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Research on Task Satellite Selection Method for Space Object Detection LEO Constellation Based on Observation Window Projection Analysis

Research on Task Satellite Selection Method for Space Object Detection LEO Constellation Based on... aerospace Article Research on Task Satellite Selection Method for Space Object Detection LEO Constellation Based on Observation Window Projection Analysis 1 , 2 , 3 , 1 , 2 1 , 2 1 , 2 Shengyu Zhang * , Zhencai Zhu , Haiying Hu and Yuqing Li Innovation Academy for Microsatellites of Chinese Academy of Sciences, Shanghai 201203, China; zhuzc@microsate.com (Z.Z.); huhy@microsate.com (H.H.); liyq@microsate.com (Y.L.) Shanghai Engineering Center for Microsatellites, Shanghai 201203, China Chinese Academy of Sciences, Beijing 100039, China * Correspondence: zhangsy@microsate.com Abstract: Aiming at the task planning and scheduling problem of space object detection LEO constellation (SODLC) for detecting space objects in deep space background, a method of SODLC task satellite selection based on observation window projection analysis is proposed. This method projects the spatial relative relationships of the SODLC observation blind zone, observation range, and the initial spatial position of the objects onto the surface of the earth for detectable analysis of satellites and targets and binds the dynamic observation conditions to the satellite trajectory after projection calculation of the visible relationship between target changes. On this basis, combined with the features of SODLC with high orbital symmetry, the task satellite selection is divided into two steps: orbit plane selection and task satellite selection. The orbit planes are selected based on the longitude range of the ascending node with the geographic location of the targets, and the task Citation: Zhang, S.; Zhu, Z.; Hu, H.; satellites are selected according to the relative motion relationship between the satellites and the Li, Y. Research on Task Satellite targets together with the constraints of observable conditions. The selection method simplifies the Selection Method for Space Object calculation process of scheduling and selecting task satellites. Simulation analysis prove the method Detection LEO Constellation Based has better task satellite selection efficiency. The method has high practical value for task planning on Observation Window Projection and scheduling for event-driven SODLC. Analysis. Aerospace 2021, 8, 156. https://doi.org/10.3390/ Keywords: space object detection LEO constellation; observation window projection; task satel- aerospace8060156 lite selection Academic Editor: Dario Modenini Received: 9 March 2021 1. Introduction Accepted: 25 May 2021 Published: 31 May 2021 Several megaconstellation projects are in progress for global communications, which are rapidly launching thousands of satellites into low earth orbits. Megaconstellations may Publisher’s Note: MDPI stays neutral have a potential catastrophic impact [1] on the space debris environment [2]. The amount with regard to jurisdictional claims in of debris may augment rapidly if the satellites are not removed from their orbit after end published maps and institutional affil- of life, which is usually short. The large number of satellites in adjacent orbits will also iations. increase the risk of collisions, which may lead to a burst of space debris [3]. With the growing number of space objects and increasing risk of LEO collisions, space object detection LEO constellation (SODLC) has been proposed to work with ground- based sensor networks to enhance the capability of space object detection, tracking, and Copyright: © 2021 by the authors. identification and to establish timely response globally for space emergency events such as Licensee MDPI, Basel, Switzerland. collisions. Du et al. proposed three Walker analog constellations to build and maintain a This article is an open access article catalog of 200,000 LEO space debris [4]. Snow et al. introduced an optimization method distributed under the terms and to the CubeSat constellation design problem for a space-based optical debris observation conditions of the Creative Commons system in which the Walker delta constellation was adopted [5]. Attribution (CC BY) license (https:// SODLC needs to complete real-time system response after emergency events such as creativecommons.org/licenses/by/ collisions. With the dynamic relative position between satellites and the target, multiple 4.0/). Aerospace 2021, 8, 156. https://doi.org/10.3390/aerospace8060156 https://www.mdpi.com/journal/aerospace Aerospace 2021, 8, 156 2 of 17 satellites in the SODLC are required to coordinate and relay information in order to achieve full-range tracking of the target. Moreover, the satellite can determine the orbit of the target with an angles-only method [6]. Therefore, an appropriate satellite and sensor management strategy is needed [7]. Hu et al. proposed a multiobjective optimization framework for the optimal design of emergency observation constellations [8]. SODLC requires autonomous mission planning and sensor scheduling [9] on the satellite to achieve dynamic resource allocation for targets. An observation sequence for a specific target is formed, and different satellites are dispatched in turn to track and detect the target [10]. In the initial stage of an event being triggered, it is particularly important to quickly and accurately select satellites suitable for observation, which is key to a successful response. At the same time, SODLC satellites are constrained by various observation conditions during target tracking. For example, for target detection, the field of view (FOV) requires a deep space background, so the line of sight (LOS) must be above the atmospheric limb; the observation distance is limited by the capability of sensors. These constraints must be used as the screening criteria for task-executing satellites in mission planning [11]. When the event is triggered, the satellite needs to screen the existing satellites in real time to form a task sequence. Yu et al. investigated the emergency scheduling problem and proposed a cooperation-oriented ant colony optimization algorithm (CO-ACO) to solve the observation sequence problem [12]. Existing methods mainly select candidate satellites by directly calculating the spatial visibility between the target and all satellites. However, constraints in the observation conditions lead to high computational complexity, high onboard resource consumption, and low timeliness of mission planning. Existing SODLC planning methods do not effectively use the inherent characteristics of SODLC and the satellite itself to optimize the selection process of task satellites. Although the target is noncooperative, it has certain temporal and spatial uncertainty as an event trigger. Previous studies have fully considered the real-time coverage per- formance of time and space when designing SODLC [13]. In order to achieve balanced spatial double coverage and intersatellite links [14], the Walker constellation adopts a configuration with very high symmetry and periodicity of motion characteristics [15]. In this study, a method is proposed that analyzes and calculates the observation con- ditions depending on the projection of the target trajectory, satellite trajectory, undetectable range of the atmospheric limb constraints, and the maximum detectable distance of the observation distance onto the surface of the earth. At the same time, the task satellite selection is divided into two steps considering the high orbital symmetry, namely orbital plan selection and task satellite selection, which greatly simplifies the calculation process for task satellite selection. After the dynamic observation conditions are projected and bound to the satellite trajectory, the visible relationship with the target change can be precisely calculated, which serves for dynamic mission planning. 2. Problem Description 2.1. Ground Projection of the SODLC Satellite Observation Range SODLC satellites need to observe the target in a deep space background above the atmospheric limb. Therefore, the LOS of the target should be at least tangent to the edge of the atmospheric limb, as shown in Figure 1. Aerospace 2021, 8, 156 3 of 17 Aerospace 2021, 8, 156 3 of 18 Sat sat tar Projection of undetectable region Maximum Projection of detectable region Detection Range e Figure 1. Observation model of the SODLC satellite. Figure 1. Observation model of the SODLC satellite. The The tar target get cannot cannot be be ob observed served w when hen it it ap appears pears in inth the e ra range nge of ofth the e int intersection ersection q of of the line from the satellite to the center of the earth and the tangent of the satellite to the the line from the satellite to the center of the earth and the tangent of the satellite to the atmospheric limb. atmospheric limb. An area centered on the subsatellite point and in range of D is obtained by projecting An area centered on the subsatellite point and in range of bD is obtained by project- the invisible observation angle range of the satellite to the target on the surface of the ing the invisible observation angle range of the satellite to the target on the surface of the earth. A target is undetectable as long as its projection on the earth surface falls within the earth. A target is undetectable as long as its projection on the earth surface falls within the range above. The undetectable range D is determined by the atmospheric limb height H , range above. The undetectable range is determined by the atmospheric limb height satellite orbit height H , and target height H . tar H , satellite orbit height H , and target height H . a s tar 8 h    i R +H R +H 1 e a 1 e a D (t) = cos cos  R , H (t) > H > RRHH b e a  11eeaa tar < R +H R +H (t) e s e D (t )  cosh  cios tar  R ，H （t） H    b e tar a 1 R +H R  H e a R Ht （） (1)   D (t) = cos e s  R , H e (t) tar H  b e a tar > R +H e s D (t) = 0, H  H   b sR  Ha 1 e a D (t )  cos  R ，H （t） H    (1) b e tar a R  H   e s   where R is the radius of the earth. D (t ) 0，H H For a circular orbit, the orbital height of the satellite is regarded as a constant and ba s the atmospheric  limb height can also be considered as a certain value, while the height of the target changes with its movement. Therefore, the undetectable range will also vary where Re is the radius of the earth. with the height of the target. When the target height is lower than the atmospheric limb For a circular orbit, the orbital height of the satellite is regarded as a constant and the height, the undetectable area is completely determined by the atmospheric limb. When the atmospheric limb height can also be considered as a certain value, while the height of the target height is greater than the atmospheric limb height, the undetectable range changes target changes with its movement. Therefore, the undetectable range will also vary with dynamically with the target height. the height of the target. When the target height is lower than the atmospheric limb height, At the same time, the detection capability affects the performance of orbit determi- the undetectable area is completely determined by the atmospheric limb. When the target nation [16]. Flohrer et al. analyzed the performance of space-based optical system with a height is greater than the atmospheric limb height, the undetectable range changes dy- 20 cm aperture, 6 field of view, and flexible integration requirements [17]. namically with the target height. Aerospace 2021, 8, 156 4 of 18 Aerospace 2021, 8, 156 4 of 17 At the same time, the detection capability affects the performance of orbit determi- nation [16]. Flohrer et al. analyzed the performance of space-based optical system with a 20 cm aperture, 6° field of view, and flexible integration requirements [17]. The The detection detection capability capability is is decided decided by by the the apertur aperture, e, optical optical system system ef efficienc ficiency y,, and and integration integration time. time. In In or or der der to to simplify simplify the the analysis analysis ofof the thpr e pro oblem, blem, the th tar e targ get is et calculated is calculated as a 10 cm diameter sphere, and the dimmest magnitude observable by the optical system as a 10 cm diameter sphere, and the dimmest magnitude observable by the optical system studied is around 17.2 M with 15 cm aperture and flexible integration. The magnitude is studied is around 17.2 M v v with 15 cm aperture and flexible integration. The magnitude is calculated by Equation (2): calculated by Equation (2): m26.58 2.5 log [A F( ) L 2 ] (2) m = 26.58 2.5 log [AgF(f)/L ] (2) where where  m is the limiting magnitude; m is the limiting magnitude;  A is area of the space object along the line of sight; A is area of the space object along the line of sight;   is the reflectivity; g is the reflectivity; F( )  is the solar phase angle; and F(f) is the solar phase angle; and  L is the observation distance. L is the observation distance. The calculation results are in Figure 2. The calculation results are in Figure 2. Figure 2. Relationship between detection capability and observation system. Figure 2. Relationship between detection capability and observation system. In Figure 2, with the dimmest magnitude of around 17.2 M in this study, the maxi- In Figure 2, with the dimmest magnitude of around 17.2 Mv in this study, the maxi- mum detection distance is 6000 km. mum detection distance is 6000 km. Because the SODLC satellite has azimuth omnidirectional maneuverability, the con- Because the SODLC satellite has azimuth omnidirectional maneuverability, the con- nection between the farthest point of detection and the center of the earth will also form a nection between the farthest point of detection and the center of the earth will also form a range on the ground with the subsatellite point as the center and D as the arc length, where range on the ground with the subsatellite point as the center and D as the arc length, where D is the maximum range projection of the observation. After eliminating the projection of D is the maximum range projection of the observation. After eliminating the projection of the undetectable area, the detectable area is an annulus with a width of D . the undetectable area, the detectable area is an annulus with a width of Dl. 2 2 2 2 2  2 <  (R +H (t)) +(R +H ) L 1 e e s tar RR  H （t）   H  L     D(t) = cos  R , H (t) > H ee tar s 1 e a  tar  2 R +H (t) (R +H ) ( e ) e s (3) D(t ) cos  R ，H （t） H tar  e tar a  2 R  H （t） R  H      (3) D(t) = 0, H (tee )  H tar s tar  D(t ) 0，H （t） H  tar a Similarly, the maximum length of the observable range D(t) also varies with the Similarly, the maximum length of the observable range Dt () also varies with the H (t) height of the target. When H (t) is less than the atmospheric limb, there is no tar tar detectable range, i.e., D(t) is 0. Ht （） height of the target. When Ht （） is less than the atmospheric limb, there is no tar tar The width of the detectable ring zone is as follows: detectable range, i.e., Dt () is 0. The width of the detectable ring zone is as follows: D (t) = D(t) D (t), H (t) > H (4) l b tar D（t）=D(t) D (t), H（t） H (4) l b tar a Above, a ring-shaped detectable area projected onto the earth’s surface is formed by the constraints of the atmospheric limb observation and the maximum observation distance. Aerospace 2021, 8, 156 5 of 18 Above, a ring-shaped detectable area projected onto the earth’s surface is formed by Aerospace 2021, 8, 156 5 of 17 the constraints of the atmospheric limb observation and the maximum observation dis- tance. 2.2. Dynamic Detectability Analysis of Targets 2.2. Dynamic Detectability Analysis of Targets Because the spatial positions of the target and the satellite are in a highly dynamic Because the spatial positions of the target and the satellite are in a highly dynamic process, the visibility of a target to a specific satellite should be judged under a dynamic process, the visibility of a target to a specific satellite should be judged under a dynamic condition. Therefore, it is necessary to combine the undetectable area Dt () centered on condition. Therefore, it is necessary to combine the undetectable area D ( bt) centered on the the satellite’s satellite’subsatellite s subsatellite point point with with the th detectable e detectable area area D (tD)（ and t） the and satellite’s the satellite subsatellite ’s subsat- l l point trajectory to form a judgment on the detectability condition of a specific target at a ellite point trajectory to form a judgment on the detectability condition of a specific target specific time. The relationship between the projection point of the target on the earth’s at a specific time. The relationship between the projection point of the target on the earth’s surface and the projection of different detection characteristics is shown in Figure 3. surface and the projection of different detection characteristics is shown in Figure 3. Sat HS ( (tt ),  ) tt (XY , ) tar tar Ground Track Figure 3. Dynamic observation area analysis. Figure 3. Dynamic observation area analysis. For For the the tar tar get, get, at ata a given giventime time t,t,the the tar taget’s rget’s geographic geographic longitude longitudeX X , geographic , geographic tar tar latitude Y , and target height H (t) are all determined. latitude tY ar , and target height taHt r （） are all determined. tar tar Similarly, at a given time t, the geographic longitude l(t) and geographic latitude Similarly, at a given time t, the geographic longitude () t and geographic latitude j t of the subsatellite point of a specific satellite Sat are also determined, and the satellite ( ) t of the subsatellite point of a specific satellite Sat are also determined, and the satel- height is still considered as a fixed value. lite height is still considered as a fixed value. For a certain orbit, the geographic longitude l(t) and geographic latitude j(t) of the subsatellite For a certa point in orbit are , th de e termined geograph by ic longit the inclination ude () t of and th ege satellite ographorbit ic latit and udethe  tr t ue of   anomaly at time t. the subsatellite point are determined by the inclination of the satellite orbit and the true The calculation formula for the geographic longitude of the satellite subsatellite point anomaly at time t. is as follows: The calculation formula for the geographic longitude of the satellite subsatellite point l(t) = W + arctan[cos i tan(w + q(t))] (5) g0 is as follows: (t)  arctan cosi tan  (t) The calculation formula for the geographical latitude  ofthe satellite subsatellite point (5) g 0  is as follows: The calculation formula for the geographical latitude of the satellite subsatellite point j(t) = arcsin[sin i sin(w + q(t))] (6) is as follows: Among them, the orbit inclination i is a fixed value for determining the orbit, and ! is a fixed value for the argument of perigee. Aerospace 2021, 8, 156 6 of 17 The true anomaly at a specific time t is as follows: q(t) = q + nt (7) where q is the true anomaly at the initial moment (epoch). n = (8) 5 3 2 where a is the semimajor axis of the orbit, and m = 3.986006  10 km /s . At a specific time t, the arc length D between the subsatellite point on the earth’s HS surface and the target projection point can be calculated as follows: 1 t t t D (t) = R  cos cos(Y ) cos(j(t)) cos(X l(t)) + sin(Y ) sin(j(t)) (9) HS e tar tar tar where l(t) is the geographic longitude and j(t) is geographic latitude of the specific t t satellite Sat’s subsatellite point, X is the geographic longitude and Y is geographic tar tar latitude of the target. According to the length of the arc connecting the subsatellite point and the target projection point, it can be judged whether it is in the detectable area. If DET stands for the number of satellites that have conditions for observing a specific target, DET = 1, D (t) < D (t)  D (t) b HS l (10) DET = 0, D (t)  D (t)[ D (t) > D (t) HS HS b l then, when the length of the arc connecting the subsatellite point and the target projec- tion point D t is greater than the undetectable arc D (t) and less than the maximum ( ) HS detection distance arc D (t), the DET count equals 1. 3. Task Satellite Selecting Method 3.1. Analysis of the Relative Relationship between the SODLC and the Target The SODLC adopts the Walker constellation. In this study, the 24/4/1 constellation configuration was chosen for the simulation analysis. The specific parameters of the seed Satellite1 can be seen in Table 1. Table 1. Orbital parameters of Satellite1. Parameters Value Semimajor axis 7978.14 km Eccentricity 1.47826  10 Inclination 60 RAAN 1.11991  10 Argument of perigee 0 True anomaly 0 The main constraints considered include the observation height of the atmospheric limb, the maximum detection distance, etc. The main simulation input parameters are shown in Table 2. Table 2. Simulation configuration parameters. Parameters Value Atmospheric limb height 80 km Maximum detection distance 6000 km Satellite pointing range Azimuth 360 , pitch  85 Aerospace 2021, 8, 156 7 of 17 3.2. Task Satellite Selection Method Based on Observation Window Projection For the constellation, the target will have visibility to multiple satellites, especially the target with a long trajectory. Therefore, multiple satellites are required to complete the relay tracking of the target during its flight. After a target appears, the system needs to perform task planning and resource scheduling and then select the task satellites. The existing method of selecting task satellites for the SODLC is to calculate the visibility and space observation constraints of the target and all satellites in orbit after the target appearance and then complete the task satellite selection after sorting according to the calculation results. The calculation is more complicated due to the dynamic characteristics of the satellite, the target, the constraints themselves, and the inherent characteristics of the satellite orbit, which are not fully considered to optimize calculation. In this paper, a method of projecting and screening task satellite observation windows is specially proposed. At the same time, the inherent characteristics of the constellation orbit and the relative relationship between the target and the satellite projected to the ground are used to quickly select task satellites. This method reduces unnecessary computing overhead and is adaptive to the task planning and resource scheduling process for dynamic changes. Because the SODLC generally uses fewer orbital planes, analyses in the related litera- ture have also used 3 to 4 orbital planes [18]. For each orbital plane, no matter how many satellites are distributed on this orbital plane at the time, the ascending node longitudes of all satellites on the same orbital surface are distributed in a specific interval at this specific time [19]. R is the width of distribution interval for the ascending or descending nodes of all tracks in an orbital period. R = T w (11) where T is the orbital period of the orbital plane, and w is the earth’s rotation speed. For example, for an orbit with an orbit height of 1600 km and an orbital inclination of 60 degrees, the longitude of the satellite’s ascending node in an orbit is distributed in a longitude interval with a width of 29.549 . Based on the characteristics of the SODLC, the candidate orbital plane can be quickly selected by judging the distribution relationship between the target and the geographic longitude of the ascending node of the orbit. After the specific orbital plane is selected, the relative motion relationship between the target and the satellite can be used to select the candidate orbital plane and then the candidate observation satellites. 3.3. Orbit Plane Selection From Formula (10), a distribution interval of the ascending node longitude of the orbital plane is obtained. To compare the target and this interval, it is necessary to compare the position of the target and the position of the orbital interval on the equator, as shown in Figure 4. The geographical longitude distribution range of the ascending node of the orbital plane can be calculated by the instantaneous root of any satellite in the orbital plane. The calculation of the ascending orbit is shown in Formula (12): W = l tan j ctani > G0 0 0 < q W = W w   T GE0 G0 2p (12) W = W + w  1  T > e GW0 G0 2p W = W  R GC0 GW0 W 2 Aerospace 2021, 8, 156 8 of 17 The calculation of descending orbit is shown in Formula (13): W = l + 180 + tan j ctani > G0 0 2 0 > b < q W = W + 180 + w   T GE0 G0 e 2p (13) W = W + 180 w  1  T > e GW0 G0 2p W = W  R GC0 GW0 W where W is the geographic longitude of the satellite’s ascending node, W is the east G0 GE0 extreme value of the longitude interval, W is the west extreme value of the longitude GW0 interval, and W is the middle value of the longitude interval. a = 6356.755 km is the GC0 polar radius of the earth, and b = 6378.140 km is the equatorial radius. q is the true anomaly of the satellite for the initial state, l is the longitude at the time, and j is the 0 0 latitude at the time. At this moment, we assume that the geographic location of the target has a virtual satellite, calculate the geographic longitude of the virtual satellite’s ascending node, obtain the projection of the target on the equator X that characterizes the orbital G0 plane characteristics of the constellation, and calculate the difference between the center of Aerospace 2021, 8, 156 8 of 18 each orbital surface distribution range and X , filtering the track surface corresponding to G0 the minimum value X W . j j G0 GC0 Direction of orbit track shift Distribution range of ascending node GW0 XG0 Ω G0 ΩGE0 Longitude range of detectable region projection GED0 GWD0 Figure 4. Selection method based on longitude section of ascending node. Figure 4. Selection method based on longitude section of ascending node. The geographical longitude distribution range of the ascending node of the orbital 3.4. Task Satellite Selection Analysis plane can be calculated by the instantaneous root of any satellite in the orbital plane. After selecting the orbital planes, it is necessary to select candidate satellites on The calculation of the ascending orbit is shown in Formula (12): the selected orbital planes. The selection of candidate satellites is mainly based on the relative motion relationship between the satellite and the target with the constraints of    tan ctan i  G 0 0 2 0 observation conditions. To summarize the relative  motion relationship between the target and the satellite,     T GE00 G e the main situation can be seen  in Figure 5. The 2 target and the satellite are moving in (12) completely opposite directions called opposite flight. While they are moving in the same      1 T GW00 G e  direction called codirectional flight. The tangential horizontal flight can be divided into 2  two situations with the same latitude and longitude deviation.  =R    GC0 GW 0   2 The calculation of descending orbit is shown in Formula (13):  a    180  tan ctan i  G 0 0 0    180   T GE00 G e  2 (13)      180   1 T GW00 G e 2   =R    GC0 GW 0   2 where  is the geographic longitude of the satellite’s ascending node,  is the east G 0 GE 0 extreme value of the longitude interval, is the west extreme value of the longitude GW 0 interval, and is the middle value of the longitude interval. a = 6356.755 km is the GC0 polar radius of the earth, and b = 6378.140 km is the equatorial radius.  is the true anomaly of the satellite for the initial state,  is the longitude at the time, and  is the 0 0 latitude at the time. At this moment, we assume that the geographic location of the target has a virtual satellite, calculate the geographic longitude of the virtual satellite’s ascending node, obtain the projection of the target on the equator that characterizes the orbital G 0 plane characteristics of the constellation, and calculate the difference between the center Aerospace 2021, 8, 156 9 of 18 of each orbital surface distribution range and X , filtering the track surface correspond- G 0 ing to the minimum value X  . GG 0 C0 3.4. Task Satellite Selection Analysis After selecting the orbital planes, it is necessary to select candidate satellites on the selected orbital planes. The selection of candidate satellites is mainly based on the relative motion relationship between the satellite and the target with the constraints of observation conditions. To summarize the relative motion relationship between the target and the satellite, the main situation can be seen in Figure 5. The target and the satellite are moving in com- pletely opposite directions called opposite flight. While they are moving in the same di- Aerospace 2021, 8, 156 9 of 17 rection called codirectional flight. The tangential horizontal flight can be divided into two situations with the same latitude and longitude deviation. Tangential flight Co-directional flight Opposite flight Tangential flight Figure 5. Relative motion between satellite and target. Figure 5. Relative motion between satellite and target. 3.4.1. Codirectional Flight 3.4.1. Codirectional Flight The situation of the satellite and the target flying in the same direction can be seen The situation of the satellite and the target flying in the same direction can be seen in in Figure 5. For time-sequence trajectories, the high-precision orbit propagator (HPOP) Figure 5. For time-sequence trajectories, the high-precision orbit propagator (HPOP) was was adopted in the simulation. However, trajectory propagation is not the main research adopted in the simulation. However, trajectory propagation is not the main research com- component of this article, and the propagation time was less than 1 h. Therefore, the model ponent of this article, and the propagation time was less than 1 h. Therefore, the model was simplified, the space targets were calculated as a 10 cm diameter sphere, and the was simplified, the space targets were calculated as a 10 cm diameter sphere, and the sat- satellites were calculated as an 80 cm cube. ellites were calculated as an 80 cm cube. In Figure 6, the red spots represent the space trace of the target, the blue spots denote In Figure 6, the red spots represent the space trace of the target, the blue spots denote the space trace of the satellite, and the green line is the line of sight. It can be seen from the the space trace of the satellite, and the green line is the line of sight. It can be seen from figure that the satellite can detect the target almost all the way, the range of LOS adjustment the figure that the satellite can detect the target almost all the way, the range of LOS ad- is very small, and the observation conditions are better. justment is very small, and the observation conditions are better. The changes in observation conditions during the observation process can be seen in Figure 7, where the green line is the maximum observation projection distance, the red line is the undetectable projection distance, and the blue line is the projection distance between the satellite and the target. The green area is the width of the observable area. It can be seen from the figure that the distance between the target and the satellite stays in the observable area between the maximum observation and the unobservable projection distance until the target height continues to decrease to unobservable. Aerospace 2021, 8, 156 10 of 18 Aerospace 2021, 8, 156 10 of 17 Aerospace 2021, 8, 156 10 of 18 Figure 6. Trajectory of satellite and target with access link. The changes in observation conditions during the observation process can be seen in Figure 7, where the green line is the maximum observation projection distance, the red line is the undetectable projection distance, and the blue line is the projection distance between the satellite and the target. The green area is the width of the observable area. It can be seen from the figure that the distance between the target and the satellite stays in the observable area between the maximum observation and the unobservable projection Figure 6. Trajectory of satellite and target with access link. Figure 6. Trajectory of satellite and target with access link. distance until the target height continues to decrease to unobservable. The changes in observation conditions during the observation process can be seen in Figure 7, where the green line is the maximum observation projection distance, the red line is the undetectable projection distance, and the blue line is the projection distance between the satellite and the target. The green area is the width of the observable area. It can be seen from the figure that the distance between the target and the satellite stays in the observable area between the maximum observation and the unobservable projection distance until the target height continues to decrease to unobservable. Figure 7. Time sequence of detection area variation. Figure 7. Time sequence of detection area variation. 3.4.2. Tangential Flight 3.4.2. Tangential Flight The situation of the tangential flight between the satellite and the target can be seen in The situation of the tangential flight between the satellite and the target can be seen Figures 8–10, respectively. They are the deviation of longitude and latitude in the same in Figures 8–10, respectively. They are the deviation of longitude and latitude in the same direction and the deviation of latitude and longitude in the same direction. The first case direction and the deviation of latitude and longitude in the same direction. The first case can be seen in Figure 8. Only part of the arc of the target can be detected by the satellite. can be seen in Figure 8. Only part of the arc of the target can be detected by the satellite. The changes in observation conditions during the observation process can be seen in Figure 9 for this case. The main constraint on the length of the observation arc is that the Figure 7. Time sequence of detection area variation. distance between the satellite and the target exceeds the maximum observable distance. In Figures 10 and 11, it can be seen that the same observation arc is limited when the lat- 3.4.2. Tangential Flight itude and longitude deviate in the same direction, and the main constraint comes from the The situation of the tangential flight between the satellite and the target can be seen observation distance, which exceeds the maximum observation distance. The observation in Figures 8–10, respectively. They are the deviation of longitude and latitude in the same efficiency of tangential direction flight is lower than that of the same direction flight. direction and the deviation of latitude and longitude in the same direction. The first case can be seen in Figure 8. Only part of the arc of the target can be detected by the satellite. Aerospace 2021, 8, 156 11 of 18 AerAer ospospace ace 2021 2021 , 8, ,18 5,6156 11 of 1118 of 17 Figure 8. Trajectory of satellite and target with access link. The changes in observation conditions during the observation process can be seen in Figure 9 for this case. The main constraint on the length of the observation arc is that the Figure 8. Trajectory of satellite and target with access link. Figure 8. Trajectory of satellite and target with access link. distance between the satellite and the target exceeds the maximum observable distance. The changes in observation conditions during the observation process can be seen in Figure 9 for this case. The main constraint on the length of the observation arc is that the distance between the satellite and the target exceeds the maximum observable distance. Aerospace 2021, 8, 156 12 of 18 Figure 9. Time sequence of detection area variation. Figure 9. Time sequence of detection area variation. In Figures 10 and 11, it can be seen that the same observation arc is limited when the latitude and longitude deviate in the same direction, and the main constraint comes from Figure 9. Time sequence of detection area variation. the observation distance, which exceeds the maximum observation distance. The obser- vation efficiency of tangential direction flight is lower than that of the same direction In Figures 10 and 11, it can be seen that the same observation arc is limited when the flight. latitude and longitude deviate in the same direction, and the main constraint comes from the observation distance, which exceeds the maximum observation distance. The obser- vation efficiency of tangential direction flight is lower than that of the same direction flight. Figure 10. Trajectory of satellite and target with access link. Figure 10. Trajectory of satellite and target with access link. Figure 11. Time sequence of detection area variation. 3.4.3. Opposite Directional Flight The situation of the satellite and the target flying in the opposite direction can be seen in Figure 12. From Figures 12 and 13, it can be seen that in the case of opposite directional flight, the observable arc of the target is extremely limited, which is mainly due to the target quickly approaching and entering the unobservable area. Therefore, when flying in oppo- site directions, the observation benefit is the lowest. Aerospace 2021, 8, 156 12 of 18 Aerospace 2021, 8, 156 12 of 17 Figure 10. Trajectory of satellite and target with access link. Figure 11. Time sequence of detection area variation. Figure 11. Time sequence of detection area variation. 3.4.3. Opposite Directional Flight Aerospace 2021, 8, 156 13 of 18 3.4.3. Opposite Directional Flight The situation of the satellite and the target flying in the opposite direction can be seen The situation of the satellite and the target flying in the opposite direction can be seen in Figure 12. in Figure 12. From Figures 12 and 13, it can be seen that in the case of opposite directional flight, the observable arc of the target is extremely limited, which is mainly due to the target quickly approaching and entering the unobservable area. Therefore, when flying in oppo- site directions, the observation benefit is the lowest. Figure 12. Trajectory of satellite and target with access link. Figure 12. Trajectory of satellite and target with access link. From Figures 12 and 13, it can be seen that in the case of opposite directional flight, the observable arc of the target is extremely limited, which is mainly due to the target quickly approaching and entering the unobservable area. Therefore, when flying in opposite directions, the observation benefit is the lowest. Figure 13. Time sequence of detection area variation. 3.5. Task Satellite Selection Factor In the selected orbital plane, the weight of three factors are proposed [20]: the relative angle influence factor Q is obtained by analyzing the relative motion relationship be- ra tween the target and the satellite, Q is obtained by analyzing the distance relationship dst between the target and the satellite, and Q is obtained by analyzing the relationship bd between the target and the unobservable area. The overall task satellite selection factor SF is calculated as follows: n n n n SF  w Q  w Q  w Q (14) sat ra ra dst dst bd bd w w where is the weight for the relative motion relationship, is the weight for ra dst the relative distance observation, and is the weight for the blind zone. Observing a bd target requires no less than two satellites at the same time, and considering the continuity of the entire process, two orbital planes and two satellites on the orbital plane were se- lected at the initial stage of selection. The selection factors of each satellite were calculated in the orbital plane, and the satellite with the highest factor value was selected as the first choice, while the satellite with the second highest choice factor was chosen as the second Aerospace 2021, 8, 156 13 of 18 Aerospace 2021, 8, 156 13 of 17 Figure 12. Trajectory of satellite and target with access link. Figure 13. Time sequence of detection area variation. Figure 13. Time sequence of detection area variation. 3.5. Task Satellite Selection Factor 3.5. Task Satellite Selection Factor In the selected orbital plane, the weight of three factors are proposed [20]: the relative In the selected orbital plane, the weight of three factors are proposed [20]: the relative angle influence factor Q is obtained by analyzing the relative motion relationship be- n ra angle influence factor Q is obtained by analyzing the relative motion relationship be- ra tween the target and the satellite, Q is obtained by analyzing the distance relationship dst tween the target and the satellite, Q is obn tained by analyzing the distance relationship dst between the target and the satellite, and Q is obtained by analyzing the relationship bd bet between ween th the e ttar arget get an and d the the unobservable satellite, and ar Qea. The is ob overall tained task by analy satellite zing selection the relation factor ship SF bd is calculated as follows: between the target and the unobservable area. The overall task satellite selection factor SF is calculated as follows: n n n n SF = w  Q + w  Q + w  Q (14) n ra n ra n n sat dst dst bd bd SF  w Q  w Q  w Q (14) sat ra ra dst dst bd bd where w is the weight for the relative motion relationship, w is the weight for where w isra the weight for the relative motion relationship, w is dst the weight for the ra dst relative distance observation, and w is w the weight for the blind zone. Observing a target the relative distance observation, and is the weight for the blind zone. Observing a bd bd requires no less than two satellites at the same time, and considering the continuity of the target requires no less than two satellites at the same time, and considering the continuity entire process, two orbital planes and two satellites on the orbital plane were selected at of the entire process, two orbital planes and two satellites on the orbital plane were se- the initial stage of selection. The selection factors of each satellite were calculated in the lected at the initial stage of selection. The selection factors of each satellite were calculated orbital plane, and the satellite with the highest factor value was selected as the first choice, in the orbital plane, and the satellite with the highest factor value was selected as the first while the satellite with the second highest choice factor was chosen as the second choice. choice, while the satellite with the second highest choice factor was chosen as the second The Monte Carlo simulation was used to determine the weight values. The simulation was divided into two stages. In the first stage, the satellites were selected with 0.1 as the weight step value for all three weights. Then, the length of the observation windows were calculated between 10 random targets and the selected satellite. After 10,000 iterations, a selection result with a length of 0.1 weight interval was obtained based on the longest observation window. In the second stage, the weight step setting was 0.01 in the chosen weight interval, and another 10,000 iterations were carried out to determine the weight settings, as seen in Table 3. Table 3. Weight configuration. Weight Value Relative motion weight 0.14 Relative distance weight 0.65 Blind zone influence weight 0.21 4. Results and Discussion Different latitudes and different moving trajectory targets were used to simulate and verify the screening method of the constellation. The main parameters of the target used in the simulation verification are shown in Table 4. The mid-latitude opposing flying target, the low-latitude tangential flying target, the mid-latitude tangentially biased remote Aerospace 2021, 8, 156 14 of 17 target, and the high-latitude long-range target flying in the same direction were selected to simulate the selection of candidate orbits and task satellites. Table 4. Coordinate of the trajectory shadow ends. Target and Position Longitude Latitude Target1 Position1 143.505 38.230 Target1 Position2 145.707 36.227 Target2 Position1 145.966 15.569 Target2 Position2 142.945 17.621 Target3 Position1 118.793 41.002 Target3 Position2 126.851 38.689 Target4 Position1 115.154 40.315 Target4 Position2 118.583 50.013 The selection results of candidate orbits and task satellites for the mid-latitude oppos- ing flying target (target 1) can be seen in Figure 14. Among them, the satellite flying in the opposite direction of the target (the trajectory in purple-red line) had an observation window for the satellite. When flying in the opposite direction, it was the first satellite of the second selected orbit (SOFS), and the second selected satellite in second selected orbit (SOSS) with the black line in the trajectory had the ability to observe the target early. The blue trajectory was the first satellite of the first orbit (FOFS), which had the longest observation arc to the target. The green trajectory followed as the first orbit second satellite (FOSS). Although flying tangentially to the target, it had a better observation window due Aerospace 2021, 8, 156 15 of 18 to the relative distance from the further point to the near point. The optimization results of orbits and task satellites were consistent with the actual observation conditions. Figure 14. Selection of orbit planes and satellites for target1. Figure 14. Selection of orbit planes and satellites for target1. Figure 15 shows the satellite selection results of tangential flying targets at low lati- Figure 15 shows the satellite selection results of tangential flying targets at low lati- tudes. The target was tangential to the first orbit and opposite to the second orbit. There- tudes. The target was tangential to the first orbit and opposite to the second orbit. Therefore, fore, the selection results were consistent with the actual observation conditions. the selection results were consistent with the actual observation conditions. Figure 15. Selection of orbit planes and satellites for target2. Figure 16 shows the satellite selection results of the mid-latitude long-distance fly- ing target, the opposing flight orbit was selected as the first orbit, although there were fewer observing blind spots in the opposite direction. The four selected satellites were also the satellites with the best observation conditions under actual analysis. Aerospace 2021, 8, 156 15 of 18 Figure 14. Selection of orbit planes and satellites for target1. Figure 15 shows the satellite selection results of tangential flying targets at low lati- Aerospace 2021, 8, 156 15 of 17 tudes. The target was tangential to the first orbit and opposite to the second orbit. There- fore, the selection results were consistent with the actual observation conditions. Figure 15. Selection of orbit planes and satellites for target2. Figure 15. Selection of orbit planes and satellites for target2. Fig Figur ure 16 e 16 sho shows ws th the e s satellite atellite se selection lection result results s of of the the mid-latitude mid-latitude long-distance long-distance flying fly- target, the opposing flight orbit was selected as the first orbit, although there were fewer ing target, the opposing flight orbit was selected as the first orbit, although there were Aerospace 2021, 8, 156 16 of 18 observing blind spots in the opposite direction. The four selected satellites were also the fewer observing blind spots in the opposite direction. The four selected satellites were also satellites with the best observation conditions under actual analysis. the satellites with the best observation conditions under actual analysis. Figure 16. Selection of orbit planes and satellites for target3. Figure 16. Selection of orbit planes and satellites for target3. For high latitude target 4, the satellite selection result is shown in Figure 17. The orbit For high latitude target 4, the satellite selection result is shown in Figure 17. The orbit that actually had the longest observation window was selected as the suboptimal orbit. that actually had the longest observation window was selected as the suboptimal orbit. The The se selected lected four four s satellites atellites wer were e the thfour e four satellites satellites with with th the best e best actual actual observation observation con conditions, di- tions, but b ther ut th e wer ere e were discr d epancies iscrepancie in the s in orbit the orbit and a satellite nd satell orite dering. order The ing. results The reshowed sults show that ed the selection of orbital planes based on the longitude of the ascending node was more sensitive that the selection of orbital planes based on the longitude of the ascending node was more to the latitude distribution of the target. The reason for this is that the input constellation sensitive to the latitude distribution of the target. The reason for this is that the input con- orbits were densely distributed in high-latitude regions, and the observation conditions stellation orbits were densely distributed in high-latitude regions, and the observation conditions of each orbital plane were less different; therefore, optimally and suboptimally, the actual observational gain difference on the orbital surface was close. Therefore, alt- hough the order of satellite selection was different from the actual one, the selected satel- lite was the one with the best observation profit. Figure 17. Selection of orbit planes and satellites for target4. Aerospace 2021, 8, 156 16 of 18 Figure 16. Selection of orbit planes and satellites for target3. For high latitude target 4, the satellite selection result is shown in Figure 17. The orbit that actually had the longest observation window was selected as the suboptimal orbit. The selected four satellites were the four satellites with the best actual observation condi- tions, but there were discrepancies in the orbit and satellite ordering. The results showed Aerospace 2021, 8, 156 16 of 17 that the selection of orbital planes based on the longitude of the ascending node was more sensitive to the latitude distribution of the target. The reason for this is that the input con- stellation orbits were densely distributed in high-latitude regions, and the observation conditions of each orbital plane were less different; therefore, optimally and suboptimally, of each orbital plane were less different; therefore, optimally and suboptimally, the actual the actual observational gain difference on the orbital surface was close. Therefore, alt- observational gain difference on the orbital surface was close. Therefore, although the hough the order of satellite selection was different from the actual one, the selected satel- order of satellite selection was different from the actual one, the selected satellite was the lite was the one with the best observation profit. one with the best observation profit. Figure 17. Selection of orbit planes and satellites for target4. Figure 17. Selection of orbit planes and satellites for target4. 5. Conclusions This study proposes a method that fully considers the constellation orbit charac- teristics for event-driven SODLC. After the target appears, based on the initial limited information, the candidate satellites with the observation conditions are quickly screened to meet the needs of high-efficiency mission planning and scheduling. The observation window projection screening method can quickly screen the observation satellites with better observation conditions through less calculation. Calculation and simulation analysis show this method is able to select orbital planes with optimal observation conditions and the corresponding observation satellites when calculating mid-latitude and low-latitude targets. When calculating high-latitude area targets, the optimal satellites that are consistent with the actual observation benefits can be correctly selected, but there is a deficiency of insensitivity to the priority order of the orbital surface, which can be the subject of future optimization studies. The constraints considered in this work were mainly the atmospheric limb height and the observation distance, and more specific constraints such as the sun avoidance angle and full moon avoidance angle were not considered, which can also be studied in future work. The observation window projection screening method proposed in this paper has better task satellite selection efficiency, timeliness, and practical value for event-driven mission planning and scheduling of SODLC. Author Contributions: Conceptualization: S.Z. and Z.Z.; methodology: S.Z.; supervision: Z.Z. and H.H.; writing—review and editing: S.Z. and Y.L. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the Innovation Laboratory Fund Program of the Chinese Academy of Sciences, grant number CXJJ17S014. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not applicable. Aerospace 2021, 8, 156 17 of 17 Conflicts of Interest: The authors declare no conflict of interest. References 1. Sanchez, A.H.; Soares, T.; Wolahan, A. Reliability aspects of mega-constellation satellites and their impact on the space debris environment. In Proceedings of the 2017 Annual Reliability and Maintainability Symposium (RAMS), Orlando, FL, USA, 23–26 January 2017. [CrossRef] 2. Lewis, H.G. Evaluation of debris mitigation options for a large constellation. J. Space Saf. 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Chang, L. Research on Object Tracking in Limited Scale Optical Surveillance Satellite Constellation System. Master ’s Dissertation, National University of Defense Technology, Changsha, Hunan, China, 2017. 10. Budianto, I.A.; Olds, J.R. A Collaborative Optimization Approach to Design and Deployment of a Space Based Infrared System Constellation. In Proceedings of the Aerospace Conference, Big Sky, MT, USA, 18–25 March 2000; IEEE: Piscataway, NJ, USA, 11. Wang, X.; Zhang, H.; Bai, S.; Yue, Y. Design of agile satellite constellation based on hybrid-resampling particle swarm optimization method. Acta Astronaut. 2021, 178, 595–605. [CrossRef] 12. Yu, Y.; Hou, Q.; Zhang, J.; Zhang, W. Mission scheduling optimization of multi-optical satellites for multi-aerial targets staring surveillance. J. Frankl. Inst. 2020, 357, 8657–8677. [CrossRef] 13. Shtark, T.; Gurfil, P. Low Earth orbit satellite constellation for regional positioning with prolonged coverage durations. Adv. Space Res. 2019, 63, 2469–2494. [CrossRef] 14. Ge, H.; Li, B.; Nie, L.; Ge, M.; Schuh, H. LEO constellation optimization for LEO enhanced global navigation satellite system (LeGNSS). Adv. Space Res. 2020, 66, 520–532. [CrossRef] 15. Chen, Y.; Zhao, L.; Liu, H.; Li, L.; Liu, J. Analysis of Configuration and Maintenance Strategy of LEO Walker Constellation. J. Astronaut. 2019, 40, 1296–1303. 16. Sciré, G.; Santoni, F.; Piergentili, F. Analysis of orbit determination for space based optical space surveillance system. Adv. Space Res. 2015, 56, 421–428. [CrossRef] 17. Flohrer, T.; Krag, H.; Klinkrad, H.; Schildknecht, T. Feasibility of performing space surveillance tasks with a proposed space-based optical architecture. Adv. Space Res. 2011, 47, 1029–1042. [CrossRef] 18. Buzzi, P.G.; Selva, D.; Hitomi, N.; Blackwell, W.J. Assessment of constellation designs for earth observation: Application to the Tropics mission. Acta Astronaut. 2019, 161, 166–182. [CrossRef] 19. Noullez, A.; Tsiganis, K. Design of low-altitude Martian orbits using frequency analysis. Adv. Space Res. 2021, 67, 477–495. [CrossRef] 20. Kim, H.; Chang, Y.-K. Optimal mission scheduling for hybrid synthetic aperture radar satellite constellation based on weighting factors. Aerosp. Sci. Technol. 2020, 107, 106287. [CrossRef] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Aerospace Multidisciplinary Digital Publishing Institute

Research on Task Satellite Selection Method for Space Object Detection LEO Constellation Based on Observation Window Projection Analysis

Zhang, Shengyu; Zhu, Zhencai; Hu, Haiying; Li, Yuqing
Aerospace , Volume 8 (6) – May 31, 2021
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aerospace Article Research on Task Satellite Selection Method for Space Object Detection LEO Constellation Based on Observation Window Projection Analysis 1 , 2 , 3 , 1 , 2 1 , 2 1 , 2 Shengyu Zhang * , Zhencai Zhu , Haiying Hu and Yuqing Li Innovation Academy for Microsatellites of Chinese Academy of Sciences, Shanghai 201203, China; zhuzc@microsate.com (Z.Z.); huhy@microsate.com (H.H.); liyq@microsate.com (Y.L.) Shanghai Engineering Center for Microsatellites, Shanghai 201203, China Chinese Academy of Sciences, Beijing 100039, China * Correspondence: zhangsy@microsate.com Abstract: Aiming at the task planning and scheduling problem of space object detection LEO constellation (SODLC) for detecting space objects in deep space background, a method of SODLC task satellite selection based on observation window projection analysis is proposed. This method projects the spatial relative relationships of the SODLC observation blind zone, observation range, and the initial spatial position of the objects onto the surface of the earth for detectable analysis of satellites and targets and binds the dynamic observation conditions to the satellite trajectory after projection calculation of the visible relationship between target changes. On this basis, combined with the features of SODLC with high orbital symmetry, the task satellite selection is divided into two steps: orbit plane selection and task satellite selection. The orbit planes are selected based on the longitude range of the ascending node with the geographic location of the targets, and the task Citation: Zhang, S.; Zhu, Z.; Hu, H.; satellites are selected according to the relative motion relationship between the satellites and the Li, Y. Research on Task Satellite targets together with the constraints of observable conditions. The selection method simplifies the Selection Method for Space Object calculation process of scheduling and selecting task satellites. Simulation analysis prove the method Detection LEO Constellation Based has better task satellite selection efficiency. The method has high practical value for task planning on Observation Window Projection and scheduling for event-driven SODLC. Analysis. Aerospace 2021, 8, 156. https://doi.org/10.3390/ Keywords: space object detection LEO constellation; observation window projection; task satel- aerospace8060156 lite selection Academic Editor: Dario Modenini Received: 9 March 2021 1. Introduction Accepted: 25 May 2021 Published: 31 May 2021 Several megaconstellation projects are in progress for global communications, which are rapidly launching thousands of satellites into low earth orbits. Megaconstellations may Publisher’s Note: MDPI stays neutral have a potential catastrophic impact [1] on the space debris environment [2]. The amount with regard to jurisdictional claims in of debris may augment rapidly if the satellites are not removed from their orbit after end published maps and institutional affil- of life, which is usually short. The large number of satellites in adjacent orbits will also iations. increase the risk of collisions, which may lead to a burst of space debris [3]. With the growing number of space objects and increasing risk of LEO collisions, space object detection LEO constellation (SODLC) has been proposed to work with ground- based sensor networks to enhance the capability of space object detection, tracking, and Copyright: © 2021 by the authors. identification and to establish timely response globally for space emergency events such as Licensee MDPI, Basel, Switzerland. collisions. Du et al. proposed three Walker analog constellations to build and maintain a This article is an open access article catalog of 200,000 LEO space debris [4]. Snow et al. introduced an optimization method distributed under the terms and to the CubeSat constellation design problem for a space-based optical debris observation conditions of the Creative Commons system in which the Walker delta constellation was adopted [5]. Attribution (CC BY) license (https:// SODLC needs to complete real-time system response after emergency events such as creativecommons.org/licenses/by/ collisions. With the dynamic relative position between satellites and the target, multiple 4.0/). Aerospace 2021, 8, 156. https://doi.org/10.3390/aerospace8060156 https://www.mdpi.com/journal/aerospace Aerospace 2021, 8, 156 2 of 17 satellites in the SODLC are required to coordinate and relay information in order to achieve full-range tracking of the target. Moreover, the satellite can determine the orbit of the target with an angles-only method [6]. Therefore, an appropriate satellite and sensor management strategy is needed [7]. Hu et al. proposed a multiobjective optimization framework for the optimal design of emergency observation constellations [8]. SODLC requires autonomous mission planning and sensor scheduling [9] on the satellite to achieve dynamic resource allocation for targets. An observation sequence for a specific target is formed, and different satellites are dispatched in turn to track and detect the target [10]. In the initial stage of an event being triggered, it is particularly important to quickly and accurately select satellites suitable for observation, which is key to a successful response. At the same time, SODLC satellites are constrained by various observation conditions during target tracking. For example, for target detection, the field of view (FOV) requires a deep space background, so the line of sight (LOS) must be above the atmospheric limb; the observation distance is limited by the capability of sensors. These constraints must be used as the screening criteria for task-executing satellites in mission planning [11]. When the event is triggered, the satellite needs to screen the existing satellites in real time to form a task sequence. Yu et al. investigated the emergency scheduling problem and proposed a cooperation-oriented ant colony optimization algorithm (CO-ACO) to solve the observation sequence problem [12]. Existing methods mainly select candidate satellites by directly calculating the spatial visibility between the target and all satellites. However, constraints in the observation conditions lead to high computational complexity, high onboard resource consumption, and low timeliness of mission planning. Existing SODLC planning methods do not effectively use the inherent characteristics of SODLC and the satellite itself to optimize the selection process of task satellites. Although the target is noncooperative, it has certain temporal and spatial uncertainty as an event trigger. Previous studies have fully considered the real-time coverage per- formance of time and space when designing SODLC [13]. In order to achieve balanced spatial double coverage and intersatellite links [14], the Walker constellation adopts a configuration with very high symmetry and periodicity of motion characteristics [15]. In this study, a method is proposed that analyzes and calculates the observation con- ditions depending on the projection of the target trajectory, satellite trajectory, undetectable range of the atmospheric limb constraints, and the maximum detectable distance of the observation distance onto the surface of the earth. At the same time, the task satellite selection is divided into two steps considering the high orbital symmetry, namely orbital plan selection and task satellite selection, which greatly simplifies the calculation process for task satellite selection. After the dynamic observation conditions are projected and bound to the satellite trajectory, the visible relationship with the target change can be precisely calculated, which serves for dynamic mission planning. 2. Problem Description 2.1. Ground Projection of the SODLC Satellite Observation Range SODLC satellites need to observe the target in a deep space background above the atmospheric limb. Therefore, the LOS of the target should be at least tangent to the edge of the atmospheric limb, as shown in Figure 1. Aerospace 2021, 8, 156 3 of 17 Aerospace 2021, 8, 156 3 of 18 Sat sat tar Projection of undetectable region Maximum Projection of detectable region Detection Range e Figure 1. Observation model of the SODLC satellite. Figure 1. Observation model of the SODLC satellite. The The tar target get cannot cannot be be ob observed served w when hen it it ap appears pears in inth the e ra range nge of ofth the e int intersection ersection q of of the line from the satellite to the center of the earth and the tangent of the satellite to the the line from the satellite to the center of the earth and the tangent of the satellite to the atmospheric limb. atmospheric limb. An area centered on the subsatellite point and in range of D is obtained by projecting An area centered on the subsatellite point and in range of bD is obtained by project- the invisible observation angle range of the satellite to the target on the surface of the ing the invisible observation angle range of the satellite to the target on the surface of the earth. A target is undetectable as long as its projection on the earth surface falls within the earth. A target is undetectable as long as its projection on the earth surface falls within the range above. The undetectable range D is determined by the atmospheric limb height H , range above. The undetectable range is determined by the atmospheric limb height satellite orbit height H , and target height H . tar H , satellite orbit height H , and target height H . a s tar 8 h    i R +H R +H 1 e a 1 e a D (t) = cos cos  R , H (t) > H > RRHH b e a  11eeaa tar < R +H R +H (t) e s e D (t )  cosh  cios tar  R ，H （t） H    b e tar a 1 R +H R  H e a R Ht （） (1)   D (t) = cos e s  R , H e (t) tar H  b e a tar > R +H e s D (t) = 0, H  H   b sR  Ha 1 e a D (t )  cos  R ，H （t） H    (1) b e tar a R  H   e s   where R is the radius of the earth. D (t ) 0，H H For a circular orbit, the orbital height of the satellite is regarded as a constant and ba s the atmospheric  limb height can also be considered as a certain value, while the height of the target changes with its movement. Therefore, the undetectable range will also vary where Re is the radius of the earth. with the height of the target. When the target height is lower than the atmospheric limb For a circular orbit, the orbital height of the satellite is regarded as a constant and the height, the undetectable area is completely determined by the atmospheric limb. When the atmospheric limb height can also be considered as a certain value, while the height of the target height is greater than the atmospheric limb height, the undetectable range changes target changes with its movement. Therefore, the undetectable range will also vary with dynamically with the target height. the height of the target. When the target height is lower than the atmospheric limb height, At the same time, the detection capability affects the performance of orbit determi- the undetectable area is completely determined by the atmospheric limb. When the target nation [16]. Flohrer et al. analyzed the performance of space-based optical system with a height is greater than the atmospheric limb height, the undetectable range changes dy- 20 cm aperture, 6 field of view, and flexible integration requirements [17]. namically with the target height. Aerospace 2021, 8, 156 4 of 18 Aerospace 2021, 8, 156 4 of 17 At the same time, the detection capability affects the performance of orbit determi- nation [16]. Flohrer et al. analyzed the performance of space-based optical system with a 20 cm aperture, 6° field of view, and flexible integration requirements [17]. The The detection detection capability capability is is decided decided by by the the apertur aperture, e, optical optical system system ef efficienc ficiency y,, and and integration integration time. time. In In or or der der to to simplify simplify the the analysis analysis ofof the thpr e pro oblem, blem, the th tar e targ get is et calculated is calculated as a 10 cm diameter sphere, and the dimmest magnitude observable by the optical system as a 10 cm diameter sphere, and the dimmest magnitude observable by the optical system studied is around 17.2 M with 15 cm aperture and flexible integration. The magnitude is studied is around 17.2 M v v with 15 cm aperture and flexible integration. The magnitude is calculated by Equation (2): calculated by Equation (2): m26.58 2.5 log [A F( ) L 2 ] (2) m = 26.58 2.5 log [AgF(f)/L ] (2) where where  m is the limiting magnitude; m is the limiting magnitude;  A is area of the space object along the line of sight; A is area of the space object along the line of sight;   is the reflectivity; g is the reflectivity; F( )  is the solar phase angle; and F(f) is the solar phase angle; and  L is the observation distance. L is the observation distance. The calculation results are in Figure 2. The calculation results are in Figure 2. Figure 2. Relationship between detection capability and observation system. Figure 2. Relationship between detection capability and observation system. In Figure 2, with the dimmest magnitude of around 17.2 M in this study, the maxi- In Figure 2, with the dimmest magnitude of around 17.2 Mv in this study, the maxi- mum detection distance is 6000 km. mum detection distance is 6000 km. Because the SODLC satellite has azimuth omnidirectional maneuverability, the con- Because the SODLC satellite has azimuth omnidirectional maneuverability, the con- nection between the farthest point of detection and the center of the earth will also form a nection between the farthest point of detection and the center of the earth will also form a range on the ground with the subsatellite point as the center and D as the arc length, where range on the ground with the subsatellite point as the center and D as the arc length, where D is the maximum range projection of the observation. After eliminating the projection of D is the maximum range projection of the observation. After eliminating the projection of the undetectable area, the detectable area is an annulus with a width of D . the undetectable area, the detectable area is an annulus with a width of Dl. 2 2 2 2 2  2 <  (R +H (t)) +(R +H ) L 1 e e s tar RR  H （t）   H  L     D(t) = cos  R , H (t) > H ee tar s 1 e a  tar  2 R +H (t) (R +H ) ( e ) e s (3) D(t ) cos  R ，H （t） H tar  e tar a  2 R  H （t） R  H      (3) D(t) = 0, H (tee )  H tar s tar  D(t ) 0，H （t） H  tar a Similarly, the maximum length of the observable range D(t) also varies with the Similarly, the maximum length of the observable range Dt () also varies with the H (t) height of the target. When H (t) is less than the atmospheric limb, there is no tar tar detectable range, i.e., D(t) is 0. Ht （） height of the target. When Ht （） is less than the atmospheric limb, there is no tar tar The width of the detectable ring zone is as follows: detectable range, i.e., Dt () is 0. The width of the detectable ring zone is as follows: D (t) = D(t) D (t), H (t) > H (4) l b tar D（t）=D(t) D (t), H（t） H (4) l b tar a Above, a ring-shaped detectable area projected onto the earth’s surface is formed by the constraints of the atmospheric limb observation and the maximum observation distance. Aerospace 2021, 8, 156 5 of 18 Above, a ring-shaped detectable area projected onto the earth’s surface is formed by Aerospace 2021, 8, 156 5 of 17 the constraints of the atmospheric limb observation and the maximum observation dis- tance. 2.2. Dynamic Detectability Analysis of Targets 2.2. Dynamic Detectability Analysis of Targets Because the spatial positions of the target and the satellite are in a highly dynamic Because the spatial positions of the target and the satellite are in a highly dynamic process, the visibility of a target to a specific satellite should be judged under a dynamic process, the visibility of a target to a specific satellite should be judged under a dynamic condition. Therefore, it is necessary to combine the undetectable area Dt () centered on condition. Therefore, it is necessary to combine the undetectable area D ( bt) centered on the the satellite’s satellite’subsatellite s subsatellite point point with with the th detectable e detectable area area D (tD)（ and t） the and satellite’s the satellite subsatellite ’s subsat- l l point trajectory to form a judgment on the detectability condition of a specific target at a ellite point trajectory to form a judgment on the detectability condition of a specific target specific time. The relationship between the projection point of the target on the earth’s at a specific time. The relationship between the projection point of the target on the earth’s surface and the projection of different detection characteristics is shown in Figure 3. surface and the projection of different detection characteristics is shown in Figure 3. Sat HS ( (tt ),  ) tt (XY , ) tar tar Ground Track Figure 3. Dynamic observation area analysis. Figure 3. Dynamic observation area analysis. For For the the tar tar get, get, at ata a given giventime time t,t,the the tar taget’s rget’s geographic geographic longitude longitudeX X , geographic , geographic tar tar latitude Y , and target height H (t) are all determined. latitude tY ar , and target height taHt r （） are all determined. tar tar Similarly, at a given time t, the geographic longitude l(t) and geographic latitude Similarly, at a given time t, the geographic longitude () t and geographic latitude j t of the subsatellite point of a specific satellite Sat are also determined, and the satellite ( ) t of the subsatellite point of a specific satellite Sat are also determined, and the satel- height is still considered as a fixed value. lite height is still considered as a fixed value. For a certain orbit, the geographic longitude l(t) and geographic latitude j(t) of the subsatellite For a certa point in orbit are , th de e termined geograph by ic longit the inclination ude () t of and th ege satellite ographorbit ic latit and udethe  tr t ue of   anomaly at time t. the subsatellite point are determined by the inclination of the satellite orbit and the true The calculation formula for the geographic longitude of the satellite subsatellite point anomaly at time t. is as follows: The calculation formula for the geographic longitude of the satellite subsatellite point l(t) = W + arctan[cos i tan(w + q(t))] (5) g0 is as follows: (t)  arctan cosi tan  (t) The calculation formula for the geographical latitude  ofthe satellite subsatellite point (5) g 0  is as follows: The calculation formula for the geographical latitude of the satellite subsatellite point j(t) = arcsin[sin i sin(w + q(t))] (6) is as follows: Among them, the orbit inclination i is a fixed value for determining the orbit, and ! is a fixed value for the argument of perigee. Aerospace 2021, 8, 156 6 of 17 The true anomaly at a specific time t is as follows: q(t) = q + nt (7) where q is the true anomaly at the initial moment (epoch). n = (8) 5 3 2 where a is the semimajor axis of the orbit, and m = 3.986006  10 km /s . At a specific time t, the arc length D between the subsatellite point on the earth’s HS surface and the target projection point can be calculated as follows: 1 t t t D (t) = R  cos cos(Y ) cos(j(t)) cos(X l(t)) + sin(Y ) sin(j(t)) (9) HS e tar tar tar where l(t) is the geographic longitude and j(t) is geographic latitude of the specific t t satellite Sat’s subsatellite point, X is the geographic longitude and Y is geographic tar tar latitude of the target. According to the length of the arc connecting the subsatellite point and the target projection point, it can be judged whether it is in the detectable area. If DET stands for the number of satellites that have conditions for observing a specific target, DET = 1, D (t) < D (t)  D (t) b HS l (10) DET = 0, D (t)  D (t)[ D (t) > D (t) HS HS b l then, when the length of the arc connecting the subsatellite point and the target projec- tion point D t is greater than the undetectable arc D (t) and less than the maximum ( ) HS detection distance arc D (t), the DET count equals 1. 3. Task Satellite Selecting Method 3.1. Analysis of the Relative Relationship between the SODLC and the Target The SODLC adopts the Walker constellation. In this study, the 24/4/1 constellation configuration was chosen for the simulation analysis. The specific parameters of the seed Satellite1 can be seen in Table 1. Table 1. Orbital parameters of Satellite1. Parameters Value Semimajor axis 7978.14 km Eccentricity 1.47826  10 Inclination 60 RAAN 1.11991  10 Argument of perigee 0 True anomaly 0 The main constraints considered include the observation height of the atmospheric limb, the maximum detection distance, etc. The main simulation input parameters are shown in Table 2. Table 2. Simulation configuration parameters. Parameters Value Atmospheric limb height 80 km Maximum detection distance 6000 km Satellite pointing range Azimuth 360 , pitch  85 Aerospace 2021, 8, 156 7 of 17 3.2. Task Satellite Selection Method Based on Observation Window Projection For the constellation, the target will have visibility to multiple satellites, especially the target with a long trajectory. Therefore, multiple satellites are required to complete the relay tracking of the target during its flight. After a target appears, the system needs to perform task planning and resource scheduling and then select the task satellites. The existing method of selecting task satellites for the SODLC is to calculate the visibility and space observation constraints of the target and all satellites in orbit after the target appearance and then complete the task satellite selection after sorting according to the calculation results. The calculation is more complicated due to the dynamic characteristics of the satellite, the target, the constraints themselves, and the inherent characteristics of the satellite orbit, which are not fully considered to optimize calculation. In this paper, a method of projecting and screening task satellite observation windows is specially proposed. At the same time, the inherent characteristics of the constellation orbit and the relative relationship between the target and the satellite projected to the ground are used to quickly select task satellites. This method reduces unnecessary computing overhead and is adaptive to the task planning and resource scheduling process for dynamic changes. Because the SODLC generally uses fewer orbital planes, analyses in the related litera- ture have also used 3 to 4 orbital planes [18]. For each orbital plane, no matter how many satellites are distributed on this orbital plane at the time, the ascending node longitudes of all satellites on the same orbital surface are distributed in a specific interval at this specific time [19]. R is the width of distribution interval for the ascending or descending nodes of all tracks in an orbital period. R = T w (11) where T is the orbital period of the orbital plane, and w is the earth’s rotation speed. For example, for an orbit with an orbit height of 1600 km and an orbital inclination of 60 degrees, the longitude of the satellite’s ascending node in an orbit is distributed in a longitude interval with a width of 29.549 . Based on the characteristics of the SODLC, the candidate orbital plane can be quickly selected by judging the distribution relationship between the target and the geographic longitude of the ascending node of the orbit. After the specific orbital plane is selected, the relative motion relationship between the target and the satellite can be used to select the candidate orbital plane and then the candidate observation satellites. 3.3. Orbit Plane Selection From Formula (10), a distribution interval of the ascending node longitude of the orbital plane is obtained. To compare the target and this interval, it is necessary to compare the position of the target and the position of the orbital interval on the equator, as shown in Figure 4. The geographical longitude distribution range of the ascending node of the orbital plane can be calculated by the instantaneous root of any satellite in the orbital plane. The calculation of the ascending orbit is shown in Formula (12): W = l tan j ctani > G0 0 0 < q W = W w   T GE0 G0 2p (12) W = W + w  1  T > e GW0 G0 2p W = W  R GC0 GW0 W 2 Aerospace 2021, 8, 156 8 of 17 The calculation of descending orbit is shown in Formula (13): W = l + 180 + tan j ctani > G0 0 2 0 > b < q W = W + 180 + w   T GE0 G0 e 2p (13) W = W + 180 w  1  T > e GW0 G0 2p W = W  R GC0 GW0 W where W is the geographic longitude of the satellite’s ascending node, W is the east G0 GE0 extreme value of the longitude interval, W is the west extreme value of the longitude GW0 interval, and W is the middle value of the longitude interval. a = 6356.755 km is the GC0 polar radius of the earth, and b = 6378.140 km is the equatorial radius. q is the true anomaly of the satellite for the initial state, l is the longitude at the time, and j is the 0 0 latitude at the time. At this moment, we assume that the geographic location of the target has a virtual satellite, calculate the geographic longitude of the virtual satellite’s ascending node, obtain the projection of the target on the equator X that characterizes the orbital G0 plane characteristics of the constellation, and calculate the difference between the center of Aerospace 2021, 8, 156 8 of 18 each orbital surface distribution range and X , filtering the track surface corresponding to G0 the minimum value X W . j j G0 GC0 Direction of orbit track shift Distribution range of ascending node GW0 XG0 Ω G0 ΩGE0 Longitude range of detectable region projection GED0 GWD0 Figure 4. Selection method based on longitude section of ascending node. Figure 4. Selection method based on longitude section of ascending node. The geographical longitude distribution range of the ascending node of the orbital 3.4. Task Satellite Selection Analysis plane can be calculated by the instantaneous root of any satellite in the orbital plane. After selecting the orbital planes, it is necessary to select candidate satellites on The calculation of the ascending orbit is shown in Formula (12): the selected orbital planes. The selection of candidate satellites is mainly based on the relative motion relationship between the satellite and the target with the constraints of    tan ctan i  G 0 0 2 0 observation conditions. To summarize the relative  motion relationship between the target and the satellite,     T GE00 G e the main situation can be seen  in Figure 5. The 2 target and the satellite are moving in (12) completely opposite directions called opposite flight. While they are moving in the same      1 T GW00 G e  direction called codirectional flight. The tangential horizontal flight can be divided into 2  two situations with the same latitude and longitude deviation.  =R    GC0 GW 0   2 The calculation of descending orbit is shown in Formula (13):  a    180  tan ctan i  G 0 0 0    180   T GE00 G e  2 (13)      180   1 T GW00 G e 2   =R    GC0 GW 0   2 where  is the geographic longitude of the satellite’s ascending node,  is the east G 0 GE 0 extreme value of the longitude interval, is the west extreme value of the longitude GW 0 interval, and is the middle value of the longitude interval. a = 6356.755 km is the GC0 polar radius of the earth, and b = 6378.140 km is the equatorial radius.  is the true anomaly of the satellite for the initial state,  is the longitude at the time, and  is the 0 0 latitude at the time. At this moment, we assume that the geographic location of the target has a virtual satellite, calculate the geographic longitude of the virtual satellite’s ascending node, obtain the projection of the target on the equator that characterizes the orbital G 0 plane characteristics of the constellation, and calculate the difference between the center Aerospace 2021, 8, 156 9 of 18 of each orbital surface distribution range and X , filtering the track surface correspond- G 0 ing to the minimum value X  . GG 0 C0 3.4. Task Satellite Selection Analysis After selecting the orbital planes, it is necessary to select candidate satellites on the selected orbital planes. The selection of candidate satellites is mainly based on the relative motion relationship between the satellite and the target with the constraints of observation conditions. To summarize the relative motion relationship between the target and the satellite, the main situation can be seen in Figure 5. The target and the satellite are moving in com- pletely opposite directions called opposite flight. While they are moving in the same di- Aerospace 2021, 8, 156 9 of 17 rection called codirectional flight. The tangential horizontal flight can be divided into two situations with the same latitude and longitude deviation. Tangential flight Co-directional flight Opposite flight Tangential flight Figure 5. Relative motion between satellite and target. Figure 5. Relative motion between satellite and target. 3.4.1. Codirectional Flight 3.4.1. Codirectional Flight The situation of the satellite and the target flying in the same direction can be seen The situation of the satellite and the target flying in the same direction can be seen in in Figure 5. For time-sequence trajectories, the high-precision orbit propagator (HPOP) Figure 5. For time-sequence trajectories, the high-precision orbit propagator (HPOP) was was adopted in the simulation. However, trajectory propagation is not the main research adopted in the simulation. However, trajectory propagation is not the main research com- component of this article, and the propagation time was less than 1 h. Therefore, the model ponent of this article, and the propagation time was less than 1 h. Therefore, the model was simplified, the space targets were calculated as a 10 cm diameter sphere, and the was simplified, the space targets were calculated as a 10 cm diameter sphere, and the sat- satellites were calculated as an 80 cm cube. ellites were calculated as an 80 cm cube. In Figure 6, the red spots represent the space trace of the target, the blue spots denote In Figure 6, the red spots represent the space trace of the target, the blue spots denote the space trace of the satellite, and the green line is the line of sight. It can be seen from the the space trace of the satellite, and the green line is the line of sight. It can be seen from figure that the satellite can detect the target almost all the way, the range of LOS adjustment the figure that the satellite can detect the target almost all the way, the range of LOS ad- is very small, and the observation conditions are better. justment is very small, and the observation conditions are better. The changes in observation conditions during the observation process can be seen in Figure 7, where the green line is the maximum observation projection distance, the red line is the undetectable projection distance, and the blue line is the projection distance between the satellite and the target. The green area is the width of the observable area. It can be seen from the figure that the distance between the target and the satellite stays in the observable area between the maximum observation and the unobservable projection distance until the target height continues to decrease to unobservable. Aerospace 2021, 8, 156 10 of 18 Aerospace 2021, 8, 156 10 of 17 Aerospace 2021, 8, 156 10 of 18 Figure 6. Trajectory of satellite and target with access link. The changes in observation conditions during the observation process can be seen in Figure 7, where the green line is the maximum observation projection distance, the red line is the undetectable projection distance, and the blue line is the projection distance between the satellite and the target. The green area is the width of the observable area. It can be seen from the figure that the distance between the target and the satellite stays in the observable area between the maximum observation and the unobservable projection Figure 6. Trajectory of satellite and target with access link. Figure 6. Trajectory of satellite and target with access link. distance until the target height continues to decrease to unobservable. The changes in observation conditions during the observation process can be seen in Figure 7, where the green line is the maximum observation projection distance, the red line is the undetectable projection distance, and the blue line is the projection distance between the satellite and the target. The green area is the width of the observable area. It can be seen from the figure that the distance between the target and the satellite stays in the observable area between the maximum observation and the unobservable projection distance until the target height continues to decrease to unobservable. Figure 7. Time sequence of detection area variation. Figure 7. Time sequence of detection area variation. 3.4.2. Tangential Flight 3.4.2. Tangential Flight The situation of the tangential flight between the satellite and the target can be seen in The situation of the tangential flight between the satellite and the target can be seen Figures 8–10, respectively. They are the deviation of longitude and latitude in the same in Figures 8–10, respectively. They are the deviation of longitude and latitude in the same direction and the deviation of latitude and longitude in the same direction. The first case direction and the deviation of latitude and longitude in the same direction. The first case can be seen in Figure 8. Only part of the arc of the target can be detected by the satellite. can be seen in Figure 8. Only part of the arc of the target can be detected by the satellite. The changes in observation conditions during the observation process can be seen in Figure 9 for this case. The main constraint on the length of the observation arc is that the Figure 7. Time sequence of detection area variation. distance between the satellite and the target exceeds the maximum observable distance. In Figures 10 and 11, it can be seen that the same observation arc is limited when the lat- 3.4.2. Tangential Flight itude and longitude deviate in the same direction, and the main constraint comes from the The situation of the tangential flight between the satellite and the target can be seen observation distance, which exceeds the maximum observation distance. The observation in Figures 8–10, respectively. They are the deviation of longitude and latitude in the same efficiency of tangential direction flight is lower than that of the same direction flight. direction and the deviation of latitude and longitude in the same direction. The first case can be seen in Figure 8. Only part of the arc of the target can be detected by the satellite. Aerospace 2021, 8, 156 11 of 18 AerAer ospospace ace 2021 2021 , 8, ,18 5,6156 11 of 1118 of 17 Figure 8. Trajectory of satellite and target with access link. The changes in observation conditions during the observation process can be seen in Figure 9 for this case. The main constraint on the length of the observation arc is that the Figure 8. Trajectory of satellite and target with access link. Figure 8. Trajectory of satellite and target with access link. distance between the satellite and the target exceeds the maximum observable distance. The changes in observation conditions during the observation process can be seen in Figure 9 for this case. The main constraint on the length of the observation arc is that the distance between the satellite and the target exceeds the maximum observable distance. Aerospace 2021, 8, 156 12 of 18 Figure 9. Time sequence of detection area variation. Figure 9. Time sequence of detection area variation. In Figures 10 and 11, it can be seen that the same observation arc is limited when the latitude and longitude deviate in the same direction, and the main constraint comes from Figure 9. Time sequence of detection area variation. the observation distance, which exceeds the maximum observation distance. The obser- vation efficiency of tangential direction flight is lower than that of the same direction In Figures 10 and 11, it can be seen that the same observation arc is limited when the flight. latitude and longitude deviate in the same direction, and the main constraint comes from the observation distance, which exceeds the maximum observation distance. The obser- vation efficiency of tangential direction flight is lower than that of the same direction flight. Figure 10. Trajectory of satellite and target with access link. Figure 10. Trajectory of satellite and target with access link. Figure 11. Time sequence of detection area variation. 3.4.3. Opposite Directional Flight The situation of the satellite and the target flying in the opposite direction can be seen in Figure 12. From Figures 12 and 13, it can be seen that in the case of opposite directional flight, the observable arc of the target is extremely limited, which is mainly due to the target quickly approaching and entering the unobservable area. Therefore, when flying in oppo- site directions, the observation benefit is the lowest. Aerospace 2021, 8, 156 12 of 18 Aerospace 2021, 8, 156 12 of 17 Figure 10. Trajectory of satellite and target with access link. Figure 11. Time sequence of detection area variation. Figure 11. Time sequence of detection area variation. 3.4.3. Opposite Directional Flight Aerospace 2021, 8, 156 13 of 18 3.4.3. Opposite Directional Flight The situation of the satellite and the target flying in the opposite direction can be seen The situation of the satellite and the target flying in the opposite direction can be seen in Figure 12. in Figure 12. From Figures 12 and 13, it can be seen that in the case of opposite directional flight, the observable arc of the target is extremely limited, which is mainly due to the target quickly approaching and entering the unobservable area. Therefore, when flying in oppo- site directions, the observation benefit is the lowest. Figure 12. Trajectory of satellite and target with access link. Figure 12. Trajectory of satellite and target with access link. From Figures 12 and 13, it can be seen that in the case of opposite directional flight, the observable arc of the target is extremely limited, which is mainly due to the target quickly approaching and entering the unobservable area. Therefore, when flying in opposite directions, the observation benefit is the lowest. Figure 13. Time sequence of detection area variation. 3.5. Task Satellite Selection Factor In the selected orbital plane, the weight of three factors are proposed [20]: the relative angle influence factor Q is obtained by analyzing the relative motion relationship be- ra tween the target and the satellite, Q is obtained by analyzing the distance relationship dst between the target and the satellite, and Q is obtained by analyzing the relationship bd between the target and the unobservable area. The overall task satellite selection factor SF is calculated as follows: n n n n SF  w Q  w Q  w Q (14) sat ra ra dst dst bd bd w w where is the weight for the relative motion relationship, is the weight for ra dst the relative distance observation, and is the weight for the blind zone. Observing a bd target requires no less than two satellites at the same time, and considering the continuity of the entire process, two orbital planes and two satellites on the orbital plane were se- lected at the initial stage of selection. The selection factors of each satellite were calculated in the orbital plane, and the satellite with the highest factor value was selected as the first choice, while the satellite with the second highest choice factor was chosen as the second Aerospace 2021, 8, 156 13 of 18 Aerospace 2021, 8, 156 13 of 17 Figure 12. Trajectory of satellite and target with access link. Figure 13. Time sequence of detection area variation. Figure 13. Time sequence of detection area variation. 3.5. Task Satellite Selection Factor 3.5. Task Satellite Selection Factor In the selected orbital plane, the weight of three factors are proposed [20]: the relative In the selected orbital plane, the weight of three factors are proposed [20]: the relative angle influence factor Q is obtained by analyzing the relative motion relationship be- n ra angle influence factor Q is obtained by analyzing the relative motion relationship be- ra tween the target and the satellite, Q is obtained by analyzing the distance relationship dst tween the target and the satellite, Q is obn tained by analyzing the distance relationship dst between the target and the satellite, and Q is obtained by analyzing the relationship bd bet between ween th the e ttar arget get an and d the the unobservable satellite, and ar Qea. The is ob overall tained task by analy satellite zing selection the relation factor ship SF bd is calculated as follows: between the target and the unobservable area. The overall task satellite selection factor SF is calculated as follows: n n n n SF = w  Q + w  Q + w  Q (14) n ra n ra n n sat dst dst bd bd SF  w Q  w Q  w Q (14) sat ra ra dst dst bd bd where w is the weight for the relative motion relationship, w is the weight for where w isra the weight for the relative motion relationship, w is dst the weight for the ra dst relative distance observation, and w is w the weight for the blind zone. Observing a target the relative distance observation, and is the weight for the blind zone. Observing a bd bd requires no less than two satellites at the same time, and considering the continuity of the target requires no less than two satellites at the same time, and considering the continuity entire process, two orbital planes and two satellites on the orbital plane were selected at of the entire process, two orbital planes and two satellites on the orbital plane were se- the initial stage of selection. The selection factors of each satellite were calculated in the lected at the initial stage of selection. The selection factors of each satellite were calculated orbital plane, and the satellite with the highest factor value was selected as the first choice, in the orbital plane, and the satellite with the highest factor value was selected as the first while the satellite with the second highest choice factor was chosen as the second choice. choice, while the satellite with the second highest choice factor was chosen as the second The Monte Carlo simulation was used to determine the weight values. The simulation was divided into two stages. In the first stage, the satellites were selected with 0.1 as the weight step value for all three weights. Then, the length of the observation windows were calculated between 10 random targets and the selected satellite. After 10,000 iterations, a selection result with a length of 0.1 weight interval was obtained based on the longest observation window. In the second stage, the weight step setting was 0.01 in the chosen weight interval, and another 10,000 iterations were carried out to determine the weight settings, as seen in Table 3. Table 3. Weight configuration. Weight Value Relative motion weight 0.14 Relative distance weight 0.65 Blind zone influence weight 0.21 4. Results and Discussion Different latitudes and different moving trajectory targets were used to simulate and verify the screening method of the constellation. The main parameters of the target used in the simulation verification are shown in Table 4. The mid-latitude opposing flying target, the low-latitude tangential flying target, the mid-latitude tangentially biased remote Aerospace 2021, 8, 156 14 of 17 target, and the high-latitude long-range target flying in the same direction were selected to simulate the selection of candidate orbits and task satellites. Table 4. Coordinate of the trajectory shadow ends. Target and Position Longitude Latitude Target1 Position1 143.505 38.230 Target1 Position2 145.707 36.227 Target2 Position1 145.966 15.569 Target2 Position2 142.945 17.621 Target3 Position1 118.793 41.002 Target3 Position2 126.851 38.689 Target4 Position1 115.154 40.315 Target4 Position2 118.583 50.013 The selection results of candidate orbits and task satellites for the mid-latitude oppos- ing flying target (target 1) can be seen in Figure 14. Among them, the satellite flying in the opposite direction of the target (the trajectory in purple-red line) had an observation window for the satellite. When flying in the opposite direction, it was the first satellite of the second selected orbit (SOFS), and the second selected satellite in second selected orbit (SOSS) with the black line in the trajectory had the ability to observe the target early. The blue trajectory was the first satellite of the first orbit (FOFS), which had the longest observation arc to the target. The green trajectory followed as the first orbit second satellite (FOSS). Although flying tangentially to the target, it had a better observation window due Aerospace 2021, 8, 156 15 of 18 to the relative distance from the further point to the near point. The optimization results of orbits and task satellites were consistent with the actual observation conditions. Figure 14. Selection of orbit planes and satellites for target1. Figure 14. Selection of orbit planes and satellites for target1. Figure 15 shows the satellite selection results of tangential flying targets at low lati- Figure 15 shows the satellite selection results of tangential flying targets at low lati- tudes. The target was tangential to the first orbit and opposite to the second orbit. There- tudes. The target was tangential to the first orbit and opposite to the second orbit. Therefore, fore, the selection results were consistent with the actual observation conditions. the selection results were consistent with the actual observation conditions. Figure 15. Selection of orbit planes and satellites for target2. Figure 16 shows the satellite selection results of the mid-latitude long-distance fly- ing target, the opposing flight orbit was selected as the first orbit, although there were fewer observing blind spots in the opposite direction. The four selected satellites were also the satellites with the best observation conditions under actual analysis. Aerospace 2021, 8, 156 15 of 18 Figure 14. Selection of orbit planes and satellites for target1. Figure 15 shows the satellite selection results of tangential flying targets at low lati- Aerospace 2021, 8, 156 15 of 17 tudes. The target was tangential to the first orbit and opposite to the second orbit. There- fore, the selection results were consistent with the actual observation conditions. Figure 15. Selection of orbit planes and satellites for target2. Figure 15. Selection of orbit planes and satellites for target2. Fig Figur ure 16 e 16 sho shows ws th the e s satellite atellite se selection lection result results s of of the the mid-latitude mid-latitude long-distance long-distance flying fly- target, the opposing flight orbit was selected as the first orbit, although there were fewer ing target, the opposing flight orbit was selected as the first orbit, although there were Aerospace 2021, 8, 156 16 of 18 observing blind spots in the opposite direction. The four selected satellites were also the fewer observing blind spots in the opposite direction. The four selected satellites were also satellites with the best observation conditions under actual analysis. the satellites with the best observation conditions under actual analysis. Figure 16. Selection of orbit planes and satellites for target3. Figure 16. Selection of orbit planes and satellites for target3. For high latitude target 4, the satellite selection result is shown in Figure 17. The orbit For high latitude target 4, the satellite selection result is shown in Figure 17. The orbit that actually had the longest observation window was selected as the suboptimal orbit. that actually had the longest observation window was selected as the suboptimal orbit. The The se selected lected four four s satellites atellites wer were e the thfour e four satellites satellites with with th the best e best actual actual observation observation con conditions, di- tions, but b ther ut th e wer ere e were discr d epancies iscrepancie in the s in orbit the orbit and a satellite nd satell orite dering. order The ing. results The reshowed sults show that ed the selection of orbital planes based on the longitude of the ascending node was more sensitive that the selection of orbital planes based on the longitude of the ascending node was more to the latitude distribution of the target. The reason for this is that the input constellation sensitive to the latitude distribution of the target. The reason for this is that the input con- orbits were densely distributed in high-latitude regions, and the observation conditions stellation orbits were densely distributed in high-latitude regions, and the observation conditions of each orbital plane were less different; therefore, optimally and suboptimally, the actual observational gain difference on the orbital surface was close. Therefore, alt- hough the order of satellite selection was different from the actual one, the selected satel- lite was the one with the best observation profit. Figure 17. Selection of orbit planes and satellites for target4. Aerospace 2021, 8, 156 16 of 18 Figure 16. Selection of orbit planes and satellites for target3. For high latitude target 4, the satellite selection result is shown in Figure 17. The orbit that actually had the longest observation window was selected as the suboptimal orbit. The selected four satellites were the four satellites with the best actual observation condi- tions, but there were discrepancies in the orbit and satellite ordering. The results showed Aerospace 2021, 8, 156 16 of 17 that the selection of orbital planes based on the longitude of the ascending node was more sensitive to the latitude distribution of the target. The reason for this is that the input con- stellation orbits were densely distributed in high-latitude regions, and the observation conditions of each orbital plane were less different; therefore, optimally and suboptimally, of each orbital plane were less different; therefore, optimally and suboptimally, the actual the actual observational gain difference on the orbital surface was close. Therefore, alt- observational gain difference on the orbital surface was close. Therefore, although the hough the order of satellite selection was different from the actual one, the selected satel- order of satellite selection was different from the actual one, the selected satellite was the lite was the one with the best observation profit. one with the best observation profit. Figure 17. Selection of orbit planes and satellites for target4. Figure 17. Selection of orbit planes and satellites for target4. 5. Conclusions This study proposes a method that fully considers the constellation orbit charac- teristics for event-driven SODLC. After the target appears, based on the initial limited information, the candidate satellites with the observation conditions are quickly screened to meet the needs of high-efficiency mission planning and scheduling. The observation window projection screening method can quickly screen the observation satellites with better observation conditions through less calculation. Calculation and simulation analysis show this method is able to select orbital planes with optimal observation conditions and the corresponding observation satellites when calculating mid-latitude and low-latitude targets. When calculating high-latitude area targets, the optimal satellites that are consistent with the actual observation benefits can be correctly selected, but there is a deficiency of insensitivity to the priority order of the orbital surface, which can be the subject of future optimization studies. The constraints considered in this work were mainly the atmospheric limb height and the observation distance, and more specific constraints such as the sun avoidance angle and full moon avoidance angle were not considered, which can also be studied in future work. The observation window projection screening method proposed in this paper has better task satellite selection efficiency, timeliness, and practical value for event-driven mission planning and scheduling of SODLC. Author Contributions: Conceptualization: S.Z. and Z.Z.; methodology: S.Z.; supervision: Z.Z. and H.H.; writing—review and editing: S.Z. and Y.L. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the Innovation Laboratory Fund Program of the Chinese Academy of Sciences, grant number CXJJ17S014. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not applicable. Aerospace 2021, 8, 156 17 of 17 Conflicts of Interest: The authors declare no conflict of interest. References 1. Sanchez, A.H.; Soares, T.; Wolahan, A. Reliability aspects of mega-constellation satellites and their impact on the space debris environment. In Proceedings of the 2017 Annual Reliability and Maintainability Symposium (RAMS), Orlando, FL, USA, 23–26 January 2017. [CrossRef] 2. Lewis, H.G. Evaluation of debris mitigation options for a large constellation. J. Space Saf. 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Journal

Aerospace – Multidisciplinary Digital Publishing Institute

Published: May 31, 2021

Keywords: space object detection LEO constellation; observation window projection; task satellite selection

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