基于TLE的Starlink星座第一阶段部署情况分析

近年来,随着卫星技术的快速发展和低轨（low earth orbit,LEO）卫星宽带互联网建设需求的不断增加,低轨大规模星座发展日新月异。针对Starlink星座初始化部署问题,首先论述了“星链”（Starlink）星座现状,分析在轨卫星高度变化。然后利用公开的两行轨道根数（two-line element,TLE）,从卫星发射入轨、轨道面分布两个方面,简要分析了Starlink星座的部署情况,给出升交点的变化规律;同时仿真分析了Starlink星座对地面的覆盖性能。最后,给出星座轨道面和相位分布、故障卫星处置以及可见卫星数量。所分析的结果以期为中国未来部署大规模LEO星座的建设提供借鉴。     

Towards the automated operations of large distributed satellite systems. Part 2: Classifications and tools

Recent developments have seen a trend towards larger constellations of spacecraft, with some proposals featuring constellations of more than 10.000 satellites. While similar concepts for large constellations already existed in the past, traditional satellite deployments hardly ever feature groups of more than 100 satellites. This trend towards considerably larger satellite numbers originates from non-traditional design and operations of spacecraft by non-traditional space companies. The evolution in the space sector, precipitated by new players, is often referred to as “Space 4.0” or “New Space”. It necessitates a rethinking of the way satellites and satellite constellations are planned, designed, and operated. New operational paradigms are needed to enable automatic, optimal task definition, and scheduling in a holistic approach.This is the second of two companion papers that investigate the operations of distributed satellite systems. This second article investigates the classification of distributed satellite systems and evaluates commercial tools for automated spacecraft operations, whereas the first article performed a survey of conventional and “new space”operations of spacecraft constellations.Classification metrics for constellations are derived and evaluated with respect to their informative value concerning the operation, the automation, and the scalability of the constellation. The proposed classification system is applied to the Dove and RapidEye constellation and allows for a comparison between the presented automation approaches. Commercial tools for automated spacecraft operations are evaluated for several mission task elements, such as orbit control, orbit maintenance, and collision avoidance. Subsequently, the trends, benefits, and standardization needs for operational automation are identified.     

卫星规避方案量化分析方法研究

空间碎片数量日益增多,为保护在轨卫星的运行安全,需要针对碎片碰撞制定规避方案,用来规避碰撞风险.本文在调研国外卫星规避机动流程的基础上,分别研究了卫星规避相关的轨道机动方式、轨道预报模型以及交会风险计算模型,建立了卫星规避方案量化分析方法,为规避方案的选择提供参考.      

The influence of orbital maneuver on autonomous orbit determination of an extended satellite navigation constellation

The right ascension of the ascending node is unobservable if only the inter-satellite ranging is used for autonomous orbit determination (AOD) of an Earth navigation constellation. However, if an Earth-Moon libration point satellite is added to the Earth navigation constellation to construct an extended navigation constellation, all the orbital elements can be determined with only the inter-satellite ranging. Furthermore, the extended navigation constellation can provide navigation information for interplanetary probes. For such an extended navigation constellation, orbital control needs to be considered due to the instability of the libration-point satellite orbit. This study concerns the influence of satellite orbital maneuver on the AOD of the extended navigation constellation. An AOD method under orbital maneuver is proposed. A low thrust controller is designed to achieve libration point satellite autonomous orbit maintenance by using AOD results. A navigation constellation consisting of three GPS satellites and one libration point satellite are designed for simulation. The simulation results show that libration point satellites can achieve autonomous navigation and autonomous orbit maintenance by only using inter-satellite ranging information. The rotation drift error of the Earth navigation constellation is also suppressed.     

一种双基站低轨道区域覆盖δ星座设计

在双基站理论研究基础上 ,进行了定倾角区域性覆盖双基站δ星座设计 ,采用倾角为 41°的回归轨道 ,用点覆盖数值仿真的方法设计了对地面站与空间站的一重覆盖与二重覆盖下的星座构型。且星座中各星之间 ,各星与空间站之间均可建立星际链路 ,保证数据在空间站、地面站及星座之间连续传递     

Optimal mission planning of the reconfiguration process of satellite constellations through orbital maneuvers: A novel technical framework

In this paper, a general new methodology is presented for the orbital reconfiguration of satellite constellations on the basis of Lambert targeting theorem. In view of the cost and risk reduction, it is very important to consider the problem of satellite constellation reconfiguration with the two constraints of overall mission cost minimization and the desired final configuration. Hence, the dependent non-simultaneous deployment approach is proposed to minimize overall fuel cost. Despite the fact that the satellites deploy in a non-simultaneous manner, supplementary phasing maneuvers on the target orbital pattern to achieve the desired orbital configuration are avoided. Moreover, a novel idea is presented to optimize the flight of satellites, which plays an important role in complying with the constraint of overall fuel cost minimization as much as possible. In order to achieve the global optimal solution of the satellite constellation reconfiguration problem, the efficient hybrid Particle Swarm Optimization/Genetic Algorithm (PSO/GA) technique, is implemented. Finally, to indicate the superiority of the presented method, a comparison to the simultaneous maneuver viewpoint is made on a number of representative cases. The obtained results imply significant reduction of reconfiguration costs by employing the proposed method.     

低轨导航增强卫星星座设计

针对目前全球低轨卫星快速发展的现状,对低轨导航增强卫星星座设计方法进行了详细的研究。首先推导了轨道高度与可视球冠的关系,结合太空垃圾分布,从覆盖范围、经济性及碰撞风险几方面联合确定了轨道高度。然后推导了用户仰角与轨道倾角的关系,分析了实现南北极点覆盖的轨道倾角。接着结合铱星星座,推导出单一星座构型无法实现全球范围内均匀的可见星和精度衰减因子（Dilution of Precision,DOP）值分布。最后提出了一种组合低轨卫星星座设计方法。结果表明,该方法设计的组合星座在实现全球覆盖的同时,能够实现可见星数量与DOP值在全球范围内的均匀分布。     

多等级区域侦察弹性星座设计方法

针对传统侦察星座目标单一、弹性低的问题，提出了多等级区域侦察弹性星座的设计方法。该方法将星座设计过程按区域等级信息分为多个子星座逐步设计，直到整体星座对所有的区域性能满足设计要求。以区域被划分为3个等级为例，首先对星座设计需求、设计指标及设计步骤进行了分析。其次推导了地面最低分辨率和轨道高度的关系并确定了不同子星座的轨道高度。最后考虑轨道倾角、一箭多星发射、光照和升交点漂移同步约束，构建基础星座、子星座1和子星座2的优化模型。最终设计星座为3层混合星座，共8个轨道面和70颗卫星，星座对各等级区域的最大重访时间分别为10937s，12241s和17437s，弹性指数为2213%，2420%和6361%。结果表明该方法设计的星座可实现对区域覆盖和弹性分级的设计要求，证明了方法的有效性。对比Walker星座设计方法，在同等设计要求下，Walker星座所需卫星数为156颗，多等级区域侦察弹性星座所需卫星数远低于Walker星座，结果进一步证明了该星座设计方法的优越性。     

低轨卫星的北斗反射信号海洋覆盖分析

北斗系统作为我国自行研制的导航系统，具有独特的混合星座特性，其反射事件在海洋上的空间分布和覆盖性能的研究成果较少。针对上述问题，模拟了北斗三号（Beidou System 3，BDS3）以及全球定位系统（Global Positioning System，GPS）空间星座，模拟不同性能参数的低轨接收卫星，在此仿真系统的基础上，计算反射事件在各仿真场景下的海洋覆盖率以及同时发生反射事件的卫星数量。结果表明：BDS3与GPS相比具有更大的反射事件海洋覆盖率，覆盖性能更优；仿真周期7天与1天相比,前者卫星产生的反射事件海洋覆盖率约为后者5倍；低轨道卫星（Low Earth Orbit,LEO）轨道高度越高，天线波束角度越大，反射事件海洋覆盖率越大；3颗LEO卫星下同时发生反射事件卫星数的平均值约为单颗LEO卫星的3倍。可通过设计多星组网来提高反射事件海洋覆盖率。研究结果对星载反射技术海洋遥感应用方面有一定的参考价值。     

Iridium/ORBCOMM机会信号融合定位技术

在全球导航卫星系统(GNSS)不可用情况下，低地球轨道(LEO)卫星机会信号(SOP)定位技术是一种有效的导航定位解决方案。单LEO星座机会信号定位技术面临星座构型不足或可见卫星偏少等问题，多LEO星座机会信号融合定位技术可有效解决该问题。通过分析瞬时多普勒定位原理，建立了Iridium/ORBCOMM机会信号融合定位模型，引入基于Helmert方差估计的加权最小二乘算法进一步提高定位精度。实测数据表明:基于Helmert方差估计的Iridium/ORBCOMM机会信号融合定位精度优于70 m，验证了多LEO星座机会信号融合定位的可行性和有效性。      

The impact on tsunami detection from space using GNSS-reflectometry when combining GPS with GLONASS and Galileo

The devastating Sumatra tsunami in 2004 demonstrated the need for a tsunami early warning system in the Indian Ocean. Such a system has been installed within the German-Indonesian Tsunami Early Warning System (GITEWS) project. Tsunamis are a global phenomenon and for global observations satellites are predestined. Within the GITEWS project a feasibility study on a future tsunami detection system from space has therefore been carried out. The Global Navigation Satellite System Reflectometry (GNSS-R) is an innovative way of using GNSS signals for remote sensing. It uses ocean reflected GNSS signals for sea surface altimetry. With a dedicated Low Earth Orbit (LEO) constellation of satellites equipped with GNSS-R receivers, densely spaced sea surface height measurements could be established to detect tsunamis. Some general considerations on the geometry between LEO and GNSS are made in this simulation study. It exemplary analyzes the detection performance of a GNSS-R constellation at 900 km altitude and 60° inclination angle when applied to the Sumatra tsunami as it occurred in 2004. GPS is assumed as signal source and the combination with GLONASS and Galileo signals is investigated. It can be demonstrated, that the combination of GPS and Galileo is advantageous for constellations with few satellites while the combination with GLONASS is preferable for constellations with many satellites. If all three GNSS are combined, the best detection performance can be expected for all scenarios considered. In this case an 18 satellite constellation will detect the Sumatra tsunami within 17 min with certainty, while it takes 53 min if only GPS is considered.     

移动通信卫星经济性分析

由小型近地轨道卫星组成星座,实现移动通信服务,是卫星通信发展的重要方向。近地轨道卫星和地球静止轨道卫星用作移动通信卫星网,各有其优缺点。文章从经济性角度对两类卫星网进行了比较,重点是对不同高度的轨道(包括低、中、地球静止)的移动通信系统的空间部分成本——卫星星座的研制成本与发射成本进行分析比较,给出了具体的运算公式和计算结果。其结论是:轨道高度越低,卫星网的成本越高;地球静止轨道卫星网的成本最低。但是,决定是否发展小型近地轨道通信卫星网,不能仅考虑经济因素,还要考虑对技术进步的推动作用。     

一种改进的卫星星座服务可用性评价方法

针对存在缺失卫星的轨道面,将星座中的卫星分为两组,从概率角度并采用组合方法提出了星座覆盖可用性和导航精度可用性指标的统计评价模型和仿真流程,进而通过对两项可用性指标进行加权建立了形式统一的服务可用性加权评价模型。利用该模型对单个或多个轨道面有确定数量卫星缺失的状态下,星座构型和轨道参数变化对其服务可用性的影响进行了研究。结果表明,星座轨道平面数和轨道高度均对服务可用性有较大影响。提出的服务可用性评价模型物理意义明确,可有效减少指标评价时间,研究结论有助于在概念设计阶段对星座构型和轨道参数进行优选。     

中轨道Walker导航星座在轨备份方案优化设计

针对中轨道Walker导航星座在轨备份方案的优化问题，首先提出了在轨备份星轨位优化设计方法，考虑星座运行期间在轨备份星与工作卫星存在共同提供服务的情况，选取PDOP值和可见卫星数作为轨位优化指标，建立了轨位优化模型，并基于NSGA-Ⅱ算法对不同轨位下在轨备份星对导航星座服务性能的提升效果进行仿真分析；然后，基于在轨备份星轨位的优化结果，建立在轨备份星替换的轨道机动模型，并综合考虑速度增量和替换时间，确定了以替换时间最少为优化目标的在轨备份星替换方案。结果表明，提出的在轨备份方案能有效满足备份星的设计需求，增强导航星座的服务性能，实现故障卫星的快速替换，可为导航星座备份星的建设提供借鉴。     

Assessing and minimizing collisions in satellite mega-constellations

We aim to provide satellite operators and researchers with an efficient means for evaluating and mitigating collision risk during the design process of mega-constellations. We first introduce a novel algorithm for conjunction prediction that relies on large-scale numerical simulations and uses a sequence of filters to greatly reduce its computational expense. We then use this brute-force algorithm to establish baselines of endogenous (intra-constellation), or self-induced, conjunction events for the FCC-reported designs of the OneWeb LEO and SpaceX Starlink mega-constellations. We demonstrate how these deterministic results can be used to validate more computationally efficient, stochastic techniques for close-encounter prediction by adopting a new probabilistic approach from Solar-System dynamics as a simple test case. Finally, we show how our methodology can be applied during the design phase of large constellations by investigating Minimum Space Occupancy (MiSO) orbits, a generalization of classical frozen orbits that holistically account for the perturbed-Keplerian dynamics of the Earth-satellite-Moon-Sun system. The results indicate that the adoption of MiSO orbital configurations of the proposed mega-constellations can significantly reduce the risk of endogenous collisions with nearly indistinguishable adjustments to the nominal orbital elements of the constellation satellites.     

Analysis of the orbit lifetime of CubeSats in low Earth orbits including periodic variation in drag due to attitude motion

It is estimated that more than 22,300 human-made objects are in orbit around the Earth, with a total mass above 8,400,000 kg. Around 89% of these objects are non-operational and without control, which makes them to be considered orbital debris. These numbers consider only objects with dimensions larger than 10 cm. Besides those numbers, there are also about 2000 operational satellites in orbit nowadays. The space debris represents a hazard to operational satellites and to the space operations. A major concern is that this number is growing, due to new launches and particles generated by collisions. Another important point is that the development of CubeSats has increased exponentially in the last years, increasing the number of objects in space, mainly in the Low Earth Orbits (LEO). Due to the short operational time, CubeSats boost the debris population. One of the requirements for space debris mitigation in LEO is the limitation of the orbital lifetime of the satellites, which needs to be lower than 25 years. However, there are space debris with longer estimated decay time. In LEÓs, the influence of the atmospheric drag is the main orbital perturbation, and is used in maneuvers to increment the losses in the satellite orbital energy, to locate satellites in constellations and to accelerate the decay.The goal of the present research is to study the influence of aerodynamic rotational maneuver in the CubeSat?s orbital lifetime. The rotational axis is orthogonal to the orbital plane of the CubeSat, which generates variations in the ballistic coefficient along the trajectory. The maneuver is proposed to accelerate the decay and to mitigate orbital debris generated by non-operational CubeSats. The panel method is selected to determine the drag coefficient as a function of the flow incident angle and the spinning rate. The pressure distribution is integrated from the satellite faces at hypersonic rarefied flow to calculate the drag coefficient. The mathematical model considers the gravitational potential of the Earth and the deceleration due to drag. To analyze the effects of the rotation during the decay, multiple trajectories were propagated, comparing the results obtained assuming a constant drag coefficient with trajectories where the drag coefficient changes periodically. The initial perigees selected were lower than 400 km of altitude with eccentricities ranging from 0.00 to 0.02. Six values for the angular velocity were applied in the maneuver. The technique of rotating the spacecraft is an interesting solution to increase the orbit decay of a CubeSat without implementing additional de-orbit devices. Significant changes in the decay time are presented due to the increase of the mean drag coefficient calculated by the panel method, when the maneuver is applied, reducing the orbital lifetime, however the results are independent of the angular velocity of the satellite.     

Scheduling algorithms for rapid imaging using agile Cubesat constellations

Distributed Space Missions such as formation flight and constellations, are being recognized as important Earth Observation solutions to increase measurement samples over space and time. Cubesats are increasing in size (27U, ～40?kg in development) with increasing capabilities to host imager payloads. Given the precise attitude control systems emerging in the commercial market, Cubesats now have the ability to slew and capture images within short notice. We propose a modular framework that combines orbital mechanics, attitude control and scheduling optimization to plan the time-varying, full-body orientation of agile Cubesats in a constellation such that they maximize the number of observed images and observation time, within the constraints of Cubesat hardware specifications. The attitude control strategy combines bang-bang and PD control, with constraints such as power consumption, response time, and stability factored into the optimality computations and a possible extension to PID control to account for disturbances. Schedule optimization is performed using dynamic programming with two levels of heuristics, verified and improved upon using mixed integer linear programming. The automated scheduler is expected to run on ground station resources and the resultant schedules uplinked to the satellites for execution, however it can be adapted for onboard scheduling, contingent on Cubesat hardware and software upgrades. The framework is generalizable over small steerable spacecraft, sensor specifications, imaging objectives and regions of interest, and is demonstrated using multiple 20?kg satellites in Low Earth Orbit for two case studies – rapid imaging of Landsat’s land and coastal images and extended imaging of global, warm water coral reefs. The proposed algorithm captures up to 161% more Landsat images than nadir-pointing sensors with the same field of view, on a 2-satellite constellation over a 12-h simulation. Integer programming was able to verify that optimality of the dynamic programming solution for single satellites was within 10%, and find up to 5% more optimal solutions. The optimality gap for constellations was found to be 22% at worst, but the dynamic programming schedules were found at nearly four orders of magnitude better computational speed than integer programming. The algorithm can include cloud cover predictions, ground downlink windows or any other spatial, temporal or angular constraints into the orbital module and be integrated into planning tools for agile constellations.     

基于改进MOPSO算法的区域侦察弹性星座重构方法

针对区域侦察弹性星座重构问题，提出了基于改进多目标粒子群优化算法(multi objective particle swarm optimization，MOPSO)的区域侦察弹性星座重构方法。该方法采用一箭多星发射和在轨卫星相位机动相结合的方式对受损星座重构。首先选取了星座覆盖、重构成本、重构时间和星座弹性四方面的指标；其次对一箭多星发射过程和卫星相位机动过程进行了分析，对失效轨道面内剩余正常卫星采取均匀相位的策略。以恢复原有星座性能为目的，考虑最大重访时间、重构成本、重构时间及弹性，建立了重构时间和重构成本最优的重构优化模型。最后对MOPSO算法进行了改进，提出了基于学习机制的种群更新策略，通过变量转化将离散变量转化为连续变量，解决了重构优化模型中混合变量优化问题。针对某一受损星座进行仿真，重构时间最优的重构方案为发射6颗新卫星结合在轨卫星均匀相位；重构成本最优的重构方案为发射4颗新卫星结合在轨卫星均匀相位。案例表明提出的重构方法有效，可为侦察星座的建设提供参考。     

Large constellations assessment and optimization in LEO space debris environment

Recent plans for large constellations in Low-Earth Orbit have opened the debate on both their vulnerability and their influence on the already hazardous space debris environment. In fact, given that large constellations normally employ satellites of small size, there might be situations in which cm-size debris could have enough energy to cause fragmentation of a significant part of these spacecraft upon impact, while smaller debris could affect the functionalities of critical subsystems, even compromising the success of disposal operations planned at end-of-life. In this context, this paper investigates: (1) collisions with large objects that could initiate the fragmentation of a significant part of the satellite, and (2) impacts with small debris that might perforate the spacecraft hull thus causing relevant performance/functionality degradation. These two points are merged in a simple statistical tool for risk assessment, which analyses the effects of the main parameters of the constellations on its vulnerability (i.e. operational life, number of satellites, spacecraft cross section, satellites reliability). In more details, the tool relates impact probability (for both small and large debris) to the ballistic response of spacecraft structures and protections, defining the critical configurations that might compromise the expected disposal operations. This method requires a limited knowledge of the spacecraft internal layout, as it is based on a statistical analysis of impact damage instead of a complete evaluation of the vulnerability of each subsystem. In parallel, non-debris related failures are also investigated and statistic models of spacecraft reliability characteristic are proposed. Among the results, it is shown that reducing the lifetime of individual satellites in a constellation might improve the success rate of post-mission disposal, thanks to the reduction of the spacecraft exposure to the space environment with the consequential degradation of its performance. On the other hand, reducing the lifetime would seriously affect the debris environment: the increase in traffic in the most crowded altitudes would be not counterbalanced by the higher post mission disposal success rate, causing an overall increase of the total number of uncontrolled resident objects.