Agile satellite mission preprocessing method based on dynamic step and vector geometry

Abstract

The application provides an agile satellite task preprocessing method based on a dynamic step and vector geometry, belongs to the technical field of agile imaging satellite task planning, and mainly solves the problems of unreasonable calculation resource distribution, the contradiction between the precision and efficiency of a grid coverage calculation method in a traditional fixed-step agile imaging satellite subsatellite point trajectory generation method. The application significantly improves the preprocessing efficiency and calculation precision by dynamically adjusting the agile imaging satellite subsatellite point trajectory calculation step and directly calculating the coverage area, and provides high-quality input data for a task planning algorithm.

Description

Technical Field

[0001] This invention belongs to the field of agile imaging satellite mission planning technology, specifically relating to an agile satellite mission preprocessing method based on dynamic step size and vector geometry. Background Technology

[0002] The preprocessing stage of agile imaging satellite regional observation mission planning requires generating the nadir trajectory of the agile imaging satellite and calculating coverage, providing input data for subsequent mission allocation and side-swing angle optimization. In practical applications, traditional methods suffer from two core problems: First, the fixed-step agile imaging satellite nadir trajectory generation method does not dynamically adjust the sampling density based on the distance between the agile imaging satellite nadir trajectory and the target area, leading to unreasonable allocation of computational resources. Although shortening the calculation step size of the agile imaging satellite nadir trajectory can improve the accuracy of the observation time window calculation to some extent, the computation time cost increases dramatically; conversely, increasing the calculation step size can shorten the computation time, but it will reduce the accuracy of the target observation time window calculation. Second, existing gridded coverage calculation methods discretize the target observation area into multiple grid cells. The size and number of grid cells determine the accuracy of the coverage calculation. That is, to improve the accuracy of the regional coverage calculation, it is necessary to continuously shrink the regional grid cells and increase the number of grids, resulting in a quadratic increase in the system's computational load, seriously affecting the efficiency of mission planning. To address the aforementioned issues, an efficient preprocessing method based on adaptive dynamic step size and vector geometry is needed. This method should be able to adjust the sampling density in real time according to the distance between the nadir point of the agile imaging satellite and the observation area, while employing continuous geometric calculations to avoid coverage calculation errors introduced by grid discretization. Summary of the Invention

[0003] To overcome the shortcomings of existing technologies and address the problems of unreasonable allocation of computational resources and the contradiction between accuracy and efficiency in the traditional fixed-step agile imaging satellite nadir trajectory generation method, this invention provides an agile satellite mission preprocessing method based on dynamic step size and vector geometry.

[0004] The technical solution adopted by this invention to solve its technical problem includes the following steps: Step S1: Determine the target area and its boundary vertices; construct the Earth-fixed coordinate system, the geocentric inertial coordinate system, the orbital coordinate system, and the satellite body coordinate system; calculate the coordinates from the geodetic coordinate system to the Earth-fixed coordinate system ECEF. The transformation matrix from the Earth-fixed coordinate system ECEF to the geocentric inertial coordinate system ECI. Construct an orbital dynamics model and establish it in the geocentric inertial coordinate system (ECI). The dynamic equations of the perturbation-driven agile imaging satellite are decomposed in Cartesian coordinates to obtain a set of dynamic equations. By numerically integrating these equations, the state vector of the agile imaging satellite at any time within the planning period in geocentric inertial coordinates is recursively obtained. The system calculates the geodetic longitude, geodetic latitude, and flight velocity of the agile imaging satellite at any given time. Step S2: Iteratively calculate the time step; Step S2-1: Based on the current time Given the geodetic longitude and latitude of the nadir point of the agile imaging satellite, and traversing all boundary vertices of the target area, calculate the shortest distance between the nadir point of the agile imaging satellite and the target area. ; Calculate the observation buffer distance of agile imaging satellites The difference between the shortest distance and the observation buffer distance of the agile imaging satellite is used as the distance margin between the current position and the effective observation area; If the distance margin is less than zero, adjust the time step. Set the step size to the minimum value, and set the current time... The geodetic longitude and geodetic latitude of the corresponding agile imaging satellite nadir points are added to the agile imaging satellite nadir point trajectory sequence set; the time step is used to update the next time step. , If the next moment Greater than the global observation end time If the iteration loop terminates, the set of agile imaging satellite nadir trajectory sequences is output; if the next moment... Less than or equal to the global observation end time Then As the current moment, return to step S2-1 and recalculate; the minimum step size is 1 second. If the distance margin is greater than or equal to zero, calculate the time step. Use time step Update the next moment If the next moment Greater than the global observation end time If the iteration loop terminates, the set of agile imaging satellite nadir trajectory sequences is output; if the next moment... Less than or equal to the global observation end time Then Return to step S2-1 as the current moment; Step S3: Calculate the side swing angle; the side swing angle includes an upper limit and a lower limit; divide the target area into a left area and a right area according to the trajectory segment of the agile imaging satellite nadir point; Step S3-1: Calculate the upper and lower limits of the lateral sway angle when the trajectory of the agile imaging satellite's nadir point crosses the target area; For the left region, calculate the farthest distance from the nadir point trajectory segment of the agile imaging satellite to the boundary of the left region. If this distance is greater than the limit coverage boundary distance, the upper limit of the side swing angle is the maximum side swing angle; otherwise, calculate the corresponding side swing angle by reverse calculation of the farthest distance on the left as the upper limit of the side swing angle. For the right region, the same method as for the left region is used to calculate the farthest distance from the nadir point trajectory segment of the agile imaging satellite to the boundary of the right region, and to determine the lower limit of the side sway angle. Step S3-2: Calculate the lateral sway angle when the trajectory of the agile imaging satellite's nadir point does not intersect with the target area; If the target area is located to the left of the nadir trajectory segment of the agile imaging satellite, calculate the farthest distance from the nadir trajectory segment of the agile imaging satellite to the boundary of the left area. If this distance is greater than the limit coverage boundary distance, the swing angle range is from 0 to the maximum side swing angle; otherwise, calculate the corresponding minimum side swing angle by reverse calculation of the farthest distance on the left. If the target area is located to the right of the nadir trajectory segment of the agile imaging satellite, the same method is used to determine the range of the side swing angle. The lower limit of the side swing angle is the negative minimum side swing angle or the negative maximum side swing angle, and the upper limit of the side swing angle is 0. Step S3-3: Based on the calculated side-swing angle, output the range of side-swing angle values ​​that enable the agile imaging satellite coverage strip to have an effective intersection with the target area; Step S4: Derive the ground coverage width based on the set of agile imaging satellite nadir point trajectory sequences and the side-swing angle; generate continuous observation strip vector polygons through spherical geometric projection; traverse the set of agile imaging satellite nadir point trajectory sequences, and calculate the coordinates of the corresponding left and right boundary points for each agile imaging satellite nadir point trajectory point based on the side-swing angle and field of view; connect all boundary points in sequence to construct the agile imaging satellite observation strip polygon; for each agile imaging satellite observation strip polygon, calculate the intersection of the agile imaging satellite observation strip polygon and the target area polygon to obtain the geometric polygon of the actual coverage area. If multiple observation strips exist, perform a geometric union operation on all intersecting polygons to remove overlapping parts and obtain the final total coverage area. Calculate the area of ​​the final coverage area using the polygon area, with the coverage rate being the coverage area divided by the total area of ​​the target region, and output as a percentage. Generate continuous coverage rate values ​​and intersecting geometric spatial polygons. Integrate the agile imaging satellite's nadir point trajectory sequence set, side-swing angle, and continuous coverage rate values ​​into a preprocessed constraint set. Directly output this constraint set to subsequent mission optimization and scheduling to provide accurate spatial geometric basis for agile imaging satellite mission allocation.

[0005] Furthermore, the origin of the Earth-fixed coordinate system ECEF is the Earth's center, the Z-axis points to the Earth's North Pole, the X-axis points to the intersection of the Greenwich Meridian and the Earth's equator, and the Y-axis forms a right-handed coordinate system with the X and Z axes; the origin of the geocentric inertial coordinate system ECI is at the Earth's center, the X-axis points along the intersection of the Earth's equatorial plane and the ecliptic plane to the J2000 mean vernal equinox, the Z-axis points to the J2000 mean North Pole, and the Y-axis is obtained according to the right-hand rule; the orbital coordinate system has the agile imaging satellite's center of mass as its origin, the X-axis is along the geocentric radius vector of the agile imaging satellite, the Y-axis is along the direction of orbital motion and perpendicular to the X-axis, and the Z-axis is perpendicular to the orbital plane and determined by the right-hand rule; the satellite body coordinate system has the agile imaging satellite's center of mass as its origin, and the three axes are the roll axis, pitch axis, and yaw axis of the agile imaging satellite's attitude motion.

[0006] Furthermore, the calculation of coordinates from the geodetic coordinate system to the Earth-fixed coordinate system ECEF... The process is as follows: Longitude at any point Earth's latitude as high as the earth Find the coordinates of any point in the Earth-fixed coordinate system ECEF. The formula is: ; in: for The radius of curvature of the circle at point 1; This is the first eccentricity of the Earth's ellipsoid; for exist The components of the axis; for exist The components of the axis; for exist The components of the axis.

[0007] Furthermore, the step of obtaining the transformation matrix from the Earth-fixed coordinate system ECEF to the geocentric inertial coordinate system ECI... The process is as follows: ; in The precession matrix, the precession matrix for: ; In the formula , and These are all equatorial precession parameters, expressed as follows, in radians: ; In the formula, The Julian century number is calculated using the following formula: ; for Time period (year-month-day-hour-minute-second) and its corresponding Julian day: ; Earth's rotation transformation matrix: ; In the formula, With Greenwich Mean Time The conversion relationship is as follows: ; .

[0008] Furthermore, the aforementioned orbital dynamics model is established in the geocentric inertial coordinate system (ECI). The dynamic equations of the perturbation-driven agile imaging satellite are decomposed in Cartesian coordinates to obtain a set of dynamic equations. By numerically integrating these equations, the state vector of the agile imaging satellite at any time within the planning period in geocentric inertial coordinates is recursively obtained. The steps are as follows: In the geocentric inertial coordinate system (ECI), the dynamic equations of the agile imaging satellite are: ; In the formula, This represents the position vector of the agile imaging satellite in the geocentric inertial coordinate system (ECI). The gravitational constant of Earth; This refers to the perturbation acceleration caused by the Earth's oblateness; The acceleration vector of the agile imaging satellite in the geocentric inertial coordinate system (ECI); The dynamic equations of the agile imaging satellite are decomposed in Cartesian coordinates, based on... The perturbation model yields the dynamic equations for agile imaging satellites: ; In the formula, , and These are the position components of the agile imaging satellite in the geocentric inertial coordinate system; , and These are the acceleration components of the agile imaging satellite in the geocentric inertial coordinate system; Earth's gravity Term coefficient, The average radius of the Earth's equator; By numerically integrating the dynamic equations of the agile imaging satellite, the agile imaging satellite's performance at any time within the planning period can be recursively obtained. State vector in the geocentric inertial coordinate system ; wherein, the state vector Including satellite position components and velocity vector ; Then convert to a matrix To obtain the agile imaging satellite at any time within the planning period Position vector in Earth-fixed coordinate system : ; Subsequently, the position vector in the Earth-fixed coordinate system is projected onto the Earth ellipsoid surface to calculate the geodetic longitude of the nadir point of the agile imaging satellite at any given time. and latitude ; ; ; In the formula These represent the position components in the Earth-fixed coordinate system; At the same time, by combining the satellite's velocity vector in the geocentric inertial coordinate system, the satellite's velocity vector in the Earth-fixed coordinate system is obtained through coordinate transformation.

[0009] Furthermore, the target area refers to the specific geographic spatial range that the satellite system needs to cover for observation; in the spatial geometric model, the target area is represented as a closed polygon enclosed by a series of geodetic latitude and longitude coordinates connected in sequence; the boundary vertices of the target area refer to the discrete vertices of the polygon boundary of the target area.

[0010] Furthermore, the calculation of the shortest distance between the nadir point of the agile imaging satellite and the target area... The steps are as follows: Based on the geodetic longitude and latitude of the nadir point of the agile imaging satellite, all boundary vertices of the target area are traversed. The distance from the nadir point of the agile imaging satellite to each vertex is calculated using the great circle distance formula, and the minimum value is taken as the shortest distance. : ; In the formula, The number of vertices at the boundary of the target region; For the target area The geodetic longitude and geodetic latitude of each boundary vertex; The function for calculating the distance between a sphere and a great circle is as follows: ; In the formula, The average radius of the Earth; and These represent the current position of the agile imaging satellite's nadir and the target area's position at that moment. The latitude and longitude coordinates of each boundary vertex .

[0011] Furthermore, the calculation of the observation buffer distance The steps are as follows: ; In the formula, For agile imaging satellite altitude; The radius of the Earth; This is the maximum lateral sway angle; The load field of view angle.

[0012] Furthermore, the calculation time step The process is as follows: Given the current time Based on the geodetic longitude of the nadir point of the Agile Imaging Satellite Earth's latitude and the flight speed of agile imaging satellites The time step of the next sampling time for: ; In the formula, This represents the shortest spherical distance from the nadir point of the agile imaging satellite to the boundary of the target area at the current moment. For observation buffer distance; For agile imaging satellite flight speed; The relative velocity caused by the Earth's rotation; This is the minimum time step.

[0013] Furthermore, the left and right regions are defined as follows: a Cartesian coordinate system is defined, where the straight line containing the trajectory segment of the agile imaging satellite's nadir point is the Y-axis, the flight direction of the agile imaging satellite is the positive direction, the midpoint of the trajectory segment is the origin, and the perpendicularity to the Y-axis is the X-axis. When the X-axis coordinate of a certain sub-region is negative, it is defined as the left region; otherwise, it is defined as the right region.

[0014] The beneficial effects of this invention are as follows: This invention utilizes a distance-aware dynamic step-size adaptive sampling and vector geometric continuous calculation method to dynamically adjust the sampling density based on the real-time distance between the agile imaging satellite and the target area. This significantly reduces the computation time required for agile imaging satellite nadir trajectory points in typical scenarios, while maintaining computational efficiency far exceeding that of high-resolution grid methods. Through coverage capability boundary analysis and effective side-swing angle range calculation, a complete physical constraint system is established, eliminating agile imaging satellite nadir trajectory segments where targets cannot be observed, significantly narrowing the side-swing angle optimization search space, and providing high-quality input data for subsequent mission planning. A vector geometric method is used to construct observation strip polygons and calculate the intersection area, maintaining spatial continuity and avoiding discretization errors. Maintaining a 1-second sampling accuracy within the effective observation area ensures the accuracy of coverage calculation. Compared to traditional fixed step-size and gridded methods, this invention comprehensively utilizes dynamic step-size sampling and vector geometric calculation, significantly improving preprocessing efficiency. It is particularly suitable for large-scale, long-cycle agile imaging satellite regional observation mission planning, meeting the needs of rapid response and high-precision coverage analysis. Attached Figure Description

[0015] Figure 1 This is a flowchart of the dynamic step-size agile imaging satellite nadir trajectory calculation process of this invention; Figure 2 This is a flowchart of the calculation of the effective side sway angle (upper limit side sway angle) when the nadir point trajectory of the agile imaging satellite of the present invention passes through the target area. Figure 3 This is a flowchart (lower limit side swing angle) for calculating the effective side swing angle when the nadir trajectory of the agile imaging satellite of this invention passes through the target area. Figure 4 This is a flowchart of the effective side swing angle calculation (upper limit side swing angle) when the trajectory of the agile imaging satellite nadir point and the target area do not intersect. Figure 5 This is a flowchart (lower limit side swing angle) for calculating the effective side swing angle when the trajectory of the agile imaging satellite nadir point does not intersect with the target area according to the present invention. Figure 6 This is a flowchart of the coverage calculation method based on vector geometry of the present invention. Detailed Implementation

[0016] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0017] This invention provides an agile satellite mission preprocessing method based on dynamic step size and vector geometry, comprising the following steps: S1: Coordinate System Establishment and Orbital Dynamics Modeling. This involves establishing the Earth-fixed coordinate system, the geocentric inertial coordinate system, the orbital coordinate system, and the satellite body coordinate system; deriving the transformation matrices between these coordinate systems; and establishing a system that considers… The perturbation-based orbital dynamics model lays the foundation for accurate calculation of the motion state of agile imaging satellites. The target region refers to the specific geographic spatial area that the satellite system needs to cover. In the spatial geometry model, the target region is represented as a closed polygon bounded by a series of geodetic latitude and longitude coordinates connected sequentially; the boundary vertices of the target region refer to the discrete vertices of the polygon's boundary. S1 includes: S11: Construct the Earth-fixed coordinate system ECEF, the geocentric inertial coordinate system ECI, the orbital coordinate system, and the satellite body coordinate system; The origin of the Earth-fixed coordinate system ECEF is the Earth's center, the Z-axis points to the Earth's North Pole, the X-axis points to the intersection of the Greenwich Meridian and the Earth's equator, and the Y-axis forms a right-handed coordinate system with the X and Z axes. The origin of the geocentric inertial coordinate system (ECI) is at the center of the Earth. The X-axis points to the J2000 mean vernal equinox along the intersection of the Earth's equatorial plane and the ecliptic plane. The Z-axis points to the J2000 mean north pole. The Y-axis is obtained according to the right-hand rule. The orbital coordinate system is based on the centroid of the agile imaging satellite as the origin, with the X-axis along the geocentric radius vector of the agile imaging satellite, the Y-axis along the direction of orbital motion and perpendicular to the X-axis, and the Z-axis perpendicular to the orbital plane, determined by the right-hand rule. The satellite body coordinate system has the centroid of the agile imaging satellite as the origin, and the three axes are the roll axis, pitch axis and yaw axis of the agile imaging satellite attitude motion. S12: Transformations between coordinate systems are achieved using rotation matrices. For the coverage calculation requirements of this paper, the following transformation relationships are introduced: S12-1: Calculate coordinates from the geodetic coordinate system to the Earth-fixed coordinate system ECEF. ; Longitude at any point Earth's latitude as high as the earth Find the coordinates of any point in the Earth-fixed coordinate system ECEF. The formula is: ; in: for The radius of curvature of the circle at point 1; This is the first eccentricity of the Earth's ellipsoid; for exist The components of the axis; for exist The components of the axis; for exist The components of the axis; S12-2: Calculate the transformation matrix from the Earth-fixed coordinate system ECEF to the geocentric inertial coordinate system ECI. ; ; in The precession matrix, the precession matrix for: ; In the formula , and These are all equatorial precession parameters, expressed as follows, in radians: ; In the formula, The Julian century number is calculated using the following formula: ; for Time period (year-month-day-hour-minute-second) and its corresponding Julian day: ; Earth's rotation transformation matrix: ; In the formula, With Greenwich Mean Time The conversion relationship is as follows: ; ; S13: Establish the orbital dynamics model; establish it in the geocentric inertial coordinate system (ECI). The dynamic equations of the perturbation-driven agile imaging satellite are decomposed into vector equations in the Cartesian coordinate system to obtain expressions for the three-axis acceleration components. By numerically integrating the dynamic equations of the agile imaging satellite, the state vector of the agile imaging satellite in the geocentric inertial coordinate system at any time within the planning period is recursively obtained. In the geocentric inertial coordinate system (ECI), the dynamic equations of the agile imaging satellite are: ; In the formula, This represents the position vector of the agile imaging satellite in the geocentric inertial coordinate system (ECI). The gravitational constant of Earth; This refers to the perturbation acceleration caused by the Earth's oblateness; The acceleration vector of the agile imaging satellite in the geocentric inertial coordinate system (ECI); The dynamic equations of the agile imaging satellite are decomposed in Cartesian coordinates, based on... The perturbation model yields the following set of dynamic equations for agile imaging satellites: ; In the formula, , and These are the position components of the agile imaging satellite in the geocentric inertial coordinate system; , and These are the acceleration components of the agile imaging satellite in the geocentric inertial coordinate system; Earth's gravity Term coefficient, The average radius of the Earth's equator; By numerically integrating the dynamic equations of the agile imaging satellite, the agile imaging satellite's performance at any time within the planning period can be recursively obtained. State vector in the geocentric inertial coordinate system ; wherein, the state vector Including satellite position components and velocity vector ; Then convert to a matrix To obtain the agile imaging satellite at any time within the planning period Position vector in Earth-fixed coordinate system : ; Subsequently, the position vector in the Earth-fixed coordinate system is projected onto the Earth ellipsoid surface to calculate the geodetic longitude of the nadir point of the agile imaging satellite at any given time. and latitude Simultaneously, combining the satellite's velocity vector in the geocentric inertial coordinate system, the satellite's velocity vector in the Earth-fixed coordinate system is obtained through coordinate transformation. The latitude and longitude coordinates and velocity vector of the agile imaging satellite's nadir point obtained above will serve as real-time physical state input parameters for the subsequent dynamic step size calculation in S2. ; ; In the formula These represent the position components in the Earth-fixed coordinate system; S2: Dynamic Step-Length Agile Imaging Satellite Nadir Trajectory Generation. This method generates the nadir trajectory of the agile imaging satellite using a distance-based dynamic step-length sampling method. The method dynamically adjusts the calculation step size based on the real-time distance between the agile imaging satellite's nadir trajectory and the target area. When the satellite is far from the target area, a large step size is used for sparse sampling to improve efficiency, while dense sampling is switched to ensure accuracy when approaching or entering the effective observation area, thus optimizing the allocation of computational resources. S2 includes: S21: Calculate the shortest distance between the nadir point of the agile imaging satellite and the target area. Obtain the current nadir position of the agile imaging satellite calculated by the orbital dynamics model in S1. ), traverse all boundary vertices of the target area, calculate the distance from the nadir point of the agile imaging satellite to each vertex using the great circle distance formula, and take the minimum value as the shortest distance; ; In the formula, The number of vertices at the boundary of the target region; For the target area The latitude and longitude of each boundary vertex; The function for calculating the distance between a sphere and a great circle is as follows: ; In the formula, The average radius of the Earth; and These represent the current position of the agile imaging satellite's nadir and the target area's position at that moment. The latitude and longitude coordinates of each boundary vertex ; S22: Calculate the velocity of agile imaging satellites and observation buffer distance : ; In the formula, For agile imaging satellite altitude; The radius of the Earth; This is the maximum lateral sway angle; The load field of view angle; S23: Calculate the difference between the boundary distance and the shortest distance. The difference between the boundary distance and the shortest distance represents the remaining distance between the current position and the effective observation area. This step constructs a spatial geometric initial screening mechanism through the "observation buffer distance." During trajectory extrapolation, the system directly skips invalid points outside the buffer range and only activates high-density sampling and precise lateral sway angle calculation for potential visible points entering the range. This strategy of "first defining the visible boundary, then focusing on fine calculation" significantly eliminates redundant calculations, greatly improving the efficiency of task planning and ensuring high accuracy. S24: Determine whether the satellite has entered the effective observation area. If the difference between the boundary distance and the shortest distance is less than 0, it means that the trajectory of the nadir point of the agile imaging satellite has entered the effective observation area. Set the calculation step size to the minimum value of 1 second and proceed to step S26. If the difference between the boundary distance and the shortest distance is greater than or equal to 0, it means that the trajectory of the nadir point of the agile imaging satellite is still outside the observation area. Proceed to step S25. S25: Calculate the adaptive time step; Given the current time The nadir position of the agile imaging satellite is ( Both the satellite velocity vector and the orbital dynamics model are obtained from the time step of the next sampling time. for: ; In the formula, This represents the shortest spherical distance from the nadir point of the agile imaging satellite to the boundary of the target area at the current moment. For observation buffer distance; For agile imaging satellite flight speed; The relative velocity caused by the Earth's rotation; Minimum time step; S26: Trajectory status update; The current moment The latitude and longitude information of the corresponding agile imaging satellite nadir points are recorded and appended to the agile imaging satellite nadir point trajectory sequence set; subsequently, the time update of the state variables is performed: ; S27: Determine whether the agile imaging satellite nadir trajectory generation is complete, and determine the updated time. Has the set global observation end time been exceeded? : like If the iteration loop terminates, the final set of adaptive nadir point trajectory sequences is output. like Then directly As a new input moment, return to step S21 and proceed to the next round of distance calculation and step size determination; S3: Calculation of the effective side-swing angle range. Based on the geometric relationship between the nadir trajectory of the agile imaging satellite and the target area, the range of side-swing angle values ​​that allow the agile imaging satellite coverage strip to effectively intersect with the target area is calculated. Through region division and distance determination methods, the upper and lower limits of the side-swing angle are determined, significantly narrowing the optimization search space.

[0018] S3 includes: S31: Determine the geometric relationship between the nadir trajectory of the agile imaging satellite and the target area. Based on the intersection of the nadir trajectory of the agile imaging satellite and the boundary of the target area, the geometric relationship is divided into two categories: The first category is that the nadir trajectory of the agile imaging satellite passes through the target area, that is, there is an intersection between the line segment of the nadir trajectory of the agile imaging satellite and the boundary of the target area. In this case, the agile imaging satellite has the dual capabilities of direct observation and side-swing observation. The second category is that the nadir trajectory of the agile imaging satellite does not intersect with the target area, but it may cover the target through side-swing. The judgment condition is that the shortest distance from the nadir trajectory of the agile imaging satellite to the target area is less than the limit coverage boundary distance. In this case, side-swing compensation is necessary to achieve observation. S32: Calculate the lateral sway angle when the nadir trajectory of the agile imaging satellite passes through the target area; The target area is divided into two sub-regions according to the trajectory segment of the nadir point of the agile imaging satellite; a plane rectangular coordinate system is defined, in which the straight line where the trajectory segment of the nadir point of the agile imaging satellite is located is the Y-axis, the flight direction of the agile imaging satellite is the positive direction, the midpoint of the trajectory segment is the origin, and the perpendicular to the Y-axis is the X-axis. When the X-axis coordinate of a certain sub-region is negative, it is defined as the left region; otherwise, it is defined as the right region. For the left region, calculate the farthest distance from the nadir point trajectory segment of the agile imaging satellite to the boundary of the left region. If this distance is greater than the limit coverage boundary distance, the upper limit side sway angle is the maximum side sway angle; otherwise, calculate the corresponding side sway angle by reverse calculation of the farthest distance on the left as the upper limit. For the right region, the same logic is used to calculate the farthest distance from the nadir point trajectory segment of the agile imaging satellite to the boundary of the right region, and to determine the lower limit side swing angle; it should be noted that the right side swing angle is negative, indicating the direction of swing to the right; S33: Calculation of the side sway angle when the trajectory of the agile imaging satellite's nadir point does not intersect with the target area; First, determine which side of the agile imaging satellite's nadir trajectory the target area is located on. Define a Cartesian coordinate system, where the straight line containing the agile imaging satellite's nadir trajectory segment is the Y-axis, the agile imaging satellite's flight direction is the positive direction, the midpoint of the trajectory segment is the origin, and the perpendicular to the Y-axis is the X-axis. When the X-axis coordinate within the target area is negative, the target area is defined as being on the left side of the agile imaging satellite's nadir trajectory segment; otherwise, it is defined as being on the right side. If the target area is located to the left of the agile imaging satellite's nadir trajectory segment, calculate the farthest distance from the agile imaging satellite's nadir trajectory segment to the left boundary of the area. If this distance is greater than the limit coverage boundary distance, the effective side-swing angle range is from 0 to the maximum side-swing angle; otherwise, calculate the corresponding minimum necessary side-swing angle by working backward from the farthest distance on the left. If the target area is located to the right of the agile imaging satellite's nadir trajectory segment, use the same logic to determine the effective side-swing angle range, with the lower limit being either a negative minimum necessary side-swing angle or a negative maximum side-swing angle, and the upper limit being 0. S34: Output effective side-swing angle range. Based on the upper and lower limit side-swing angles calculated above, output the range of side-swing angle values ​​that enable the agile imaging satellite coverage strip to have an effective intersection with the target area. This range provides key constraints for subsequent side-swing angle optimization algorithms, significantly reducing the optimization search space.

[0019] S4: Coverage calculation based on vector geometry. The geometric polygon of the observation strip is directly constructed using vector geometry methods. The coverage is obtained by calculating the intersection area of ​​the polygon and the target area. This method maintains spatial continuity, avoids errors caused by grid discretization, and can accurately express the geometric boundary of the coverage strip. S4 includes: S41: Extract the set of nadir points from the agile imaging satellite. Combine this with the ground coverage width derived from the effective side-swing angle range calculated in S3. Generate a continuous observation strip vector polygon through spherical geometric projection. Traverse the sequence of agile imaging satellite nadir point trajectory points. For each agile imaging satellite nadir point trajectory point, calculate the corresponding left and right boundary point coordinates based on the side-swing angle and field of view. Connect all boundary points sequentially to construct the agile imaging satellite observation strip polygon. S42: Calculate the intersection of the strip and the target region. For each observed strip polygon, calculate its intersection with the target region polygon to obtain the geometric polygon of the actual coverage area. If there are multiple observed strips, perform a geometric union operation on all intersection polygons to remove the overlapping parts and obtain the final total coverage area. S43: Calculate the coverage area and coverage rate. Using the polygon area calculation function, calculate the area of ​​the final covered region. The region coverage rate is defined as the covered area divided by the total area of ​​the target region and output as a percentage. Because the vector geometry method maintains spatial continuity, it can accurately represent the geometric boundaries of the coverage zone and avoid errors caused by mesh discretization; S44: Generates continuous region coverage values ​​and intersecting polygon geometric spatial data. This result eliminates the mesh generation error and computational redundancy caused by traditional mesh discretization methods, achieving an improvement in coverage from approximate estimation to geometric analysis; S45: Integrate the set of nadir points of the agile imaging satellite generated in S2, the effective lateral tilt angle range calculated in S3, and the continuous coverage established in S4 into a preprocessing constraint set; output this constraint set directly to the subsequent task optimization and scheduling to provide accurate spatial geometric basis for the task allocation of the agile imaging satellite.

[0020] Table 1-1 illustrates examples of dynamic step-size adaptive calculation in different scenarios: when generating the nadir trajectory over a day, the dynamic step-size sampling requires only 564 points, while the fixed step-size requires 86,400. The dynamic step-size method reduces the number of trajectory points to be calculated by 99.34%, significantly improving computational efficiency. It can be seen that the step-size gradually decreases as the satellite nadir approaches the target area. In the far-field phase, the step-size remains on the order of hundreds of seconds, while in the near-field phase, it gradually decreases to tens of seconds. When the step-size control parameter is less than the set minimum threshold (1 second), it is determined that the satellite has entered the effective observation area. The step-size is immediately limited to 1 second, and intensive sampling begins. This dynamic step-size adjustment method performs sparse sampling outside the observation area and intensive sampling within the effective observation area, improving computational efficiency.

[0021] Table 1-1 Example of Dynamic Step Size Adaptive Calculation

Claims

1. An agile satellite mission preprocessing method based on dynamic step size and vector geometry, characterized in that, Includes the following steps: Step S1: Determine the target area and its boundary vertices; construct the Earth-fixed coordinate system, the geocentric inertial coordinate system, the orbital coordinate system, and the satellite body coordinate system; calculate the coordinates from the geodetic coordinate system to the Earth-fixed coordinate system ECEF. The transformation matrix from the Earth-fixed coordinate system ECEF to the geocentric inertial coordinate system ECI. ; Construct an orbital dynamics model and establish it in the geocentric inertial coordinate system (ECI). The dynamic equations of the perturbation-driven agile imaging satellite are decomposed in Cartesian coordinates to obtain a set of dynamic equations. By numerically integrating these equations, the state vector of the agile imaging satellite at any time within the planning period in geocentric inertial coordinates is recursively obtained. The system calculates the geodetic longitude, geodetic latitude, and flight velocity of the agile imaging satellite at any given time. Step S2: Iteratively calculate the time step; Step S2-1: Based on the current time Given the geodetic longitude and latitude of the nadir point of the agile imaging satellite, and traversing all boundary vertices of the target area, calculate the shortest distance between the nadir point of the agile imaging satellite and the target area. ; Calculate the observation buffer distance of agile imaging satellites The difference between the shortest distance and the observation buffer distance of the agile imaging satellite is used as the distance margin between the current position and the effective observation area; If the distance margin is less than zero, adjust the time step. Set the step size to the minimum value, and set the current time... The geodetic longitude and geodetic latitude of the nadir points of the agile imaging satellites are added to the set of agile imaging satellite nadir point trajectory sequences; Update the next moment using the time step. , If the next moment Greater than the global observation end time If the iteration loop terminates, the set of agile imaging satellite nadir point trajectory sequences is output; if the next moment... Less than or equal to the global observation end time Then As the current moment, return to step S2-1 and recalculate; The minimum step size is 1 second; If the distance margin is greater than or equal to zero, calculate the time step. Use time step Update the next moment If the next moment Greater than the global observation end time If the iteration loop terminates, the set of agile imaging satellite nadir point trajectory sequences is output; if the next moment... Less than or equal to the global observation end time Then Return to step S2-1 as the current moment; Step S3: Calculate the side swing angle; the side swing angle includes an upper limit and a lower limit; divide the target area into a left area and a right area according to the trajectory segment of the agile imaging satellite nadir point; Step S3-1: Calculate the upper and lower limits of the lateral sway angle when the trajectory of the agile imaging satellite's nadir point crosses the target area; For the left region, calculate the farthest distance from the nadir point trajectory segment of the agile imaging satellite to the boundary of the left region. If this distance is greater than the limit coverage boundary distance, then the upper limit of the side swing angle is the maximum side swing angle. Otherwise, the upper limit of the side swing angle is obtained by calculating the corresponding side swing angle from the farthest distance on the left. For the right region, the same method as for the left region is used to calculate the farthest distance from the nadir point trajectory segment of the agile imaging satellite to the boundary of the right region, and to determine the lower limit of the side sway angle. Step S3-2: Calculate the lateral sway angle when the trajectory of the agile imaging satellite's nadir point does not intersect with the target area; If the target area is located to the left of the nadir trajectory segment of the agile imaging satellite, calculate the farthest distance from the nadir trajectory segment of the agile imaging satellite to the boundary of the left area. If this distance is greater than the limit coverage boundary distance, the swing angle range is from 0 to the maximum side swing angle; otherwise, calculate the corresponding minimum side swing angle by reverse calculation of the farthest distance on the left. If the target area is located to the right of the nadir trajectory segment of the agile imaging satellite, the same method is used to determine the range of the side swing angle. The lower limit of the side swing angle is the negative minimum side swing angle or the negative maximum side swing angle, and the upper limit of the side swing angle is 0. Step S3-3: Based on the calculated side-swing angle, output the range of side-swing angle values ​​that enable the agile imaging satellite coverage strip to have an effective intersection with the target area; Step S4: Derive the ground coverage width based on the set of nadir point trajectory sequences of the agile imaging satellite and the side sway angle; By using spherical geometric projection, a continuous observation strip vector polygon is generated. The set of agile imaging satellite nadir point trajectory sequences is traversed. For each agile imaging satellite nadir point trajectory point, the coordinates of the corresponding left and right boundary points are calculated based on the side sway angle and field of view angle. All boundary points are connected in sequence to construct the agile imaging satellite observation strip polygon. For each agile imaging satellite observation strip polygon, the intersection of the agile imaging satellite observation strip polygon and the target area polygon is calculated to obtain the geometric polygon of the actual coverage area. If there are multiple observation stripes, perform a geometric union operation on all intersecting polygons to remove the overlapping parts and obtain the final total coverage area. The area of ​​the final covered region is calculated using the polygon area. The region coverage rate is the covered area divided by the total area of ​​the target region, and then output as a percentage. Generate continuous regional coverage values ​​and intersecting geometric spatial polygons; integrate the set of nadir point trajectory sequences of agile imaging satellites, side sway angles, and continuous coverage values ​​into a preprocessed constraint set; directly output this constraint set to subsequent task optimization and scheduling, providing accurate spatial geometric basis for task allocation of agile imaging satellites.

2. The agile satellite mission preprocessing method based on dynamic step size and vector geometry according to claim 1, characterized in that, The orbital dynamics model is constructed and established in the geocentric inertial coordinate system (ECI). The dynamic equations of the perturbation-driven agile imaging satellite are decomposed in Cartesian coordinates to obtain a set of dynamic equations. By numerically integrating these equations, the state vector of the agile imaging satellite at any time within the planning period in geocentric inertial coordinates is recursively obtained. The steps are as follows: In the geocentric inertial coordinate system (ECI), the dynamic equations of the agile imaging satellite are: ； In the formula, This represents the position vector of the agile imaging satellite in the geocentric inertial coordinate system (ECI). The gravitational constant of Earth; This refers to the perturbation acceleration caused by the Earth's oblateness; The acceleration vector of the agile imaging satellite in the geocentric inertial coordinate system (ECI); The dynamic equations of the agile imaging satellite are decomposed in Cartesian coordinates, based on... The perturbation model yields the dynamic equations for agile imaging satellites: ； In the formula, , and These are the position components of the agile imaging satellite in the geocentric inertial coordinate system; , and These are the acceleration components of the agile imaging satellite in the geocentric inertial coordinate system; Earth's gravity Term coefficient, The average radius of the Earth's equator; By numerically integrating the dynamic equations of the agile imaging satellite, the agile imaging satellite's performance at any time within the planning period can be recursively obtained. State vector in the geocentric inertial coordinate system ; wherein, the state vector Including satellite position components and velocity vector ; Then convert to a matrix To obtain the agile imaging satellite at any time within the planning period Position vector in Earth-fixed coordinate system : ； Subsequently, the position vector in the Earth-fixed coordinate system is projected onto the Earth ellipsoid surface to calculate the geodetic longitude of the nadir point of the agile imaging satellite at any given time. and latitude ; ； ； In the formula These represent the position components in the Earth-fixed coordinate system; At the same time, by combining the satellite's velocity vector in the geocentric inertial coordinate system, the satellite's velocity vector in the Earth-fixed coordinate system is obtained through coordinate transformation.

3. The agile satellite mission preprocessing method based on dynamic step size and vector geometry according to claim 1, characterized in that, The calculation of the shortest distance between the nadir point of the agile imaging satellite and the target area. The steps are as follows: Based on the geodetic longitude and latitude of the nadir point of the agile imaging satellite, all boundary vertices of the target area are traversed. The distance from the nadir point of the agile imaging satellite to each vertex is calculated using the great circle distance formula, and the minimum value is taken as the shortest distance. : ； In the formula, The number of vertices at the boundary of the target region; For the target area The geodetic longitude and geodetic latitude of each boundary vertex; The function for calculating the distance between a sphere and a great circle is as follows: ； In the formula, The average radius of the Earth; and These represent the current position of the agile imaging satellite's nadir and the target area's position at that moment. The latitude and longitude coordinates of each boundary vertex .

4. The agile satellite mission preprocessing method based on dynamic step size and vector geometry according to claim 1, characterized in that, The calculation of the observation buffer distance The steps are as follows: ； In the formula, For agile imaging satellite altitude; The radius of the Earth; This is the maximum lateral sway angle; The load field of view angle.

5. The agile satellite mission preprocessing method based on dynamic step size and vector geometry according to claim 1, characterized in that, The calculation time step The process is as follows: Given the current time Based on the geodetic longitude of the nadir point of the Agile Imaging Satellite Earth's latitude and the flight speed of agile imaging satellites The time step of the next sampling time for: ； In the formula, This represents the shortest spherical distance from the nadir point of the agile imaging satellite to the boundary of the target area at the current moment. For observation buffer distance; For agile imaging satellite flight speed; The relative velocity caused by the Earth's rotation; This is the minimum time step.

6. The agile satellite mission preprocessing method based on dynamic step size and vector geometry according to claim 1, characterized in that, The target area refers to the specific geographic space range that the satellite system needs to cover for observation; In the spatial geometric model, the target region is represented as a closed polygon formed by a series of geodetic latitude and longitude coordinates connected in sequence; the boundary vertices of the target region refer to the discrete vertices of the polygon boundary of the target region.

7. The agile satellite mission preprocessing method based on dynamic step size and vector geometry according to claim 1, characterized in that, The left and right regions are defined as follows: a Cartesian coordinate system is defined, where the straight line containing the trajectory segment of the agile imaging satellite's nadir point is the Y-axis, the flight direction of the agile imaging satellite is the positive direction, the midpoint of the trajectory segment is the origin, and the perpendicularity to the Y-axis is the X-axis. When the X-axis coordinate of a certain sub-region is negative, it is defined as the left region; otherwise, it is defined as the right region.

8. The agile satellite mission preprocessing method based on dynamic step size and vector geometry according to claim 1, characterized in that, The origin of the Earth-fixed coordinate system ECEF is the Earth's center, the Z-axis points to the Earth's North Pole, the X-axis points to the intersection of the Greenwich Meridian and the Earth's equator, and the Y-axis forms a right-handed coordinate system with the X and Z axes. The origin of the geocentric inertial coordinate system ECI is at the Earth's center, the X-axis points along the intersection of the Earth's equatorial plane and the ecliptic plane to the J2000 mean vernal equinox, the Z-axis points to the J2000 mean North Pole, and the Y-axis is obtained according to the right-hand rule. The orbital coordinate system has the agile imaging satellite's center of mass as its origin, the X-axis is along the geocentric radius vector of the agile imaging satellite, the Y-axis is along the direction of orbital motion and perpendicular to the X-axis, and the Z-axis is perpendicular to the orbital plane and determined by the right-hand rule. The satellite body coordinate system has the agile imaging satellite's center of mass as its origin, and the three axes are the roll axis, pitch axis, and yaw axis of the agile imaging satellite's attitude motion.

9. The agile satellite mission preprocessing method based on dynamic step size and vector geometry according to claim 1, characterized in that, The calculation of coordinates from the geodetic coordinate system to the Earth-fixed coordinate system ECEF The process is as follows: Longitude at any point Earth's latitude as high as the earth Find the coordinates of any point in the Earth-fixed coordinate system ECEF. The formula is: ； in: for The radius of curvature of the circle at point 1; This is the first eccentricity of the Earth's ellipsoid; for exist The components of the axis; for exist The components of the axis; for exist The components of the axis. The transformation matrix from the Earth-fixed coordinate system ECEF to the geocentric inertial coordinate system ECI is obtained. The process is as follows: ； in The precession matrix, the precession matrix for: ； In the formula , and These are all equatorial precession parameters, expressed as follows, in radians: ； In the formula, The Julian century number is calculated using the following formula: ； for Time period (year-month-day-hour-minute-second) and its corresponding Julian day: ； Earth's rotation transformation matrix: ； In the formula, With Greenwich Mean Time The conversion relationship is as follows: ； 。 10. A computer-readable storage medium storing a computer program; characterized in that, When the computer program is executed by the processor, it implements an agile satellite mission preprocessing method based on dynamic step size and vector geometry as described in any one of claims 1-8.

Images