Rapid calculation method for revisit capability of global target constellation
阅读说明：本技术 一种全球目标星座重访能力快速计算方法 (Rapid calculation method for revisit capability of global target constellation ) 是由 胡建龙 安源 李贝贝 戴路 范林东 王宇 于 2021-07-02 设计创作，主要内容包括：本发明提供了一种全球目标星座重访能力快速计算方法,该方法通过建立Walker卫星星座的相对相位构型模型,根据卫星星下点轨迹的解析公式,计算目标点与卫星星下点轨迹的最短距离以判断是否访问目标,并计算得到重访时刻,最终汇总所有卫星的对目标的重访时刻得到卫星星座的重访能力。该方法使得在不依赖卫星轨道预报计算的情况下,能够实现针对全球任意纬度目标星座重访能力的计算,极大程度上提升了计算效率。(The invention provides a method for quickly calculating revisiting capacity of a global target constellation, which comprises the steps of establishing a relative phase configuration model of a Walker satellite constellation, calculating the shortest distance between a target point and a satellite point track according to an analytic formula of the satellite point track to judge whether to access the target, calculating to obtain revisiting time, and finally summarizing the revisiting time of all satellites to the target to obtain the revisiting capacity of the satellite constellation. The method can realize the calculation of the revisit capability of the target constellation at any latitude of the world without depending on the satellite orbit forecasting calculation, thereby greatly improving the calculation efficiency.)
1. A method for rapidly calculating the revisit capability of a global target constellation is characterized by comprising the following steps:
the method comprises the following steps: setting a target, Walker constellation configuration parameters and an angle range of satellite sidesway; the longitude and latitude amplitude information of the rising intersection point of one satellite in the constellation and the number of orbit circles are known, and the longitude and latitude amplitude information of the rising intersection point of all other satellites is obtained through calculation;
step two: calculating the distance of the satellite covering the earth;
step three: calculating to obtain the satellite down-satellite point track of the whole period of the satellite according to the longitude of the ascending point of the satellite in the step one and a formula of the satellite down-satellite point track;
step four: calculating the shortest distance between the tracks of the points under the satellite in the step two of setting the target distance in the step one; if the shortest distance between the set target and the substellar point track is less than or equal to the distance which the satellite can cover the earth, the satellite can access the set target in the orbit period; if the shortest distance between the set target and the substellar point track is greater than the distance which can cover the earth by the satellite, the satellite cannot access the set target in the orbit period; selecting a next satellite, and repeating the third step to the fourth step; until all satellites in the constellation finish the calculation of the access set target time in the current orbit circle;
step five: after revisit time calculation of all satellites in the constellation for the set target in all orbit circles is completed, summarizing and sequencing all revisit time, and then counting to obtain revisit capacity of the satellite constellation.
2. The method for rapidly calculating the revisit capability of the global target constellation according to claim 1, wherein the third step is capable of calculating an analytic formula of the satellite subsatellite point trajectory, and specifically comprises the following steps:
elevation intersection longitude λ of known satellite0Then, the latitude and longitude of the satellite subsatellite point track changes with the satellite latitude argument u according to the following analytic formula:
φ＝asin(sini·sinu)
where φ is the geocentric latitude of the substellar point, λ is the longitude of the substellar point, i is the orbit inclination, ω isEFor self-rotation of the earthVelocity, omega, right ascension, WΩIs the rate of change of the ascension cross point, omegauIs the satellite latitude amplitude angle change rate.
3. The method as claimed in claim 1, wherein in the fourth step, the method for calculating the shortest distance between the trajectories of the points under the satellite in the first step and the second step for setting the target distance comprises the following steps:
let the longitude and latitude of a point on the satellite subsatellite point track be [ x1,y1]Setting the longitude and latitude of the target point as [ x2,y2]The distance calculation formula of two points on the earth's surface is as follows:
S＝R·acos[cos(y1)cos(y2)cos(x1-x2)+sin(y1)sin(y2)]
setting longitude and latitude determination values of a target point; and y is1Can be composed of x1The distance formula of the observation target point relative to the track of the sub-satellite point can be abbreviated as follows: s ═ F (x)1)；
The distance differential is calculated as follows:
the step of calculating the shortest distance between the target and the sub-satellite point track by using a forward and backward method comprises the following steps:
a, given an initial point x0Initial step length h0Error tolerance err, initial search area [ a, b ]]Let h be h0，x1＝x0；
B, if dF (x)1) If the value is less than 0, turning to the step C, otherwise, turning to the step D;
C，x2＝x1+ h, if dF (x)2) > 0, then b ═ x2,a＝x1H is h/2, otherwise x1＝x2,h＝2h；
D，x2＝x1H, if dF (x)2) If > 0, then x1＝x2H is 2h, otherwise b is x2,a＝x1,h＝h/2；
E, if | b-a | < err, the result xans(a + B)/2, otherwise return value step B;
if the shortest distance x between the target and the track of the points under the satelliteansLess than the distance that the satellite can cover, the satellite can access the target during that orbital period.
Technical Field
The invention belongs to the field of spacecraft orbit design, and particularly relates to a method for rapidly calculating the revisiting capacity of a global target constellation.
Background
The revisiting capability of the satellite constellation is an important index of the service capability of the satellite constellation, and is a main design target in the design of remote sensing, communication and navigation satellite constellations. In conventional calculation of satellite constellation revisitation capability, orbit information of a satellite needs to be used. And the calculation according to the orbit forecast of the satellite and the calculation of the visible window of the target need to consume more computing resources, and the method has low computing efficiency. Meanwhile, some researches propose a brief calculation method only aiming at the revisiting capacity of the equatorial target, so that the calculation efficiency is improved, but the revisiting capacity cannot be calculated aiming at the target at any latitude.
Disclosure of Invention
Aiming at the problem of revisit capability calculation of a Walker satellite constellation, the revisit capability of the satellite to the target is judged by a forward and backward method by utilizing an intersatellite point trajectory analysis formula of the satellite, and then the revisit capability of the satellite constellation is obtained.
The technical scheme adopted by the invention for solving the technical problem is as follows:
a method for rapidly calculating the revisit capability of a global target constellation comprises the following steps:
the method comprises the following steps: setting a target, Walker constellation configuration parameters and an angle range of satellite sidesway; the longitude and latitude amplitude information of the rising intersection point of one satellite in the constellation and the number of orbit circles are known, and the longitude and latitude amplitude information of the rising intersection point of all other satellites is obtained through calculation;
step two: calculating the distance of the satellite covering the earth;
step three: calculating to obtain the satellite down-satellite point track of the whole period of the satellite according to the longitude of the ascending point of the satellite in the step one and a formula of the satellite down-satellite point track;
step four: calculating the shortest distance between the tracks of the subsatellite points of the step two of the step one of setting the target distance; if the shortest distance between the set target and the track of the subsatellite point is less than or equal to the distance which can cover the earth by the satellite, the satellite can access the set target in the orbit period; if the shortest distance between the set target and the track of the substellar points is greater than the distance which can cover the earth by the satellite, the satellite cannot access the set target in the orbit period; selecting a next satellite, and repeating the third step to the fourth step; until all satellites in the constellation finish the calculation of the access set target time in the current orbit circle;
step five: after revisit time calculation of all satellites in the constellation for the set target in all orbit circles is completed, all revisit time is collected and sequenced, and then revisit capacity of the satellite constellation is obtained through statistics.
Further, in the third step, an analytic formula of the satellite subsatellite point trajectory can be calculated, and the method specifically includes the following steps:
elevation intersection longitude λ of known satellite0Then, the latitude and longitude of the satellite subsatellite point track changes with the satellite latitude argument u according to the following analytic formula:
φ＝asin(sini·sinu)
where φ is the geocentric latitude of the substellar point, λ is the longitude of the substellar point, i is the orbit inclination, ω isEIs the rotational angular velocity of the earth, omega is the red meridian at the ascending intersection point, WΩIs the rate of change of the ascension cross point, omegauIs the satellite latitude amplitude angle change rate.
Further, in the fourth step, the calculation method of the shortest distance between the trajectories of the points under the satellite in the step one of setting the target distance and the step two of setting the target distance includes the following steps:
let the longitude and latitude of a point on the satellite subsatellite point track be [ x1,y1]Setting the longitude and latitude of the target point as [ x2,y2]The distance calculation formula of two points on the earth's surface is as follows:
S＝R·acos[cos(y1)cos(y2)cos(x1-x2)+sin(y1)sin(y2)]
setting longitude and latitude determination values of a target point; and y is1Can be composed of x1The distance formula of the observation target point relative to the track of the sub-satellite point can be abbreviated as follows: s ═ F (x)1)；
The distance differential is calculated as follows:
the step of calculating the shortest distance between the target and the sub-satellite point track by using a forward and backward method comprises the following steps:
a, given an initial point x0Initial step length h0Error tolerance err, initial search area [ a, b ]]Let h be h0， x1＝x0；
B, if dF (x)1) If the value is less than 0, turning to the step C, otherwise, turning to the step D;
C，x2＝x1+ h, if dF (x)2) > 0, then b ═ x2,a＝x1H is h/2, otherwise x1＝x2,h＝2h；
D，x2＝x1H, if dF (x)2) If > 0, then x1＝x2H is 2h, otherwise b is x2,a＝x1,h＝h/2；
E, if | b-a | < err, the result xans(a + B)/2, otherwise return value step B;
if the shortest distance x between the target and the track of the points under the satelliteansLess than the distance that the satellite can cover, the satellite can access the target during that orbital period.
The invention has the beneficial effects that: the method has the advantages that under the condition of not depending on satellite orbit prediction calculation, the revisit capability calculation is carried out on any latitude target in the world, meanwhile, the whole calculation process avoids using a satellite orbit prediction algorithm consuming calculation resources, and the calculation efficiency is greatly improved.
Drawings
Fig. 1 is a flowchart of a method for rapidly calculating a global target constellation revisiting capability.
FIG. 2 is a flow chart of the advancing and retreating method.
Figure 3 access time diagrams of a satellite constellation to a target.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and examples.
As shown in fig. 1, a method for fast calculating a global target constellation revisiting capability includes the following steps:
the method comprises the following steps: setting a target, Walker constellation configuration parameters and an angle range of satellite sidesway;
the configuration parameter format of the Walker satellite constellation is as follows: and (3) WalkerT/P/F, wherein T is the total number of satellites in the constellation, P is the number of orbital planes contained in the constellation, and F is a constellation phase factor.
If the relative latitude argument and relative elevation longitude of the first satellite in the satellite constellation are assumed to be 0. The latitude argument of each satellite in the constellation relative to the first satellite is:
where p is the orbital plane number of the satellite and s is the satellite number within the orbital plane.
Meanwhile, when the track turn is nlapIn the meantime, the elevation longitude of each satellite in the constellation relative to the first satellite is:
wherein omegaproFor the precession angle of the rising intersection of each intersection period, ΩspreThe distribution range of the right ascension at the ascending points of the constellation.
Therefore, by knowing the longitude and latitude amplitude information of the intersection point of one satellite in the constellation and the number of orbit turns, the longitude and latitude amplitude information of all other satellites can be calculated by the parameters of the Walker constellation.
Step two: calculating the distance of the satellite covering the earth;
the coverage of the satellite, which includes the yaw maneuvering range and the load beam half-cone angle of the satellite, is a major factor affecting the ability of the satellite to revisit. I.e. delta-phimax+αs. Where, δ is the satellite coverage, φmaxFor maximum yaw maneuvering angle, αsIs the load beam half-cone angle.
According to trigonometric function sine theorem, the half cone angle psi of the earth center angle of the satellite coverage is as follows:
wherein R isEIs the earth radius and h is the satellite orbital height.
The distance S covered by the satellitecovComprises the following steps:
Scov＝REψ
step three: calculating to obtain the satellite down-satellite point track of the whole period of the satellite according to the longitude of the ascending point of the satellite in the step one and a formula of the satellite down-satellite point track;
under the condition of considering the perturbation of the earth oblateness, the longitude and latitude change rate of the satellite subsatellite point track is as follows:
wherein u is the amplitude angle of the orbit latitude, i is the inclination angle of the orbit, phi is the geocentric latitude of the point under the satellite, lambda is the longitude of the point under the satellite, alpha is the right ascension, omegaEIs the rotational angular velocity of the earth, omega is the red meridian at the ascending intersection point, WΩThe rate of change of the right ascension at the ascending crossing point.
The earth center latitude of the satellite subsatellite point is derived by the formula as follows:
the satellite sub-satellite longitude is given by:
therefore, the latitude and longitude of the satellite subsatellite point can be calculated by an analytic formula of the satellite latitude argument.
If the longitude of the ascending point of the satellite is known, the analytic formula of the latitude and longitude of the satellite subsatellite point track is as follows:
φ＝asin(sini·sinu)
wherein, ω isuIs the rate of change of the latitude argument, λ, of the satellite0Is the elevation longitude of the satellite.
Step four: calculating the shortest distance between the tracks of the subsatellite points of the step two of the step one of setting the target distance; if the shortest distance between the set target and the track of the subsatellite point is less than or equal to the distance which can cover the earth by the satellite, the satellite can access the set target in the orbit period; if the shortest distance between the set target and the track of the substellar points is greater than the distance which can cover the earth by the satellite, the satellite cannot access the set target in the orbit period; selecting a next satellite, and repeating the third step to the fourth step; until all satellites in the constellation finish the calculation of the access set target time in the current orbit circle;
and judging whether the satellite can access the target in a certain orbit circle, and calculating the shortest distance of the target point relative to the satellite sub-satellite point track. Because the longitude and latitude of the earth surface do not accord with the attributes of the plane rectangular coordinate system, the shortest distance point cannot be calculated by a formula analysis method or a derivation method. Therefore, the shortest distance point can only be found by a method of searching in a range of solution intervals. Therefore, the shortest distance from the target point to the track is calculated by adopting a forward-backward method.
Empirically, if the longitude of the target point is x0Then the longitude of the corresponding closest distance point on the satellite subsatellite point track is located at [ x [ ]0-Δx,x0+Δx]Within the range, where Δ x is the solution interval size.
The distance between two points on the earth's surface is calculated as follows:
S＝R·acos[cos(y1)cos(y2)cos(x1-x2)+sin(y1)sin(y2)]
wherein, [ x ]1,y1],[x2,y2]Longitude and latitude of two points. Let [ x)2,y2]Is an observed target point, which is a defined value. [ x ] of1,y1]Is a point on the orbit of the satellite's subsatellite point, and y1Can be composed of x1The distance formula of the observation target point relative to the track of the substellar point can be abbreviated as follows: s ═ F (x)1)。
The distance differential is calculated as follows:
as shown in fig. 2, the step of calculating the shortest distance between the target and the sub-satellite point trajectory by using the forward-backward method is as follows:
a, given an initial point x0Initial step length h0Error tolerance err, initial search area [ a, b ]]Let h be h0， x1＝x0；
B, if dF (x)1) If the value is less than 0, turning to the step C, otherwise, turning to the step D;
C，x2＝x1+ h, if dF (x)2) > 0, then b ═ x2,a＝x1H is h/2, otherwise x1＝x2,h＝2h；
D，x2＝x1H, if dF (x)2) If > 0, then x1＝x2H is 2h, otherwise b is x2,a＝x1,h＝h/2；
E, if | b-a | < err, the result xans(a + B)/2, otherwise return value step B;
step five: after revisit time calculation of all satellites in the constellation for the set target in all orbit circles is completed, all revisit time is collected and sequenced, and then revisit capacity of the satellite constellation is obtained through statistics.
After the access judgment of one satellite to the target in one orbit circle is completed, if the access is available, the latitude argument u of the closest distance point on the track is recordedvisitAnd the current simulation round k.
Wherein u isvisit＝xansI.e. the solution of the forward and backward method.
The time for the satellite to visit the target point is as follows:
wherein, PnodIs the intersection period of the satellite.
Sequencing the access time of each satellite to obtain a time set of a satellite constellation access target point as follows: [ T ]visit_1,Tvisit_2,...Tvisit_i...,Tvisit_N,]。
Then the set of revisit times for the satellite constellation is: [ T ]gap_1,Tgap_2,...Tgap_i...,Tgap_N-1,]Wherein T isgap_i＝Tvisit_i+1-Tvisit_i。
For example, the constellation and satellite parameters of a constellation of remote sensing satellites are shown in the following table:
TABLE 1 constellation configuration parameters
Serial number
Item
Numerical value
1
Track height/km
535
2
Orbital inclination angle/°
60
3
Maximum yaw angle/°
30
4
Load half cone angle/° c
1
5
WalkerN/P/F
Walker60/10/1
6
Distribution of ascending crossing points and right ascension angle
100
7
Latitude/degree of target
40
The revisiting capability of the satellite constellation is simulated by using the method, the access time of the satellite constellation to the target is shown in figure 3, and the vertical coordinate value corresponding to the access time of the constellation to the target is 1.
The revisit capability of the satellite constellation to the target is obtained by counting the visit time as shown in the following table:
TABLE 2 satellite constellation revisitation Capacity
Serial number
Item
Numerical value
1
Average number of single daily visits/visit
48.8
2
Average revisit time/min
26.4
3
Maximum revisit time/min
586.7