A latitude zone full-coverage non-linear time-varying load constellation configuration analytical design method

Abstract

The application discloses a kind of latitude zone full coverage nonlinear time-varying load constellation configuration analytical design methods, comprising: according to satellite orbit altitude and load detection geometry constraint, the analytical model of fan-shaped load ground detection coverage is established, the latitude and longitude extreme value of fan-shaped coverage area and nonlinear time-varying relationship changing with orbit position are obtained;According to the latitude and longitude extreme value of fan-shaped coverage area and nonlinear time-varying relationship changing with orbit position, and target latitude zone range, by solving orbit inclination, satellite number in orbit plane, orbit plane number and orbit plane satellite phase difference gradually through analytical constraint model, the constellation configuration parameters satisfying target latitude zone full coverage requirement are obtained;Satellite constellation system is designed and deployed according to constellation configuration parameters.The method of the application can be directly used for satellite launch into orbit after orbit deployment and on-orbit operation control, without additional numerical iteration optimization.

Description

Technical Field

[0001] This invention belongs to the field of satellite systems engineering, and in particular relates to an analytical design method for a nonlinear time-varying payload constellation configuration with full latitudinal coverage. Background Technology

[0002] With the rapid development of aerospace remote sensing technology, achieving continuous, high-frequency coverage of the globe or specific latitudinal zones using satellite constellations has become a core requirement in fields such as resource exploration, disaster early warning, and environmental monitoring. Analytical constellation configuration design methods, by establishing mathematical models and directly deriving the optimal combination of orbital parameters under coverage performance constraints, are a key means to improve constellation design efficiency. Currently, mature analytical configuration design theories are mostly based on modeling the coverage characteristics of communication payloads. The ground coverage area of ​​such payloads is usually simplified to a circular region centered on the nadir point. Under this model, the coverage band width is constant and the edges are straight. Designers can use spherical trigonometric functions to directly derive the total number of satellites, the number of orbital planes, and the phase relationship required to achieve complete coverage of the target area, forming a linear or quasi-linear analytical design system.

[0003] However, in practical applications, remote sensing payloads are constrained by the lower viewing angle and azimuth angle, and their instantaneous coverage area typically presents a fan-shaped or more complex geometric shape. Under the coupling effect of satellite orbital motion and Earth's rotation, the coverage area of ​​such payloads undergoes complex rotation and deformation around the nadir point, resulting in the coverage edge becoming a complex curve that changes nonlinearly with latitude and time. Existing analytical design methods based on circular coverage models cannot accurately describe this nonlinear time-varying characteristic, and its linear geometric relationship is difficult to directly transfer to a fan-shaped coverage scenario. This often leads to reliance on large-scale numerical simulations for parameter iteration and verification during the design process, which not only reduces the accuracy of constellation configuration design but also affects design efficiency and the interpretability of the scheme. Summary of the Invention

[0004] The purpose of this invention is to provide an analytical design method for nonlinear time-varying payload constellation configurations that addresses the need for full latitudinal coverage. This method, considering the complex and dynamically changing ground projection shape of nonlinear time-varying payloads, leverages the uniform and symmetrical distribution of the Walker constellation. By studying the spatial geometric distribution of constellation nodes, a complementary mathematical model of coverage edges within the same orbital plane and between adjacent orbital planes is established. Through analytical constraints and the derivation of no-miss coverage conditions for the two worst-coverage regions near the equator and near the latitudinal boundaries, an analytical design for full coverage configurations within a specific latitudinal range is achieved. This provides an orbital element configuration scheme that can be directly applied to engineering implementation for deploying actual satellite constellation systems.

[0005] To provide engineering configuration schemes for constructing practical satellite constellation systems, this invention offers an analytical design method for nonlinear time-varying payload constellation configurations with full latitudinal coverage, comprising: Based on the satellite orbital altitude and payload detection geometric constraints, an analytical model of the sector-shaped payload's Earth detection coverage is established to obtain the extreme values ​​of latitude and longitude of the sector-shaped coverage area and its nonlinear time-varying relationship with orbital position. Based on the extreme values ​​of latitude and longitude of the sector coverage area and their nonlinear time-varying relationship with orbital position, as well as the target latitude zone range, the orbital inclination, the number of satellites in the orbital plane, the number of orbital planes, and the phase difference between satellites in the orbital plane are solved step by step through the analytical constraint model to obtain the constellation configuration parameters that meet the full coverage requirements of the target latitude zone.

[0006] Preferably, the process of obtaining the orbital inclination angle includes: Based on the coverage overlap model of adjacent satellites in the same orbital plane, the upper or lower intersection point of the coverage boundary of adjacent satellites is calculated according to the range of the target latitude zone to determine the boundary latitude of continuous coverage. Redundancy design is carried out in combination with the boundary loss caused by orbital plane separation, and the analytical solution of orbital inclination is obtained.

[0007] Preferably, the process of obtaining the orbital inclination angle further includes: When the target latitude zone has bidirectional coverage from south to north latitude, in the scenario at the southernmost end of the orbit, the lower boundary latitude of continuous coverage is extracted by comparing the intersection point of the ground coverage of adjacent satellites with the height of the inner arc dome of the single-satellite fan-shaped payload. This lower boundary latitude is then combined with the upper boundary latitude of continuous coverage determined by the upper intersection point to form the coverage boundary, in order to calculate the orbital inclination.

[0008] Preferably, the process of obtaining the number of satellites in the orbital plane includes: A spatial geometric model is constructed based on the sub-satellite points of adjacent satellites and the intersection of their coverage areas to determine the spatial topological relationship between the phase difference of adjacent satellites and the vertical coverage arc length within the orbital plane. Based on the spatial topology, an analytical mapping equation between the number of satellites in the orbital plane and the vertical coverage arc length is derived. Then, based on the range of the target latitude zone and the orbital inclination, the minimum vertical coverage arc length threshold required to ensure continuous coverage in high-latitude areas is calculated, thereby solving for the number of satellites required for each orbital plane.

[0009] Preferably, the process of obtaining the number of orbital planes includes: A spatial geometric model is established at the furthest distance between adjacent orbital planes to determine the analytical mapping equation between the included angle of the orbital planes and the orbital inclination and the difference in right ascension of the ascending node. Based on the coverage range of the sector payload and the overlap of coverage with adjacent satellites, a coverage complementarity criterion between adjacent orbital planes is set to determine the maximum critical threshold of the angle between orbital planes, and the maximum critical threshold of the difference in right ascension of the ascending node and the number of orbital planes are calculated.

[0010] Preferably, the process of setting coverage complementarity criteria between adjacent orbital planes includes: By comparing the intersection of the coverage areas of adjacent satellites with the height of the inner arc dome of the single-satellite sector payload, the larger of the two is selected as the main reference point for complementary criteria, and the smaller of the two is selected as the auxiliary reference point. Ensure that the outer arc dome of the satellite sector payload on the adjacent orbital plane covers the main reference point, and that the upper intersection point of the sector payload covers the auxiliary reference point.

[0011] Preferably, the process of obtaining the satellite phase difference between the orbital planes includes: The basic constellation configuration is constructed based on the number of orbital planes and the number of satellites required for each orbital plane. A spatial geometric model is established at the furthest point between adjacent orbits, consisting of the sub-satellite points of satellites on adjacent orbital planes and the ascending nodes of the orbital planes. Based on the selected complementary criterion reference point type, the true anomaly angles of corresponding satellites on adjacent orbital planes are calculated using the spatial geometric model, and then the phase difference between corresponding satellites on orbital planes is obtained.

[0012] Preferably, the process of calculating the true anomaly angle of corresponding satellites on adjacent orbital planes includes: When the inner arc arch of the single-star sector load is taken as the main reference point, the nadir points of the first satellite on the first orbital plane and the target satellite on the second orbital plane are respectively located at the position with the maximum normal distance on the orbital plane. The large arc length between the nadir points of the two satellites and the ascending node of their respective orbital planes is calculated by the spatial geometric model and converted into the true anomaly angles of the first satellite and the target satellite respectively.

[0013] Preferably, the process of calculating the true anomaly angle of corresponding satellites on adjacent orbital planes further includes: When the lower intersection of the coverage areas of adjacent satellites is taken as the main reference point, the lower intersection of the coverage areas of the first satellite on the first orbital plane and the nadir point of the target satellite on the second orbital plane are respectively located at the position with the maximum normal distance on the orbital plane. The large arc length between the nadir points of the first satellite and its adjacent satellites on the first orbital plane, and the nadir point of the target satellite on the second orbital plane and their respective ascending nodes on the orbital plane are calculated by the spatial geometric model, and converted into the true anomaly angles of the first satellite and the target satellite respectively.

[0014] Preferably, the constellation configuration parameters that meet the requirement of full coverage of the target latitude zone include the number of orbital planes, the number of satellites in each orbital plane, and the phase difference between corresponding satellites between orbital planes.

[0015] Compared with the prior art, the present invention has the following advantages and technical effects: This invention addresses the complex and dynamically changing ground projection shape of nonlinear time-varying loads. First, by establishing an analytical model of the instantaneous load coverage under a spherical Earth model, it quantifies the rotation and deformation patterns of the sector-shaped load under the coupling effect of orbital motion and Earth's rotation, solving the problem that existing circular coverage models cannot describe nonlinear time-varying characteristics. Second, leveraging the uniform symmetry of the Walker constellation, this invention transforms the complex overall constellation coverage problem into a geometric coverage boundary constraint problem within the same orbital plane and between adjacent orbital planes. Through step-by-step analytical derivation of orbital inclination, number of satellites in the plane, number of orbital planes, and phase difference between orbital planes, it achieves rapid closed-form solution of constellation configuration parameters for coverage requirements of a specified latitude zone. This avoids the drawbacks of existing technologies that rely on large-scale numerical searches and simulation verification, significantly improving computational efficiency and design accuracy. Finally, this invention establishes analytical constraint models for the two worst-coverage regions near the equator and at the boundaries of latitude zones. By calculating the upper / lower intersection points of the coverage boundaries of adjacent satellites and the height of the inner arc dome, the mapping relationship between the orbital plane angle and the phase offset is established and the critical value is calculated. Under the premise of considering the boundary loss caused by orbital plane separation, reasonable redundancy is provided for the orbital inclination, realizing a full-coverage closed design of the target latitude zone in the spatiotemporal dimension. This effectively overcomes the technical difficulty of closing the coverage boundary under nonlinear time-varying load scenarios in existing methods, and provides an orbital element configuration scheme that can be directly applied to engineering implementation for the deployment of actual satellite constellation systems.

[0016] The constellation configuration parameters (including orbital inclination, number of satellites in each orbital plane, number of orbital planes, and phase difference between satellites in orbital planes) obtained by the method of this invention can be used as core input parameters for satellite orbit design and can be directly used for orbit deployment and on-orbit operation control after satellite launch and insertion into orbit, without the need for additional numerical iteration optimization.

[0017] The constellation configuration parameters obtained by the method of this invention, through the engineering implementation of these parameters, can ensure that the constellation system composed of multiple satellites achieves continuous and uninterrupted coverage of the target latitude zone in the spatiotemporal dimension, meeting the requirements of continuous observation data for application tasks such as resource exploration, disaster early warning, and environmental monitoring.

[0018] The method of this invention avoids the design process of relying on large-scale numerical simulation for parameter traversal in traditional methods by analytically solving constellation configuration parameters. It can significantly shorten the cycle from conceptual design to engineering deployment of constellation system and reduce system design and verification costs. Attached Figure Description

[0019] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings: Figure 1 This is a schematic diagram of the method flow according to an embodiment of the present invention. Detailed Implementation

[0020] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0021] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0022] This embodiment provides an analytical design method for a latitude-zone full-coverage nonlinear time-varying load constellation configuration, including: Based on the satellite orbital altitude and payload detection geometric constraints, an analytical model of the sector-shaped payload's Earth detection coverage is established to obtain the extreme values ​​of latitude and longitude of the sector-shaped coverage area and its nonlinear time-varying relationship with orbital position. Based on the extreme values ​​of latitude and longitude of the sector coverage area and their nonlinear time-varying relationship with orbital position, as well as the target latitude zone range, the orbital inclination, the number of satellites in the orbital plane, the number of orbital planes, and the phase difference between satellites in the orbital plane are solved step by step through the analytical constraint model to obtain the constellation configuration parameters that meet the full coverage requirements of the target latitude zone.

[0023] In the above embodiments, the constellation configuration parameters obtained in this embodiment that meet the full coverage requirements of the target latitude zone are used to deploy a satellite constellation system that achieves continuous and uninterrupted coverage of the target latitude zone. This provides an orbital element configuration scheme that can be directly applied to engineering implementation for deploying actual satellite constellation systems, so that the constellation system can achieve spatiotemporal continuous coverage of the target latitude zone during operation.

[0024] Specifically, such as Figure 1 As shown, the constellation configuration analytical design method in this embodiment involves the use of the following modules, including: In the payload Earth observation coverage calculation module, an analytical model of the payload's instantaneous coverage under the Earth spherical model is first established based on the given satellite orbital altitude and payload detection geometric constraints. The coverage capability of the sector payload's Earth observation, i.e., the central angle of the sphere in the latitude and longitude direction, is calculated from the input angle and azimuth of the payload detection. Subsequently, the extreme values ​​of latitude and longitude of the sector coverage area and their relationship with the orbital position are derived to characterize the instantaneous coverage capability and geometric deformation law of the payload at different latitudes, providing a reference for subsequent constellation coverage complementary analysis.

[0025] In the constellation configuration analysis and design module, the orbital inclination design module first establishes a sector coverage overlap model of adjacent satellites on the same orbital plane. By calculating the intersection point of the overlapping coverage of adjacent satellites and performing inclination compensation, the preliminary design result of the orbital inclination that meets the high-latitude coverage requirements is obtained. In the scenario at the southernmost end of the orbit, the lower boundary latitude of continuous coverage is extracted by comparing the intersection point of the ground coverage of adjacent satellites with the inner camber height of the single-satellite sector payload. The boundary analysis criterion is used to verify the envelope of the coverage zone on the target latitude zone, and the analytical solution of the orbital inclination and the maximum north and south latitude threshold that the sub-satellite point must reach are obtained.

[0026] Subsequently, in the satellite number design module within the orbital plane, based on the spatial geometric relationship between the nadir points of adjacent satellites and the coverage edge, a conversion model of the phase difference between adjacent satellites in the same orbital plane and the overlapping coverage depth is constructed. Using spherical trigonometric geometry, the maximum allowable phase difference between adjacent satellites under the constraint of maximum payload detection capability is calculated. Combining the upper and lower limits of target coverage latitude and the analytical solution of orbital inclination, the critical vertical distance between the intersection point of adjacent satellite coverage and the nadir point trajectory is determined to ensure continuous coverage in high-latitude areas. Then, the critical value of the phase difference between adjacent satellites in the same orbital plane is obtained. The number of satellites required for each orbital plane is calculated by rounding according to the principle of circumferential phase bisector.

[0027] Next, in the orbital plane number design module, a geometric analysis model is established at the furthest point of the normal distance between adjacent orbital planes. Boundary constraints are established to meet the requirement of complementary coverage of the intersection point under the overlap of the outer arc of the sector load and the adjacent satellites. Using spherical trigonometric relations, an analytical mapping is constructed between the difference in right ascension of the ascending node between adjacent orbital planes, the orbital inclination, and the angle between the orbital planes. Based on the central angle of the sector load coverage in the latitudinal direction, the critical normal distance between the corresponding satellites of adjacent orbital planes that ensure the closure of the coverage zone is determined. The critical value of the difference in right ascension of the ascending node is calculated through the mapping relationship. The required number of orbital planes is calculated by rounding according to the principle of bisecting the right ascension of a circle.

[0028] Finally, in the inter-orbital satellite phase difference design module, a spatial position model of satellites in adjacent orbital planes at the maximum normal distance is established, the geometric mapping relationship between the satellite nadir point and the intersection of the orbital plane equator is established, the spherical arc length between the reference satellite nadir point and the intersection of the orbital plane equator is calculated using spherical trigonometric geometry, the reference true anomaly angle of corresponding satellites in adjacent orbital planes is determined, and then the satellites in the target orbital plane are numbered and matched using the true anomaly angle interval determination algorithm, the index of the corresponding satellite is extracted, and the phase offset of satellites with the same or related serial numbers in adjacent orbital planes is calculated comprehensively to obtain the analytical solution of inter-orbital satellite phase difference that meets the requirement of no missing coverage.

[0029] Furthermore, the process of obtaining the orbital inclination angle includes: Based on the coverage overlap model of adjacent satellites in the same orbital plane, the upper or lower intersection point of the coverage boundary of adjacent satellites is calculated according to the range of the target latitude zone to determine the boundary latitude of continuous coverage. Redundancy design is carried out in combination with the boundary loss caused by orbital plane separation, and the analytical solution of orbital inclination is obtained.

[0030] Furthermore, the process of obtaining the orbital inclination angle also includes: When the target latitude zone has bidirectional coverage from south to north latitude, in the scenario at the southernmost end of the orbit, the lower boundary latitude of continuous coverage is extracted by comparing the intersection point of the ground coverage of adjacent satellites with the height of the inner arc dome of the single-satellite fan-shaped payload. This lower boundary latitude is then combined with the upper boundary latitude of continuous coverage determined by the upper intersection point to form the coverage boundary, in order to calculate the orbital inclination.

[0031] Furthermore, the analytical design method for the latitude-zone full-coverage nonlinear time-varying load constellation configuration in this embodiment includes the following steps: Based on the satellite payload detection capabilities and the Earth sphere model, the geocentric angle of the nonlinear payload at a specific orbital altitude is calculated, the calculation capability of the sector payload for Earth detection coverage is constructed, and the extreme values ​​of latitude and longitude of the projection of the sector payload coverage area onto the Earth's surface and its relationship with the satellite position are derived.

[0032] The user selects the target latitude zone to be observed and inputs the satellite orbital altitude, target latitude zone range, and payload viewing angle and azimuth into the payload Earth observation coverage calculation module.

[0033] In the orbital inclination design module, based on the mapping relationship between the overlapping coverage area of ​​adjacent satellites on the same orbital plane and the phase difference between adjacent satellites, within a reasonable range of adjacent satellite phase differences, this embodiment discusses three cases according to the range included in the target latitude zone: the latitude zone between the equator and north latitude, the latitude zone between south latitude and the equator, and the latitude zone between south latitude and north latitude. (1) For the latitude zone from the equator to the north latitude, the satellite is set to be in a prograde orbit and the sector payload is viewed from the left (the overall direction is north). When two adjacent satellites move to the symmetrical positions on both sides of the northernmost end of the nadir point trajectory, the upper intersection of their coverage boundaries is calculated, and this is used as the upper latitude of the continuous coverage to constrain the orbital inclination design.

[0034] (2) For the latitude zone from the south latitude to the equator, the analysis logic is the same as that in case (1). Calculate the intersection point of the coverage of adjacent satellites, determine the upper limit latitude of continuous coverage, and switch the sector payload to the right view direction when generating the constellation.

[0035] (3) For the latitude zone from south latitude to north latitude, in addition to case (1), the boundaries at both the north and south ends also need to be taken into account. When the satellite moves to the southernmost point of the nadir trajectory, the latitude value closer to the equator is selected as the lower boundary latitude of continuous coverage by comparing the intersection point of the fan-shaped coverage of adjacent satellites with the height of the inner arc dome of the single-satellite fan-shaped payload.

[0036] The orbit inclination design module will take into account the continuous coverage upper and lower boundaries or bidirectional boundaries obtained from the above situations, calculate its envelope coverage capability of the target latitude zone, and give redundancy under the premise of considering the boundary loss caused by orbital surface separation, and finally calculate the analytical solution of the orbit inclination that meets the requirements.

[0037] Furthermore, the process of obtaining the number of satellites in orbit includes: A spatial geometric model is constructed based on the sub-satellite points of adjacent satellites and the intersection of their coverage areas to determine the spatial topological relationship between the phase difference of adjacent satellites and the vertical coverage arc length within the orbital plane. Based on spatial topology, an analytical mapping equation between the number of satellites in the orbital plane and the vertical coverage arc length is derived. Then, based on the range of the target latitude zone and the orbital inclination, the minimum vertical coverage arc length threshold required to ensure continuous coverage in high-latitude areas is calculated, thereby solving for the number of satellites required for each orbital plane.

[0038] Furthermore, in this embodiment, the number of satellites in the orbital plane is calculated based on the analytical solution of the satellite orbital inclination angle and the coverage range of the sector payload for Earth detection in the orbital plane design module.

[0039] First, due to the near-circular orbit satellite and the Earth's spherical model, the area of ​​Earth covered by the satellite remains approximately constant during its operation. Based on this, a system is established using the sub-satellite points of adjacent satellites. , and the intersection of its coverage area The constructed spatial geometric model determines the phase difference between adjacent satellites within the orbital plane and the vertical coverage arc length. The spatial topological relationship between them is then established. Secondly, based on this spatial topological relationship, an analytical mapping equation between the number of satellites in the orbital plane and the vertical coverage arc length is derived. Then, according to the range of the target latitude zone and the analytical solution of the orbital inclination obtained above, the minimum vertical coverage arc length threshold required to ensure no missed coverage in high-latitude regions is calculated. Finally, the number of satellites required for each orbital plane to satisfy the coverage boundary closure condition is calculated. The analytical design results for the number of satellites in the orbital plane were obtained.

[0040] Furthermore, the process of obtaining the number of orbital planes includes: A spatial geometric model is established at the furthest distance between adjacent orbital planes to determine the analytical mapping equation between the included angle of the orbital planes and the orbital inclination and the difference in right ascension of the ascending node. Based on the coverage range of the sector payload and the overlap of coverage with adjacent satellites, a coverage complementarity criterion between adjacent orbital planes is set to determine the maximum critical threshold of the angle between orbital planes, and the maximum critical threshold of the difference in right ascension of the ascending node and the number of orbital planes are calculated.

[0041] Furthermore, the process of setting coverage complementarity criteria between adjacent orbital planes includes: By comparing the intersection of the coverage areas of adjacent satellites with the height of the inner arc dome of the single-satellite sector payload, the larger of the two is selected as the main reference point for complementary criteria, and the smaller of the two is selected as the auxiliary reference point. Ensure that the outer arc of the satellite sector payload on the adjacent orbital plane covers the main reference point, and that the upper intersection point of the sector payload covers the auxiliary reference point.

[0042] Furthermore, in this embodiment, the orbital plane number design module is used to solve for the number of orbital planes based on the analytical solution of the satellite orbital inclination and the coverage range of the sector payload for Earth detection.

[0043] First, based on the complementary requirements of the Earth detection coverage of sector-shaped loads between adjacent orbital planes, a spatial geometric model is established at the furthest distance between the orbital planes to determine the geocentric angle corresponding to the maximum normal distance between the orbital planes, i.e., the orbital plane angle. Second, the orbital plane angle is derived on a sphere. With orbital inclination difference in right ascension of ascending nodes The analytical mapping equation between them is then established. Next, based on the overlap between the payload's coverage area and that of adjacent satellites, the lower intersection point of the adjacent satellite coverage areas and the height of the inner arc dome of the single-satellite sector payload are compared. The larger of the two is selected as the primary reference point for the complementarity criterion, and the smaller one is selected as the secondary reference point. Based on this, a coverage complementarity criterion between adjacent orbital planes is established: ensuring that the outer arc dome of the satellite sector payload on adjacent orbital planes covers the primary reference point, and simultaneously ensuring that the upper intersection point of the satellite sector payload on adjacent orbital planes covers the secondary reference point. Finally, the maximum critical threshold for the orbital plane angle is determined. And solve for the maximum ascending node right ascension difference threshold that satisfies the requirement of complementary coverage. and the number of orbital planes The analytical design results of the orbital plane number were obtained.

[0044] Furthermore, the process of obtaining the phase difference between satellites in orbital planes includes: The basic constellation configuration is constructed based on the number of orbital planes and the number of satellites required for each orbital plane. A spatial geometric model is established at the furthest point between adjacent orbits, consisting of the sub-satellite points of satellites on adjacent orbital planes and the ascending nodes of the orbital planes. Based on the selected complementary criterion reference point type, the true anomaly angles of corresponding satellites on adjacent orbital planes are calculated using a spatial geometric model, and then the phase difference between corresponding satellites on orbital planes is obtained.

[0045] Furthermore, the process of calculating the true anomaly angle of corresponding satellites on adjacent orbital planes includes: When the inner arc arch of the single-star sector load is taken as the main reference point, the nadir points of the first satellite on the first orbital plane and the target satellite on the second orbital plane are located at the positions with the largest normal distance on the orbital plane. The large arc length between the nadir points of the two satellites and the ascending nodes of their respective orbital planes is calculated by the spatial geometric model and converted into the true anomaly angles of the first satellite and the target satellite, respectively.

[0046] Furthermore, the process of calculating the true anomaly angle of corresponding satellites on adjacent orbital planes also includes: When the lower intersection of the coverage areas of adjacent satellites is taken as the main reference point, the lower intersection of the coverage areas of the first satellite on the first orbital plane and the nadir point of the target satellite on the second orbital plane are respectively located at the position with the maximum normal distance on the orbital plane. The large arc length between the nadir points of the first satellite and its adjacent satellites on the first orbital plane, and the nadir point of the target satellite on the second orbital plane and their respective ascending nodes on the orbital plane are calculated by the spatial geometric model, and then converted into the true anomaly angles of the first satellite and the target satellite respectively.

[0047] Furthermore, the constellation configuration parameters that meet the requirement of full coverage of the target latitude zone include the number of orbital planes, the number of satellites in each orbital plane, and the phase difference between corresponding satellites between orbital planes.

[0048] Furthermore, in this embodiment, the satellite phase difference design module between orbital planes analyzes the distribution of satellites between adjacent orbital planes that can achieve complementary coverage based on the obtained design results, and completes the solution of satellite phase difference between orbital planes.

[0049] First, based on the number of orbital planes Number of satellites required for each orbital plane The basic constellation configuration is constructed, and a spatial geometric model is established at the furthest point between adjacent orbits, consisting of the satellite's nadir point and the ascending node of the orbital plane. Secondly, methods for solving the true anomaly angle of the satellite are discussed and categorized according to the selected complementary criterion reference point types. (1) If the inner arc arch of the single-star sector load is taken as the main reference point, then the nadir points of satellite 1 on orbital plane 1 and satellite k on orbital plane 2 are respectively located at the position with the largest normal distance on the orbital plane. The large arc length between the nadir points of the satellites on the two orbital planes and the ascending intersection of the orbital planes is calculated by the spatial geometric model and converted into the true anterior angles of satellite 1 and satellite k respectively.

[0050] (2) If the lower intersection of the coverage areas of adjacent satellites is taken as the main reference point, then let the lower intersection of the coverage areas of satellite 1 and adjacent satellites on orbital plane 1 and the nadir of satellite k on orbital plane 2 be located at the positions with the largest normal distance on the orbital plane. Calculate the nadir of satellite 1 and its adjacent satellites on orbital plane 1, as well as the large arc length between the nadir of satellite k on orbital plane 2 and their respective ascending intersections on the orbital plane through the spatial geometric model, and convert them into the true anomaly angles of satellite 1 and satellite k respectively.

[0051] Next, the true anomaly angle of satellite k is compared with the true anomaly angles of all satellites in orbital plane 1 to determine the satellite number of satellite k in orbital plane 2. Finally, the difference in true anomaly angle between satellite k and the corresponding satellite in orbital plane 1 is calculated, which is the analytical solution for the phase difference between corresponding satellites in orbital planes that satisfies the requirement of full latitudinal coverage.

[0052] Organize and store the calculated satellite orbit elements and constellation configuration parameters, including the number of orbital planes, the number of satellites in the orbital plane, and the phase difference between corresponding satellites in the orbital plane.

[0053] This embodiment addresses the sector projection characteristics of remote sensing payloads constrained by the lower viewing angle and azimuth angle. By establishing an analytical model of the payload's instantaneous coverage under the Earth's spherical model, it quantifies the nonlinear time-varying characteristics such as rotation generated by the payload under the coupling effect of orbital motion and Earth's rotation, providing a reference for the analytical design of constellation configurations.

[0054] This embodiment utilizes the uniform symmetry of the Walker constellation to transform the complex overall constellation coverage problem into a geometric coverage boundary constraint problem within the same orbital plane and between adjacent orbital planes. Through step-by-step analytical derivation of orbital inclination, number of satellites in the plane, number of orbital planes, and phase difference between orbital planes, a rapid closed-form solution for constellation configuration parameters oriented towards coverage requirements of a specified latitude zone is achieved. This avoids large-scale numerical searches and simulation verification, and has the advantages of high computational efficiency, high accuracy, and ease of maintenance.

[0055] This embodiment establishes an analytical constraint model for the two most poorly covered sensitive areas: near the equator and at the boundaries of latitudinal zones. By calculating the upper / lower intersections of adjacent satellite coverage boundaries and the height of the inner arc dome, the mapping relationship between the orbital plane angle and the phase offset is established, and the critical value is calculated. Considering the boundary loss caused by orbital plane separation, reasonable redundancy is provided for the orbital inclination, achieving a closed-loop design for full spatiotemporal coverage of the target latitudinal zone.

[0056] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. An analytical design method for a nonlinear time-varying load constellation configuration with full latitudinal coverage, characterized in that, include: Based on the satellite orbital altitude and payload detection geometric constraints, an analytical model of the sector-shaped payload's Earth detection coverage is established to obtain the extreme values ​​of latitude and longitude of the sector-shaped coverage area and its nonlinear time-varying relationship with orbital position. Based on the extreme values ​​of latitude and longitude of the sector coverage area and their nonlinear time-varying relationship with orbital position, as well as the target latitude zone range, the orbital inclination, number of satellites in the orbital plane, number of orbital planes, and phase difference between satellites in the orbital plane are solved step by step through the analytical constraint model to obtain the constellation configuration parameters that meet the full coverage requirements of the target latitude zone. Design and deploy a satellite constellation system based on the constellation configuration parameters.

2. The method according to claim 1, characterized in that, The process of obtaining the orbital inclination angle includes: Based on the coverage overlap model of adjacent satellites in the same orbital plane, the upper or lower intersection point of the coverage boundary of adjacent satellites is calculated according to the range of the target latitude zone to determine the boundary latitude of continuous coverage. Redundancy design is carried out in combination with the boundary loss caused by orbital plane separation, and the analytical solution of orbital inclination is obtained.

3. The method according to claim 1, characterized in that, The process of obtaining the orbital inclination angle also includes: When the target latitude zone has bidirectional coverage from south to north latitude, in the scenario at the southernmost end of the orbit, the lower boundary latitude of continuous coverage is extracted by comparing the intersection point of the ground coverage of adjacent satellites with the height of the inner arc dome of the single-satellite fan-shaped payload. This lower boundary latitude is then combined with the upper boundary latitude of continuous coverage determined by the upper intersection point to form the coverage boundary, in order to calculate the orbital inclination.

4. The method according to claim 1, characterized in that, The process of obtaining the number of satellites in the orbital plane includes: A spatial geometric model is constructed based on the sub-satellite points of adjacent satellites and the intersection of their coverage areas to determine the spatial topological relationship between the phase difference of adjacent satellites and the vertical coverage arc length within the orbital plane. Based on the spatial topology, an analytical mapping equation between the number of satellites in the orbital plane and the vertical coverage arc length is derived. Then, based on the range of the target latitude zone and the orbital inclination, the minimum vertical coverage arc length threshold required to ensure continuous coverage in high-latitude areas is calculated, thereby solving for the number of satellites required for each orbital plane.

5. The method according to claim 1, characterized in that, The process of obtaining the number of orbital planes includes: A spatial geometric model is established at the furthest distance between adjacent orbital planes to determine the analytical mapping equation between the included angle of the orbital planes and the orbital inclination and the difference in right ascension of the ascending node; Based on the coverage range of the sector payload and the overlap of coverage with adjacent satellites, a coverage complementarity criterion between adjacent orbital planes is set to determine the maximum critical threshold of the angle between orbital planes, and the maximum critical threshold of the difference in right ascension of the ascending node and the number of orbital planes are calculated.

6. The method according to claim 5, characterized in that, The process of setting coverage complementarity criteria between adjacent orbital planes includes: By comparing the intersection of the coverage areas of adjacent satellites with the height of the inner arc dome of the single-satellite sector payload, the larger of the two is selected as the main reference point for complementary criteria, and the smaller of the two is selected as the auxiliary reference point. Ensure that the outer arc dome of the satellite sector payload on the adjacent orbital plane covers the main reference point, and that the upper intersection point of the sector payload covers the auxiliary reference point.

7. The method according to claim 1, characterized in that, The process of obtaining the satellite phase difference between the orbital planes includes: The basic constellation configuration is constructed based on the number of orbital planes and the number of satellites required for each orbital plane. A spatial geometric model is established at the furthest point between adjacent orbits, consisting of the sub-satellite points of satellites on adjacent orbital planes and the ascending nodes of the orbital planes. Based on the selected complementary criterion reference point type, the true anomaly angles of corresponding satellites on adjacent orbital planes are calculated using the spatial geometric model, and then the phase difference between corresponding satellites on orbital planes is obtained.

8. The method according to claim 7, characterized in that, The process of calculating the true anomaly angle of corresponding satellites on adjacent orbital planes includes: When the inner arc arch of the single-star sector load is taken as the main reference point, the nadir points of the first satellite on the first orbital plane and the target satellite on the second orbital plane are respectively located at the position with the maximum normal distance on the orbital plane. The large arc length between the nadir points of the two satellites and the ascending node of their respective orbital planes is calculated by the spatial geometric model and converted into the true anomaly angles of the first satellite and the target satellite respectively.

9. The method according to claim 7, characterized in that, The process of calculating the true anomaly angle of corresponding satellites on adjacent orbital planes also includes: When the lower intersection of the coverage areas of adjacent satellites is taken as the main reference point, the lower intersection of the coverage areas of the first satellite on the first orbital plane and the nadir point of the target satellite on the second orbital plane are respectively located at the position with the maximum normal distance on the orbital plane. The large arc length between the nadir points of the first satellite and its adjacent satellites on the first orbital plane, and the nadir point of the target satellite on the second orbital plane and their respective ascending nodes on the orbital plane are calculated by the spatial geometric model, and converted into the true anomaly angles of the first satellite and the target satellite respectively.

10. The method according to claim 1, characterized in that, The constellation configuration parameters that meet the requirement of full coverage of the target latitude zone include the number of orbital planes, the number of satellites in each orbital plane, and the phase difference between corresponding satellites between orbital planes.

Images