverage problem. Specifically, the field of view mapping domain of the constellation to the GEO target is as follows:

[0149]

[0150] Among them, Γ G denoted as the field of view mapping domain of the constellation to the GEO target, and N as the number of space-based observation satellites included in the constellation.

[0151] For example, taking the first satellite in the first orbital plane of the constellation as the reference satellite, by calculating the right ascension of the relative ascending node and the relative latitude argument of each satellite relative to the reference satellite, the relative mapping domain of each satellite can be obtained using the relative mapping method in this embodiment. Thus, in (Ω... G The field-of-view mapping domain of a homogeneous constellation is obtained on a two-dimensional plane (u). The constellation's field-of-view mapping is obtained entirely through a linear translation of the single-star's field-of-view mapping domain, and its shape is identical to that of the single-star's field-of-view mapping domain. The constellation's field-of-view mapping possesses time-invariant properties. Therefore, by introducing the constellation's field-of-view mapping, the problem of multi-star coverage of space targets can be transformed into a single-star coverage problem with multiple time-invariant mapping domains. As the constellation size increases, constructing the constellation's field-of-view mapping domain can reduce the complexity of coverage analysis and improve computational efficiency.

[0152] The coverage analysis method in this embodiment will be further explained below with specific simulation examples.

[0153] This example verifies the visibility window of the space-based observation platform for GEO targets, the coverage analysis results of different observation payloads, the visibility window of the space-based observation platform for quasi-GEO targets at different orbital altitudes, and the coverage analysis results of the space-based observation constellation for targets. By comparing the calculation results with those of STK (System Tool Kit) software, the calculation accuracy and efficiency of the method proposed in this embodiment are verified.

[0154] First, a space-based situational awareness scenario is established. The space-based observation platform is set as a low-Earth orbit satellite. Referring to the orbital parameters of the STSS-ATRR advanced technology satellite of the space-based space surveillance system, the space-based observation platform can be designed as a sun-synchronous orbit with an orbital altitude of 850km. The simulation scenario starts at 00:00:00 on August 1, 2024, and the simulation duration is 24 hours. The orbital parameters of the space-based observation platform at the initial moment are shown in Table 1 below. The satellite's orbit prediction model is set as J2.

[0155] Table 1 Orbital parameters of the space-based observation platform

[0156]

[0157] The field-of-view mapping domain of this embodiment can be applied to any satellite payload field of view. The payload types selected in the experiment include conical, rectangular, and hexagonal. Any GEO target can be selected for simulation experiments. Let the latitude and longitude of the nadir point of the GEO target be G1: (0, 144.14), G2: (0, -111.17), and G3: (0, -95), respectively.

[0158] The geostationary orbit target is located in an orbit with a semi-major axis of 42,166.259 km. To verify the coverage performance of the method in this embodiment for quasi-GEO targets, the semi-major axes of the quasi-GEO targets are set to 20,000 km, 25,000 km, and 35,000 km, respectively, to verify the performance of the coverage analysis algorithm. Subsequent experiments are all conducted based on this initially set scenario.

[0159] Assuming the payload of the space-based observation platform is a conical field of view with a payload half-angle set to 20°, the coverage analysis results of the low-Earth orbit space-based observation platform payload on the three designated GEO targets are as follows: Figure 9 As shown, the closed regions enclosed by different linear curves represent the field-of-view mapping domains of the observation payload for targets G1, G2, and G3, respectively. The black solid line with arrows indicates the low-orbit observation satellite's position within (Ω). G The trajectory on the u) plane, the intersection of the satellite trajectory and the field of view mapping domain, are the start and end times of the observation of the corresponding GEO target. According to the method of this embodiment, the time window can be solved. Simultaneously from... Figure 9 It is not difficult to see that the field of view mapping domains of different GEO targets only have a translation in the horizontal axis direction, while there is no difference in the vertical axis direction. This is because the three GEO targets only have a phase difference, and the calculation process will affect Ω through equations (28) and (29). G The solution results are obtained by solving the problem, while the calculation results for the latitude argument u are unaffected. The simulation results are consistent with the theoretical analysis, which also verifies the correctness of the method applied in this embodiment.

[0160] Table 2 shows the calculation results of the visible windows of the space-based observation platform for high-orbit targets G1, G2, and G3. The trajectory intersection method is the coverage analysis method proposed in this embodiment. The table displays the calculation results of STK and provides a comparative analysis. The start and end times represent the endpoint times of the observation interval of the observation payload for the GEO targets, respectively. The absolute error shows the average error at the start and end times. Table 2 shows that the space-based observation platform has three visible windows for targets G1 and G2, and two visible windows for target G3. Figure 9 It can be observed that the satellite trajectory and the field of view mapping domain of target G3 intersect at orbital orbits 4 and 10, and the results correspond. Furthermore, at orbital orbit 4, the space-based observation platform has a visible range for target G2 [24288.166, 24761.931] and a visible range for target G3 [24210.072, 24719.911]. Figure 8 The table shows that the visible window for G2 is contained within the visible range for G3, which corresponds perfectly with the calculation results in Table 2.

[0161] Table 2 shows the calculation results of the visible window for different GEO targets.

[0162]

[0163] Comparing the method of this embodiment with the calculation results of STK, it can be found that the average error of the window calculation result is 0.0234s, with a maximum calculation error of 0.0467s, which reflects the calculation accuracy of the method of this embodiment. Meanwhile, statistics on the time consumption of the solution process show that, using the method of this embodiment to calculate the visible windows of the space-based observation platform for targets G1, G2, and G3, the program takes approximately 0.031s, 0.033s, and 0.025s respectively, verifying the efficiency of the method of this embodiment. This is because the method of this embodiment is an analytical solution, which improves the solution efficiency compared to iterative algorithms.

[0164] The method described in this embodiment is applicable to coverage analysis of any payload type. The applicability of the payload types is verified through simulation experiments. The following payload types can be configured for the low-Earth orbit space-based observation platform: 1) a conical payload with a half-cone angle of 30°; 2) a rectangular payload with both vertical and horizontal half-angles of 20°; 3) a hexagonal payload with a payload half-angle of 15°. The visible window of target G2 is calculated using the above three payloads respectively, and the field-of-view mapping domain results are as follows: Figure 10 As shown.

[0165] Figure 10The regions enclosed by different linear curves represent the field-of-view mapping domains of the conical, rectangular, and hexagonal loads on target G2, respectively. It can be observed that the conical load has the largest field-of-view mapping domain, completely encompassing the other two mapping domains. The hexagonal load's mapping domain is also included within the rectangular load's mapping domain. This indicates that the size of the mapping domain is related to the size of the load's field of view; the larger the load's field of view, the larger the mapping domain (Ω). G The larger the mapping domain on the u) plane, the more times it will intersect with the trajectory of the space-based observation platform. At the same time, it can be found that the mapping domains of rectangular and hexagonal loads are not regular polygons, and the mapping domain of conical loads is an irregular closed circle. This is because the field of view mapping process shown in equations (24)-(26) is a nonlinear transformation process. Therefore, the shape of the mapping domain is different from the load field of view, but the result of the mapping domain still retains the geometric similarity with the load field of view.

[0166] Table 3 shows the calculation results of the visible windows of the high-orbit target G2 by space-based platforms carrying different imaging payloads. The conical, rectangular, and hexagonal payloads have 4, 3, and 2 visible windows for G2, respectively, which is consistent with... Figure 10 The geometric intersection results shown are consistent. Due to the differences in the field of view among the three types of loads, the average observation time for the high-orbit target G2 under the conical load is statistically calculated to be 663.621 s, exceeding the 504.753 s for the rectangular load and the 314.011 s for the hexagonal load. This indicates that a larger load field of view corresponds to a longer observable time for the target. Comparing the results with the STK calculations, it is evident that the method in this embodiment has high computational accuracy; the average error between the three sets of experimental results and the STK calculations is 0.0233 s, meeting the engineering requirement of a computational accuracy better than 1 s. Because the method in this embodiment uses analytical solving, the computation process is highly efficient, with the program running time under different loads not exceeding 0.1 s. Meanwhile, the half-angle of the conical load in this example is 30°. It can be seen that the method of this embodiment can achieve high calculation accuracy under different sizes of conical load fields of view. Therefore, the experiment can verify the applicability of the proposed algorithm to different sizes and types of load fields of view, reflecting the good applicability of the method of this embodiment. It can be used for space-based situational awareness platforms carrying different types of loads.

[0167] Table 3. Calculation results of the visible window for different loads on GEO targets.

[0168]

[0169] This example demonstrates a coverage analysis method for quasi-GEO targets at different orbital altitudes. Based on space-based observations, coverage analysis experiments were conducted on quasi-GEO orbital targets with semi-major axes of 20,000 km, 25,000 km, and 35,000 km. The right ascension of the ascending node of the target star was set to -95°, and the three quasi-GEO orbital targets can be designated as G4, G5, and G6, respectively. The space-based observation platform carried a conical payload with a semi-cone angle of 40°. The calculation results of the visible window of the payload for quasi-GEO orbital targets at different orbital altitudes are shown in Table 4. The first column displays the number and semi-major axis of the different quasi-GEO targets.

[0170] Table 4 shows the calculation results of the visible window for quasi-GEO targets at different altitudes.

[0171]

[0172]

[0173] As can be seen from Table 4, the space-based observation platform has more observation windows for quasi-GEO targets in higher orbits. Specifically, there are 6 visible windows for target G6, and 4 visible windows each for targets G4 and G5. The average window durations for targets G4, G5, and G6 are 748.201 s, 830.605 s, and 906.853 s, respectively. This indicates that the higher the orbital altitude of the quasi-GEO target, the longer the average observation time for the space-based observation platform. This is because the farther the target satellite is from the space-based observation platform, the greater the extension of the platform's payload field of view boundary into space, and the larger the corresponding visible time window interval. Comparing the results with those calculated by STK, the average calculation error for the visible window is found to be 0.0169 s, indicating that the proposed method has high computational accuracy for coverage analysis of quasi-GEO targets.

[0174] The field-of-view mapping results of the space-based observation platform for the quasi-GEO target G6 with a semi-major axis of 35,000 km are as follows: Figure 11 As shown, the closed area enclosed by the solid line is the field-of-view mapping domain of the conical payload. It can be seen that there are 6 sets of intersections between the satellite trajectory and the mapping domain, corresponding to the 6 visible time intervals in Table 4. Figure 9 and Figure 10 By comparison, it can be found that there are differences in the slope of the trajectory of the space-based observation platform and the interval between adjacent trajectories on the horizontal axis. G The interval on the coordinate axis is 2π / K, when the equivalent rotational angular velocity ω′ E The higher the slope, the smaller the slope of the trajectory, which leads to a corresponding increase in the coordinate interval between adjacent trajectories. The theoretical analysis and experimental results are consistent.

[0175] This embodiment proposes the concepts of relative field-of-view mapping and constellation field-of-view mapping in space-based situational awareness scenarios. These concepts can be used for coverage analysis of GEO and quasi-GEO targets by homogeneous constellations. This example also verifies the applicability of the method in the aforementioned scenarios. Using the space-based observation platform defined in Table 1 as the reference satellite, a Walker constellation in the form of 4 / 1 / 0 is established, including four low-Earth orbit observation satellites. Coverage analysis results are calculated for a constellation carrying a 30° conical payload aligned with GEO target G2, and for a constellation carrying a rectangular payload with a vertical half-angle of 25° and a horizontal half-angle of 15° aligned with GEO target G6.

[0176] The field-of-view mapping results of the Walker constellation carrying the conical load for target G2 are as follows: Figure 12 As shown in Table 5, the closed area enclosed by the black solid line is the mapping domain result of the reference satellite to the target, and the other three dashed areas are the relative field-of-view mapping domains of other satellites in the Walker constellation. By intersecting the satellite trajectory with different mapping domains, the visible time window of the constellation to the GEO target can be obtained. The specific results are shown in Table 5. The first two columns represent the satellite number in the Walker constellation and the orbit number of the reference satellite in which the payload is visible to the target.

[0177] Table 5. Calculation results of the visible window of constellations to GEO targets.

[0178]

[0179] As shown in Table 5, each satellite in the constellation has four visible windows for the target within the simulation scenario. The average observation durations of these windows are 663.621s, 692.772s, 687.961s, and 669.956s, respectively. Since the satellite orbital altitude and payload type are consistent, the average window lengths do not differ significantly, which is consistent with the analysis results. Comparing the results with those calculated by STK, the average error of the 16 sets of window calculations is found to be 0.02s, verifying the applicability and computational accuracy of the method in this embodiment for constellation coverage analysis.

[0180] To verify the coverage analysis effect of the method in this embodiment on the GEO orbit target, a rectangular load was used to simulate the coverage of target G6. The mapping domain results are as follows: Figure 13 As shown, the mapping domain of the rectangular payload field of view is approximately rectangular in shape. The closed area enclosed by the black solid line is the mapping domain of the reference satellite. The other three dashed areas are the relative mapping domain results of other satellites in the constellation, respectively. By introducing constellation field of view mapping, the problem of multi-satellite Earth coverage is transformed into a single-satellite coverage problem with time-invariant multi-mapping domains. Moreover, the constellation field of view mapping has the same properties as that of a single satellite. The calculation results of the visible window can be obtained by intersecting the trajectory of the space-based observation platform with the mapping domain.

[0181] Table 6 shows the coverage analysis results of the rectangular payload constellation aligned with the GEO target G6. The fourth satellite has five visible windows. Figure 12 Correspondingly, the satellite trajectories and the mapping domain intersect at the 3rd / 4th / 8th / 9th / 14th orbital cycles, and the results are consistent. Comparison with the calculation results of STK shows that the calculation results for the constellation across 15 time windows are highly consistent with STK results, with an average error of 0.023s and a maximum error of 0.0969s. This error of less than 0.1s reflects the accuracy of the algorithm proposed in this embodiment. Furthermore, calculating the alignment of the four satellite constellations carrying rectangular payloads with the GEO target takes only 0.0996s, demonstrating the efficiency of the method in this embodiment and its ability to meet the application requirements of rapid coverage analysis for large-scale constellations.

[0182] Table 6. Calculation results of the visible window of the constellation aligned with the GEO target.

[0183]

[0184] The above description is merely a preferred embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent structural transformations made using the contents of the present invention's specification and drawings under the inventive concept of the present invention, or direct / indirect applications in other related technical fields, are included within the patent protection scope of the present invention.

Claims

1. A GEO target coverage analysis method based on a field-of-view mapping model, characterized in that, Includes the following steps: Step 1: Based on the geometric relationship between the space-based observation platform and the GEO target, construct the payload apparent equation for the space-based observation platform's observation of the GEO target. Specifically, the payload apparent equation is as follows: in, i For the track inclination angle, a For the semi-major axis of the space-based observation platform's orbit, e For orbital eccentricity, ω The perigee argument, x 0=[1,0,0] T It is the identity matrix. T This is the transpose of the matrix. ρ This refers to the distance between the space-based observation platform and the GEO target. α The azimuth angle of the view element vector. β Let the pitch angle be the view vector. λ , φ ( ) represents the latitude and longitude of the point where the GEO target is projected onto the Earth's surface. a 0 represents the semi-major axis of the GEO target's orbit. R x , R y , R z They represent circumference respectively. , , The coordinate transformation matrix for the corresponding angle of axis rotation; Step 2, using the longitude Ω of the ascending node G The horizontal axis and the latitude argument are shown. u Establish a two-dimensional coordinate plane (Ω) with the vertical axis as the ordinate. G , u The analytical solution of the load apparent element equation is calculated to obtain the two-dimensional coordinate plane (Ω). G , u The field of view mapping domain of the space-based observation platform for GEO targets; Step 3: Project the trajectory of the space-based observation platform onto the two-dimensional coordinate plane (Ω). G , u On, and based on the two-dimensional coordinate plane (Ω) G , u The intersection of the field of view mapping domain and the trajectory of the space-based observation platform described above is used to obtain the visible window of the space-based observation platform for the GEO target, thus completing the coverage analysis of the space-based observation platform for the GEO target. When the rotational angular velocity of the GEO target is equal to the rotational angular velocity of the Earth... ω E At the same time, the trajectory of the space-based observation platform is projected onto the two-dimensional coordinate plane (Ω). G , u The process is as follows: Set up a virtual Earth and set its rotation angular velocity. It has the same rotational angular velocity as the GEO target, making its Earth perturbation force, semi-major axis, semi-minor axis, and Earth gravitational constant the same as the real Earth; When considering J During orbital perturbations, the latitude argument of the space-based observation platform is obtained. Longitude of the ascending intersection The average rate of change is: in, t For time parameters, K u The rate of change of latitude angle. μ The gravitational constant of Earth, R E For the Earth's semi-major axis, K Ω The rate of change of longitude at the ascending node; because K u , K Ω All are parameters, therefore the space-based observation platform is in the two-dimensional coordinate plane (Ω) G , u The movement on the slope can be represented as a series of movements with a fixed slope. K The equidistant lines are: This allows us to plot the space-based observation platform in a two-dimensional coordinate plane (Ω). G , u Projection of the motion trajectory onto the surface; The rotational angular velocity of the GEO target and the rotational angular velocity of the virtual Earth. The calculation process is as follows: Considering the shift of the ascending node Δλ1 caused by the Earth's rotational angular velocity and the shift of the ascending node Δλ2 caused by the Earth's oblateness, the following equation is established: in, ω S The rotational angular velocity of the GEO target; When the orbital eccentricity of the celestial observation platform is 0, the simplified result is: The orbital inclination of the celestial observation platform i When = 0, further simplification yields: Substituting the semi-major axis of the GEO target at different orbital altitudes into the above formula, we can obtain the rotational angular velocity of the GEO target. ω S And the rotational angular velocity of the virtual Earth = ω S .

2. The GEO target coverage analysis method based on the field-of-view mapping model according to claim 1, characterized in that, Step 2, calculating the analytical solution of the load apparent element equation specifically includes: When the orbital eccentricity of the celestial observation platform is 0, the load apparent element equation is simplified to: Set intermediate parameters n 0 is: You will then receive: Then the solution is obtained ; Introduce intermediate parameters that meet the following conditions λ 0、 φ 0: And the intermediate parameters were calculated. λ 0、 φ 0 is: intermediate parameters λ 0、 φ Substituting 0 into the load apparent equation, we get: Let intermediate parameters γ Ω λ satisfy , ,available: Let the intermediate parameters Ψ and Θ be: Intermediate parameters can then be obtained. γ Ω λ Two sets of solutions γ 1. Ω λ1 and γ 2. Ω λ2 They are respectively: Where Π represents pi; set up( γ 1,Ω λ1 )and( γ 2,Ω λ2 ) is an intermediate parameter γ Ω λ The correct solution, and substitute it into cos( γ cos( φ 0) = cos(Ω) λ cos( φ Perform verification; if the verification passes, output directly () γ 1,Ω λ1 )and( γ 2,Ω λ2 Otherwise let Ω λ1 =Π-arcsin(Θ),Ω λ2 =arcsin(Θ) outputs ( γ 1,Ω λ1 )and( γ 2,Ω λ2 ); Finally, the analytical solution of the load apparent element equation can be obtained as follows: in,( u 1,Ω G1 )and( u 2,Ω G2 That is, the load apparent equation with respect to the latitude angle. Longitude of the ascending intersection The two sets of analytical solutions, corresponding to the two-dimensional coordinate plane (Ω) G , u The two field-of-view mapping domains of the space-based observation platform for the GEO target.

3. The GEO target coverage analysis method based on the field-of-view mapping model according to claim 1, characterized in that, When the GEO target is stationary relative to the Earth, the trajectory of the space-based observation platform is projected onto the two-dimensional coordinate plane (Ω). G , u The process is as follows: When considering J During orbital perturbations, the latitude argument of the space-based observation platform is obtained. Longitude of the ascending intersection The average rate of change is: in, t For time parameters, K u The rate of change of latitude angle. μ The gravitational constant of Earth, R E For the Earth's semi-major axis, K Ω The rate of change of longitude at the ascending node. ω E This is the Earth's rotational angular velocity; because K u , K Ω All are parameters, therefore the space-based observation platform is in the two-dimensional coordinate plane (Ω) G , u The movement on the slope can be represented as a series of movements with a fixed slope. K The equidistant lines are: This allows us to plot the space-based observation platform in a two-dimensional coordinate plane (Ω). G , u The projection of the motion trajectory on the surface.

4. The GEO target coverage analysis method based on the field-of-view mapping model according to any one of claims 1 to 3, characterized in that, When performing coverage analysis of GEO targets by a constellation of multiple space-based observation satellites, the following steps are used: A space-based observation satellite is randomly selected from the constellation as a reference star, and a two-dimensional coordinate plane (Ω) is obtained based on steps 1 and 2. G , u The field of view mapping domain of the reference satellite for the GEO target; Calculate the relative ascending node right ascension and relative latitude argument between other space-based observation satellites in the constellation and the reference satellite; Based on the field of view mapping domain of the reference satellite to the GEO target and the relative ascending node right ascension and relative latitude argument of the reference satellite and other space-based observation satellites, a two-dimensional coordinate plane (Ω) is obtained. G , u By mapping the field of view of the constellation to the GEO target, the problem of multi-star coverage of the GEO target can be transformed into a time-invariant, multi-mapping-domain single-star coverage problem.

5. The GEO target coverage analysis method based on the field-of-view mapping model according to claim 4, characterized in that, The relative ascending node right ascension and relative latitude argument between the other space-based observation satellites in the constellation and the reference satellite are specifically as follows: Where, ΔΩ j Δ u j Each of the constellations is the first j The relative ascending node right ascension and relative latitude argument between the individual observation satellites and the reference satellite, Ω j , u j Each of the constellations is the first j Right ascension of the ascending node and arc of latitude of each base observation satellite, Ω f , u f These are the right ascension of the ascending node and the argument of latitude of the reference star, respectively. The specific field-of-view mapping domain of the constellation for the GEO target is as follows: Among them, Γ G For the field of view mapping of the constellation to the GEO target, α The azimuth angle of the view element vector. β Let the pitch angle be the view vector. λ , φ ( ) represents the latitude and longitude of the point where the GEO target is projected onto the Earth's surface. N This represents the number of space-based observation satellites included in the constellation.

Images