Angles-only relative orbit determination in low earth orbit

The paper provides an overview of the angles-only relative orbit determination activities conducted to support the Autonomous Vision Approach Navigation and Target Identification (AVANTI) experiment. This in-orbit endeavor was carried out by the German Space Operations Center (DLR/GSOC) in autumn 2016 to demonstrate the capability to perform spaceborne autonomous close-proximity operations using solely line-of-sight measurements. The images collected onboard have been reprocessed by an independent on-ground facility for precise relative orbit determination, which served as ultimate instance to monitor the formation safety and to characterize the onboard navigation and control performances. During two months, several rendezvous have been executed, generating a valuable collection of images taken at distances ranging from 50?km to only 50?m. Despite challenging experimental conditions characterized by a poor visibility and strong orbit perturbations, angles-only relative positioning products could be continuously derived throughout the whole experiment timeline, promising accuracy at the meter level during the close approaches. The results presented in the paper are complemented with former angles-only experience gained with the PRISMA satellites to better highlight the specificities induced by different orbits and satellite designs.     

Accurate orbit predictions for debris orbit manoeuvre using ground-based lasers

Orbit manoeuvre of low Earth orbiting (LEO) debris using ground-based lasers has been proposed as a cost-effective means to avoid debris collisions. This requires the orbit of the debris object to be determined and predicted accurately so that the laser beam can be locked on the debris without the loss of valuable laser operation time. This paper presents the method and results of a short-term accurate LEO (<900 km in altitude) debris orbit prediction study using sparse laser ranging data collected by the EOS Space Debris Tracking System (SDTS). A main development is the estimation of the ballistic coefficients of the LEO objects from their archived long-term two line elements (TLE). When an object is laser tracked for two passes over about 24 h, orbit prediction (OP) accuracy of 10–20 arc seconds for the next 24–48 h can be achieved – the accuracy required for laser debris manoeuvre. The improvements in debris OP accuracy are significant in other applications such as debris conjunction analyses and the realisation of daytime debris laser tracking.     

Radiative transitions in few-electron quasi-molecules

The review is aimed at the discussion of recent results on spectral profiles produced in collisions of few-electron atoms/ions. Calculations of spectral profiles produced by atom/ion collisions need some preliminary quantum-chemical information such as potential energy surfaces, dipole transition moments, etc. The main advantage of few-electron systems is that all input data can be obtained ab initio or analytically, thus the profiles calculated do not include any fit parameters. Two specific examples have been discussed. The first one deals with radiative transitions accompanying charge-exchange in collisions of one-electron ions with bare nuclei. The second example concerns radiative transitions produced by H⁻ + H collisions.     

埋藏卫星尸体的轨道墓地

2009年2月11日,美国一颗通信卫星与俄罗斯一颗已经报废的卫星在太空中相撞.这次事件产生了大量太空垃圾,可能会对国际空间站的安全造成威胁.目前科学家在探讨有效清理太空垃圾的方法,以防类似事件再次发生.     

The LAGEOS satellites orbit and Yukawa-like interactions

LAGEOS II general relativity pericenter precession has been analysed in terms of the errors produced by the mismodelling of both the gravitational and non-gravitational perturbations acting on the satellite orbit. The accuracy in the pericenter determination may be considered as an upper-bound value for the estimate of the strength α of a possible new-long-range-interaction described by a Yukawa-like potential. In the present work we have focused on the constraints in α that can be obtained with the current best multi-satellites gravity field model EGM96 (α < 2.6 × 10⁻¹⁰) and also with the first promising models from the CHAMP (α < 1.8 × 10⁻¹⁰) and GRACE (α < 1.2 × 10⁻¹⁰) gravimetric missions. These results represent, potentially, an improvement of two or three orders-of-magnitude with respect to the best constraints obtained in the past with Earth–LAGEOS and Lunar–LAGEOS data (|α| < 10⁻⁵–10⁻⁸). The impact of the non-gravitational perturbations mismodelling in the final error budget has been determined together with the improvements obtainable in the constraint of the strength α with the proposed LARES satellite.     

飞行器轨道的特征点

针对飞行器轨道的数据处理问题,首次提出了轨道的特征点概念。轨道的特征点是飞行器动力突变的真实反映,轨道特征点的客观存在,要求我们在测量数据处理中,在多项式表示轨道时应以特征点为端点,或以特征点为轨道样条表示的当然节点,否则将带来轨道的表示误差,在残差数据中波动现象。介绍了提取轨道特征点的方法,仿真与实际测量数据的处理结果表明：特征点提取方法准确度较镐;特征点为当然节点的样条函数表示轨道能消除节点选     

Space debris mitigation in geosynchronous orbit

In order to preserve the geosynchronous region, the Inter-Agency Space Debris Coordination Committee (IADC) proposed and endorsed a re-orbiting strategy for spacecraft at the end-of-life: they should be disposed above the synchronous altitude and passivated, to reduce the risk of inadvertent explosions. The recommended perigee altitude of the disposal orbit took into account all relevant perturbations and was a function of the expected perturbing acceleration induced by solar radiation pressure. It was intended to prevent any further interference with a properly defined geostationary protected region.     

Cosmic dust measurements in lunar orbit

On 15th February 1992, ISAS space engineering satellite HITEN was successfully inserted into an elliptical orbit around the moon with perilune between some 100 km and 8000 km and apolune of about 50.000 km. On board was a small scientific experiment designed to detect cosmic dust particles, MDC - Munich Dust Counter. During a period of more than one year, until Hiten's hard landing on the moon surface at 10th of April 1993 (UTC), measurements of impact velocity, mass and crude flight direction of micrometeoroid particles have been performed. In total 150 cosmic dust impacts were detected and evaluated. From these measurements, the impact rate versus time and the dust flux versus distance from the moon are derived. The evidence of moon ejecta and some indications of particles which are orbiting the moon will be discussed. The spatial distribution of the measured particles is shown in lunarcentric as well as in heliocentric coordinate systems. The directional distribution is also given, showing the different populations of cosmic dust particles. Finally, the gathered data will be compared with previous results from measurements in the vicinity of the Earth and in the geomagnetic tail region.     

CHAMP and GRACE accelerometer calibration by GPS-based orbit determination

Current and planned Earth observation missions are equipped with highly sensitive accelerometers. Before using the data, the instrument has to be calibrated by determining scale and bias parameters for each axis. Here, the accelerometer measurements are used in a GPS-based reduced-dynamic orbit determination approach, replacing the non-gravitational force models, and nominally daily calibration parameters are estimated. Additional empirical accelerations are estimated to account for deficiencies in the applied force models. This method is applied to 5 years of CHAMP and GRACE data, resulting in an orbit precision at the level of a few centimeters. In along-track direction the calibration parameters can be estimated freely, scale factors of 0.96 ± 0.014 and 0.95 ± 0.015 are obtained for GRACE A and B, and 0.85 ± 0.024 for CHAMP. A constant scale factor results in the smoothest bias series, with clear trends and occasional jumps. In radial and cross-track direction tight constraints to a priori biases have to be applied. Furthermore, the determined orbits are analyzed with respect to reference trajectories, and SLR, phase and KBR residuals are presented.     

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.     

Stereoscopic imaging from polar orbit and synthetic stereo imaging

The photogrammetric determination of cloud top heights from stereoscopic satellite images seems to be a very good solution to this hitherto unresolved problem. Whereas in the U.S.A., stereoscopic imaging is done by use of geosynchronous weather satellites, in Europe such a system cannot be used because there is only one geosynchronous satellite (METEOSAT). An alternative could be a Stero Line Scanner (SLS) operating on a polar orbiter.SLS would scan twice, forward and backward, producing in this way two image strips for steroscopic viewing and photogrammetric measurements from pole to pole. Because of the cloud motion between the two scans, a SLS needs additional independent height information for reference points, e.g. from a Laser Ranger (LAR). The advantage of this method is that cloud motion, and therefore wind, can also be determined for these reference points. Another solution is a system of two SLS satellites flying one after the other and scanning the same area simultaneously. This allows cloud motion determination across the whole image. The use of infrared channels also allows night operation and provides additional data such as improved seas surface temperatures.The DFVLR is currently studying these problems. Synthetic stereoscopic imaging is being used in a forerunner programm to the SLS project and also for simulation in SLS studies.     

ERS-1 and ERS-2 operational and precise orbit determination

This paper presents the European Space Operations Centre's orbit determination and prediction systems for the ERS-1 mission. The routine operational orbit determination and prediction subsystem is discussed briefly, and statistics of the accuracy compared to the requirements are given. The precise orbit determination subsystem is then described, and the accuracy of its results are compared to those of the operational orbit system and to the D-PAF preliminary orbit solutions. Some geophysical results from the altimeter data, processed in these orbit determinations, are also presented. The ESOC/OAD ‘ERS-1 Orbit Report’ is introduced as a document providing this information on a monthly basis. Finally, this paper describes how the experience gained with the precise orbit determination will be exploited to further improve the accuracy of the routine system that will be used for ERS-2, and provides an estimate of this accuracy.     

Energetic particle environment in near-Earth orbit.

The hazard of exposure to high doses of ionizing radiation is one of the primary concerns of extended manned space missions and a continuous threat for the numerous spacecraft in operation today. In the near-Earth environment the main sources of radiation are solar energetic particles (SEP), galactic cosmic rays (GCR), and geomagnetically trapped particles, predominantly protons and electrons. The intensity of the SEP and GCR source depends primarily on the phase of the solar cycle. Due to the shielding effect of the Earth's magnetic field, the observed intensity of SEP and GCR particles in a near-Earth orbit will also depend on the orbital parameters altitude and inclination. The magnetospheric source strength depends also on these orbital parameters because they determine the frequency and location of radiation belt passes. In this paper an overview of the various sources of radiation in the near-Earth orbit will be given and first results obtained with the Solar, Anomalous, and Magnetospheric Particle Explorer (SAMPEX) will be discussed. SAMPEX was launched on 3 July 1992 into a near polar (inclination 82 degrees) low altitude (510 x 675 km) orbit. The SAMPEX payload contains four separate instruments of high sensitivity covering the energy range 0.5 to several hundred MeV/nucleon for ions and 0.4 to 30 MeV for electrons. This low altitude polar orbit with zenith-oriented instrumentation provides a new opportunity for a systematic study of the near-Earth energetic particle environment.     

Precision orbit determination performance for CryoSat-2

In this paper we discuss our efforts to perform precision orbit determination (POD) of CryoSat-2 which depends on Doppler and satellite laser ranging tracking data. A dynamic orbit model is set-up and the residuals between the model and the tracking data is evaluated. The average r.m.s. of the 10?s averaged Doppler tracking pass residuals is approximately 0.39?mm/s; and the average of the laser tracking pass residuals becomes 1.42?cm. There are a number of other tests to verify the quality of the orbit solution, we compare our computed orbits against three independent external trajectories provided by the CNES. The CNES products are part of the CryoSat-2 products distributed by ESA. The radial differences of our solution relative to the CNES precision orbits shows an average r.m.s. of 1.25?cm between Jun-2010 and Apr-2017. The SIRAL altimeter crossover difference statistics demonstrate that the quality of our orbit solution is comparable to that of the POE solution computed by the CNES. In this paper we will discuss three important changes in our POD activities that have brought the orbit performance to this level. The improvements concern the way we implement temporal gravity accelerations observed by GRACE; the implementation of ITRF2014 coordinates and velocities for the DORIS beacons and the SLR tracking sites. We also discuss an adjustment of the SLR retroreflector position within the satellite reference frame. An unexpected result is that we find a systematic difference between the median of the 10 s Doppler tracking residuals which displays a statistically significant pattern in the South Atlantic Anomaly (SSA) area where the median of the velocity residuals varies in the range of ?0.15 to +0.15?mm/s.     

Precise orbit determination and baseline consistency assessment for Swarm constellation

Precise orbit determination (POD) and precise baseline determination (PBD) of Swarm satellites with 4 years of data are investigated. Ambiguity resolution (AR) plays a crucial role in achieving the best orbit accuracy. Swarm POD and PBD based on single difference (SD) AR and traditional double difference (DD) AR methods are explored separately. Swarm antenna phase center variation (PCV) corrections are developed to further improve the orbit determination accuracy. The code multipath of C1C, C1W and C2W observations is first evaluated and clear variations in code noise related to different receiver settings are observed. Carrier phase residuals of different time periods and different loop tracking settings of receiver are studied to explore the effect of ionospheric scintillation on POD. The reduction of residuals in the polar and geomagnetic equator regions confirms the positive impact of the updated carrier tracking loops (TLs) on POD performance. The SD AR orbits and orbits with float ambiguity (FA) are compared with the Swarm precise science orbits (PSOs). An average improvement of 27 %, 4 % and 16 % is gained in along-track, cross-track and radial directions by fixing the ambiguity to integer. For Swarm-A/B and Swarm-B/C formations, specific days are selected to perform the DD AR-based POD during which the average distance of the formation satellites is less than 5000 km. Satellite laser ranging (SLR) observations are employed to validate the performance of FA, SD AR and DD AR orbits. The consistency between the SD AR orbits and SLR data is at a level of 10 mm which shows an improvement of 25 % when comparing with the FA results. An SLR residuals reduction of 15 % is also achieved by the DD AR solution for the selected days. Precise relative navigation is also an essential aspect for spacecraft formation flying missions. The closure error method is proposed to evaluate the baseline precision in three dimensions. A baseline precision of 1–3 mm for Swarm-A/C formation and 3–5 mm for Swarm-A/B and Swarm-B/C satellite pairs is verified by both the consistency check and closure error method.     

A simple and valid analysis method for orbit anomaly detection

A simple analysis method for orbit anomaly detection, called semi-major axis change method (SACM) was presented by using a relationship between the change of orbit parameters and velocity increments. In this method, the mean value and standard deviation of the semi-major axis change in different time intervals were first calculated according to historical data. Then, these two parameters, the mean value and standard deviation of the semi-major axis change, are chosen as basis variables and combined as an anomalous criterion. For orbit objects with different characteristic, anomalous thresholds were given in different time intervals for identifying the anomalies of the orbital objects. Finally, this method is used for low earth orbit (LEO) satellites and American–Russian breakup debris. By adopting this method, the characteristics of the orbit change were given. The accuracy rate of anomaly analysis for LEO satellites and American–Russian breakup debris can reach to 100%, which demonstrates that the method was rapid and valid.     

Dynamical evolution of debris clouds in geosynchronous orbit

Optical observations have discovered a substantial amount of decimeter sized objects in orbits close to the geosynchronous altitude. Most of these are probably the result of a still undetermined number of explosions occurred to spacecraft and upper stages. So far, however, only two or three fragmentations have been confirmed near GEO and the identification of further explosions at a so high altitude is made difficult by the long time passed since the occurrence of the events and by the effects of the orbital perturbations on the resulting debris clouds. In order to assist the optical observers in identifying debris clouds due to explosions in proximity of the geosynchronous region, a set of fragmentations has been simulated, taking into account a reasonable range of ejection velocities as a function of the fragment size. The resulting debris clouds have been propagated, including all the relevant orbital perturbations, for several decades and the results obtained are presented as snapshots, at given post-explosion times, in the orbital elements space.     

Galileo real-time orbit determination with multi-frequency raw observations

Real-time GNSS-based applications require corresponding real-time orbit products. While traditional GNSS orbits are generated with the dual-frequency IF (Ionosphere-Free) model, the increase of multi-frequency signal satellites brings new challenges for the data processing. Therefore, real-time orbit determination with the multi-frequency UC (Uncombined) model is introduced in this study considering its flexibility. With the derived mathematical model conforming to IGS (International GNSS Service) dual-frequency clock definition and one-week triple-frequency Galileo observation data from 90 IGS network stations, the convergence and accuracy of real-time orbits is assessed and the characteristics of satellite IFCB (Inter-Frequency Clock Bias) are analyzed. Results indicate that the model differences, including dual-frequency IF model, dual-frequency UC model and triple-frequency UC model, contribute to only cm-level differences with CODE (Center for Orbit Determination in Europe) final orbits after a convergence time of around 12 h. The constellation-mean RMS (Root Mean Square) differences of the converged real-time orbits with the CODE final orbits reaches about 5.0 cm, 7.0 cm and 5.0 cm for the radial, tangential and normal directions. The convergence of satellite IFCB is much faster than that of satellite orbit, which reflects a loose correlation between these two parameters. While the Galileo satellite IFCB are temporally stable, the modeling of satellite IFCB may be unreliable when over constrained and becomes even more unstable with commonly encountered datum changes. In summary, real-time GNSS orbit determination with multi-frequency raw observations is feasible and extendable with proper treatment of IFCB.     

Improving orbit prediction accuracy through supervised machine learning

Due to the lack of information such as the space environment condition and resident space objects’ (RSOs’) body characteristics, current orbit predictions that are solely grounded on physics-based models may fail to achieve required accuracy for collision avoidance and have led to satellite collisions already. This paper presents a methodology to predict RSOs’ trajectories with higher accuracy than that of the current methods. Inspired by the machine learning (ML) theory through which the models are learned based on large amounts of observed data and the prediction is conducted without explicitly modeling space objects and space environment, the proposed ML approach integrates physics-based orbit prediction algorithms with a learning-based process that focuses on reducing the prediction errors. Using a simulation-based space catalog environment as the test bed, the paper demonstrates three types of generalization capability for the proposed ML approach: (1) the ML model can be used to improve the same RSO’s orbit information that is not available during the learning process but shares the same time interval as the training data; (2) the ML model can be used to improve predictions of the same RSO at future epochs; and (3) the ML model based on a RSO can be applied to other RSOs that share some common features.