Rapid visible time window calculation method for large-scale satellite group collaboration

Abstract

The invention relates to a rapid visible time window calculation method for large-scale satellite group cooperation. The method comprises the following steps: establishing an analytic relationship between time and a satellite latitude argument based on a rapid analytic orbit model; calculating a rough moment when the sub-satellite point trajectory of the satellite intersects with the target declination circle; screening potential coverable circles in combination with satellite side sway and a field angle; for each circle, accurately calculating the positive side-looking moment of the satellite to the target by iterating the spherical geometrical relationship; and finally, by taking the moment as a reference, performing forward and backward recursion by using a high-precision model in combination with a dichotomy to determine accurate starting and ending moments of the visible window. According to the method, the defects that a tracking propagation method is high in calculation precision but high in calculation cost can be overcome, and the preprocessing efficiency of a ground or satellite-borne task planning system is improved; meanwhile, the problem of low precision in the prior art is solved, a solution is provided for satellite-borne window calculation of a large-scale satellite group cooperative task planning system, and online and high-precision calculation of single-satellite and satellite group visible windows during large-scale satellite group cooperation is realized.

Description

Technical Field

[0001] This invention relates to the field of multi-satellite collaborative mission planning technology, specifically to a method for calculating the fast visible time window for large-scale satellite constellation collaboration. Background Technology

[0002] Calculating the visible time window of a satellite relative to ground targets is the foundation and prerequisite for almost all space activities (such as Earth observation, data transmission, and telemetry, tracking, and command). With the explosive growth in the number of satellites in orbit, especially in the context of large-scale constellation and swarm collaborative mission planning, how to efficiently and accurately calculate visible window resources has become an increasingly important challenge.

[0003] With the explosive growth in the number of satellites in orbit, how to efficiently and accurately calculate visibility window resources has become an increasingly important challenge in the field of aerospace mission planning. The traditional method for calculating the satellite coverage time window for ground targets is the tracking propagation method. This method typically uses a fixed step size to numerically calculate the satellite's orbital position and utilizes sensor coverage geometry to perform visibility analysis on the target point, thereby obtaining the start and end times of the satellite's coverage time window for the target point. For example, Chinese invention patent CN116996115A typically uses a fixed or variable step size to numerically extrapolate the satellite orbit and combines this with sensor coverage geometry to determine the target's visibility. This method is highly accurate, but because the step size is limited by the accuracy of orbit calculation, it often requires frequent searches, resulting in a large computational load and significant time consumption, making it difficult to meet the needs of rapid planning for large-scale satellite constellations. Another example is Chinese invention patent CN116996115A, which, although reducing some computational load through ground station classification and orbit filtering, is still essentially based on numerical extrapolation and search, and its filtering logic depends on the ground station's perspective, making it unsuitable for generalized and rapid calculation of satellite coverage for arbitrary ground point targets. In addition, some published literature proposes approximate analytical calculation methods, most of which solve for the satellite's time window by comparing the latitude or longitude of the nadir point. For example, Chinese invention patent CN116821566A uses a two-body or simplified dynamic model and utilizes the geometric relationship between the nadir point trajectory and the latitude circle for approximate solution to quickly screen potential coverage areas. However, these methods suffer from insufficient accuracy in window calculation due to the overly simplified orbital dynamics model, which greatly limits their practical application in tasks requiring high-precision planning (such as agile satellite imaging).

[0004] The shortcomings of existing technologies are mainly reflected in the following aspects:

[0005] (1) Tracking propagation method and corresponding improvement methods generally adopt the orbit numerical calculation method and recursively calculate with fixed or variable step size. Due to the consideration of orbit calculation accuracy, the step size is generally controlled within tens of seconds, which leads to frequent visible window search, huge amount of calculation, and a lot of time consumption.

[0006] (2) To quickly calculate the time window, most approximate analytical methods currently employ a two-body model or a simplified perturbation model, utilizing the geometric relationship between the nadir point trajectory and the latitude circle to solve the problem, thereby quickly screening potential coverage circles or approximate windows. However, because the orbital mechanics model used in these methods is too simple, the window calculation accuracy is insufficient, which greatly limits the practical application of these methods. Summary of the Invention

[0007] In view of the above-mentioned technical problems, this invention proposes a fast visible time window calculation method for large-scale constellation coordination. While ensuring the calculation accuracy is comparable to that of traditional high-precision methods, it can significantly reduce the number of invalid searches by integrating fast analytical orbit models, spherical geometric iterative algorithms and high-precision model binary search methods, thereby achieving fast and high-precision calculation of the visible time window.

[0008] The technical solution to the technical problem of this invention is: a fast visible time window calculation method for large-scale constellation coordination, comprising the following steps:

[0009] Step S1: Obtain the initial orbital parameters of the satellite. Based on the preset fast analytical orbital dynamics model, establish the analytical relationship between the satellite's orbital time and the satellite's perigee argument, mean perigee angle, and latitude argument.

[0010] Step S2: Based on the location information of the ground target and the satellite orbital inclination, calculate the first latitude argument of the satellite when its nadir point trajectory intersects with the latitude circle where the target point is located;

[0011] Step S3: Based on the analytical relationship established in step S1, solve for the first time set corresponding to the first latitude argument, as the potential coarse visible time of the satellite to the target point;

[0012] Step S4: Based on the satellite's attitude maneuverability and payload field of view, select potential coverage orbits from the potential visible coarse moments;

[0013] Step S5: For the selected potential coverage circles, the second moment of the satellite's frontal and side-view imaging of the target point is obtained by constructing the spherical geometric relationship between the satellite, the target point and the Earth's center and performing iterative calculations.

[0014] Step S6: Using the second time point as a reference, and employing a high-precision analytical orbit model combined with a bisection search strategy, calculate the precise start and end times of the precise visible time window of the satellite to the target.

[0015] According to one technical solution of the present invention, in step S1, with As input, the analytical relationship between satellite orbit time and satellite perigee argument, mean perigee angle, and satellite latitude argument is expressed as follows:

[0016] ;

[0017] in, For the semi-major axis of the track, For eccentricity, For the track inclination angle, For the near point angle, For the track semi-major, For average motion, For satellite operating time, Right ascension of the ascending node, The perigee argument, For the angle of near point, The latitude argument of the satellite. The gravitational constant of Earth, To account for the second-order zonal harmonic coefficients of the Earth's oblateness, For the Earth's radius, These are the average motion at the initial moment, the first time derivative of the average motion, and the second time derivative of the average motion, respectively.

[0018] According to one technical solution of the present invention, in step S2, the location information of the ground target includes at least the longitude and latitude of the ground target.

[0019] According to a technical solution of the present invention, in step S5, obtaining the second moment of satellite frontal and side-view imaging of the target point by constructing spherical geometric relationships and performing iterative calculations specifically includes:

[0020] Step S51: Select an initial time t0 from the potential visible coarse times, determine the position of the satellite nadir point S0 in the geocentric equatorial inertial coordinate system at time t0, and the first position A1 of the target point in the geocentric equatorial inertial coordinate system, and calculate the arc connecting the target point and the nadir point. The central angle in radians;

[0021] Step S52: Construct an arc passing through the Earth's center. This makes the spherical angle ∠S0S1A1 90 degrees in the spherical triangle △S0S1A1.

[0022] Step S53: Calculate the spherical angle ∠S1S0A1 based on the satellite orbital plane normal vector and the plane normal vector determined by the three points A1 and S0.

[0023] Step S54: Calculate the arc based on the spherical triangle relationship. The central angle radian and the arc The central angle in radians;

[0024] Step S55: According to the arc Calculate the time t1 when the satellite reaches point S1, based on the central angle radians and the average motion of the satellite;

[0025] Step S56: Based on the Earth's rotation, calculate the second position A2 of the target point in the geocentric equatorial inertial coordinate system at time t1;

[0026] Step S57: Using S0 and A2 as vertices, repeat steps S52 to S56 to iteratively calculate the time when the satellite is at the updated position.

[0027] Step S58: Repeat the iteration process until the preset convergence condition is met, and take the satellite time obtained in the last iteration as the second time, that is, the satellite frontal side view imaging time.

[0028] According to one technical solution of the present invention, in step S53, the spherical angle ∠S1S0A1 is calculated by the following formula:

[0029]

[0030] in, The normal vector to the satellite's orbital plane. Let be the normal vector of the plane containing the Earth's center, the target point A1, and the sub-satellite point S0.

[0031] According to one technical solution of the present invention, in step S54, The central angle in radians is expressed as:

[0032]

[0033] in, Let be the central angle in radians between the target point A1 and the nadir point S0 at time t0.

[0034] According to a technical solution of the present invention, in step S54, the arc The central angle in radians is expressed as:

[0035] .

[0036] According to one technical solution of the present invention, in step S6, the high-precision analytical orbit model is the SGP4 model.

[0037] According to a technical solution of the present invention, in step S6, the recursive calculation using a high-precision analytical orbit model combined with the bisection method specifically involves: starting from the second moment, dynamically adjusting the recursive step size using the bisection method; when the satellite's visibility of the target point changes, reducing the step size for precise positioning until the critical point between visibility and invisibility is found, which are respectively used as the precise start time and precise end time.

[0038] Compared with the prior art, the present invention has the following beneficial effects:

[0039] This invention presents a fast visible time window calculation method for large-scale constellation coordination. It introduces a fast analytical orbital model for preliminary screening and innovatively proposes a method for calculating the frontal and side-view times based on spherical geometry iteration. This avoids the problem of traditional tracking and propagation methods requiring a large number of blind searches with fixed small step sizes throughout the entire mission cycle, thus reducing computational complexity.

[0040] This invention offers high computational accuracy. After quickly locating the midpoint of the visible window (frontal / side-view time), it switches to using high-precision orbital models such as SGP4, and employs a bisection method for fine-grained searching only near the start and end points of the window. This method inherits the advantages of high-precision models while limiting their application to an extremely short time interval, thus achieving overall accuracy comparable to using high-precision models throughout the entire process, while significantly reducing the computational load.

[0041] This invention is highly versatile, as it does not depend on specific ground stations or mission scenarios. It directly processes the geometric relationship between satellites and fixed ground targets, making it suitable for visibility analysis in various Earth observation and data transmission missions. It is especially suitable for rapid visibility preprocessing in large-scale satellite constellation collaborative planning.

[0042] This invention has good engineering practicality, with clear steps. Both the model and algorithm are analytical or semi-analytical, ensuring stable and reliable computation. The fast analytical model can control the latitude argument prediction error within 0.3% within 24 hours, fully meeting the accuracy requirements of the initial screening of visible windows in the task planning. Attached Figure Description

[0043] Figure 1 This invention compares the latitude argument calculated by the fast analytical orbital model and the high-precision SGP4 model.

[0044] Figure 2 This invention defines the geometric relationship between the trajectory of a fixed ground target moving along the declination circle and the trajectory of the satellite's nadir point in the geocentric equatorial inertial coordinate system.

[0045] Figure 3 The iterative process and geometric relationship for determining the satellite's side-view time of the target are used in this invention;

[0046] Figure 4 This is a flowchart of the fast visible window calculation process for large-scale constellation coordination according to the present invention. Detailed Implementation

[0047] To more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the accompanying drawings used in the embodiments will be briefly described below. Obviously, the drawings described below are merely some embodiments of the present invention, and those skilled in the art can obtain other drawings based on these drawings without any creative effort.

[0048] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. The embodiments cannot be described in detail here, but the embodiments of the present invention are not limited to the following embodiments.

[0049] This invention discloses a fast visible time window calculation method for large-scale constellation coordination. The method uses a fast analytical orbital dynamics model to directly obtain the potential orbit number and approximate visible time, and uses an analytical iterative method to obtain a high-precision frontal and side-view time to obtain the midpoint of the visible window. Then, it uses a higher-precision SGP4 analytical orbital calculation model and a bisection method with variable step size to obtain the accurate initial time of the visible window, which greatly reduces the number of time window searches, thereby overcoming the shortcomings of the prior art and improving the calculation efficiency and accuracy.

[0050] like Figures 1 to 4 As shown, the present invention provides a fast visible time window calculation method for large-scale constellation coordination, comprising the following steps:

[0051] Step S1: Obtain the initial orbital parameters of the satellite. Based on the preset fast analytical orbital dynamics model, establish the analytical relationship between the satellite's orbital time and the satellite's perigee argument, mean perigee angle, and latitude argument.

[0052] Input the initial orbital data or position and velocity data of the satellite, and considering the characteristics of near-circular orbits of large-scale satellite constellations, take into account J2 perturbation and atmospheric drag perturbation, and use a fast analytical orbital dynamics model to establish the mathematical relationship between time and the satellite's perigee argument and mean perigee angle.

[0053]

[0054] in, For the semi-major axis of the track, For eccentricity, For the track inclination angle, For the near point angle, For the track semi-major, For average motion, For satellite operating time, Right ascension of the ascending node, The perigee argument, For the angle of near point, The latitude argument of the satellite. The gravitational constant of Earth, To account for the second-order zonal harmonic coefficients of the Earth's oblateness, For the Earth's radius, These are the average motion at the initial moment, the first time derivative of the average motion, and the second time derivative of the average motion, respectively.

[0055] Taking a low-Earth orbit near-circular orbit satellite as an example, the latitude argument obtained from the aforementioned rapid analytical orbital dynamics model has a small error compared to the latitude argument calculated by the widely used high-precision SGP4 model, with a deviation of less than 0.3% within 24 hours, meeting the accuracy requirements for mission planning and visible window calculations. More detailed results can be found... Figure 1 As shown.

[0056] Step S2: Based on the location information of the ground target and the satellite orbital inclination, calculate the first latitude argument of the satellite when its nadir point trajectory intersects with the latitude circle where the target point is located;

[0057] Based on the location information of the ground target and the satellite orbital inclination, the location information of the ground target includes at least its longitude and latitude. In the geocentric equatorial inertial coordinate system, the latitudinal argument of the satellite when its nadir trajectory intersects the target point's declination circle is calculated; this is called the first latitudinal argument. The intersection of the satellite nadir trajectory and the target point's trajectory along the declination circle can be seen in the diagram. Figure 2 .

[0058] Step S3: Based on the analytical relationship established in step S1, solve for the first time set corresponding to the first latitude argument, as the potential coarse visible time of the satellite to the target point;

[0059] Step S4: Based on the satellite's attitude maneuverability and payload field of view, select potential coverage orbits from the potential visible coarse moments;

[0060] Step S5: For the selected potential coverage circles, the second moment of the satellite's frontal and side-view imaging of the target point is obtained by constructing the spherical geometric relationship between the satellite, the target point and the Earth's center and performing iterative calculations.

[0061] Considering that the satellite's forward and side-view time of the target generally falls within the middle of a time window, the target point is projected onto the surface of an imaginary Earth sphere fixed to a geocentric equatorial inertial coordinate system. Based on the geometric relationship of the satellite's forward and side-view of the target, a high-precision forward and side-view time is obtained through iterative calculations. The iterative process and geometric relationship for determining the satellite's forward and side-view time of the target are detailed below. Figure 3 .

[0062] In some embodiments of the present invention, step S5 specifically includes:

[0063] Step S51: Select an initial time t0 from the potential visible coarse times, determine the position of the satellite nadir point S0 in the geocentric equatorial inertial coordinate system at time t0, and the first position A1 of the target point in the geocentric equatorial inertial coordinate system, and calculate the arc connecting the target point and the nadir point. The central angle in radians;

[0064] Based on the target's declination, determine the declination of point S below the satellite, and then determine the satellite's latitudinal argument. And determine the time when the satellite's nadir point reaches the target point's declination. and determine The position of the target in the geocentric equatorial inertial coordinate system at any given time coordinate ,Right now And the arc can be calculated. The central angle radian is as follows:

[0065] .

[0066] Step S52: Construct an arc passing through the Earth's center. This makes the spherical angle ∠S0S1A1 90 degrees in the spherical triangle △S0S1A1.

[0067] Step S53: Calculate the spherical angle ∠S1S0A1 based on the satellite orbital plane normal vector and the plane normal vector defined by the three points A1 and S0. The specific process is as follows:

[0068] Based on three points (the Earth's center, the ascending node, ... Determine the normal vector of the orbital plane. ;

[0069] Based on three points (the Earth's center, the Earth's core, the ... , Determine the normal vectors of the plane containing the target point and the nadir point. ;

[0070] We can obtain:

[0071] .

[0072] Step S54: Calculate the arc based on the spherical triangle relationship. The central angle radian and the arc The central angle in radians;

[0073] The central angle in radians is expressed as:

[0074]

[0075] in, Let be the central angle in radians between the target point A1 and the nadir point S0 at time t0.

[0076] In step S54, the arc The central angle in radians is expressed as:

[0077] .

[0078] Step S55: According to the arc Using the central angle in radians and the average angular velocity of the satellite, calculate the time t1 when the satellite reaches point S1, expressed as:

[0079] .

[0080] Step S56: Based on the Earth's rotation, calculate the second position A2 of the target point in the geocentric equatorial inertial coordinate system at time t1. The coordinates of the second position A2 are expressed as follows: ;

[0081] Step S57: Using S0 and A2 as vertices, repeat steps S52 to S56 to iteratively calculate the time when the satellite is at the updated position.

[0082] Construct a spherical right triangle Following steps S52 to S56, the satellite's position is iteratively calculated. The moment And calculate the target at time . Location coordinate ;

[0083] Step S58: Repeat the iteration process until the preset convergence condition is met, and take the satellite time obtained in the last iteration as the second time, that is, the satellite frontal side view imaging time.

[0084] Similarly, construct a spherical right triangle Following steps S52 to S56, the satellite's position is iteratively calculated. The moment In the geocentric equatorial inertial coordinate system, the target's velocity due to the Earth's rotation is relatively small compared to the satellite's velocity, resulting in a rapid convergence of the iterative process. The appropriate number of iterations can be selected based on the required accuracy within the actual visible window. Finally, the time obtained from the iterations... It is the moment when the satellite is closest to the target, that is, the moment when the satellite performs a side-view imaging.

[0085] Step S6: Using the second time point as a reference, and employing a high-precision analytical orbit model combined with a bisection search strategy, calculate the precise start and end times of the precise visible time window of the satellite to the target.

[0086] The high-precision analytical trajectory model is the SGP4 model.

[0087] The recursive calculation using a high-precision analytical orbit model combined with the bisection method is as follows: starting from the second moment, the recursive step size is dynamically adjusted using the bisection method. When the satellite's visibility of the target point changes, the step size is reduced for precise positioning until the critical point between visibility and invisibility is found, which is taken as the precise start time and precise end time, respectively.

[0088] like Figure 4 As shown, the complete process of fast visible time window calculation for constellation coordination according to the present invention includes the following specific steps:

[0089] (1) Input and preprocessing

[0090] Input the "initial orbital parameters of the satellite", process them through the "rapid analytical orbital dynamics model" to obtain the "position (right ascension, declination) of the satellite's nadir point in the geocentric equatorial inertial coordinate system";

[0091] Input the "target location (longitude, latitude)", and after "conversion from Earth-fixed coordinate system to geocentric equatorial inertial coordinate system", you will get the "position of the fixed ground target (right ascension, declination) in the geocentric equatorial inertial coordinate system".

[0092] Input "Platform attitude maneuverability" and "Load field of view" to calculate "Observable range (geocentric angle)".

[0093] (2) Rough time and circle selection

[0094] By combining the "satellite nadir position" and the "target position", calculate the "argument of latitude when the satellite nadir trajectory intersects the declination circle of the target point";

[0095] Based on the "observable range (geocene angle)", filter the "circumferences with potential visible windows";

[0096] The above results together determine the "rough time of the frontal side view, i.e. the initial time value t0 of the iteration".

[0097] (3) Iterative calculation of forward and side view time

[0098] Based on t0, "construct the geometric relationship of the satellite's frontal and side views of the target, and use the spherical geometric relationship to iteratively calculate a more accurate frontal and side view time";

[0099] Convergence check on the iteration results: Verify "|tti If |<ε” is true, return and iterate again; if true, then obtain the “frontal side view time t”. i ".

[0100] (4) Determine the final visible window

[0101] Based on "frontal and lateral viewing time t" i The process ends when the start and end times of the visible window are determined using the SGP4 recursor and binary search method.

[0102] This invention addresses the shortcomings of the tracking propagation method, which offers high accuracy but comes at a high computational cost, and can significantly improve the preprocessing efficiency of ground-based or spaceborne mission planning systems. Simultaneously, it solves the problem of low accuracy in most fast window calculation methods, providing a solution for spaceborne window calculation in large-scale constellation collaborative mission planning systems, enabling online, high-precision calculation of visible windows for single stars and constellations during large-scale constellation collaboration.

[0103] According to one aspect of the present invention, an electronic device is provided, comprising: one or more processors, one or more memories, and one or more computer programs; wherein the processor is connected to the memory, and the one or more computer programs are stored in the memory; when the electronic device is running, the processor executes the one or more computer programs stored in the memory to cause the electronic device to perform a fast visible time window calculation method for large-scale constellation coordination as described in any of the above technical solutions.

[0104] The processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor can be a microprocessor or any conventional processor.

[0105] The memory can be an internal storage unit of the terminal device, such as a hard drive or RAM. Alternatively, it can be an external storage device, such as a plug-in hard drive, Smart Media Card (SMC), Secure Digital (SD) card, or Flash Card. Furthermore, the memory can include both internal and external storage units. The memory is used to store the computer program and other programs and data required by the terminal device. It can also be used to temporarily store data that has been output or will be output.

[0106] According to one aspect of the present invention, a computer-readable storage medium is provided for storing computer instructions, which, when executed by a processor, implement a fast visible time window calculation method for large-scale constellation coordination as described in any of the above technical solutions.

[0107] For example, computer-readable storage media can be read-only memory (ROM), random access memory (RAM), read-only optical disc (CD-ROM), magnetic tape, floppy disk, and optical data storage devices. They can be implemented using computer-executable program code, thus allowing them to be stored in a storage device for execution by a computing device, or they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. Therefore, this invention is not limited to any particular hardware and software combination.

[0108] In summary, this invention proposes a rapid visible time window calculation method for large-scale constellation coordination. It employs a rapid analytical orbital dynamics model to directly obtain potential orbits and approximate visible times, and uses an analytical iterative method to obtain high-precision frontal and side-view times to determine the midpoint of the visible window. Then, it utilizes a higher-precision SGP4 analytical orbital calculation model, employing a bisection method with variable step size to obtain the precise initial visible window time, significantly reducing the number of time window searches and overcoming the shortcomings of existing technologies, thus improving computational efficiency and accuracy. This invention is implemented through the following technical solutions: 1. Considering that most large-scale constellations or star groups currently use near-circular orbits with a mission planning cycle of 24 hours, a rapid analytical orbital dynamics model is used to establish an analytical relationship between the satellite's latitude argument at any given time and the initial orbital parameters and time, based on the satellite's initial orbital parameters; 2. Based on the position of the ground fixed point target and the satellite's orbital inclination, the latitude argument of the satellite when its nadir intersects with the target point's latitude circle is calculated; 3. Based on the equality of the two latitude argument relationships, a preliminary screening of coverable targets is performed. The process involves: 1) determining several approximate times for the satellite's coverage; 2) using the sub-satellite point position (right ascension, declination), the satellite's maximum attitude yaw angle, and the payload's field of view to obtain the geocentric angle corresponding to the satellite's reachable Earth coverage area, and then filtering out potential coverage rings based on the target's position (right ascension, declination) at that moment; 3) considering that the satellite's forward and backward side-view of the target generally falls within the middle of the time window, projecting the target point onto the surface of an imaginary Earth sphere fixed to the geocentric equatorial inertial coordinate system, and using iterative calculations based on the geometric relationship of the satellite's forward and backward side-view of the target to obtain a high-precision forward and backward side-view time; and 4) using analytical orbits such as SGP4 to recursively push points forward and backward with varying step sizes, combined with the bisection method, to obtain the starting time of the high-precision visible window.

[0109] Furthermore, it should be noted that the embodiments of the present invention may take the form of a computer program product implemented on one or more computer-usable storage media containing computer-usable program code.

[0110] Embodiments of the present invention are described with reference to flowchart illustrations and / or block diagrams of methods, terminal devices (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, embedded processor, or other programmable data processing terminal device to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing terminal device, generate instructions for implementing the flowchart illustrations. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0111] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing terminal device to operate in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The functions specified in one or more boxes. These computer program instructions may also be loaded onto a computer or other programmable data processing terminal equipment to cause a series of operational steps to be performed on the computer or other programmable terminal equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable terminal equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0112] It should also be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or terminal device that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or terminal device. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or terminal device that includes said element.

[0113] Finally, it should be noted that the above description represents a preferred embodiment of the present invention. It should be pointed out that although preferred embodiments have been described, those skilled in the art, once they understand the basic inventive concept of the present invention, can make various improvements and modifications without departing from the principles described herein. These improvements and modifications should also be considered within the scope of protection of the present invention. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the embodiments of the present invention.

Claims

1. A fast visible time window calculation method for large-scale constellation coordination, characterized in that, Includes the following steps: Step S1: Obtain the initial orbital parameters of the satellite. Based on the preset fast analytical orbital dynamics model, establish the analytical relationship between the satellite's orbital time and the satellite's perigee argument, mean perigee angle, and latitude argument. Step S2: Based on the location information of the ground target and the satellite orbital inclination, calculate the first latitude argument of the satellite when its nadir point trajectory intersects with the latitude circle where the target point is located; Step S3: Based on the analytical relationship established in step S1, solve for the first time set corresponding to the first latitude argument, as the potential coarse visible time of the satellite to the target point; Step S4: Based on the satellite's attitude maneuverability and payload field of view, select potential coverage orbits from the potential visible coarse moments; Step S5: For the selected potential coverage circles, the second moment of the satellite's frontal and side-view imaging of the target point is obtained by constructing the spherical geometric relationship between the satellite, the target point and the Earth's center and performing iterative calculations. Step S6: Using the second time point as a reference, and employing a high-precision analytical orbit model combined with a bisection search strategy, calculate the precise start and end times of the precise visible time window of the satellite to the target.

2. The method according to claim 1, characterized in that, In step S1, with As input, the analytical relationship between satellite orbit time and satellite perigee argument, mean perigee angle, and satellite latitude argument is expressed as follows: ； in, For the semi-major axis of the satellite orbit, For eccentricity, For the track inclination angle, For the near point angle, For the track semi-major, For average motion, For satellite operating time, Right ascension of the ascending node, The perigee argument, For the angle of near point, The latitude argument of the satellite. The gravitational constant of Earth, To account for the second-order zonal harmonic coefficients of the Earth's oblateness, For the Earth's radius, These are the average motion at the initial moment, the first time derivative of the average motion, and the second time derivative of the average motion, respectively.

3. The method according to claim 1, characterized in that, In step S2, the location information of the ground target includes at least the longitude and latitude of the ground target.

4. The method according to claim 1, characterized in that, In step S5, the step of obtaining the second moment of satellite frontal and side-view imaging of the target point by constructing spherical geometric relationships and performing iterative calculations specifically includes: Step S51: Select an initial time t0 from the potential visible coarse times, determine the position of the satellite nadir point S0 in the geocentric equatorial inertial coordinate system at time t0, and the first position A1 of the target point in the geocentric equatorial inertial coordinate system, and calculate the arc connecting the target point and the nadir point. The central angle in radians; Step S52: Construct an arc passing through the Earth's center. This makes the spherical angle ∠S0S1A1 90 degrees in the spherical triangle △S0S1A1. Step S53: Calculate the spherical angle ∠S1S0A1 based on the satellite orbital plane normal vector and the plane normal vector determined by the three points A1 and S0. Step S54: Calculate the arc based on the spherical triangle relationship. The central angle radian and the arc The central angle in radians; Step S55: According to the arc Calculate the time t1 when the satellite reaches point S1, based on the central angle radians and the average motion of the satellite; Step S56: Based on the Earth's rotation, calculate the second position A2 of the target point in the geocentric equatorial inertial coordinate system at time t1; Step S57: Using S0 and A2 as vertices, repeat steps S52 to S56 to iteratively calculate the time when the satellite is at the updated position. Step S58: Repeat the iteration process until the preset convergence condition is met, and take the satellite time obtained in the last iteration as the second time, that is, the satellite frontal side view imaging time.

5. The method according to claim 4, characterized in that, In step S53, the spherical angle ∠S1S0A1 is calculated using the following formula: in, The normal vector to the satellite's orbital plane. Let be the normal vector of the plane containing the Earth's center, the target point A1, and the sub-satellite point S0.

6. The method according to claim 4, characterized in that, In step S54, The central angle in radians is expressed as: in, Let be the central angle in radians between the target point A1 and the nadir point S0 at time t0.

7. The method according to claim 6, characterized in that, In step S54, the arc The central angle in radians is expressed as: 。 8. The method according to claim 1, characterized in that, In step S6, the high-precision analytical orbit model is the SGP4 model.

9. The method according to claim 1 or 8, characterized in that, In step S6, the recursive calculation using a high-precision analytical orbit model combined with the bisection method is specifically as follows: starting from the second moment, the recursive step size is dynamically adjusted using the bisection method. When the visibility state of the satellite to the target point changes, the step size is reduced for precise positioning until the critical point between visibility and invisibility is found, which are respectively used as the precise start time and precise end time.

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