Orbital evolution of the first upper stages used for the new European and Chinese navigation satellite systems

The solutions adopted for the disposal of the upper stages used to put in orbit the first satellites of the new European (Galileo) and Chinese (Beidou) navigation constellations were analyzed. The orbit evolution of the rocket bodies was modeled for 200 years, taking into account all relevant perturbations, and the chosen disposal options were evaluated in terms of their long-term consequences for the debris environment. The results obtained, when applicable, were also discussed in the context of the eccentricity instability problem, pointed out in previous studies. In addition, the long-term evolution of the fragments resulting from a Beidou rocket body breakup, and of simulated high area-to-mass ratio objects released in the disposal orbits of the first two Galileo upper stages, was investigated.Eight out of ten Beidou upper stages were found to have an orbital lifetime <25 years and the other two resulted in a dwell time of approximately 6 years below 2000 km. It was also found that the perigee heights of the two upper stages used to deploy the first Galileo test spacecraft will remain more than 169 km above the constellation nominal altitude, never crossing the existing or planned navigation systems. In spite of an inclination resonance possibly leading to the exponential growth of the eccentricity over several decades, the optimal choice of the disposal orbital elements was able to prevent such an outcome, by maintaining the orbit nearly circular. Therefore, the upper stage disposal strategies used so far for Beidou and Galileo have generally been quite successful in averting the long-term interference of such rocket bodies with the navigation constellations, provided that accidental breakups are prevented.     

大型低轨航天器与星座卫星的碰撞风险研究

针对商业小卫星星座迅猛发展对航天器飞行安全造成潜在威胁的问题，以600 km高度星座和大型低轨航天器为研究对象，通过区域方法(BOX)和碰撞概率风险评估方法，分析了星座与大型低轨航天器的碰撞风险。根据星座轨道演化分析表明，整个星座卫星与大型低轨航天器可能发生碰撞的时间相对集中，持续时间约 1~ 2年。BOX方法计算结果表明，每颗卫星与大型低轨航天器交会，并进入红色预警门限的交会次数约10次左右。碰撞概率计算结果表明，约有5%的卫星进入红色预警门限，星座如果在寿命末期采取无控再入将对大型低轨航天器在1~2年内产生较大的威胁。     

GNSS服务空域空间信号可用性比较与分析

通过基本参数对全球卫星导航系统（GPS、GLONASS、Galileo和北斗）空间信号可用性影响实验,得出四系统的A knee 值分别为3800km、1100km、3800km和1000km,对应的平均可见卫星数为25、16、22和14/22（亚太地区、MEO星座/混合星座）。分析了三种典型轨道用户的卫星可见性,北斗和GLONASS对MEO和HEO用户的空间信号可用性能较GPS和Galileo稍差,而在LEO用户的应用中,北斗空间信号可用性能却表现最优,平均可见卫星数约为20颗,可用性时间分布比较均匀。最后对GNSS空间有效持续时间段进行统计,随着用户高度的增加,有效持续时间段数增多、总有效持续时间减少;四系统提供全弧段有效服务空间分别为地面至6100km、1600km、6100km和1700km。     

New insights on the orbital debris collision hazard at GEO

An analysis is performed of the orbital debris collision hazard to operational spacecraft at geosynchronous orbit (GEO). As part of the examination, the contribution of individual components of the population are considered and presented to provide a clearer linkage between object characteristic and resulting risk. Our examination of GEO collision risk reveals several critical new insights: (1) the current probability of collision in GEO is relatively low, yet the future is difficult to predict due to our limited ability to observe objects in GEO and the uncertainty in past and future debris-generating events in GEO; (2) the probability of collision in GEO is not uniform by longitude — it is seven times greater in regions centered about the geopotential wells; (3) the probability of a mission-terminating collision is greatly dependent upon the approximately 2200 objects in the 10 cm–1 m range observed in GEO but not yet cataloged; (4) hardware relocated to GEO “graveyard” disposal orbits pose a potential additional, but not fully understood, collision hazard to operational GEO satellites; and (5) the collision hazard throughout the course of a day or year is highly episodic (i.e. non-uniform).     

一类适用于各种轨道类型的导航卫星广播星历研究

导航卫星广播星历是卫星导航定位的基础,要求有较高的精度和实时性。GPS和GLONASS广播星历形式适合于某一类卫星轨道,但存在一定局限性。利用切比雪夫多项式拟合导航卫星轨道,拟合系数作为广播星历的参数发布,这是一种新的广播星历形式,可作为各种轨道类型的导航卫星的广播星历参数,而且具有精度高、计算速度快等特点。     

全球导航星座星间链路技术发展建议

美国全球定位系统（GPS）的Block IIR和Block IIF系列导航卫星安装了UHF频段的星间链路收发设备,未来的GPS Ⅲ系列导航卫星将用Ka频段星间链路替代UHF频段星间链路,提高星间数据通信容量,增强抗干扰能力;俄罗斯全球导航卫星系统（GLONASS）的新一代GLONASS-K系列导航卫星开始安装S频段星间链路收发设备;欧洲的伽利略（Galileo）卫星导航系统也在规划全球导航星座的星间链路体系;我国北斗（Compass）卫星导航系统正处在由区域覆盖向全球覆盖的过渡阶段,全球星座的星间链路正处在多种系统体制的抉择中。文章在对国外各种星间链路研究的基础上,从导航星座星间链路需求和特点出发,提出建议：1）建设高频段星间链路;2）加强星间天线与卫星总体的联合设计;3）星间网络协议要具有灵活性;4）尽可能保持每颗卫星的星间链路设备状态一致。文章考虑了现有国内技术储备和国外未来技术发展方向,提出的观点可以作为我国全球卫星导航系统对星间链路选择的参考,对我国Compass系统建设技术先进的星间链路有一定的指导意义。     

32颗GPS卫星星座空间覆盖特性建模与仿真

GPS卫星要准确完成定位功能可见卫星数应不少于4颗.通过建立针对低轨、中高轨和大椭圆轨道目标卫星的GPS信号空间几何覆盖模型,利用Matlab计算针对低轨、中高轨和大椭圆轨道的可见卫星数,对目前美国32颗GPS卫星星座的空间覆盖特性进行仿真.仿真结果显示,32颗GPS卫星星座不仅可以对低轨目标实现全轨道覆盖,而且对中高轨和大椭圆轨道也有所覆盖,大大扩展了24颗GPS卫星星座的空间应用.     

The Investigation of Possible Approaches of Cataloged Space Objects to Manned Spacecraft

Initial orbital parameter errors are used to examine the miss distance between a spacecraft and an ensemble of tracked objects by a Monte Carlo-type analysis. The radial separation between orbits is evaluated and a keep-out zone is determined, which reduces the risk of collision to an acceptable level.An operational prediction methodology is suggested based on a catalog database, which identifies potentially hazardous approaches and computes the probability of collision for selected spacecraft. An example for the Mir Space Station is presented, which estimates the collision probability and the cross-sectional flux of cataloged objects for the time frame of interest. The results appear to be in good agreement with those of other space debris models.     

Local debris congestion in the geosynchronous environment with population augmentation

Forecasting of localized debris congestion in the geostationary (GEO) regime is performed to investigate how frequently near-miss events occur for each of the longitude slots in the GEO ring. The present-day resident space object (RSO) population at GEO is propagated forward in time to determine current debris congestion conditions, and new probability density functions that describe where GEO satellites are inserted into operational orbits are harnessed to assess longitude-dependent congestion in “business-as-usual” launch traffic, with and without re-orbiting at end-of-life. Congestion forecasting for a 50-year period is presented to illustrate the need for appropriately executed mitigation measures in the GEO ring. Results indicate that localized debris congestion will double within 50 years under current 80% re-orbiting success rates.     

GPS-based relative navigation for the Proba-3 formation flying mission

The primary objective of the Proba-3 mission is to build a solar coronagraph composed of two satellites flying in close formation on a high elliptical orbit and tightly controlled at apogee. Both spacecraft will embark a low-cost GPS receiver, originally designed for low-Earth orbits, to support the mission operations and planning during the perigee passage, when the GPS constellation is visible. The paper demonstrates the possibility of extending the utilization range of the GPS-based navigation system to serve as sensor for formation acquisition and coarse formation keeping. The results presented in the paper aim at achieving an unprecedented degree of realism using a high-fidelity simulation environment with hardware-in-the-loop capabilities. A modified version of the flight-proven PRISMA navigation system, composed of two single-frequency Phoenix GPS receivers and an advanced real-time onboard navigation filter, has been retained for this analysis. For several-day long simulations, the GPS receivers are replaced by software emulation to accelerate the simulation process. Special attention has been paid to the receiver link budget and to the selection of a proper attitude profile. Overall the paper demonstrates that, despite a limited GPS tracking time, the onboard navigation filter gets enough measurements to perform a relative orbit determination accurate at the centimeter level at perigee. Afterwards, the orbit prediction performance depends mainly on the quality of the onboard modeling of the differential solar radiation pressure acting on the satellites. When not taken into account, this perturbation is responsible for relative navigation errors at apogee up to 50 m. The errors can be reduced to only 10 m if the navigation filter is able to model this disturbance with 70% fidelity.     

星座设计中避免卫星碰撞问题的研究

随着小卫星技术的发展 ,越来越多的航天任务采用小卫星星座来完成 ,在星座的设计过程中需要考虑的因素众多。本文从星座运行的安全性角度 ,分析了星座中卫星发生碰撞的机会和碰撞概率 ,对星座中存在的卫星之间可能发生的碰撞问题进行了研究 ,并提出了解决方法     

Mapping orbits with low station keeping costs for constellations of satellites based on the integral over the time of the perturbing forces

The present paper is concerned with the search for orbits that have potential to require low fuel consumption for station-keeping maneuvers for constellations of satellites. The method used to study this problem is based on the integral over the time of the undesired perturbing forces. This integral measures the change of velocity caused by the perturbation forces acting on the satellite, so mapping orbits that are less perturbed, which generates good candidates for orbits that requires low fuel consumption for station-keeping maneuvers. The integral over the time depends only on the orbit of the spacecraft and the dynamical system considered. The type of engine and the control technique applied to the spacecraft are not considered to search for those orbits. It can be a good strategy to be applied for a first mapping of orbits. For this search, it is analyzed the integral of orbits with different values of the Keplerian elements in order to find the best ones with respect to this criterion. The perturbations considered are the ones caused by the third body, which includes the Sun and the Moon, and the J₂ term of the geopotential. The results presented here show numerical simulations to obtain the integral of those perturbing forces for different orbits. The GPS and the Molniya constellations are used as examples for those calculations.     

多GNSS掩星大气探测卫星星座设计

为减少无线电掩星(RO)大气探测星座的卫星数量并增加探测数据量,将北斗（BD）和GPS、Galileo、GLONASS共同作为探测信源,提出一种多全球导航卫星系统（GNSS）掩星大气探测星座概念和优化设计方法。融合先验大气模型和二维射线追踪算法,建立兼容多GNSS信源的掩星事件前向模拟算法,实现掩星事件快速精确仿真;给出多GNSS掩星大气探测星座参数对探测性能的影响特性,降低了星座模型的复杂度;并利用改进的蚁群算法实现星座参数寻优。设计结果与COSMICII星座相比,卫星数量减少2颗,探测数据量增加了40%,探测均匀性提高了67%。     

A vector method for synthesis of orbits and the structure of satellite constellations for multiswath periodic coverage of the Earth

Single satellites and multisatellite constellations for the periodic coverage of the Earth are considered. The main feature is the use of several cameras with different swath widths. A vector method is proposed which makes it possible to find orbits minimizing the periodicities of coverage of a given area of Earth uniformly for all swaths. Their number is not limited, but the relative dimensions should satisfy the Fibonacci series or some new numerical sequences. The results apply to constellations of any number of satellites. Formulas were derived for calculating their structure, i.e., relative position in the constellation. Examples of orbits and the structure of constellations for the Earth’s multiswath coverage are presented.     

Evaluation of a satellite constellation for active debris removal

This paper analyzes an example of a three-dimensional constellation of debris removal satellites and proposes an effective constellation using a delta-V analysis that discusses the advisability of rendezvousing satellites with space debris. Lambert?s Equation was used to establish a means of analysis to construct a constellation of debris removal satellites, which has a limit of delta-V injection by evaluating the amount of space debris that can be rendezvoused by a certain number of removal satellite. Consequently, we determine a constellation of up to 38 removal satellites for debris removal, where the number of space debris rendezvoused by a single removal satellite is not more than 25, removing up to 584 pieces of debris total. Even if we prepare 38 removal satellites in their respective orbits, it is impossible to remove all of the space debris. Although many removal satellites, over 100 for example, can remove most of the space debris, this method is economically disproportionate. However, we can also see the removal satellites are distributed nearly evenly. Accordingly, we propose a practical two-stage strategy. The first stage is to implement emergent debris removal with the 38 removal satellites. When we find a very high probability of collision between a working satellite and space debris, one of the removal satellites in the constellation previously constructed in orbit initiates a maneuver of emergent debris removal. The second stage is a long-term space debris removal strategy to suppress the increase of space debris derived from collisions among the pieces of space debris. The constellation analyzed in this paper, which consists of the first 38 removal satellites, can remove half of the over 1000 dangerous space debris among others, and then the constellation increases the number of the following removal satellites in steps. At any rate, an adequate orbital configuration and constellation form is very important for both space debris removal and economic efficiency. Though the size of constellation of debris removal satellites would be small originally, such a constellation of satellites should be one of the initial constellations of removal satellites to ensure the safety of the future orbital environment.     

基于遗传算法的全球导航星座重构研究

全球卫星导航系统在部分卫星失效的情况下会引起地面导航性能下降甚至造成导航服务中断,但卫星数量众多的全球导航星座本身具有一定冗余性,在少数卫星失效时可以通过调整剩余工作卫星的轨道来降低失效影响。这种星座重构的维护方式具有快速响应故障和故障针对性强的特点。在星座重构中涉及到选取调整卫星及其轨道参数的问题。分析了用遗传算法实现星座重构方案优化的编码、适应度选取和进化过程,利用C 结合STK和GALIB完成了对24MEO 4GEO构成的全球导航星座在3颗以下MEO卫星失效时的星座重构方案优化,并对多种星座重构的轨道机动方案进行了对比。     

低轨大规模星座对空间碎片环境的影响及其应对措施（英文）

Large constellations have developed rapidly in recent years because of their unique advantages, but they will inevitably have a major negative impact on the space debris environment, leading to its deterioration. The key to mitigate the impact is the success rate and duration of the post-mission disposal(PMD) process. Aiming at solving this problem, this paper further studies the impact of large constellations on other space assets under different PMD strategies through simulation, and proposes corresponding strategies and suggestions for mitigation.According to OneWeb's large constellation launch plan, the dangerous intersection of the large constellation with existing space assets at different stages of the constellations life cycle is calculated by simulation. Based on this, the influence of the large constellation operation on existing space assets at different times and strategies of PMD is analyzed. The conclusion shows that in the PMD stage, large constellations have the greatest impact on existing space assets; the PMD duration and number of satellites performing PMD at the same time are key factors to the degree of negative impact. The faster the PMD is, the less threat it poses to other spacecraft. More results and conclusions are still being analyzed.     

Analysis of the effect of various disturbing factors on high-precision forecasts of spacecraft orbits

The necessity of taking many force components disturbing spacecraft (SC) orbits into account is demonstrated for the example of forecasts of GLONASS ephemerides. The disturbances of SCs in high-earth orbits (HEO) and low-earth orbits (LEO) are systematized, and the degree of their effect on SC motion is estimated. Disturbance models are developed that provide essential increases of the accuracy of one-day forecasts of GLONASS and GPS ephemerides. Modeling results are presented that allow, depending on the required accuracy of SC orbit forecasts, the determination of the necessary list of disturbances included in the model.     

面向飞行器自主导航的铱星/星链星座覆盖性及可见性分析

针对低轨星座机会信号导航中单星座构型和可见星数无法同时满足高精度、高可用性的难题,基于铱星、星链轨道参数,建立了单星座和混合星座模型,探究了各个星座覆盖重数、覆盖率及飞行器对上述星座的可见性。研究结果表明：飞行器可见星数随飞行高度增加而减少,随飞行器最小观测仰角增大而减少,星链和铱星的融合可显著增加纬度60°以上区域可见星数。铱星对全球不同纬度、不同时间具有100%全覆盖;星链目前覆盖区域向两极拓展,对全球覆盖重数最大为56,最小为0,未实现全球不同纬度、全时段100%的覆盖率,但中国区域星链覆盖率均优于美国区域。星链和铱星的混合星座使全球覆盖重数优于10,不同纬度、不同时间覆盖率达到100%,显著优于单星座。