Application of a Multiple Hypothesis Filter to near GEO high area-to-mass ratio space objects state estimation

Optical surveys have identified a class of high area-to-mass ratio (HAMR) objects in the vicinity of the Geostationary Earth Orbit (GEO) regime. The nature of these objects is not well known, though their proximity to the GEO belt implies origins from space objects (SOs) near GEO. These HAMR objects pose a collision hazard as they transit through the vicinity of active GEO satellites. Due to their high area-to-mass ratios (AMRs), ranging from 0.1 to 20 m²/kg and higher, the effective solar radiation pressure perturbs their orbits significantly. Improvements in detection sensitivity will result in large numbers of uncorrelated tracks from surveys. A Multiple Hypothesis Filter (MHF) approach to the initial state estimation and track association provides a potentially automated and efficient approach to the processing of multiple un-correlated tracks.The availability of long-term optical angles data collected for a set of near GEO HAMR objects provides the means for testing candidate estimation processes such as the MHF. A baseline orbit determination (OD) process uses an Extended Kalman Filter/Smoother to manually estimate the 6 orbital elements and the effective area-to-mass ratio (AMR) which drives the solar radiation pressure perturbations on the orbital trajectories. In addition to allowing the characterization of the long-term behavior of the AMR, this process establishes a pseudo-truth trajectory to which the MHF analysis can be compared. An Unscented Kalman Filter (UKF) is applied in the MHF estimation process to estimate the 6 orbital elements and AMR, with no a priori state assumptions, and the results are compared to the pseudo-truth results for validation.The work to be presented summarizes the UKF/MHF process and assesses state estimation performance based on selected data for selected near GEO HAMR objects having a range of AMR value and variations. The prediction accuracy is also assessed by comparing predictions derived from filter updates to segments of the pseudo-truth trajectory determined from data not included in the updates.     

Application of a Multiple Hypothesis Filter to near GEO high area-to-mass ratio space objects state estimation

Optical surveys have identified a class of high area-to-mass ratio (HAMR) objects in the vicinity of the Geostationary Earth Orbit (GEO) regime. The nature of these objects is not well known, though their proximity to the GEO belt implies origins from space objects (SOs) near GEO. These HAMR objects pose a collision hazard as they transit through the vicinity of active GEO satellites. Due to their high area-to-mass ratios (AMRs), ranging from 0.1 to 20 m²/kg and higher, the effective solar radiation pressure perturbs their orbits significantly. Improvements in detection sensitivity will result in large numbers of uncorrelated tracks from surveys. A Multiple Hypothesis Filter (MHF) approach to the initial state estimation and track association provides a potentially automated and efficient approach to the processing of multiple un-correlated tracks.The availability of long-term optical angles data collected for a set of near GEO HAMR objects provides the means for testing candidate estimation processes such as the MHF. A baseline orbit determination (OD) process uses an Extended Kalman Filter/Smoother to manually estimate the 6 orbital elements and the effective area-to-mass ratio (AMR) which drives the solar radiation pressure perturbations on the orbital trajectories. In addition to allowing the characterization of the long-term behavior of the AMR, this process establishes a pseudo-truth trajectory to which the MHF analysis can be compared. An Unscented Kalman Filter (UKF) is applied in the MHF estimation process to estimate the 6 orbital elements and AMR, with no a priori state assumptions, and the results are compared to the pseudo-truth results for validation.The work to be presented summarizes the UKF/MHF process and assesses state estimation performance based on selected data for selected near GEO HAMR objects having a range of AMR value and variations. The prediction accuracy is also assessed by comparing predictions derived from filter updates to segments of the pseudo-truth trajectory determined from data not included in the updates.     

Searching for lost fragments in GEO

This paper attempts to search the lost fragments from the near-synchronous US TitanIIIC transtage explosion of February 21, 1992, known as the second major fragmentation of a TitanIIIC transtage. This breakup was accidentally observed by the Maui GEODSS sensor, and then a total of 23 objects were reported from the breakup, no orbital data on any fragments has been generated by the SSN. In order to evaluate the debris cloud orbital evolution, we demonstrate the actual US TitanIIIC transtage explosion by using breakup model and orbit propagator. The perturbing accelerations, considered in this analysis are the non-spherical part of the Earth's gravitational attraction, the gravitational attraction due to the Sun and Moon, and the solar radiation pressure effects. Finally, we will present a search strategy based on distribution of the right ascension of the ascending node about the catalogued objects and the debris particles from the US TitanIIIC transtage explosion.     

地球静止轨道空间碎片的处置

介绍了国际机构间碎片协调委员会提出的关于地球静止轨道（GEO）空间碎片问题的研究结果和碎片处置的建议，主要内容包括：GEO与GEO环的概念、EGO上物体现状，EGO空间碎片处置的基本原则和8条具体处置措施建议。该建议已于2000年2月提交联合国和平利用外层空间委员会科技小组委员会第37届会议。     

Searching for lost fragments in GEO

This paper attempts to search the lost fragments from the near-synchronous US TitanIIIC transtage explosion of February 21, 1992, known as the second major fragmentation of a TitanIIIC transtage. This breakup was accidentally observed by the Maui GEODSS sensor, and then a total of 23 objects were reported from the breakup, no orbital data on any fragments has been generated by the SSN. In order to evaluate the debris cloud orbital evolution, we demonstrate the actual US TitanIIIC transtage explosion by using breakup model and orbit propagator. The perturbing accelerations, considered in this analysis are the non-spherical part of the Earth's gravitational attraction, the gravitational attraction due to the Sun and Moon, and the solar radiation pressure effects. Finally, we will present a search strategy based on distribution of the right ascension of the ascending node about the catalogued objects and the debris particles from the US TitanIIIC transtage explosion.     

Use of Optical Characteristics to Identify Orbiting Material

Knowledge of the observable properties of orbital debris is necessary to validate debris models for both the low Earth orbit (LEO) and the geosynchronous Earth orbit (GEO). Current methods determine the size and mass of orbital debris based on knowledge or assumption of the material type of the piece. Improvement in the knowledge of material is the goal of the research described herein. The process of using spectral absorption features to determine the material type is explored. A review of the optical measurements of orbital debris as well as current research in the area is discussed. Reflectances of common spacecraft materials are compared. The need for, and advances made possible by obtaining real data are explored. The prospects of the venture are investigated.     

Further analysis of infrared spectrophotometric observations of high area to mass ratio (HAMR) objects in GEO

Optical surveys have identified a class of high area-to-mass ratio (HAMR) objects in the vicinity of the Geostationary Earth Orbit (GEO) ring^. The exact origin and nature of these objects are not well known, although their proximity to the GEO belt poses a hazard to active GEO satellites. The prevalent conjecture is that many of these objects may be thermal materials shed from derelict spacecraft in ‘graveyard’ orbits above the GEO ring. Due to their high area-to-mass ratios and unknown attitude dynamics and material characteristics, solar radiation pressure (SRP) perturbs their orbits in ways that makes it difficult to predict their orbital trajectories over periods of time exceeding a week or less. To better understand and track these objects and infer their origins, we have made observations that allow us to determine physical characteristics that will improve the non-conservative force modeling used for orbit determination (OD) and prediction. Information on their temperatures, areas, emissivities, and albedos may be obtained from thermal infrared and visible measurements. Simultaneous observations in the thermal infrared and visible wavelengths may allow disentangling of projected area, albedo, and object emissivity.Further analysis and modeling of observational data on certain of the HAMR objects collected at the AMOS observatory 3.6 m AEOS telescope are presented. The thermal-IR spectra of these geosynchronous orbit objects acquired by the Broadband Array Spectrograph System (BASS) span wavelengths 3 to 13 μm and constitute a unique data set, providing a means of measuring object fluxes in the infrared and visible wavelengths. These, in turn, allow temperatures and emissivity-area products to be calculated, and in some cases provide information on rotation rates. We compare our observational results with the outputs of simple models, in terms of visible and infrared flux and orbital characteristics. The resulting temperatures and rotation rates are used in SRP acceleration models to demonstrate improvements in OD and prediction performance relative to models which assume default ambient temperature and static attitude dynamics. Additionally, we have the capability and plans to measure material properties with the same instrument in the lab as used at the telescope to facilitate direct comparisons.     

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.     

Strategy for detection of eccentric objects near the geosynchronous region

Detection of eccentric objects near the geosynchronous region is a very important issue. However, the extremely narrow fields-of-view of optical telescopes hinders us from identifying eccentric objects. An observation strategy to systematically detect these objects and determine their orbits precisely with one telescope is outlined in this presentation. Basically, one specific geosynchronous location (not one specific celestial position) is observed on two nights. Objects which pass through that location in the first night must pass through that location again in the second night. By identifying the same objects from two nights of data, rough orbits for those objects are determined. A third night is needed for precise orbital determination. An application of this strategy to the observation for Titan fragments is also discussed.     

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).     

在轨物体接近算法研究

根据NORAD公布的在轨物体(空间碎片或航天器) 的轨道数据,给出了计算在轨物体两两间发生接近事件的方法。该方法结合了计算在轨物体 接近的运动学筛选法和相对距离函数法,以提高计算效率。以该方法为基础,提出了特定航 天器与全体在轨物体间的接近事件算法。算法采用了改进后的几何筛选法。该方法并不求解 两轨道的最近点,而是求解包含最近点的时间窗口,从而解决了原方法漏报接近事件的问题 。该方法在理论上可以检测到所有的接近事件,数值仿真验证支持了该结论。在计算效率 上新方法相对于原算法也有约10倍的提高。     

Continuum Model for Space Debris Evolution with Account of Collisions and Orbital Breakups

The paper discusses the mathematical modeling of long-term orbital debris evolution taking into account mutual collisions of space debris particles of different sizes. Investigations and long-term forecasts of orbital debris environment evolution in low Earth orbits are essential for future space mission hazard evaluation and for adopting rational space policies and mitigation measures. The paper introduces a new approach to space debris evolution mathematical modeling based on continuum mechanics incorporating partial differential equations. This is an alternative to the traditional approaches of celestial mechanics incorporating ordinary differential equations to model fragments evolution. The continuum approach to orbital debris evolution modeling has essential advantages for describing the evolution of a large number of particles, because it replaces the traditional tracking of space objects by modeling the evolution of their density of distribution.     

美国DMSP-F13卫星解体事件对空间碎片环境影响分析

2015 年2 月3 日,美国DMSP-F13 卫星发生爆炸解体,产生了百余块编目空间碎片。该卫星解体碎片主要分布在轨道高度600～1200 km 范围内,其中近50%的编目碎片在轨寿命将超过20 年,会对未来空间碎片环境构成长期影响。结合我国空间碎片环境工程模型SDEEM 对DMSP-F13 解体事件的分析结果显示,此次解体事件造成邻近轨道区域内空间碎片空间密度增加,对该区域航天器安全运行产生影响。     

Ground assisted rendezvous with geosynchronous satellites for the disposal of space debris by means of Earth-oriented tethers

Previous studies have shown that extended length Earth-oriented tethers in the geosynchronous (GEO) region can be used to re-orbit satellites to disposal orbits. One such approach involves the extension of a GEO based tether, collection of a debris object, and retraction of the tether, which transfers the retracted configuration to a higher energy orbit for debris disposal. The re-extension of the tether after debris disposal returns the configuration to the near-GEO altitude. The practical feasibility of such a system depends on the ability to collect GEO debris objects, attach them to a deployed tether system, and retract the tethers for transfer to the disposal orbits.This study addresses the collection and delivery of debris objects to the deployed tether system in GEO. The investigation considers the number, type and the characteristics of the debris objects as well as the collection tug that can be ground controlled to detect, rendezvous and dock with the debris objects for their delivery to the tethers system.A total of more than 400 objects are in drift orbits crossing all longitudes either below or above the geostationary radius. More than 130 objects are also known to librate around the stable points in GEO with periods of libration up to five or more years. A characterization of the position and velocity of the debris objects relative to the collection tug is investigated. Typical rendezvous performance requirements for uncooperative GEO satellites are examined, and the similarities with other approaches such as the ESA's CX-OLEV commercial mission proposal to extend the life of geostationary telecommunication satellites are noted.     

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.     

Collision Risk Mitigation in Geostationary Orbit

The short- and long-term effects of spacecraft explosions, as a function of the end-of-life re-orbit altitude above the geostationary orbit (GEO), were analyzed in terms of their additional contribution to the debris flux in the GEO ring. The simulated debris clouds were propagated for 72yrs, taking into account all the relevant orbital perturbations.The results obtained show that 6–7 additional explosions in GEO would be sufficient, in the long term, to double the current collision risk with sizable objects in GEO. Unfortunately, even if spacecraft were to re-orbit between 300 and 500km above GEO, this would not significantly improve the situation. In fact, an altitude increase of at least 2000km would have to be adopted to reduce by one order of magnitude the long-term risk of collision among geostationary satellites and explosion fragments. The optimal debris mitigation strategy should be a compromise between the reliability and effectiveness of spacecraft end-of-life passivation, the re-orbit altitude and the acceptable debris background in the GEO ring. However, for as long as the re-orbit altitudes currently used are less than 500km above GEO, new spacecraft explosions must be avoided in order to preserve the geostationary environment over the long term.     

Design and development of correlation techniques to maintain a space surveillance system catalogue

A growing interest exists in a future, autonomous European Space Surveillance System (ESSS). Currently, most of the knowledge about Earth-orbiting space objects is based on information provided by the USASPACECOM. This paper presents the required initial orbit determination (IOD) and correlation techniques to process optical measurements. Former studies were focused on the handling of radar measurements, which are summarised with the aim of describing a global procedure for processing hybrid measurement types (combination of radar and optic data for catalogue maintenance). The introduction of manoeuvres are presented due to their importance in the space object catalogue maintenance.The detection of uncatalogued objects and the successful correlation of already catalogued objects involve two different tasks for telescopes: survey and tasking. Assumptions for both strategies are developed on the basis of the previous work developed at the University of Berne (see [T. Flohrer, T. Schildknecht, R. Musci, E. Stöveken, Performance estimation for GEO space surveillance, Advances in Space Research 35 (2005). [1]; T. Flohrer, T. Schildknecht, R. Musci, Proposed strategies for optical observations in a future European Space Surveillance Network, presented in the 36th COSPAR Scientific Assembly (2006). [2]; R. Musci, T. Schildknecht, M. Ploner, Orbit improvement for GEO objects using follow-up observations, Advances in Space Research 34 (2004). [3]; R. Musci, T. Schildknecht, M. Ploner, G. Beutler, Orbit improvement for GTO objects using follow-up observations, Advances in Space Research 35 (2005). [4]; R. Musci, T. Schildknecht, T. Flohrer, G. Beutler, Concept for a catalogue of space debris in GEO, Proceedings of the Fourth European Conference on Space Debris, (ESA SP-587, 2005). [5]]). When a new object appears in the field of view, initial orbit determination must be performed. When only one telescope per site is available, the initial measurements are separated by only a few seconds. Therefore, the initial orbit determination is quite inaccurate due to bad mathematical conditioning of the problem. In order to improve the accuracy of the initial orbit determination, several follow-up observations of the object are required. This implies that the telescope needs to track the detected objects over a long period, and therefore the time available for surveying is reduced. By processing the additional follow-up measurements, separated now by a few hours, the initial orbit determination gives more accurate results and the object can be recovered after an orbital revolution. When several telescopes per site are available, the optical strategies may be modified. The survey tasks can be distributed between the available telescopes. In this way the number of images corresponding to each object increases and to track the detected object over long periods is not always needed. Numerical results will be shown in order to evaluate the accuracy and features of the different telescope strategies. A key point for performing efficiently the cataloguing process is the calculation of the estimated state vector covariance matrix. The covariance matrix analysis allows an adaptive tasking-survey telescope scheduling. Moreover, the implementation of a proper batch orbit determination process by means of a square root information filter (SRIF) requires a realistic initial covariance matrix.Hybrid measurements are available from objects that can be observed through both radar and optical sensors (e.g. GTO objects). The batch orbit determination and correlation process of hybrid measurements is also based on SRIF using an extended measurement model. Both the initial orbit determination methods using radar and optical measurements have to be sufficiently accurate to initialise SRIF correctly. In order to avoid filter divergence, the estimated covariance must be correctly updated after processing both kinds of measurements. The implemented algorithms are explained and their performance is shown through realistic simulations.Techniques to detect and characterise object manoeuvres during the cataloguing process have been developed and implemented. Four main groups of manoeuvre objects have been established by means of their observed permitted orbital ranges (GEO, LEO, MEO–GPS, Molniya). The study is based on the historical TLEs files. When an object with an uncatalogued orbit appears, a comparison between the new orbit and the orbits contained in the permitted ranges of one of the manoeuvre groups is performed. If the required Δa and/or Δi to convert the lost orbit into the detected orbit seems to be feasible, a manoeuvre will be identified and the orbit will be updated in the catalogue. Otherwise, it will be decided that a new object was found. For this purpose, a procedure to estimate the manoeuvres and reset orbits have been developed.     

Detection technique for artificially illuminated objects in the outer solar system and beyond

Existing and planned optical telescopes and surveys can detect artificially illuminated objects, comparable in total brightness to a major terrestrial city, at the outskirts of the Solar System. Orbital parameters of Kuiper belt objects (KBOs) are routinely measured to exquisite precisions of<10(-3). Here, we propose to measure the variation of the observed flux F from such objects as a function of their changing orbital distances D. Sunlight-illuminated objects will show a logarithmic slope α ≡ (d log F/d log D)=-4, whereas artificially illuminated objects should exhibit α=-2. The proposed Large Synoptic Survey Telescope (LSST) and other planned surveys will provide superb data and allow measurement of α for thousands of KBOs. If objects with α=-2 are found, follow-up observations could measure their spectra to determine whether they are illuminated by artificial lighting. The search can be extended beyond the Solar System with future generations of telescopes on the ground and in space that would have the capacity to detect phase modulation due to very strong artificial illumination on the nightside of planets as they orbit their parent stars.     

低轨航天器磁推进方法

基于地球空间磁场的磁作用效应,提出了一类低轨航天器无工质消耗的磁推进方法,并对航天器的高度保持进行了研究。该方法具有作用机理明晰、物理结构简单、控制策略灵活等特征。以磁场对磁体作用的磁矩理论为基础,建立了带磁航天器飞行的磁推力模型,提出了基于磁力线追踪策略的轨道高度保持方法。利用熟知的IGRF11地磁模型,通过数值仿真计算,验证了磁推进方法对于600～1000km圆轨道航天器进行高度保持的有效性。     

基于计算机的低地球轨道航天器设计与观测的轨道碎片环境模型

文章介绍了一个半经验的基于计算机的轨道碎片模型。该模型将轨道环境简化为6个不同的倾角带,每个倾角带都有各自的半长轴和近地点分布及根据不同的碎片来源有其各自的尺寸分布。用碰撞概率方程将轨道碎片分布与航天器上的碎片通量或通过地面探测器视角的通量联系起来。经比较,碎片的半长轴、近地点和倾角分布与美国空间司令部大于10cm的碎片目录是一致的。对于较小的碎片,这些分布与地面望远镜、“干草堆”雷达的测量结果一致,同时也与LDEF卫星和航天飞机的测量结果一致。