CN117421518A - Method and system for calculating ground coverage time window of low-orbit satellite - Google Patents
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Abstract
The invention relates to a method and a system for calculating a time window of a low-orbit satellite covering the ground, which calculate the visible time of the satellite to a user or a ground area by combining the satellite motion direction by using a method of plane geometric relation and coordinate system conversion, and comprises the following steps: step S1: converting the longitude and latitude elevation of the satellite, the satellite lower point and the user into ECEF coordinate values; step S2: solving an equation of a tangential plane Q of a point under a satellite in an ECEF coordinate system; step S3: solving a projection point coordinate P1 of a user on the tangent plane Q at the point below the satellite; step S4: converting the coordinate P1 of the projection point in a three-dimensional coordinate system into a coordinate P2 in a two-dimensional plane coordinate system; step S5: calculating chord lengths in a satellite coverage approximate circle of which the user is consistent with the satellite motion direction; step S6: the satellite's time of visibility to the user is calculated. The invention improves the calculation efficiency and calculation precision of the low orbit satellite to the user visible time.
Description
Technical Field
The invention belongs to the field of low-orbit satellite communication, and particularly relates to a method and a system for calculating a ground coverage time window of a low-orbit satellite.
Background
The development of aerospace technology and information technology makes a low-orbit internet satellite communication system gradually become an industry hotspot, and satellite internet also becomes one of important contents of a new building of the country.
In a low-orbit satellite system, since the low-orbit satellite has a small coverage area on the ground and moves at a high speed relative to the ground, the satellite has a very short time to be visible to the user on the ground, and the longest time to be visible varies from several minutes to tens of minutes. In particular, for low-orbit internet satellites at heights of hundreds to thousands of kilometers, the longest visible time for a user is only a few minutes to tens of minutes. Therefore, the user needs to switch frequently between different satellites, so that the switching overhead is increased, and the link can be interrupted and unreliable, so that the use experience of the user is affected.
In order to reduce the user's hand-off between different satellites, the user needs to select a satellite access system with a long visible time. Thus, the calculation of the visible time has important significance for reducing the switching overhead, improving the user experience and improving the system resource management and utilization efficiency.
Currently, a common algorithm for calculating the time of visibility is the track-and-broadcast method, which calculates the time window by determining the observability of continuously sampled satellite orbit positions on the target. Subsequently, multi-sensor coverage algorithms, large circle approximate fast algorithms, simplified earth shape and computation models, simplified rectangular coverage models, etc. have emerged. The algorithm is accurate in calculation, but low in calculation efficiency and high in resource consumption; or the model is simplified, the calculation efficiency is high, but the precision is not high, and the requirement cannot be met.
In the satellite Internet, the system operation and control requirements can provide more efficient real-time calculation service while ensuring certain precision, so as to carry out real-time and accurate control on the dynamic topology of a constellation and the switching of users/areas among different satellites, and avoid the untimely switching control caused by delay generated by the calculation of a large number of concurrences. The existing visual time calculation method is used for calculating a time window based on the observability of the satellite orbit positions for judging continuous sampling on a target or based on a simplified model, so that the calculation complexity is high, or the calculation precision cannot be guaranteed, and the calculation precision and the calculation time cannot be well balanced.
Disclosure of Invention
The invention aims to: the invention provides a method and a system for calculating a time window of a low-orbit satellite covering a ground, which are used for solving the problem that the calculation efficiency and the calculation precision of the low-orbit satellite for the visible time of a user cannot be considered.
The technical scheme is as follows: a method for calculating a ground coverage time window for a low-orbit satellite, comprising the steps of:
step S1: converting the longitude and latitude elevation of the satellite, the satellite lower point and the user into ECEF coordinate values;
step S2: solving an equation of a tangential plane Q of a point under a satellite in an ECEF coordinate system;
step S3: solving a projection point coordinate P1 of a user on the tangent plane Q at the point below the satellite;
step S4: converting the coordinate P1 of the projection point in a three-dimensional coordinate system into a coordinate P2 in a two-dimensional plane coordinate system;
step S5: calculating chord lengths in a satellite coverage approximate circle of which the user is consistent with the satellite motion direction;
step S6: the satellite's time of visibility to the user is calculated.
Specifically, in the step S1, the longitude, latitude and elevation of the low-orbit satellite and the low-orbit satellite user are converted into XYZ coordinates in the ECEF coordinate system, and the specific algorithm is as follows:
，
wherein,the length of a long half shaft of the earth ellipsoid model is;eccentricity and flatness of ellipsoidal model；For the geographic latitude of the satellite or user,is the longitude of the satellite or the user,for the geographic altitude/elevation of the satellite or user,for the x-coordinate values of the satellite or user in the ECEF coordinate system,for the y-coordinate value of the satellite or user in the ECEF coordinate system,z coordinate values in an ECEF coordinate system for a satellite or a user;
the longitude and latitude elevation distribution of the low orbit satellite, the user and the satellite lower point of the low orbit satellite is arranged as、Andlow railECEF coordinates obtained by satellite longitude and latitude elevation conversion areECEF coordinates obtained by converting longitude and latitude elevation of user areECEF coordinates obtained by low-orbit satellite lower-satellite point longitude and latitude elevation conversion are。
Specifically, the step S2 further includes: the tangent plane method perpendicular to the ground center satellite connecting line at the position of the sub-satellite is as follows:
；
wherein,the longitude and latitude elevation coordinates of the satellite lower point of the low orbit satellite in the ECEF coordinate system.
Specifically, the step S3 further includes:
step S31, a parameter equation from the user to the perpendicular to the tangent plane Q where the undersea point is located:
；
step S32, substituting x, y, and z in the step S31 into the following tangential plane equation to obtain the parameter t as:
；
step S33, according to the parameter t obtained in the step S32, the coordinates of the projection point P1 of the user coordinates on the tangential plane are obtained as follows:
；
wherein,，，parameters of a parametric equation representing a straight line in three-dimensional space,ECEF coordinates obtained by converting longitude and latitude elevations of the low-orbit satellites,ECEF coordinates obtained by converting longitude and latitude elevation of the user,and ECEF coordinates obtained by converting longitude and latitude elevations of the satellite points below the low-orbit satellite.
Specifically, the step S4 converts coordinates and equations in the three-dimensional coordinate system into coordinates and equations in the two-dimensional coordinate system, uses the track inclination angle as the slope, and further includes:
step S41, obtaining three-dimensional vectors as two coordinate axes of a two-dimensional plane under a three-dimensional coordinate system by an approximation method、The normal vector of the plane is；
Step S42, transforming the three-dimensional plane coordinate system into the transformation matrix of the original coordinate system into a 4×4 matrix T:
，
wherein,representing three-dimensional vectorsAnd so on;
step S43, coordinates of the projection points in the three-dimensional coordinate systemSupplement is as follows；
Step S44, converting the projection point of the user on the plane under the three-dimensional coordinate system into a point under the two-dimensional plane:
then P2 is；
Step S45: shortening the coordinates of the P2 to obtain the coordinates of the projection point in a two-dimensional plane coordinate system。
Specifically, the step S5 further includes:
step S51, calculating an equivalent radius R of an approximate circle covered by the satellite on the ground;
step S52, calculating in a two-dimensional plane, and obtaining a projection linear equation of satellite motion in the two-dimensional plane by using the inclination angle, the direction and the projection point coordinates of the satellite motion: the straight line equation isPoint thenThe distance to the straight line is:；
the dip angle of satellite motion isIf the satellite moves from the south to the north, thenThe method comprises the steps of carrying out a first treatment on the surface of the If the satellite moves from north to south, then，，；
Step S53: the distance from the origin of the two-dimensional plane to the projection of the satellite motion track on the plane is as follows:
；
step S54: calculating a straight line passing through the projection point, wherein the direction is the satellite motion direction, and the chord length in a satellite coverage area circle on a two-dimensional plane, namely the total visible distance between the satellite and a user is as follows:；
step S55: the remaining visual distance is calculated by a trigonometric formula.
Specifically, the step S6 further includes:
step S61, calculating satellite motion speed as follows:；
step S62, the equivalent motion speed of the projection point of the satellite on the two-dimensional plane is as follows:；
step S63, calculating total visible time as follows:；
step S64, calculating the remaining visible time；
Wherein G is a universal gravitation coefficient; m is the mass of the earth;is the effective radius of the earth;is the satellite orbit altitude.
A computing system for a low-orbit satellite-to-ground coverage time window, comprising the following modules:
module 1: converting the longitude and latitude elevation of the satellite, the satellite lower point and the user into ECEF coordinate values;
module 2: solving an equation of a tangential plane Q of a point under a satellite in an ECEF coordinate system;
module 3: solving a projection point coordinate P1 of a user on the tangent plane Q at the point below the satellite;
module 4: converting the coordinate P1 of the projection point in a three-dimensional coordinate system into a coordinate P2 in a two-dimensional plane coordinate system;
module 5: calculating chord lengths in a satellite coverage approximate circle of which the user is consistent with the satellite motion direction;
and (6) module 6: the satellite's time of visibility to the user is calculated.
The beneficial effects are that: the method has the advantages that the low-orbit satellite height is considered to be low, the arc area covered by the ground can be approximately three-dimensional plane, so that the visible time of the satellite to a user or the ground area is calculated by combining the method of plane geometric relation and coordinate system conversion and the satellite motion direction, the calculation efficiency of the low-orbit satellite to the visible time of the user is improved, the calculation time and calculation resources are saved, and the method has good suitability and application value for satellite selection and satellite cutting decision calculation of a satellite terminal with limited calculation freedom.
Drawings
Fig. 1 is a flowchart of the whole technical scheme of the present invention.
FIG. 2 is a flow chart of a coordinate solution projected on a tangential plane by a user in accordance with the present invention.
FIG. 3 is a flow chart of converting three-dimensional coordinates of a projection point to two-dimensional coordinates according to the present invention.
FIG. 4 is a flow chart of satellite and user visible distance calculation according to the present invention.
Detailed Description
The technical scheme of the invention is further specifically described below through examples and with reference to the accompanying drawings.
As shown in fig. 1, which is a flowchart illustrating the whole technical scheme of the present invention, the present invention provides a method for calculating a time window of coverage of a low-orbit satellite to a ground, comprising the following steps:
step S1: converting the longitude and latitude elevation of the satellite, the satellite lower point and the user into ECEF coordinate values;
step S2: solving an equation of a tangential plane Q of a point under a satellite in an ECEF coordinate system;
step S3: solving a projection point coordinate P1 of a user on the tangent plane Q at the point below the satellite;
step S4: converting the coordinate P1 of the projection point in a three-dimensional coordinate system into a coordinate P2 in a two-dimensional plane coordinate system;
step S5: calculating chord lengths in a satellite coverage approximate circle of which the user is consistent with the satellite motion direction;
step S6: the satellite's time of visibility to the user is calculated.
As a further improvement of the present invention, the step S1 converts the longitude, latitude and altitude of the low orbit satellite and the low orbit satellite user into XYZ coordinates in the ECEF coordinate system, and the specific algorithm is as follows:
，
wherein,the length of a long half shaft of the earth ellipsoid model is;eccentricity and flatness of ellipsoidal model；For the geographic latitude of the satellite or user,is the longitude of the satellite or the user,for the geographic altitude/elevation of the satellite or user,for the x-coordinate values of the satellite or user in the ECEF coordinate system,for the y-coordinate value of the satellite or user in the ECEF coordinate system,z coordinate values in an ECEF coordinate system for a satellite or a user;
the longitude and latitude elevation distribution of the low orbit satellite, the user and the satellite lower point of the low orbit satellite is arranged as、Andthe ECEF coordinate obtained by the elevation conversion of the longitude and latitude of the low orbit satellite isECEF coordinates obtained by converting longitude and latitude elevation of user areECEF coordinates obtained by low-orbit satellite lower-satellite point longitude and latitude elevation conversion are。
As a further improvement of the present invention, the step S2 further includes: the tangent plane method perpendicular to the ground center satellite connecting line at the position of the sub-satellite is as follows:
；
wherein,the longitude and latitude elevation coordinates of the satellite lower point of the low orbit satellite in the ECEF coordinate system.
As a further improvement of the present invention, as shown in fig. 2, the step S3 further includes:
step S31, a parameter equation from the user to the perpendicular to the tangent plane Q where the undersea point is located:
；
step S32, substituting x, y, and z in the step S31 into the following tangential plane equation to obtain the parameter t as:
；
step S33, according to the parameter t obtained in the step S32, the coordinates of the projection point P1 of the user coordinates on the tangential plane are obtained as follows:
；
wherein,，，parametric square for representing straight line in three-dimensional spaceThe parameters of the process are set to be,ECEF coordinates obtained by converting longitude and latitude elevations of the low-orbit satellites,ECEF coordinates obtained by converting longitude and latitude elevation of the user,and ECEF coordinates obtained by converting longitude and latitude elevations of the satellite points below the low-orbit satellite.
As a further improvement of the present invention, as shown in fig. 3, the step S4 of converting coordinates and equations in a three-dimensional coordinate system into coordinates and equations in a two-dimensional coordinate system, using the track inclination angle as a slope, further includes:
step S41, obtaining three-dimensional vectors as two coordinate axes of a two-dimensional plane under a three-dimensional coordinate system by an approximation method、The normal vector of the plane is；
Step S42, transforming the three-dimensional plane coordinate system into the transformation matrix of the original coordinate system into a 4×4 matrix T:
，
wherein,representing three-dimensional vectorsAnd so on;
step S43, coordinates of the projection points in the three-dimensional coordinate systemSupplement is as follows；
Step S44, converting the projection point of the user on the plane under the three-dimensional coordinate system into a point under the two-dimensional plane:
then P2 is；
Step S45: shortening the coordinates of the P2 to obtain the coordinates of the projection point in a two-dimensional plane coordinate system。
As a further improvement of the present invention, as shown in fig. 4, the step S5 further includes:
step S51, calculating an equivalent radius R of an approximate circle covered by the satellite on the ground;
step S52, calculating in a two-dimensional plane, and obtaining a projection linear equation of satellite motion in the two-dimensional plane by using the inclination angle, the direction and the projection point coordinates of the satellite motion: the straight line equation isPoint thenThe distance to the straight line is:；
the dip angle of satellite motion isIf the satellite moves from the south to the north, thenThe method comprises the steps of carrying out a first treatment on the surface of the If the satellite moves from north to south, then，，；
Step S53: the distance from the origin of the two-dimensional plane to the projection of the satellite motion track on the plane is as follows:
；
step S54: calculating a straight line passing through the projection point, wherein the direction is the satellite motion direction, and the chord length in a satellite coverage area circle on a two-dimensional plane, namely the total visible distance between the satellite and a user is as follows:；
step S55: the remaining visual distance is calculated by a trigonometric formula.
As a further improvement of the present invention, the step S6 further includes:
step S61, calculating satellite motion speed as follows:；
step S62, the equivalent motion speed of the projection point of the satellite on the two-dimensional plane is as follows:；
step S63, calculating total visible time as follows:；
step S64, calculating the remaining visible time；
Wherein G is a universal gravitation coefficient; m is the mass of the earth; r0 is the effective radius of the earth; h0 is satellite orbit height.
A computing system for a low-orbit satellite-to-ground coverage time window, comprising the following modules:
module 1: converting the longitude and latitude elevation of the satellite, the satellite lower point and the user into ECEF coordinate values;
module 2: solving an equation of a tangential plane Q of a point under a satellite in an ECEF coordinate system;
module 3: solving a projection point coordinate P1 of a user on the tangent plane Q at the point below the satellite;
module 4: converting the coordinate P1 of the projection point in a three-dimensional coordinate system into a coordinate P2 in a two-dimensional plane coordinate system;
module 5: calculating chord lengths in a satellite coverage approximate circle of which the user is consistent with the satellite motion direction;
and (6) module 6: the satellite's time of visibility to the user is calculated.
In the following, we can see through specific comparative analysis of results that the satellite time of visibility to the user calculated by the algorithm is substantially identical to the time of visibility calculated by the STK, as shown in the following table. However, compared with the STK, the visibility is calculated from time point to time point, so that the visibility time can be calculated by one flow of the algorithm. Therefore, in an application scene (such as a user star selection decision, a star cutting decision and the like) which only needs to calculate the visible time, the algorithm greatly shortens the calculation time, saves the calculation resources, breaks away from the dependence on STK, has better suitability for satellite terminals with limited calculation capacity and has higher application value.
TABLE 1
| Satellite latitude (°) | Satellite longitude (°) | Satellite elevation (km) | User latitude (°) | User longitude (°) | User elevation (km) | Satellite movement direction | STK Total visible time(s) | Algorithm total visible time(s) |
| 42.266 | 85.358 | 1034.630 | 47.2 | 83.34 | 0 | From north to south | 600.261 | 593.720 |
| 26.704 | 94.019 | 1029.293 | 36 | 100 | 0 | From north to south | 548.577 | 441.450 |
| 3.081 | -91.696 | 1025.061 | 10 | -82 | 0 | From north to south | 526.340 | 531.179 |
| 9.838 | -90.054 | 1025.620 | 20 | -87 | 0 | From north to south | 590.603 | 584.367 |
| 30.061 | 93.043 | 1030.336 | 36 | 110 | 0 | From north to south | 295.014 | 300.631 |
| 24.381 | 99.207 | 853.621 | 32 | 100 | 0 | From north to south | 398.502 | 400.384 |
| 27.734 | -84.892 | 854.604 | 24 | -78 | 0 | From north to south | 376.995 | 380.075 |
| 28.670 | 93.600 | 854.894 | 31 | 93 | 0 | From north to south | 445.931 | 444.311 |
| 28.670 | 93.600 | 854.894 | 36 | 105 | 0 | From north to south | 263.761 | 259.061 |
As described above, although the present invention has been shown and described with reference to certain preferred embodiments, it is not to be construed as limiting the invention itself. Various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (8)
1. A method for calculating a ground coverage time window for a low-orbit satellite, comprising the steps of:
step S1: converting the longitude and latitude elevation of the satellite, the satellite lower point and the user into ECEF coordinate values;
step S2: solving an equation of a tangential plane Q of a point under a satellite in an ECEF coordinate system;
step S3: solving a projection point coordinate P1 of a user on the tangent plane Q at the point below the satellite;
step S4: converting the coordinate P1 of the projection point in a three-dimensional coordinate system into a coordinate P2 in a two-dimensional plane coordinate system;
step S5: calculating chord lengths in a satellite coverage approximate circle of which the user is consistent with the satellite motion direction;
step S6: the satellite's time of visibility to the user is calculated.
2. The method of claim 1, wherein the step S1 further comprises:
the longitude and latitude and elevation of the low orbit satellite and the low orbit satellite user are converted into XYZ coordinates in an ECEF coordinate system, and the specific algorithm is as follows:
，
wherein,the length of a long half shaft of the earth ellipsoid model is; />Eccentricity, flatness of ellipsoidal model +.>；/>For the geographical latitude of the satellite or the user, +.>Longitude for satellite or user, +.>Geographic altitude/elevation for satellite or user, < ->X-coordinate values in ECEF coordinate system for satellites or users, < >>Y-coordinate value in ECEF coordinate system for satellite or user, < >>Z coordinate values in an ECEF coordinate system for a satellite or a user;
the longitude and latitude elevation distribution of the low orbit satellite, the user and the satellite lower point of the low orbit satellite is arranged as、/>Andthe ECEF coordinate obtained by converting the longitude and latitude elevation of the low-orbit satellite is +.>ECEF coordinates obtained by converting longitude and latitude elevation of user are +.>Low rail guardECEF coordinates obtained by converting longitude and latitude elevations of points under stars are。
3. The method of claim 1, wherein the step S2 further comprises: the tangent plane method perpendicular to the ground center satellite connecting line at the position of the sub-satellite is as follows:
；
wherein,the longitude and latitude elevation coordinates of the satellite lower point of the low orbit satellite in the ECEF coordinate system.
4. The method of claim 1, wherein the step S3 further comprises:
step S31, a parameter equation from the user to the perpendicular to the tangent plane Q where the undersea point is located:
；
step S32, substituting x, y, and z in the step S31 into the following tangential plane equation to obtain the parameter t as:
；
step S33, according to the parameter t obtained in the step S32, the coordinates of the projection point P1 of the user coordinates on the tangential plane are obtained as follows:
；
wherein,，/>，/>parameters of the parametric equation representing a straight line in three-dimensional space, < >>ECEF coordinates obtained by converting longitude and latitude elevation of low-orbit satellite>ECEF coordinates obtained by converting longitude and latitude elevation of the user,and ECEF coordinates obtained by converting longitude and latitude elevations of the satellite points below the low-orbit satellite.
5. The method according to claim 1, wherein the step S4 converts coordinates and equations in a three-dimensional coordinate system into coordinates and equations in a two-dimensional coordinate system, uses the orbital tilt angle as a slope, and further comprises:
step S41, obtaining three-dimensional vectors as two coordinate axes of a two-dimensional plane under a three-dimensional coordinate system by an approximation method、The normal vector of the plane is +.>；
Step S42, transforming the three-dimensional plane coordinate system into the transformation matrix of the original coordinate system into a 4×4 matrix T:
，
wherein,representing a three-dimensional vector +.>And so on;
step S43, coordinates of the projection points in the three-dimensional coordinate systemSupplement is->；
Step S44, converting the projection point of the user on the plane under the three-dimensional coordinate system into a point under the two-dimensional plane:
then P2 is->；
Step S45: shortening the coordinates of the P2 to obtain the coordinates of the projection point in a two-dimensional plane coordinate system。
6. The method of claim 1, wherein the step S5 further comprises:
step S51, calculating an equivalent radius R of an approximate circle covered by the satellite on the ground;
step S52, calculating in a two-dimensional plane, and obtaining a projection linear equation of satellite motion in the two-dimensional plane by using the inclination angle, the direction and the projection point coordinates of the satellite motion: the straight line equation isPoint->The distance to the straight line is:；
the dip angle of satellite motion isIf the satellite moves from north to south, & gt>The method comprises the steps of carrying out a first treatment on the surface of the If the satellite moves from north to south, then，/>，/>；
Step S53: the distance from the origin of the two-dimensional plane to the projection of the satellite motion track on the plane is as follows:
；
step S54: calculating a straight line passing through the projection point, wherein the direction is the satellite motion direction, and the chord length in a satellite coverage area circle on a two-dimensional plane, namely the total visible distance between the satellite and a user is as follows:；
step S55: the remaining visual distance is calculated by a trigonometric formula.
7. The method of claim 1, wherein the step S6 further comprises:
step S61, calculating satellite motion speed as follows:；
step S62, the equivalent motion speed of the projection point of the satellite on the two-dimensional plane is as follows:；
step S63, calculating total visible time as follows:；
step S64, calculating the remaining visible time；
Wherein G is a universal gravitation coefficient; m is the mass of the earth;is the effective radius of the earth; />Is the satellite orbit altitude.
8. A computing system for a low-orbit satellite-to-ground coverage time window, comprising the following modules:
module 1: converting the longitude and latitude elevation of the satellite, the satellite lower point and the user into ECEF coordinate values;
module 2: solving an equation of a tangential plane Q of a point under a satellite in an ECEF coordinate system;
module 3: solving a projection point coordinate P1 of a user on the tangent plane Q at the point below the satellite;
module 4: converting the coordinate P1 of the projection point in a three-dimensional coordinate system into a coordinate P2 in a two-dimensional plane coordinate system;
module 5: calculating chord lengths in a satellite coverage approximate circle of which the user is consistent with the satellite motion direction;
and (6) module 6: the satellite's time of visibility to the user is calculated.
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