Rapid calculation method for coverage rate of constellation over-the-ground target area

Abstract

The invention discloses a rapid calculation method for the coverage rate of a constellation over-the-ground target area. Aiming at the problems that the number of satellites is large, the coverage rate calculation amount is large, and the calculation precision is low, the calculation method capable of rapidly positioning related satellites, rapidly calculating the coverage rate and keeping high precision is designed. Firstly, satellite orbit recursion is carried out, and satellites related to a target area are rapidly positioned based on a dichotomy. Secondly, calculating a beam coverage area of a satellite to the ground according to a satellite load type; and finally, abstracting the beam coverage area into a planar polygon, calculating an intersection of the satellite-to-ground beam coverage strip polygon and the ground target area polygon, and quickly calculating the coverage rate of the satellite to the ground target area. Aiming at the problems that the number of satellites is large, the coverage rate calculation amount is large, and the calculation precision is low, related satellites can be rapidly positioned, the coverage rate can be rapidly calculated, and the high precision is kept.

Description

Technical Field

[0001] The invention belongs to the technical field of aerospace reconnaissance, and in particular to a method for quickly calculating the coverage rate of a constellation to a ground target area. Background Art

[0002] Space reconnaissance technology usually integrates multiple sensors, combined with optical, radar and electronic reconnaissance technology, to detect ground targets around the clock, which can provide more comprehensive and accurate intelligence information. The key point of this technology is the coverage analysis of the ground area, and all information comes from the observable area. In practical application, studying efficient and fast calculation methods of constellation coverage rate is the key to evaluating the effectiveness of constellation coverage rate.

[0003] The existing calculation method of satellite coverage of ground target area is suitable for calculating the coverage of a single satellite. When the scale of satellites increases, the number of traversals of the ground grid area increases sharply, which seriously affects the calculation speed. In addition, to improve the calculation accuracy, it is necessary to divide the target area into more refined grids, which increases the impact on the calculation speed exponentially.

[0004] Patent with publication number CN116975504A discloses a method for quickly calculating targets in satellite reconnaissance coverage areas. Although this method can quickly calculate satellite reconnaissance coverage areas, it has not been applied to constellations. Patent with publication number CN116975501A discloses a method for optimizing satellite payload coverage calculations for ground targets. Although this method can solve the problem of long time and interval calculation time for satellite payloads to cover ground targets, it does not quickly calculate the coverage rate of the coverage area. Patent with publication number CN117493796A discloses a method for calculating satellite beam coverage multiplicity based on the grid point method. This method can be used to calculate satellite beam coverage multiplicity, but the calculation efficiency using the grid method is relatively low. Summary of the invention

[0005] The purpose of the present invention is to propose a fast calculation method for the coverage rate of a constellation to a ground target area in order to solve the problems of a large number of satellites, diversified ground target areas, and time-consuming coverage calculation. The method can efficiently and accurately calculate the coverage rate of a constellation to a ground target area.

[0006] The technical solution to achieve the purpose of the present invention is: a method for quickly calculating the coverage of a constellation to a ground target area, and the specific implementation steps are as follows:

[0007] Step (1): Perform rough orbit recursion on the constellation satellites to obtain satellite orbit data and calculate the coverage relationship of all satellites to all ground target areas;

[0008] Step (2): Based on the coverage relationship between the satellite and the ground target area, use a dynamic step size to quickly locate the sub-satellite position of the satellite before and after entering and leaving the ground target area;

[0009] Step (3): Calculate all beam coverage areas of the same satellite relative to the same ground target area, and merge all beam coverage areas into one beam coverage strip;

[0010] Step (4): Calculate the intersection of the beam coverage strip of the same satellite relative to the same ground target area and the target area, which is the area of ​​the ground target area covered by a single satellite;

[0011] Step (5): Count the parts of the same ground target area covered by each relevant satellite and calculate their union. Then, based on the ratio of the union to the ground target area, the coverage rate of the constellation to the ground target area can be obtained.

[0012] Compared with the prior art, the present invention has the following significant advantages: (1) The calculation speed of the coverage problem of a single satellite is fast and accurate. The present invention uses a dynamic step size to recursively infer the satellite orbit, which greatly reduces the calculation time of the satellite orbit. At the same time, by judging whether the maximum beam profile of the satellite and the maximum profile of the ground area intersect, the satellite related to the ground target area is screened, and the calculation efficiency is higher. For the calculation of the satellite coverage area, the coverage area is abstracted into a polygon in the geodetic coordinate system, and the polygon intersection and union operation rules are used for fast calculation. This calculation method is fast and accurate. Compared with the traditional grid method, the calculation efficiency is not affected by the accuracy. (2) For the ground coverage problem of the constellation, the relevant satellite can be quickly located. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 The present invention is a flowchart of a method for quickly calculating the coverage rate of a constellation to a ground target area. DETAILED DESCRIPTION

[0014] The present invention will be further described below in conjunction with the accompanying drawings.

[0015] like Figure 1 As shown, the present invention is a method for quickly calculating the coverage of a constellation to a ground target area, comprising the following steps:

[0016] Step (1): Perform a rough orbit recursion on the constellation satellites to obtain satellite orbit data and calculate the matching relationship between all satellites and all target areas. The specific description is as follows:

[0017] Perform large-step recursion on all satellites in the constellation according to the orbit model, and mark all satellites that may have coverage with the target area according to the distance relationship between the satellite sub-satellite trajectory and the center of the target area, satisfying the following constraints:

[0018] (1)

[0019] in, is the maximum beam coverage radius of satellite i, is the maximum contour radius of the target area j, is the sum of the maximum radii of satellite i and target area j, is the distance between the subsatellite point of satellite i and the center of target area j.

[0020] Step (2): Based on the matching relationship between the satellite and the target area, use the dynamic step size to quickly locate the sub-satellite position of the satellite before and after entering and leaving the ground area. The specific process is as follows:

[0021] For the satellites and ground areas that may have an overlapping relationship in step (1), at the moment of overlapping,

[0022] The satellite orbit is dynamically recursively calculated with a step length between the minimum step length of 1 second and the maximum preset step length of n seconds. A binary selection is made, and formula (1) is used as the binary judgment criterion. If it is true, the step length is increased, and if it is false, the step length is reduced until the orbit recursion stops when there is no intersection between the satellite and the target area and the step length is the minimum value. At this time, the sub-satellite position of the satellite before and after entering and leaving the ground area can be quickly located, as described as follows:

[0023] (2)

[0024] in, The set of satellite sub-satellite points representing the entry and exit times, represents the set of all recursive satellite sub-satellite points, Represents the input ground target area set.

[0025] Step (3): Calculate all beam coverage areas of the same satellite relative to the same ground target area, and merge all areas into one beam coverage strip, as described below:

[0026] For the satellites and ground areas that may have a coverage relationship in step (2), calculate the beam coverage range around the sub-satellite point of the satellite when a coverage event occurs. The coverage range is expressed as a polygon in the geodetic coordinate system. Calculate the union of all beam coverage polygons around the sub-satellite point. This set is the beam coverage strip of the same satellite relative to the same ground target area, which is described as follows:

[0027] (3)

[0028] in, is the satellite beam coverage strip, It is the intersection of the satellite instantaneous beam coverage area and the ground target area.

[0029] Step (4): Calculate the intersection of the beam coverage strip of the same satellite relative to the same ground target area and the ground target area. This area is the area of ​​the ground target area covered by a single satellite. The specific process is as follows:

[0030] For the beam coverage strip of the same satellite relative to the same ground target area calculated in step (3), the strip is also expressed in the form of a polygon in the geodetic coordinate system, and the ground target area is also expressed in the form of a polygon. By calculating the intersection of the two polygons, the coverage area of ​​the same satellite relative to the same ground target area can be obtained. This area is the area covered by the satellite, which is described as follows:

[0031] (4)

[0032] in, It is the portion of the ground target area covered by the satellite beam coverage strip.

[0033] Step (5): Count the parts of the same ground target area covered by each relevant satellite, calculate their union, and then calculate the ratio of the union to the area of ​​the ground target area to obtain the coverage rate of the constellation to the ground target area. The specific process is as follows:

[0034] For the intersection of the beam coverage strip and the target area of ​​the same satellite relative to the same ground target area calculated in step (4), the coverage area of ​​each satellite in the entire constellation for the same ground target area is counted, and the union of all the coverage area polygons is calculated. Finally, the ratio of the area of ​​the union polygon to the area of ​​the ground target area is calculated, and the coverage rate of the constellation over the ground target area can be obtained.

[0035] (5)

[0036] in, is the coverage rate of the entire constellation over the target area on the ground, is the area of ​​the same ground target area covered by all satellites, is the area of ​​the ground target area.

[0037] The present invention will be further described below in conjunction with the embodiments.

[0038] In order to illustrate the effectiveness of the method of the present invention and fully demonstrate that the method has the function of quickly calculating the coverage rate of the constellation to the ground target area, the experiment is completed as follows:

[0039] (1) Experimental initial conditions and parameter settings

[0040] This simulation setting includes a constellation of 24 satellites, a total of five ground target areas, including two circular areas and three polygonal areas, and calculates the coverage of these five ground areas within one day. The experiment mainly demonstrates the rapidity of the present invention by comparing the time consumption of the algorithm before and after the improvement; the coverage of STK is used as the standard value, and the absolute error between the coverage calculated before the improvement and the coverage calculated by the present invention and the standard value is used to demonstrate the accuracy of the present invention.

[0041] The experimental hardware platform is as follows:

[0042] Processor: Intel(R) Core(TM) i9-14900HX; Memory: 32.0 GB; Operating system: Windows 11; Development tools: Visual Studio 2022.

[0043] Take some satellites of the constellation as an example, and their orbital parameters are as follows:

[0044] Table 1 Some satellite orbit experiment parameters

[0045] serial number Semi-major axis / m Eccentricity Orbital inclination / radian Ascending node right ascension / arc Argument of perigee / radian Mean anomaly / radians 96555 7800112.963 0.000237 0.997103 1.164218 0.006596 5.119367 15427 7800173.156 0.000181 0.997112 0.174367 0.006358 6.055764 25338 7800373.646 0.000394 0.967305 4.934166 2.102729 1.348544 43491 8001387.127 0.000098 0.967473 0.533865 2.106277 5.749572 41882 7577501.174 0.000255 0.865928 2.669889 5.258907 3.778072 40749 7577436.629 0.000155 0.866244 2.682812 4.371374 3.760869 85133 7800081.941 0.000248 0.993511 4.077237 0.005177 2.205499 94166 7800134.609 0.000267 0.993633 3.697344 0.006156 2.585557 10159 7800365.774 0.000283 0.963437 0.161579 4.200273 6.122774 43707 7800384.411 0.000158 0.963415 5.658801 4.199234 0.625344

[0046] Take some satellites of the constellation as an example, and their payload parameters are as follows:

[0047] Table 2 Experimental parameters of some satellite payloads

[0048] serial number Orbital Time / UNIX Satellite Type Circular beam angle / ° Rectangular X-direction beam angle / ° Rectangular Y-direction beam angle / ° 96555 1722293913 Electronic Detective 15 15427 1722293913 Electronic Detective 20 25338 1722293913 Electronic Detective 15 43491 1722293913 Electronic Detective 10 41882 1722293913 Optics 15 10 40749 1722293913 Optics 20 15 85133 1722293913 Optics 15 10 94166 1722293913 Optics 10 20 10159 1722293913 Optics 15 15 43707 1722293913 Electronic Detective 10

[0049] The ground target area parameters are as follows:

[0050] Table 3 Experimental parameters of ground target area

[0051] Area No. Region Type Parameter value / (longitude / °, latitude / °) radius KM 1 Round （129.943452，43.764194） 500 2 Round （111.440943，39.652754） 500 3 Polygon （99.522030, 38.479572 ）（98.522030, 41.479572）（102.522030, 42.479572） （101.522030,38.479572） 4 Polygon （092.489663, 38.479572） （90.489663, 40.479572） （93.489663, 42.479572） （94.489663,40.479572） （94.489663, 38.479572） 5 Polygon （76.346035, 38.415383） （74.346035, 40.415383） （77.346035, 42.415383） （78.346035,40.415383） （78.346035, 38.415383）

[0052] (2) Analysis of experimental results

[0053] In one day, the coverage of the preset constellation for five target areas on the ground is as follows:

[0054] Table 4 Ground target area coverage

[0055] Area No. 1 2 3 4 5 Coverage before improvement 0.517 0.942 0.962 0.947 0.996 Invention coverage 0.395 0.849 0.877 0.823 0.892 STK Coverage 0.528 0.977 1 1 0.996

[0056] The absolute errors before improvement and the present invention relative to STK are shown in the following table:

[0057] Table 5 Absolute error table with STK coverage

[0058] Area No. Error type The present invention Before improvement 1 Absolute error 0.011 0.133 2 Absolute error 0.035 0.128 3 Absolute error 0.038 0.123 4 Absolute error 0.053 0.177 5 Absolute error 0.000 0.104

[0059] The time consumption of the algorithm of the present invention and the time consumption of the algorithm before improvement are as follows:

[0060] Table 6 Algorithm time consumption

[0061] algorithm Time consumed / s Before improvement 35.732 The present invention 7.224

[0062] From the analysis of the above table, it can be seen that the average absolute error of the present invention is 0.027, while the average absolute error of the algorithm before improvement is 0.133. The coverage error calculated by the present invention is only 20.3% of that before improvement, and the time consumption is only 20.2% of that before improvement.

[0063] In summary, the present invention can quickly and accurately calculate the coverage rate of the constellation to the ground target area.

[0064] Finally, it should be noted that the above is only 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 above embodiments, those skilled in the art can still modify the technical solutions described in the above embodiments or replace some of the technical features therein by equivalents. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for quickly calculating the coverage of a constellation to a ground target area, characterized in that: The steps include: Step (1): Perform rough orbit recursion on the constellation satellites to obtain satellite orbit data and calculate the coverage relationship of all satellites to all ground target areas; Step (2): Based on the coverage relationship between the satellite and the ground target area, use a dynamic step size to locate the sub-satellite position of the satellite before and after entering and leaving the ground target area; Step (3): Calculate all beam coverage areas of the same satellite relative to the same ground target area, and merge all areas into one beam coverage strip; Step (4): Calculate the intersection of the beam coverage strip of the same satellite relative to the same ground target area and the ground target area. This area is the area of ​​the ground target area covered by a single satellite. Step (5): Count the parts of the same ground target area covered by each relevant satellite, calculate their union, and calculate the ratio of the area of ​​the union area to the area of ​​the ground target area, so as to obtain the coverage rate of the constellation to the ground target area.

2. The method for rapidly calculating the coverage of a constellation-oriented ground target area according to claim 1, characterized in that: The specific implementation method of step (1) is as follows: Perform large-step recursion on all satellites in the constellation according to the orbit model, and mark all satellites that may have coverage relationship with the target area according to the distance relationship between the satellite sub-satellite point trajectory and the center of the target area, as follows: (1) in, For satellite The beam covers the maximum radius, Target area The maximum contour radius, For satellite and target area The sum of the maximum radii of For satellite Subsatellite point and target area Distance from center.

3. The method for rapidly calculating the coverage rate of a constellation-oriented ground target area according to claim 2, characterized in that: The specific implementation method of step (2) is as follows: In view of the coverage relationship between the satellite and the ground target area in step (1), at the moment of coverage, the satellite orbit is dynamically recursively stepped, and a binary selection is made between the minimum step length of 1 second and the maximum preset step length of n seconds. Formula (1) is used as the binary judgment standard. If it is true, the step length is increased, and if it is false, the step length is reduced until the orbit recursion stops when there is no intersection between the satellite and the target area and the step length is the minimum value. At this time, the sub-satellite position of the satellite before and after entering and leaving the ground target area can be located, which is described as follows: (2) in, The set of satellite sub-satellite points representing the entry and exit times, represents the set of all recursive satellite sub-satellite points, Represents the input ground target area set.

4. The method for rapidly calculating the coverage rate of a constellation-oriented ground target area according to claim 1, characterized in that: The specific implementation method of step (3) is as follows: According to the coverage relationship between the satellite and the ground target area in step (2), the beam coverage range around the sub-satellite point of the satellite in the event of a coverage event is calculated. The coverage range is expressed as a polygon in the geodetic coordinate system. The union of the beam coverage polygons around all sub-satellite points is calculated. This set is the beam coverage strip of the same satellite relative to the same ground target area, which is described as follows: (3) in, is the satellite beam coverage strip, It is the intersection of the satellite instantaneous beam coverage area and the ground target area.

5. The method for rapidly calculating the coverage rate of a constellation-oriented ground target area according to claim 1, characterized in that: The specific implementation method of step (4) is as follows: For the beam coverage strip of the same satellite relative to the same ground target area calculated in step (3), the strip is also expressed in the form of a polygon in the geodetic coordinate system, and the ground target area is also expressed in the form of a polygon. By finding the intersection of these two polygons, the coverage area of ​​the same satellite relative to the same ground target area can be calculated. This area is the area covered by the satellite in the target area, which is described as follows: (4) in, It is the part of the ground target area covered by the satellite beam coverage strip. is the satellite beam coverage strip, Represents the input ground target area set.

6. The method for rapidly calculating the coverage rate of a constellation-oriented ground target area according to claim 1, characterized in that: The specific implementation method of step (5) is as follows: For the intersection of the beam coverage strip and the target area of ​​the same satellite relative to the same target area calculated in step (4), the coverage area of ​​each satellite in the entire constellation for the same ground target area is counted, and the union of all coverage area polygons is calculated. The union is the coverage area of ​​all satellites covering the same ground area. Finally, the ratio of the area of ​​the union polygon to the area of ​​the ground target area is calculated to obtain the coverage rate of the constellation for the ground target area, which is described as follows: (5) in, is the coverage rate of the entire constellation over the target area on the ground, is the area of ​​the same ground target area covered by all satellites, The area of ​​the ground target region.

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