Estimating low resolution gravity fields at short time intervals to reduce temporal aliasing errors

The Gravity Recovery and Climate Experiment (GRACE) satellite mission has been estimating temporal changes in the Earth’s gravitational field since its launch in 2002. While it is not yet fully resolved what the limiting source of error is for GRACE, studies on future missions have shown that temporal aliasing errors due to undersampling signals of interest (such as hydrological variations) and errors in atmospheric, ocean, and tide models will be a limiting source of error for missions taking advantage of improved technologies (flying drag-free with a laser interferometer). This paper explores the option of reducing the effects of temporal aliasing errors by directly estimating low degree and order gravity fields at short time intervals, ultimately resulting in data products with improved spatial resolution. Three potential architectures are considered: a single pair of polar orbiting satellites, two pairs of polar orbiting satellites, and a polar orbiting pair of satellites coupled with a lower inclined pair of satellites. Results show that improvements in spatial resolution are obtained when one estimates a low resolution gravity field every two days for the case of a single pair of satellites, and every day for the case of two polar pairs of satellites. However, the spatial resolution for these cases is still lower than that provided by simply destriping and smoothing the solutions via standard GRACE post-processing techniques. Alternately, estimating daily gravity fields for the case of a polar pair of satellites coupled with a lower inclined pair results in solutions with superior spatial resolution than that offered by simply destriping and smoothing the solutions.     

Assessment of the close approach frequency and collision probability for satellites in different configurations of large constellations

The Earth orbital environment is drastically changing due to an intensification of the space activities. In particular, several projects of large constellations, proposed for the next years for communications purpose like global internet access, Internet of Things, or for Earth observations, will lead to the deployment of several thousands of new satellites at an unprecedented rate. It is a crucial challenge for space traffic management, which will deal with a great number of satellite conjunctions, potentially causing a collision with damaging consequences for the constellation itself and the space environment sustainability.In this paper, we investigate the close approach frequency and the cumulative collision probability for each referenced constellation. For this purpose, we compute the orbital evolution of satellites in different constellations during the lifecycle, from the deployment to the decommissioning, and we apply the CUBE algorithm and the Foster method to assess the collision probability with the background space debris population assuming a constant uncertainty in position. We show the variation of risk defined by the close approach frequency and the cumulative collision probability as a function of the proposed configuration. In particular, satellites of the Iridium and Kuiper constellation, but also satellite of the Telesat constellation on polar orbits are the most exposed at a collision. Moreover, the decommissioning phase contribute for a major part to the final cumulative collision probability.     

关于星座设计中碰撞检测问题的探讨

对于卫星数量较多的星座, 在星座设计过程中就应当考虑避免星座运行过程中卫星之间的碰撞现象。文章首先针对发生在赤道上空的严格碰撞现象进行了研究, 提出了避免赤道碰撞的星座参数配置方法; 进一步从广义碰撞检测要求出发, 对星座中卫星间的相对距离变化规律进行了研究, 并给出了设计阶段解决碰撞问题的方案。文中的内容对星座设计工作有一定的帮助。     

Impact of the time span selected to calibrate the ballistic parameter on spacecraft re-entry predictions

The trajectory modeling of satellites that are re-entering the Earth’s atmosphere, as a result of natural orbital decay, has always been a challenging task. Residual lifetime estimations and re-entry predictions are affected by substantial uncertainties, associated with atmospheric density models, with the forecasts of the relevant solar and geomagnetic activity indices and with tracking data, which for uncontrolled re-entries are usually sparse and not particularly accurate. Furthermore, modeling the aerodynamic forces that act on low altitude satellites is a formidable task, especially for objects of a complex shape and unknown attitude evolution.     

Collision probability and spacecraft disposition in the geostationary orbit

Since 1963 approximately 300 satellites have been launched into the geostationary orbit, followed possibly by another additional 200 satellites up to the year 2000. Ground surveillance with radar and optical sensors able to detect objects of 1 m minimum size in the geostationary ring indicates a total population of several hundred which includes active and defunct satellites and spent upper stages. In addition, a population of untrackable objects is conjectured, whose size can only be estimated, possibly several thousand of smaller objects.

The purpose of this paper is to review the long-term evolution of orbits in the geostationary ring and at higher altitude, the collision probabilities and disposition options.

The major perturbations are considered including attitude-orbit cross-coupling effects which could cause secular orbit perturbations.

Collision probabilities for current and projected populations are reviewed considering different approaches, such as a deterministic treatment of the uncontrolled population and a stochastic modeling for the controlled satellites. Also, colocation, that is sharing of the same longitude slot by several operational satellites, is a potential source for collision, if no preventive measures are taken.

As regards spacecraft disposition options, the conclusion is that reorbiting is currently the only practical measure to safeguard the geostationary orbit. In this recommended procedure the defunct satellites are inserted into a so-called graveyard orbit, located suffieciently high above the geostationary orbit.     

基于代理模型的卫星编队重构最短距离建模

针对编队卫星成员数量较多时,编队重构规划考虑碰撞规避会带来的巨大的计算开销。为降低计算开销和提升优化效率,基于CW方程和双脉冲轨道机动策略,建立了能够快速预测编队卫星重构过程最短距离的多种代理模型,并基于三种大小不同的训练集,从模型精度和效率两方面进行了对比。结果表明,克里金（KRG）模型在各种代理模型中精度最高,而且随着训练量的增加,克里金和人工神经网络（ANN）模型的性能得到了明显改善,模型精度有一定的保证。研究还发现,尽管KRG模型预测时间高于其他代理模型,但和真实模型相比,其耗时仍然很短,因此可用于提高考虑避碰约束时卫星编队重构轨迹优化的效率。     

利用人工势函数法的卫星电磁编队控制

卫星电磁编队是指利用卫星之间相互作用的电磁力进行卫星相对运动控制,对控制律的要求主要是计算量小和能避免碰撞.以目标星对参考星的相对运动矢量作为控制对象,分析了使用电磁力控制卫星编队的可行性,结果是如果编队卫星磁矩能够任意控制,那么卫星相对运动也能完全控制.设计了人工势函数,以相对位置和相对速度矢量作为变量,人工势函数在达到控制目标时为最小值,在碰撞的位置具有局部最大值.设计的控制律能够实时调整控制参数,能够保证电磁线圈控制电流不至于饱和,以及人工势函数导数在控制过程中小于零.仿真表明,所设计的控制律能生成编队构型并避免碰撞,而且具有一定的抗干扰性.     

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。     

利用TLE数据分析LEO卫星轨道异常的新方法——————综合判据法

及时准确地发现在轨卫星的轨道异常意义重大. 通过有效的异常算法, 能够找出发生轨道异常的碎片或航天器, 为空间碎片碰撞预警系统分析和验证碰撞事件提供数据支持. 通过对利用TLE (Two Line Elements)数据分析LEO在轨卫星轨道异常的方法研究, 提出了一个利用单个卫星相邻根数时间差控制加综合判据的判别方法. 分析表明, 相对于取单一因素阈值的判别方法, 综合判据法能够最大限度地减少漏判, 并且保持相对较高的判断准确率.      

数据收集系统的电文碰撞和计算机模拟

数据收集系统是利用人造卫星中继地球环境资料的一种无线电遥测系统。近地卫星(如美国的陆地卫星、泰罗斯-N气象卫星)所属的数据收集系统一般都采取随机取数的方法。在这类系统设计中,电文碰撞规律是涉及到系统容量的重要问题。本文在古典概率的基础上,经适当修改,得到符合计算机模拟结果的理论公式。并提供针对不同系统方案的电文碰撞概率的计算方法。      

Differential code bias estimation based on uncombined PPP with LEO onboard GPS observations

Differential Code Bias (DCB) is an essential correction that must be provided to the Global Navigation Satellite System (GNSS) users for precise position determination. With the continuous deployment of Low Earth Orbit (LEO) satellites, DCB estimation using observations from GNSS receivers onboard the LEO satellites is drawing increasing interests in order to meet the growing demands on high-quality DCB products from LEO-based applications, such as LEO-based GNSS signal augmentation and space weather research. Previous studies on LEO-based DCB estimation are usually using the geometry-free combination of GNSS observations, and it may suffer from significant leveling errors due to non-zero mean of multipath errors and short-term variations of receiver code and phase biases. In this study, we utilize the uncombined Precise Point Positioning (PPP) model for LEO DCB estimation. The models for uncombined PPP-based LEO DCB estimation are presented and GPS observations acquired from receivers onboard three identical Swarm satellites from February 1 to 28, 2019 are used for the validation. The results show that the average Root Mean Square errors (RMS) of the GPS satellite DCBs estimated with onboard data from each of the three Swarm satellites using the uncombined PPP model are less than 0.18 ns when compared to the GPS satellite DCBs obtained from IGS final daily Global Ionospheric Map (GIM) products. Meanwhile, the corresponding average RMS of GPS satellite DCBs estimated with the conventional geometry-free model are 0.290, 0.210, 0.281 ns, respectively, which are significantly larger than those obtained with the uncombined PPP model. It is also noted that the estimated GPS satellite DCBs by Swarm A and C satellites are highly correlated, likely attributed to their similar orbit type and space environment. On the other hand, the Swarm receiver DCBs estimated with uncombined PPP model, with Standard Deviation (STD) of 0.065, 0.037 and 0.071 ns, are more stable than those obtained from the official Swarm Level 2 products with corresponding STD values of 0.115, 0.101, and 0.109 ns, respectively. The above indicates that high-quality DCB products can be estimated based on uncombined PPP with LEO onboard observations.     

LEO enhanced Global Navigation Satellite System (LeGNSS) for real-time precise positioning services

Global Navigation Satellite System (GNSS) has been widely used in many geosciences areas with its Positioning, Navigation and Timing (PNT) service. However, GNSS still has its own bottleneck, such as the long initialization period of Precise Point Positioning (PPP) without dense reference network. Recently, the concept of PNTRC (Positioning, Navigation, Timing, Remote sensing and Communication) has been put forward, where Low Earth Orbit (LEO) satellite constellations are recruited to fulfill diverse missions. In navigation aspect, a number of selected LEO satellites can be equipped with a transmitter to transmit similar navigation signals to ground users, so that they can serve as GNSS satellites but with much faster geometric change to enhance GNSS capability, which is named as LEO constellation enhanced GNSS (LeGNSS). As a result, the initialization time of PPP is expected to be shortened to the level of a few minutes or even seconds depending on the number of the LEO satellites involved. In this article, we simulate all the relevant data from June 8th to 14th, 2014 and investigate the feasibility of LeGNSS with the concentration on the key issues in the whole data processing for providing real-time PPP service based on a system configuration with fourteen satellites of BeiDou Navigation Satellite System (BDS), twenty-four satellites of the Global Positioning System (GPS), and sixty-six satellites of the Iridium satellite constellations. At the server-end, Precise Orbit Determination (POD) and Precise Clock Estimation (PCE) with various operational modes are investigated using simulated observations. It is found out that GNSS POD with partial LEO satellites is the most practical mode of LeGNSS operation. At the user-end, the Geometry Dilution Of Precision (GDOP) and Signal-In-Space Ranging Error (SISRE) are calculated and assessed for different positioning schemes in order to demonstrate the performance of LeGNSS. Centimeter level SISRE can be achieved for LeGNSS.     

卫星编队飞行动力学仿真及其应用

由若干颗小卫星编队飞行组成一个虚拟卫星,其功能相当或超过一颗大卫星,这将开拓小卫星一个完全崭新的应用领域。文章首先研究轨道动力学,系统地研究编队飞行三种动力学模型,其次进行定位卫星和区域导航系统两个实例数学仿真,分析研究各种数学模型的精度和它们的应用场合。     

Improved orbit predictions using two-line elements

The density of orbital space debris constitutes an increasing environmental challenge. There are two ways to alleviate the problem: debris mitigation and debris removal. This paper addresses collision avoidance, a key aspect of debris mitigation. We describe a method that contributes to achieving a requisite increase in orbit prediction accuracy for objects in the publicly available two-line element (TLE) catalog. Batch least-squares differential correction is applied to the TLEs. Using a high-precision numerical propagator, we fit an orbit to state vectors derived from successive TLEs. We then propagate the fitted orbit further forward in time. These predictions are validated against precision ephemeris data derived from the international laser ranging service (ILRS) for several satellites, including objects in the congested sun-synchronous orbital region. The method leads to a predicted range error that increases at a typical rate of 100 m per day, approximately a 10-fold improvement over individual TLE’s propagated with their associated analytic propagator (SGP4). Corresponding improvements for debris trajectories could potentially provide conjunction analysis sufficiently accurate for an operationally viable collision avoidance system based on TLEs only.     

Use of two-line element data for thermosphere neutral density model calibration

Traditional empirical thermospheric density models are widely used in orbit determination and prediction of low-Earth satellites. Unfortunately, these models often exhibit large density errors of up to around 30% RMS. Density errors translate into orbit errors, adversely affecting applications such as re-entry operations, manoeuvre planning, collision avoidance and precise orbit determination for geodetic missions. The extensive database of two-line element (TLE) orbit data contains a wealth of information on satellite drag, at a sufficiently high spatial and temporal resolution to allow a calibration of existing neutral density models with a latency of one to two days. In our calibration software, new TLE data for selected objects is converted to satellite drag data on a daily basis. The resulting drag data is then used in a daily adjustment of density model calibration parameters, which modify the output of an existing empirical density model with the aim of increasing its accuracy. Two different calibration schemes have been tested using TLE data for about 50 objects during the year 2000. The schemes involve either height-dependent scale factors to the density or corrections to CIRA-72 model temperatures, which affect the density output based on a physical model. Both schemes have been applied with different spherical harmonic expansions of the parameters in latitude and local solar time. Five TLE objects, varying in perigee altitude between 280 and 530 km, were deliberately not used during calibration, in order to provide independent validation. Even with a single daily parameter, the RMS density model error along their tracks can already be reduced from the 30% to the 15% level. Adding additional parameters results in RMS errors lower than 12%.     

Prospects of de-tumbling large space debris using a two-satellite electromagnetic formation

Capturing large space debris with complex rotational motion is extremely challenging. A de-tumbling phase before capturing may be necessary to reduce the risk of collision with debris. This paper proposes a new noncontact de-tumbling method using a two-satellite electromagnetic formation, in which two small electromagnetic satellites, each having a high-temperature superconducting coil, generate control torques to reduce the rotation rate of debris prior to making any physical contact. The electromagnetic interaction of the target-satellite system is analyzed. A relative translational dynamics of the target–satellite system and the attitude dynamics of the target are established. Simulation results show that the proposed method effectively eliminates the rotational motion of the target. It can be safely concluded that the noncontact method for de-tumbling space debris using a two-satellite electromagnetic formation is feasible and potentially applicable to on-orbit capture.     

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.     

Improving DORIS geocenter time series using an empirical rescaling of solar radiation pressure models

Even if Satellite Laser Ranging (SLR) remains the fundamental technique for geocenter monitoring, DORIS can also determine this geophysical parameter. Gobinddass et al. (2009) found that part of the systematic errors at 118 days and 1 year can be significantly reduced by rescaling the current solar radiation pressure models using satellite-dependent empirical models. Here we extend this study to all DORIS satellites and propose a complete set of empirical solar radiation parameter coefficients. A specific problem related to SPOT-5 solar panel realignment is also detected and explained. New DORIS geocenter solutions now show a much better agreement in amplitude with independent SLR solutions and with recent geophysical models. Finally, the impact of this refined DORIS data strategy is discussed in terms of Z-geocenter monitoring as well as for other geodetic products (altitude of high latitude station such as Thule in Greenland) and Precise Orbit Determination. After reprocessing the full 1993.0-2008.0 DORIS data set, we confirm that the proposed strategy allows a significant reduction of systematic errors at periods of 118 days and 1 year (up to 20 mm), especially for the most recent data after 2002.5, when more DORIS satellites are available for geodetic purposes.     

Characterization of the cataloged Fengyun-1C fragments and their long-term effect on the LEO environment

The intentional breakup of Fengyun-1C on 11 January 2007 created the most severe orbital debris cloud in history. The altitude where the event occurred was probably the worst location for a major breakup in the low Earth orbit (LEO) region, since it was already highly populated with operational satellites and debris generated from previous breakups. The addition of so many fragments not only poses a realistic threat to operational satellites in the region, but also increases the instability (i.e., collision cascade effect) of the debris population there.     

空间碎片预警中的碰撞概率方法研究

由于空间碎片对飞行在地球轨道上的航天器危害日益严重,所以必须采取一些有效的防护措施,对于那些直径大于10 cm的碎片,通常是采用主动规避的方法来进行防护.为了避免传统的Box判据造成的过多错误预警,碰撞概率模型开始被应用于空间碎片预警,本文以空间站为例,将碰撞概率方法与传统Box区域判定法进行比较,介绍碰撞概率计算模型的建立方法,基于位置误差矩阵的碰撞概率Pc的算法,并针对实际交会事例进行了计算和分析.