A method for rapid calculation of the transit time window of Walker constellation to ground area

Abstract

The application discloses a kind of Walker constellation's transit time window fast calculation method to ground area.This method is for the fast calculation of ground area transit time, first, given time range information, constellation orbit information and ground area information are acquired, second, the intersection of orbit plane and ground area is analyzed, the time window of satellite possible transit event is screened, then, the characteristics of Walker constellation satellite uniform distribution on orbit plane are combined, the satellite orbit position in potential transit time window is quickly calculated, finally, the transit time window is obtained by judging whether the subpoint is inside or outside the area.The method can quickly calculate the time window of satellite transit ground area by analyzing the intersection of orbit plane and ground area, and combining the characteristics of Walker constellation satellite uniform distribution on orbit plane.The advantages of the method are: (1) significantly improve the calculation efficiency; (2) suitable for large-scale Walker satellite constellation.

Description

Technical Field

[0001] This invention belongs to the field of aerospace technology, specifically a method for rapidly calculating the transit time window of the Walker constellation over a ground region. Background Technology

[0002] For ground areas, the satellite transit time window is calculated using target orbit prediction data to determine the time range during which an in-orbit satellite passes over the target ground area. Transit time window calculations are widely used in aerospace tracking and control networks and satellite mission planning and control.

[0003] In existing technologies, patent CN117875029A proposes a method for analyzing the transit of land observation satellites. This method combines a long-term coarse prediction model based on orbital regression characteristics with a short-term precise prediction model based on the SGP4 algorithm. First, a long-term coarse calculation model based on sun-synchronous regression patterns and a short-term precise calculation model based on TLE-SGP4 are established. Then, the model is automatically selected according to the mission period to perform spatial relationship calculations on point / regional targets, quickly outputting imaging parameters such as transit time, side-swing angle, and solar angle. The results are automatically reported to the mission system via the FTP protocol, achieving integration of long-term overall planning and short-term precise observation. However, when dealing with large-scale systems such as the Walker constellation, problems such as low computational efficiency exist. Summary of the Invention

[0004] The purpose of this invention is to propose a method for rapidly calculating the transit time window of the Walker constellation over the ground region. This method analyzes the intersection between the orbital plane and the ground region, and combines the characteristic of the Walker constellation being evenly distributed on the orbital plane, to quickly calculate the transit time window of the satellite over the ground region.

[0005] The technical solution to achieve the purpose of this invention is as follows: a method for quickly calculating the transit time window of the Walker constellation over a ground area. First, the intersection of the orbital plane and the ground area is analyzed to screen the time windows in which satellites may transit events. Then, combined with the characteristic that Walker constellation satellites are evenly distributed on the orbital plane, the satellite orbital positions within the potential transit time window are quickly calculated. Finally, the transit time window is obtained by determining whether the nadir point is inside or outside the area.

[0006] The specific implementation steps are as follows:

[0007] Step (1): Obtain the given time range information, satellite constellation orbit information, and ground area information.

[0008] Step (2): In the first Select the j-th satellite on the orbital plane. and adjacent satellites The HPOP orbital recursive model was used to predict the orbital parameters of two satellites during the simulation time, including position and velocity.

[0009] Step (3): Based on the types of circular and polygonal areas on the ground, design a geometric method to determine the intersection between the track surface and the ground area.

[0010] Step (4): Using satellite and satellite Using the current position as a reference, and leveraging known orbital parameters and the relative positions of other satellites in the orbit, the method for calculating the positions of satellites in the same orbit is applied to further deduce the time window of intersection of other satellites on the current orbital plane. The position of the track within.

[0011] Step (5): In the intersection time window Within this framework, linear interpolation is used to calculate the transit time window for each satellite over circular or polygonal regions on the ground.

[0012] Step (6): For all unanalyzed orbital planes, repeat steps (2) to (5) to perform calculations in sequence until all orbital planes are traversed, and finally calculate the transit time of all satellites in different time windows.

[0013] A system for rapidly calculating the transit time window of the Walker constellation over a ground region includes:

[0014] The information acquisition module is used to acquire information within a given time range, satellite constellation orbit information, and ground area information;

[0015] Parameter prediction module, in the first Select the first orbital plane satellite and adjacent satellites The HPOP orbital recursive model was used to predict the orbital parameters of the two satellites during the simulation time, including their position and velocity.

[0016] The filtering and judgment module is used to select a matching geometric method to determine the intersection between the track surface and the ground area based on the different types of ground areas.

[0017] Location calculation module, based on satellite and satellite Using the current position as a reference, and leveraging known orbital parameters and the relative positions of other satellites in the orbit, the method for calculating the positions of satellites in the same orbit is applied to further deduce the time window of intersection of other satellites on the current orbital plane. The orbital position within;

[0018] The transit time window calculation module calculates the time windows in the intersecting time windows. Within the system, linear interpolation is used to calculate the transit time window for each satellite in circular or polygonal regions on the ground. For all unanalyzed orbital planes, the calculation is repeated sequentially until all orbital planes are traversed, and finally, the transit times of all satellites in different time windows are calculated.

[0019] Compared with the prior art, the present invention has the following significant advantages: (1) It can significantly improve the calculation efficiency by screening the time window that may pass through the intersection judgment; (2) It can quickly calculate the position and velocity of the satellite by utilizing the characteristic that the Walker constellation is evenly distributed on the orbital plane, which is suitable for large-scale Walker satellite constellations. Attached Figure Description

[0020] Figure 1 This is a flowchart of a method for rapidly calculating the transit time window of the Walker constellation over a ground region, according to the present invention.

[0021] Figure 2 This is a flowchart illustrating the calculation of the time window for the Walker constellation's transit over the ground region, as described in a specific embodiment of the present invention. Detailed Implementation

[0022] The present invention will now be further described with reference to the accompanying drawings.

[0023] like Figure 1 As shown, this invention provides a method for rapidly calculating the transit time window of the Walker constellation over a ground region, comprising the following steps:

[0024] Step (1): Obtain the given time range information, satellite constellation orbit information, and ground area information;

[0025] Step (2): In the first Select the j-th satellite on the orbital plane. and adjacent satellites The HPOP orbital recursive model was used to predict the orbital parameters of two satellites during the simulation time, including position and velocity.

[0026] Step (3): Based on the types of circular and polygonal areas on the ground, design a geometric method to determine the intersection between the track surface and the ground area.

[0027] Step 3.1: Select two non-overlapping satellites on the orbital plane. and ECEF coordinates and Calculate the normal vector of the circle in the orbital plane. ,in and These represent the position vectors of the two satellites on the orbital plane in the ECEF coordinate system.

[0028] (1)

[0029] And obtain the unit vector of the plane circle normal vector. :

[0030] (2)

[0031] Step 3.2: For the spherical circular region, the method of determining the intersection of the planar circle and the spherical circular region is adopted.

[0032] Calculate the center of the circular region on the sphere Distance to the plane circle :

[0033] (3)

[0034] When D is less than the spherical angle corresponding to the radius of the spherical circular region At that time, the planar circle intersects with the spherical circular region.

[0035] Step 3.3: For spherical polygon regions, use the method of determining the intersection of the planar circle and the spherical polygon region.

[0036] Step 3.3.1: Let the vertices of the polygonal region be... Choose two orthogonal unit vectors in the plane. and Using the plane circle as a parameterized basis, the parameterized equation of the plane circle is calculated. Substituting this equation into the equation of the sphere yields the equation of the intersection circle of the plane circle and the sphere.

[0037] Step 3.3.2: Select one edge of the spherical polygon The great circle containing that side The plane normal vector is Then the intersection circle and the great circle The formula for calculating the intersection point is as follows:

[0038] (4)

[0039] (5)

[0040] Step 3.3.3: For each intersection point Calculate the decision condition t k :

[0041] (6)

[0042] in, for and The central angle between them This represents the proportional parameter along the direction of the intersection point along the edge of the larger circle. If ,but Located on the edge superior.

[0043] Step 3.3.4: Determine all edges of the polygonal region. When the intersection circle and the spherical polygonal region have two intersection points, the planar circle intersects the spherical polygonal region.

[0044] Step 3.4: Based on the methods in Steps 3.2 and 3.3, calculate the time window in which the orbital plane intersects with the ground region, i.e., the potential time period for the satellite to pass through the ground region. ;

[0045] Step (4): Using satellite and satellite Using the current position as a reference, and leveraging known orbital parameters and the relative positions of other satellites in the orbit, the method for calculating the positions of satellites in the same orbit is applied to further deduce the time window of intersection of other satellites on the current orbital plane. The orbital position within;

[0046] Step 4.1: For the Walker-Delta constellation with parameters N / P / F, satellites are uniformly distributed on the same orbital plane, where N represents the total number of satellites in the constellation, P represents the number of orbital planes, and F represents the phase factor. Specify the... If a satellite in an orbital plane is designated as satellite number 0, and the other satellites in the same orbital plane are numbered from west to east relative to satellite number 0, then the satellites in that orbital plane are numbered as follows: It means that among them Let be the number of satellites in a single orbital plane. satellite The ECEF position coordinates are Number satellite The ECEF position coordinates are Considering that the satellites are located on the same plane, they are numbered as follows: satellite Corresponding ECEF position vector Depend on and The linear representation is as follows:

[0047] (7)

[0048] in, and The coefficients to be determined;

[0049] Step 4.2: The angle between the line connecting two adjacent satellites on the same orbital plane and the Earth's center is... You can get and The included angle is , and The included angle is Based on the definition of the angle between vectors, we obtain the following system of equations:

[0050] (8)

[0051] Will Substituting into the above equation, we get

[0052] (9)

[0053] Step 4.3: Solve the system of equations to obtain the coefficients. and Substitute the value This allows us to obtain the specific coordinates of satellite C in the ECEF coordinate system.

[0054] Step (5): In the intersection time window Within this framework, linear interpolation is used to calculate the transit time window for each satellite over circular or polygonal regions on the ground.

[0055] Step (6): For all unanalyzed orbital planes, repeat steps (2) to (5) to calculate in turn until all orbital planes are traversed, and finally calculate the transit time of all satellites.

[0056] A system for rapidly calculating the transit time window of the Walker constellation over a ground region includes:

[0057] The information acquisition module is used to acquire information within a given time range, satellite constellation orbit information, and ground area information;

[0058] Parameter prediction module, in the first Select the first orbital plane satellite and adjacent satellites The HPOP orbital recursive model was used to predict the orbital parameters of the two satellites during the simulation time, including their position and velocity.

[0059] The filtering and judgment module is used to select a matching geometric method to determine the intersection between the track surface and the ground area based on the different types of ground areas.

[0060] Location calculation module, based on satellite and satellite Using the current position as a reference, and leveraging known orbital parameters and the relative positions of other satellites in the orbit, the method for calculating the positions of satellites in the same orbit is applied to further deduce the time window of intersection of other satellites on the current orbital plane. The orbital position within;

[0061] The transit time window calculation module calculates the time windows in the intersecting time windows. Within the system, linear interpolation is used to calculate the transit time window for each satellite in circular or polygonal regions on the ground. For all unanalyzed orbital planes, the calculation is repeated sequentially until all orbital planes are traversed, and finally, the transit times of all satellites in different time windows are calculated.

[0062] Example

[0063] To demonstrate the effectiveness of the algorithm of this invention and fully showcase its ability to quickly calculate the transit time of a target, the following experiment was conducted:

[0064] (1) Initial conditions and parameter settings of the experiment

[0065] The simulation uses Coordinated Universal Time (UTC), starting at 00:00:00 on December 10, 2024, and ending at 00:00:00 on December 11, 2024, for a duration of 24 hours. The experiment selected four ground regions within China for transit analysis, including two circular regions, one quadrilateral region, and one pentagonal region. Specific parameters are as follows:

[0066] Table 1 Experimental parameters for the circular ground area

[0067]

[0068] Table 2 Experimental parameters for polygonal ground regions

[0069]

[0070] The low-Earth orbit (LEO) satellite constellation chosen is Constellation 2 from Starlink's Phase 1 LEO constellation plan. This constellation consists of 1584 satellites, with the following specific parameters:

[0071] Table 3 Starlink Constellation 2 Parameters

[0072]

[0073] In the experiment of calculating the transit time window of the Walker constellation, this invention selected the tracking propagation method as the comparison algorithm.

[0074] (2) Analysis of experimental results

[0075] The experiment selected a time step of 1s for the tracking propagation method and a time step of 20s for the Walker constellation transit fast algorithm. First, the single-satellite fast transit algorithm was used to calculate the transit time windows of the Walker constellation for two types of ground areas. Second, the proposed Walker constellation transit time window fast algorithm was used for analysis. The required CPU time is shown in Table 4.

[0076] Table 4 CPU Time Required for Transit Time Calculation

[0077]

[0078] Table 5 shows the calculation results of the transit time window portion of the ground area using the algorithm of this invention.

[0079] Table 5 Calculation results of the method of the present invention

[0080]

[0081] As shown in Table 4, the method of this invention has significant advantages over the tracking propagation algorithm. While maintaining accuracy, the method of this invention requires 1582 s of CPU time to calculate the time window of the satellite's transit circular region, while the tracking propagation method with a sampling step size of 1 s requires 110320 s. The time required by the method of this invention is only 1.434% of that of the tracking propagation algorithm, and the time required to calculate the time window of the transit polygonal region is also only 1.527% of that of the tracking propagation algorithm. Therefore, the Walker constellation transit time window fast algorithm has higher computational efficiency and accuracy than the traditional tracking propagation method.

[0082] Finally, it should be noted that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for rapidly calculating the transit time window of the Walker constellation over a ground region, characterized in that, Includes the following steps: Step (1): Obtain the given time range information, satellite constellation orbit information, and ground area information; Step (2): In the first Select the first orbital plane satellite and adjacent satellites The HPOP orbital recursive model was used to predict the orbital parameters of the two satellites during the simulation time, including their position and velocity. Step (3): Select the appropriate geometric method to determine the intersection between the track surface and the ground area based on the different types of ground areas; Step (4): Using satellite and satellite Using the current position as a reference, and leveraging known orbital parameters and the relative positions of other satellites in the orbit, the method for calculating the positions of satellites in the same orbit is applied to further deduce the time window of intersection of other satellites on the current orbital plane. The orbital position within the track; the specific implementation method is as follows: Step 4.1: For the Walker-Delta constellation with parameters N / P / F, satellites are evenly distributed on the same orbital plane, where N represents the total number of satellites in the constellation, P represents the number of orbital planes, and F represents the phase factor; specify the... If a satellite in an orbital plane is designated as satellite number 0, and the other satellites in the same orbital plane are numbered from west to east relative to satellite number 0, then the satellites in that orbital plane are numbered as follows: It means that, among them Let the number of satellites in one orbital plane be denoted as . satellite The ECEF position coordinates are Number satellite The ECEF position coordinates are Considering that the satellites are located on the same plane, they are numbered as follows: satellite Corresponding ECEF position vector Depend on and The linear representation is as follows: (7) in, and The coefficients to be determined; Step 4.2: The angle between the line connecting two adjacent satellites on the same orbital plane and the Earth's center is... You can get and The included angle is , and The included angle is Based on the definition of the angle between vectors, we obtain the following system of equations: (8) Will Substituting into the above equation, we get (9) Step 4.3: Solve the system of equations to obtain the coefficients. and Substitute the value This allows us to obtain the time window in which satellite C intersects. Specific coordinates in the inner ECEF coordinate system; Step (5): In the intersection time window Within this framework, linear interpolation is used to calculate the transit time window for each satellite over circular or polygonal regions on the ground. Step (6): For all unanalyzed orbital planes, repeat steps (2) to (5) to perform calculations in sequence until all orbital planes are traversed, and finally calculate the transit time of all satellites in different time windows.

2. The method for rapidly calculating the transit time window of the Walker constellation over the ground region according to claim 1, characterized in that, The specific implementation method of step (3) is as follows: Step 3.1: Select two non-overlapping satellites on the orbital plane. and ECEF coordinates , Calculate the normal vector of the circle in the orbital plane. ,in and These represent the position vectors of the two satellites on the orbital plane in the ECEF coordinate system. (1) And obtain the unit vector of the plane circle normal vector. : (2) Step 3.2: For the spherical circular region, the intersection judgment method between the planar circle and the spherical circular region is used to determine the intersection between the track surface and the ground region; Calculate the center of the circular region on the sphere Distance to the plane circle : (3) When D is less than the spherical angle corresponding to the radius of the spherical circular region At that time, the planar circle intersects with the circular region of the sphere; Step 3.3: For the spherical polygon region, use the method of judging the intersection of the planar circle and the spherical polygon region to determine the intersection of the track surface and the ground region; Step 3.4: Based on the intersection judgment method, calculate the time window of intersection between the orbital plane and the ground region, that is, the potential time period for the satellite to pass through the ground region. .

3. The method for rapidly calculating the transit time window of the Walker constellation over the ground region according to claim 2, characterized in that, The specific implementation method of step 3.3 is as follows: Step 3.3.1: Let the vertices of the polygonal region be... Choose two orthogonal unit vectors in the plane. and Using the parametric basis, the parametric equation of the plane circle is calculated, and the equation of the intersection circle of the plane circle and the sphere is obtained by substituting it into the equation of the sphere. Step 3.3.2: Select one edge of the spherical polygon The great circle containing that side The plane normal vector is Then the intersection circle and the great circle The formula for calculating the intersection point is as follows: (4) (5) Step 3.3.3: For each intersection point Calculate the judgment conditions : (6) in, for and The central angle between them This represents the proportional parameter along the direction of the intersection point along the side of the larger circle; if ,but Located on the edge superior; Step 3.3.4: Determine all edges of the polygonal region. When the intersection circle and the spherical polygonal region have two intersection points, the planar circle intersects the spherical polygonal region.

4. A system for rapidly calculating the transit time window of the Walker constellation over a ground region, characterized in that, This system is based on a fast calculation method for the transit time window of the Walker constellation over the ground area, and includes the following steps: Step (1): Obtain the given time range information, satellite constellation orbit information, and ground area information; Step (2): In the first Select the first orbital plane satellite and adjacent satellites The HPOP orbital recursive model was used to predict the orbital parameters of the two satellites during the simulation time, including their position and velocity. Step (3): Select the appropriate geometric method to determine the intersection between the track surface and the ground area based on the different types of ground areas; Step (4): Using satellite and satellite Using the current position as a reference, and leveraging known orbital parameters and the relative positions of other satellites in the orbit, the method for calculating the positions of satellites in the same orbit is applied to further deduce the time window of intersection of other satellites on the current orbital plane. The orbital position within the track; the specific implementation method is as follows: Step 4.1: For the Walker-Delta constellation with parameters N / P / F, satellites are evenly distributed on the same orbital plane, where N represents the total number of satellites in the constellation, P represents the number of orbital planes, and F represents the phase factor; specify the... If a satellite in an orbital plane is designated as satellite number 0, and the other satellites in the same orbital plane are numbered from west to east relative to satellite number 0, then the satellites in that orbital plane are numbered as follows: It means that, among them Let the number of satellites in one orbital plane be denoted as . satellite The ECEF position coordinates are Number satellite The ECEF position coordinates are Considering that the satellites are located on the same plane, they are numbered as follows: satellite Corresponding ECEF position vector Depend on and The linear representation is as follows: (7) in, and The coefficients to be determined; Step 4.2: The angle between the line connecting two adjacent satellites on the same orbital plane and the Earth's center is... You can get and The included angle is , and The included angle is Based on the definition of the angle between vectors, we obtain the following system of equations: (8) Will Substituting into the above equation, we get (9) Step 4.3: Solve the system of equations to obtain the coefficients. and Substitute the value This allows us to obtain the time window in which satellite C intersects. Specific coordinates in the inner ECEF coordinate system; Step (5): In the intersection time window Within this framework, linear interpolation is used to calculate the transit time window for each satellite over circular or polygonal regions on the ground. Step (6): For all unanalyzed orbital planes, repeat steps (2) to (5) to calculate in turn until all orbital planes are traversed, and finally calculate the transit time of all satellites in different time windows; The system includes: The information acquisition module is used to acquire information within a given time range, satellite constellation orbit information, and ground area information; Parameter prediction module, in the first Select the first orbital plane satellite and adjacent satellites The HPOP orbital recursive model was used to predict the orbital parameters of the two satellites during the simulation time, including their position and velocity. The filtering and judgment module is used to select a matching geometric method to determine the intersection between the track surface and the ground area based on the different types of ground areas. Location calculation module, based on satellite and satellite Using the current position as a reference, and leveraging known orbital parameters and the relative positions of other satellites in the orbit, the method for calculating the positions of satellites in the same orbit is applied to further deduce the time window of intersection of other satellites on the current orbital plane. The orbital position within; The transit time window calculation module calculates the time windows in the intersecting time windows. Within the system, linear interpolation is used to calculate the transit time window for each satellite in circular or polygonal regions on the ground. For all unanalyzed orbital planes, the calculation is repeated sequentially until all orbital planes are traversed, and finally, the transit times of all satellites in different time windows are calculated.

5. The Walker constellation transit time window fast calculation system for ground areas according to claim 4, characterized in that, The filtering and judgment module is implemented as follows: Take two non-overlapping satellites on the orbital plane. and ECEF coordinates , Calculate the normal vector of the circle in the orbital plane. ,in and These represent the position vectors of the two satellites on the orbital plane in the ECEF coordinate system. (1) And obtain the unit vector of the plane circle normal vector. : (2) For a spherical circular region, the intersection of the planar circle and the spherical circular region is used to determine the intersection between the track surface and the ground region; Calculate the center of the circular region on the sphere Distance to the plane circle : (3) When D is less than the spherical angle corresponding to the radius of the spherical circular region At that time, the planar circle intersects with the circular region of the sphere; For spherical polygon regions, the intersection of a planar circle and a spherical polygon region is used to determine the intersection between the track surface and the ground region; Based on the intersection determination method, the time window of intersection between the orbital plane and the ground region is calculated, which is the potential time period for the satellite to pass through the ground region. .

6. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 3.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 3.

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