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.     

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.     

对接靠拢段的一种相对导航算法研究

自主相对导航技术是空间交会对接靠拢段的关键技术之一。Unscented卡尔曼滤波(UKF)是基于Unscented Transform(UT)变换的一种新型滤波器,它避免了扩展卡尔曼滤波(EKF)的线性化误差,不必计算Jacobian矩阵,而且其状态估计精度要比EKF的高。本文研究了基于UKF滤波器的自主相对导航算法。该算法根据追踪航天器上交会雷达的测量值,采用UKF滤波器对追踪航天器和目标航天器之间的相对位置和速度进行了估计,仿真结果表明该算法可以满足位置和速度估计精度的要求。     

基于UKF的航天器最小参数姿态矩阵估计方法

钊对航天器的惯性-星光姿态确定系统，选取基于矢量观测的最小参数姿态矩阵估计方法为定姿算法。但是由于系统模型是非线性的，针对系统模型的非线性，将UKF（Unscented Kalman Filter）与最小参数姿态矩阵估计方法结合，设计了一种针对MEMS陀螺和CMOS APS星敏感器的UKF姿念估计器。仿真结果表明：在敏感器精度较差的情况下，该UKF、姿态估计器能够满足大多数航天器对姿态确定精度的要求。此外，UKF和EKF（Extended Kalman Filter）的仿真对比结果表明：UKF滤波器的收敛速度高于EKF滤波器，状态估计的精度也优于EKF滤波器，且数值稳定性好。     

A preliminary study of pulse-laser powered orbital launcher

An air-breathing pulse-laser powered orbital launcher has been proposed as an alternative to conventional chemical launch systems. The aim of the present study is to assess its feasibility through the estimation of its achievable payload mass per unit beam power and launch cost. A transfer trajectory from the ground to a geosynchronous Earth orbit (GEO) is proposed, and the launch trajectory to its geosynchronous transfer orbit (GTO) is computed using the realistic performance modeled in the pulsejet, ramjet, and rocket flight modes of the launcher. Results show that the launcher can transfer 0.084 kg of payload per 1 MW beam power to a geosynchronous earth orbit. The cost becomes a quarter of existing systems if one can divide a single launch into 24,000 multiple launches.     

基于"天基红外系统"对弹道导弹主动段估计滤波算法研究

美国的"天基红外系统"(SBIRS)包括高轨和低轨两类预警星座,前者主要用于弹道导弹主动段探测,后者主要用于被动段的跟踪测量.文章利用其高轨静止星座,对只有角测量条件下的主动段弹道估计滤波算法进行了分析比较.首先给出主动段状态方程和测量方程,然后分别结合扩展卡尔曼滤波、无迹卡尔曼滤波和粒子滤波这三类典型非线性滤波估计算...     

General solution for the optimal trajectory of an AFE-type spacecraft

The aeroassisted flight experiment (AFE) refers to an experimental spacecraft to be launched and then recovered by the Space Shuttle. It simulates a transfer from a geosynchronous Earth orbit (GEO) to a low Earth orbit (LEO). In this paper, with reference to an AFE-type spacecraft, an actual GEO-to-LEO transfer is considered under the following assumptions: the GEO and LEO orbital planes are identical; both the initial and final orbits are circular; the initial phase angle is given, while the final phase angle is free. The aeroassisted orbital transfer trajectory involves three branches: a preatmospheric branch, GEO-to-entry; an atmospheric branch, entry-to-exit; a post-atmospheric branch, exit-to-LEO. The optimal trajectory is determined by minimizing the total characteristic velocity. The optimization is performed with respect to the velocity impulses at GEO, LEO, and the time history of the angle of bank during the atmospheric pass. It is assumed that the entry path inclination is free and that the angle of attack is constant, = 17.0 deg. The sequential gradient-restoration algorithm is used to compute the optimal trajectory and it is shown that the best atmospheric pass is to be performed with constant angle of bank. The resulting optimal trajectory constitutes an ideal nominal trajectory for the generation of guidance trajectories for two reasons: the fact that the low value of the characteristic velocity is accompanied by relatively low values of the peak heating rate and the peak dynamic pressure; and the simplicity of the control distribution, requiring constant angle of bank.     

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).     

A Geosynchronous Orbit Search Strategy

Since more than 10 years there is evidence that small-size space debris is accumulating in the geosynchronous orbit (GEO), probably as the result of breakups. Two break-ups have been reported in GEO. The 1978 break-up of an EKRAN 2 satellite, SSN 10365, was identified in 1992, and in 1992 a Titan 3C Transtage, SSN 3432, break-up produced at least twenty observable pieces. Subsequently several nations performed optical surveys of the GEO region in the form of independent observation campaigns. Such surveys suffer from the fact that the field of view of optical telescopes is small compared with the total area covered by the GEO ring. As a consequence only a small volume of the orbital element-magnitude-space is covered by each individual survey. Results from these surveys are thus affected by observational biases and therefore difficult to compare. This paper describes the development of a common search strategy to overcome these limitations. The strategy optimizes the sampling for objects in orbits similar to the orbits of the known GEO population but does not exclude the detection of objects with other orbital planes. A properly designed common search strategy clearly eases the comparison of results from different groups and the extrapolation from the sparse (biased) samples to the entire GEO environment.     

UKF参数估计在航天器气动辅助变轨问题中的应用

为快速精确地求解气动辅助变轨问题，提出一种基于无损卡尔曼滤波(UKF)参数估计的数值求解方法。首先，针对气动辅助变轨问题，利用极大值原理将其转化为对应的两点边值问题;然后，以协态变量的初值作为估计参数，以末端条件为期望观测值，将该两点边值问题转化为参数估计问题，并应用UKF滤波算法求解。该算法基于估计理论，避免了计算传统数值方法所需要的梯度矩阵，同时克服了猜测协态变量初值的困难，降低了求解气动辅助变轨问题的难度。数值仿真表明，该算法结构简单，求解效率高，具有良好的鲁棒性。     

Optical orbital debris spotter

The number of man-made debris objects orbiting the Earth, or orbital debris, is alarmingly increasing, resulting in the increased probability of degradation, damage, or destruction of operating spacecraft. In part, small objects (<10 cm) in Low Earth Orbit (LEO) are of concern because they are abundant and difficult to track or even to detect on a routine basis. Due to the increasing debris population it is reasonable to assume that improved capabilities for on-orbit damage attribution, in addition to increased capabilities to detect and track small objects are needed. Here we present a sensor concept to detect small debris with sizes between approximately 1.0 and 0.01 cm in the vicinity of a host spacecraft for near real time damage attribution and characterization of dense debris fields and potentially to provide additional data to existing debris models.     

基于简化Unscented变换的FMSRUKF算法及其目标跟踪性能分析

研究Unscented变换的基本原理及Unscented Kalman Filter(UKF)算法。为了降低跟踪系统计算复杂性,在Unscented变换中引入单位矩阵,以简单的数值计算取代复杂的矩阵分解求解矩阵平方根的过程,把UKF改进为FM- SRUKF。对三维坐标系下的变加速运动目标进行跟踪仿真。结果表明FMSRUKF具有更好的精度和鲁棒性。     

Density and mass distributions of orbital debris

Area-to-mass ratios for orbital debris tracked by the U.S. Space Command were calculated from observed changes in apogee and perigee altitude due to atmospheric drag. The area-to-masses observed for the orbital debris were similar to those found for debris from laboratory breakups, and suggest that much of the debris is composed of crumpled thin plates or of insulation material with low effective density. Areas for the debris objects were derived from radar cross-section data. Object masses were calculated from the ratio of the RCS-derived area to the area-to-mass ratio. Analysis of the distributions of fragment masses from the breakups suggests that in many cases, only a portion of the initial object breaks up into small fragments.     

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.     

Longitude-dependent effects of fragmentation events in the geosynchronous orbit regime

The effects of on-orbit fragmentation events on localized debris congestion in each of the longitude slots of the geosynchronous orbit (GEO) regime are evaluated by simulating explosions and collisions of uncontrolled rocket bodies in multiple orbit configurations, including libration about one or both of the gravitational wells located at 75°E and 105°W. Fragmentation distributions are generated with the NASA Standard Breakup Model, which samples fragment area-to-mass ratio and delta-velocity as a function of effective diameter. Simulation results indicate that the long-term severity and consequence of a GEO fragmentation event is strongly dependent upon parent body longitude at the epoch of fragmentation, which can spawn bi-annual “fragment storms” in high-risk longitude slots, driven by lower-energy fragments that have been captured and have started librating around the nearby gravitational well.     

基于滤波算法的拟平均轨道根数自主实时确定方法

针对卫星长期自主运行的发展要求,首次提出了基于滤波算法的卫星自主计算拟平均轨道根数的在轨实时方法。首先以受地球非球形摄动影响的低轨卫星为研究对象,推导了拟平均轨道根数的变化率并考虑了J2平方项补偿;以拟平均轨道根数为状态变量并以卫星瞬时速度和位置作为观测量建立了滤波方程,然后分别应用平方根无迹卡尔曼滤波(SR UKF)和扩展卡尔曼滤波(EKF)对拟平均轨道根数进行估计。仿真结果表明,两种滤波方法均能有效地计算拟平均轨道根数,其中平方根UKF滤波具有更高的精度和稳定度,且都可以满足卫星在轨自主实时计算拟平均轨道根数的需求。     

Some Methods of Automatic Control of Relative Motion of Objects in Near-Earth Orbits

The methods of automatic control of motion of a free-flight platform near the orbital space station are considered. The satellite-inspector intended for service of the International Space Station is an example of such objects. The algorithms of control of the platform motion along a trajectory specified by the space station operator are developed, and control of the station keeping mode for visual observation of the state of the space station's external surface is considered. The problem of control of a platform landing on a specially equipped docking unit of the orbital space station is also considered.     

International Practices to Protect the Geostationary Ring

Since more than 20 years reorbiting of geostationary satellites at the end of their mission is recommended and partially performed to protect the GEO environment. Now a worldwide accepted reorbiting altitude was defined by the Inter-Agency Space Debris Coordination Committee (IADC). Still only one-third of the aging satellites follow this IADC rule. Based on orbital data in the DISCOS database, the situation in the geostationary ring is analyzed. From 878 known objects, 305 are controlled inside their longitude slots, 353 are drifting above, below or through GEO, and 125 are in a libration orbit (status of January 2001). In the last four years (1997–2000) 58 spacecraft reached end-of-life. Twenty of them were reorbited in compliance with the IADC recommendations, 16 were reorbited below this recommendation and 22 were abandoned without any end-of-life disposal manoeuvre.     

Nonlinear effects in the correlation of tracks and covariance propagation

Even though there are methods for the nonlinear propagation of the covariance the propagation of the covariance in current operational programs is based on the state transition matrix of the 1st variational equations, thus it is a linear propagation. If the measurement errors are zero mean Gaussian, the orbit errors, statistically represented by the covariance, are Gaussian. When the orbit errors become too large they are no longer Gaussian and not represented by the covariance. One use of the covariance is the association of uncorrelated tracks (UCTs). A UCT is an object tracked by a space surveillance system that does not correlate to another object in the space object data base. For an object to be entered into the data base three or more tracks must be correlated. Associating UCTs is a major challenge for a space surveillance system since every object entered into the space object catalog begins as a UCT. It has been proved that if the orbit errors are Gaussian, the error ellipsoid represented by the covariance is the optimum association volume. When the time between tracks becomes large, hours or even days, the orbit errors can become large and are no longer Gaussian, and this has a negative effect on the association of UCTs. This paper further investigates the nonlinear effects on the accuracy of the covariance for use in correlation. The use of the best coordinate system and the unscented Kalman Filter (UKF) for providing a more accurate covariance are investigated along with assessing how these approaches would result in the ability to correlate tracks that are further separated in time.     

基于地磁场测量估计卫星姿态的UKF算法

提出了利用UKF（Unscented Kalman Filter）处理地磁场测量数据进行低轨道（LEO）卫星自主定姿的算法。通过使用估计姿态、轨道参数和国际地磁场参考（IGRF）计算得到的地磁矢量与三轴磁强计（TAM）的测量矢量之差作为更新信息，可以实现实时的姿态角和角速度估计。针对卫星稳态定姿、大角度快速机动的定姿以及姿态失控状态下的定姿等三种任务，分别用UKF和传统的EKF（Extended Kalman Filter）进行了数值仿真。仿真结果显示出本文提出的定姿算法的优越性。