A combination method using evolutionary algorithms in initial orbit determination for too short arc

With the combination of two evolutionary algorithms EDA and DE, a new method of initial orbit determination for satellites based on ground-based too-short-arc is established. Compared with other algorithms, the proposed method focuses on the most densely populated region in the solution space rather than the individual with best fitness value. Both the global information and local information are well fused in the search of optimum. In the method $(a,e,M)$ are treated as variables of the optimization, and the optimization procedure is carried out as a two-stage hierarchical optimization problem which has three variables for each stage. Kernel density estimation is applied to build the probability distribution model without any assumptions of the specified distribution, accompanied by handling semi-major axis and eccentricity as a pair of dependent variables in the construction of the probability for the correlation between them in the practice. Numerical experiments with real ground-based observations show that the proposed method is applicable to too-short-arc with even 3?s, and the result of bias in several kilometers can be achieved with $5^{″}$ error added to angular measurements.     

Precision analysis of autonomous orbit determination using star sensor for Beidou MEO satellite

This paper focuses on the autonomous orbit determination accuracy of Beidou MEO satellite using the onboard observations of the star sensors and infrared horizon sensor. A polynomial fitting method is proposed to calibrate the periodic error in the observation of the infrared horizon sensor, which will greatly influence the accuracy of autonomous orbit determination. Test results show that the periodic error can be eliminated using the polynomial fitting method. The User Range Error (URE) of Beidou MEO satellite is less than 2?km using the observations of the star sensors and infrared horizon sensor for autonomous orbit determination. The error of the Right Ascension of Ascending Node (RAAN) is less than 60?$\mathrm{\mu }\text{rad}$ and the observations of star sensors can be used as a spatial basis for Beidou MEO navigation constellation.     

A robust semi-analytic method to solve the minimum ΔV two-impulse rendezvous problem

A novel semi-analytic approach is developed to determine the minimum $\mathrm{\Delta }V$ for a two-impulse rendezvous and validated both empirically and analytically. A previously published closed-form $\mathrm{\Delta }V$ estimate and the Lambert minimum energy transfer is used to establish upper and lower bounds of the minimum $\mathrm{\Delta }V$ transfer between two orbits. These bounds, in conjunction with the bisection method, operate on a nonlinear radical cost function to guarantee linear convergence. This approach has several real world applications including a low earth orbit (LEO) to highly elliptical orbit (HEO), and a HEO to retrograde geosynchronous orbit transfer. The minimum $\mathrm{\Delta }V$ estimates are better than those reported in the existing literature, while run times improved as much as two orders of magnitude over a fixed time Lambert solver. All singularity cases were addressed such that any orbital geometry, including Hohmann and radial elliptic transfers, converged to the global minimum $\mathrm{\Delta }V$. This approach will work for both coplanar and non-coplanar 3D geometries for any orbit type.     

Autonomous broadcast ephemeris improvement for GNSS using inter-satellite ranging measurements

This paper discusses the concept of using inter-satellite ranging (ISR) measurements of the satellites of a Global Navigation Satellite System (GNSS) for autonomous broadcast ephemeris improvement. Firstly the inter-satellite ranging is modeled to obtain the clock and orbit error observables. The orbit error observable is analyzed and its observation equation is provided. Both least-squares estimation and Kalman Filter approach are proposed to estimate satellite clock errors, while solely the Kalman Filter is used to estimate the orbit errors. All these algorithms are validated using true broadcast ephemeris and precise ephemeris of GPS along with the simulated ranging noise. Based on the settings adopted in the test, the result shows that the orbit accuracy of the precise ephemeris using the proposed method is around 20–50 cm and the accuracy of the satellite clock can reach 20 cm while ranging noise is assumed to be 0.45 m (1σ). The User Ranging Error (URE) is improved from 1.05 m to 0.34 m, which is comparable to other sources of precise ephemeris or even better, while the proposed approach has many advantages such as compatibility and accessibility. It is also noted that the proposed method may provide useful functions in determining inter-constellation coordinate and time differences autonomously for better interoperability and interchangeability in the multi GNSS operation era.     

GRACE accelerometer calibration by high precision non-gravitational force modeling

The precise modeling and knowledge of non-gravitational forces acting on satellites is of big interest to many scientific tasks and missions. Since 2002, the twin GRACE satellites have measured these forces in a low Earth orbit with highly precise accelerometers, for about 15?years. Besides the significance for the GRACE mission, these measurement data allow the evaluation of modeling approaches and the improvement of force models. Unfortunately, before any scientific usage, the accelerometer measurements need to be calibrated, namely scale factor and bias have to be regularly estimated.In this study we demonstrate an accelerometer calibration approach, solely based on high precision non-gravitational force modeling without any use of empirically or stochastically estimated parameters, using our in-house developed satellite simulation tool XHPS. The aim of this work is twofold, first we use the accelerometer data and the residuals resulting from the calibration to quantitatively analyze and validate different non-gravitational force model approaches. In a second step, we compare the calibration results to three different calibration methods from different authors, based on gravity field recovery, GPS-based precise orbit determination, and based on modeled accelerations.We consider atmospheric drag forces and winds, as well as radiation forces due to solar radiation pressure, albedo, Earth infrared and thermal radiation (TRP) of the satellite itself. For TRP, we investigate different transient temperature calculation approaches for the satellite surfaces with absorbed power from the aforementioned radiation sources. A detailed finite element model of the satellite is utilized for every force, considering orientation, material properties and shadowing conditions for each element.For cross-track and radial direction, which are mainly affected by the radiative forces, our calibration residuals are quite small when drag is not super dominant (1–3?$\text{nm}/{\text{s}}^2$ for total accelerations around $\pm$50?$\text{nm}/{\text{s}}^2$). For these directions the calibration seems to perform better than the other compared methods, where some bigger differences were found. For the drag dominated along-track direction it is vice versa, here our method is not sensitive enough because the difference between modeled and measured drag is bigger (e.g. residuals around 10?$\text{nm}/{\text{s}}^2$ for total accelerations around $\pm$70?$\text{nm}/{\text{s}}^2$ for low solar activity). In along-track direction the orbit determination based methods are more sensitive and produce more reliable results. Results for the complete GRACE mission time span from 2003 to 2017 are shown, covering different seasonal environmental conditions.     

Yarkovsky-Schach effect on space debris motion

The Yarkovsky-Schach effect is a small perturbation affecting Earth satellites and space debris illuminated by the Sun. It was first applied to the orbit of LAGEOS satellites as an explanation of the residuals in orbital elements. In this work, we carry out several numerical integration tests taking into consideration various orbit and rotation parameters, in order to analyse this effect in a broader context. The semi-major axis variations remain small and depend on the spin axis attitude with respect to the Sun. We show that the force amplitude is maximised for orbits inclined with $i\approx$?20–30°. We also observe the influence on other orbital elements, notably on the orbit inclination. However, these effects are clearly observed only on long timescales; in our simulations, we propagated the orbits for 200?y. The Yarkovsky-Schach effect is thus confirmed to have a minuscule magnitude. It should be taken into account in studies requiring high-precision orbit determination, or on expanded timescales.     

Optimal Earth’s reentry disposal of the Galileo constellation

Nowadays there is international consensus that space activities must be managed to minimize debris generation and risk. The paper presents a method for the end-of-life (EoL) disposal of spacecraft in Medium Earth Orbit (MEO). The problem is formulated as a multiobjective optimisation one, which is solved with an evolutionary algorithm. An impulsive manoeuvre is optimised to reenter the spacecraft in Earth’s atmosphere within 100?years. Pareto optimal solutions are obtained using the manoeuvre $\mathrm{\Delta }v$ and the time-to-reentry as objective functions to be minimised. To explore at the best the search space a semi-analytical orbit propagator, which can propagate an orbit for 100?years in few seconds, is adopted. An in-depth analysis of the results is carried out to understand the conditions leading to a fast reentry with minimum propellant. For this aim a new way of representing the disposal solutions is introduced. With a single 2D plot we are able to fully describe the time evolution of all the relevant orbital parameters as well as identify the conditions that enables the eccentricity build-up. The EoL disposal of the Galileo constellation is used as test case.     

地基行星大气掩星观测资料流程和数据整理

在中国火星探测萤火一号(YH-1)计划中, 包括了地基掩星观测反演火星大气的科研任务. 观测资料整理是反演流程的第一步. 本文描述了地基火星大气掩星观测处理软件系统的观测数据流程和观测资料整理模块,并详细介绍了观测资料整理模块的结构和功能, 其中包括时间系统转换、历表插值、坐标系变换、信号时延改正以及掩星平面建立. 利用行星数据系统公布的火星快车无线电科学数据和由SPICE得到的地球、火星历表以及火星快车的轨道数据, 结合本文的算法, 得到了一些实验结果.      

Onboard orbit determination using GPS observations based on the unscented Kalman filter

Spaceborne GPS receivers are used for real-time navigation by most low Earth orbit (LEO) satellites. In general, the position and velocity accuracy of GPS navigation solutions without a dynamic filter are 25 m (1σ) and 0.5 m/s (1σ), respectively. However, GPS navigation solutions, which consist of position, velocity, and GPS receiver clock bias, have many abnormal excursions from the normal error range for space operation. These excursions lessen the accuracy of attitude control and onboard time synchronization. In this research, a new onboard orbit determination algorithm designed with the unscented Kalman filter (UKF) was developed to improve the performance. Because the UKF is able to obtain the posterior mean and covariance accurately by using the second-order Taylor series expansion through the sampled sigma points that are propagated by using the true nonlinear system, its performance can be better than that of the extended Kalman filter (EKF), which uses the linearized state transition matrix to predict the covariance. The dynamic models for orbit propagation applied perturbations due to the 40 × 40 geo-potential, the gravity of the Sun and Moon, solar radiation pressure, and atmospheric drag. The 7(8)th-order Runge–Kutta numerical integration was applied for orbit propagation. Two types of observations, navigation solutions and C/A code pseudorange, can be used at the user’s discretion. The performances of the onboard orbit determination were verified using real GPS data of the CHAMP and KOMPSAT-2 satellites. The results of the orbit determination were compared with the precision orbit ephemeris (POE) of the CHAMP and KOMPSAT-2 satellites.     

Entry of dust particles into planetary magnetospheres

While interplanetary dust constitutes a primary source of cosmic particulate matter in planetary magnetospheres, the debris produced by its impact with small satellites and ring material provides an important secondary source. Internal processes, such as volcanic activity, particularly in the smaller satellites, could result in a third source. In the case of the terrestrial magnetosphere there are also artificial (internal) sources: 1–10μ sized A?₂O₃ particles injected by solid rocket mortar burns between near earth and geosynchronous orbit constitute one such source, while the fragments of larger bodies (artificial satellites) due to explosions (e.g., “killer satellites”) and collisions constitute another. Finally, if we include the purely induced cometary magnetosphere among planetary magnetospheres, the injection of cometary dust into it due to entrainment by the outflowing gases constitutes another source.As a result of being immersed in a radiative and plasma environment these dust grains get electrically charged up to some potential (positive or negative). Particularly in those regions where the magnetospheric plasma is hot and dense and their own spatial density is low, the dust grains could get charged to numerically large negative potentials.While this charging may have physical consequences for the larger grains, such as electrostatic erosion (“chipping”) and disruption, it also can effect the dynamics of the smaller grains. Indeed, the small but finite capacitance of these grains, which leads to a phase lag in the gyrophase oscillation of the grain potential, could even lead to the permanent magneto-gravitational capture of interplanetary grains within planetary magnetospheres in certain situations. Here we will review the sources of dust in planetary magnetospheres and discuss their physics and their dynamics under the combined action of both planetary gravitational and magnetospheric electromagnetic forces.     

基于GPS的地球资源卫星精密星历外推新方法

随着技术的发展,通过星载GPS接收机直接确定卫星星历成为卫星定位的一个重要手段.GPS接收机获取的卫星星历数据是某一时刻的瞬时状态,要获取连续的卫星星历数据还需要进一步处理.常用的处理方法有几何法与动力学法.在GPS接收机给定瞬时星历频率较低的情况下,几何法的计算误差比较大,特别是只有一组瞬时星历时,无法用几何法进行轨道的外推.在分析地球资源卫星轨道特点的基础上,提出一种新的轨道缩减动力模型,该模型将卫星运动在直角坐标系中分解为简谐运动,利用模型实现了轨道外推的算法.通过试验验证,该算法可以达到较高的精度.      

Medium Earth Orbit dynamical survey and its use in passive debris removal

The Medium Earth Orbit (MEO) region hosts satellites for navigation, communication, and geodetic/space environmental science, among which are the Global Navigation Satellites Systems (GNSS). Safe and efficient removal of debris from MEO is problematic due to the high cost for maneuvers needed to directly reach the Earth (reentry orbits) and the relatively crowded GNSS neighborhood (graveyard orbits). Recent studies have highlighted the complicated secular dynamics in the MEO region, but also the possibility of exploiting these dynamics, for designing removal strategies. In this paper, we present our numerical exploration of the long-term dynamics in MEO, performed with the purpose of unveiling the set of reentry and graveyard solutions that could be reached with maneuvers of reasonable $\mathrm{\Delta }V$ cost. We simulated the dynamics over 120–200?years for an extended grid of millions of fictitious MEO satellites that covered all inclinations from 0 to 90°, using non-averaged equations of motion and a suitable dynamical model that accounted for the principal geopotential terms, 3rd-body perturbations and solar radiation pressure (SRP). We found a sizeable set of usable solutions with reentry times that exceed $～40$ years, mainly around three specific inclination values: 46°, 56°, and 68°; a result compatible with our understanding of MEO secular dynamics. For $\mathrm{\Delta }V?300$ m/s (i.e., achieved if you start from a typical GNSS orbit and target a disposal orbit with $e<0.3$), reentry times from GNSS altitudes exceed $～70$ years, while low-cost ($\mathrm{\Delta }V?5–35$ m/s) graveyard orbits, stable for at lest 200?years, are found for eccentricities up to $e\approx 0.018$. This investigation was carried out in the framework of the EC-funded “ReDSHIFT” project.     

附加先验轨道约束的LEO几何法实时精密定轨验证分析

低轨卫星的实时精密定轨能够极大拓展其完成复杂科学任务的能力,例如实时环境监测、机动控制和卫星自主导航等.本文根据几何法实时精密定轨模型,提出了附加LEO先验轨道约束从而改善实时定轨的精度、收敛速度和稳定性的构想.分别采用广播星历、超快速星历预报部分和实时精密星历,设计了6种实时定轨方案,并利用Swarm-A,B,C星7天的观测数据进行方案验证与分析.结果表明,使用广播星历、IGU和IGC星历的方案精度递增,附加先验轨道约束能够进一步提升精度.使用IGC星历并附加标准差为1m的先验轨道约束后,在径向、切向和法向的定轨精度分别达到6.12cm,5.55cm和4.98cm.此外,附加先验轨道约束能够显著提升收敛速度,使用IGC星历平均收敛时间约为31min,附加标准差为1m的先验轨道约束后收敛仅需约4min.      

Assimilation of Mars Global Surveyor meteorological data

The Mars Global Surveyor (MGS) Mission is more than just a return to Mars. It represents a qualitatively new type of planetary mission. This is true not only because of the capable instrumentation aboard the spacecraft and the choice of orbit and data rate, but also because of a major beneficial change in our understanding of the interplay between observation and modeling. The Thermal Emission Spectrometer (TES), for example, is capable of taking thousands of infrared spectra per day. The 15 micrometer carbon dioxide band in these spectra can be inverted to obtain atmospheric temperature profiles, amounting to some 15,000–25,000 separate measurements each day. In addition, radio occultations produce fewer, but much higher resolution, temperature and pressure profiles. How is such a quantity of data to be handled? Clearly not in the old-fashioned manner in which a single profile is studied at great length and detail. The quantity of data does not allow this; and the quality of the data does not support it. (A single atmospheric profile is bound to contain small-scale spatial and temporal variation—e.g., gravity waves—that cannot be removed unambiguously, as well as possible errors due to noise in the observations or non-uniqueness of the inversions). Furthermore, much of the atmospheric science of interest (winds, for example) depends on quantities like horizontal temperature gradients that are not directly observed. Instead, the data should be examined collectively with the aid of a model that incorporates our knowledge of the governing physics. Described here are the first results of such a data assimilation exercise with TES observations during the aerobraking hiatus period at L_s ≈ 200.     

基于位置观测的北斗广播星历速度精度分析

利用广播星历计算导航卫星的速度向量是GNSS高精度实时测速的必要条件.本文分析了仅以卫星位置向量为观测量的北斗广播星历的速度计算精度.从广播星历拟合过程出发,推导了北斗18参数模型的速度向量计算公式.基于北斗13颗在轨卫星一年的实际轨道数据,分析了全年广播星历计算卫星速度向量的精度.结果表明,利用18参数模型计算的速度误差最大在10-4m·-1量级;在相同拟合时段条件下,地球静止轨道（GEO）和倾斜地球同步轨道（IGSO）卫星的速度精度相当,高于中圆地球轨道（MEO）卫星.通过对位置残差序列分析,得出位置残差误差较小且变化趋势平稳是广播星历计算速度精度较高的原因.分析和计算结果验证了仅用位置观测量拟合北斗广播星历算法的有效性.      

Effects of space weather on the ionosphere and LEO satellites’ orbital trajectory in equatorial,low and middle latitude

We study the effects of space weather on the ionosphere and low Earth orbit (LEO) satellites’ orbital trajectory in equatorial, low- and mid-latitude (EQL, LLT and MLT) regions during (and around) the notable storms of October/November, 2003. We briefly review space weather effects on the thermosphere and ionosphere to demonstrate that such effects are also latitude-dependent and well established. Following the review we simulate the trend in variation of satellite’s orbital radius (r), mean height (h) and orbit decay rate (ODR) during 15 October–14 November 2003 in EQL, LLT and MLT. Nominal atmospheric drag on LEO satellite is usually enhanced by space weather or solar-induced variations in thermospheric temperature and density profile. To separate nominal orbit decay from solar-induced accelerated orbit decay, we compute $r\text{,}h$ and ODR in three regimes viz. (i) excluding solar indices (or effect), where $r=r_0\text{,}h=h_0$ and $\mathit{ODR}={\mathit{ODR}}_0$ (ii) with mean value of solar indices for the interval, where $r=r_m\text{,}h=h_m$ and $\mathit{ODR}={\mathit{ODR}}_m$ and (iii) with actual daily values of solar indices for the interval ($r\text{,}h$ and ODR). For a typical LEO satellite at h?=?450?km, we show that the total decay in r during the period is about 4.20?km, 3.90?km and 3.20?km in EQL, LLT and MLT respectively; the respective nominal decay ($r_0$) is 0.40?km, 0.34?km and 0.22?km, while solar-induced orbital decay ($r_m$) is about 3.80?km, 3.55?km and 2.95?km. h also varied in like manner. The respective nominal ${\mathit{ODR}}_0$ is about 13.5?m/day, 11.2?m/day and 7.2?m/day, while solar-induced ${\mathit{ODR}}_m$ is about 124.3?m/day, 116.9?m/day and 97.3?m/day. We also show that severe geomagnetic storms can increase ODR by up to 117% (from daily mean value). However, the extent of space weather effects on LEO Satellite’s trajectory significantly depends on the ballistic co-efficient and orbit of the satellite, and phase of solar cycles, intensity and duration of driving (or influencing) solar event.     

First solar observations with ALMA

The Atacama Large Millimeter-Submillimeter Array (ALMA) has opened a new window for studying the Sun via high-resolution high-sensitivity imaging at millimeter wavelengths. In this contribution I review the capabilities of the instrument for solar observing and describe the extensive effort taken to bring the possibility of solar observing with ALMA to the scientific community. The first solar ALMA observations were carried out during 2014 and 2015 in two ALMA bands, Band 3 ($\lambda =3$?mm) and Band 6 ($\lambda =1.3$?mm), in single-dish and interferometric modes, using single pointing and mosaicing observing techniques, with spatial resolution up to $～$2″ and $～$1″ in the two bands, respectively. I overview several recently published studies which made use of the first solar ALMA observations, describe current status of solar observing with ALMA and briefly discuss the future capabilities of the instrument.     

Effect of q-nonextensive hot electrons on bifurcations of nonlinear and supernonlinear ion-acoustic periodic waves

Nonlinear and supernonlinear ion-acoustic periodic waves are investigated in a three-component unmagnetized plasma which consists of mobile fluid cold ions, Maxwellian cold electrons and q-nonextensive hot electrons employing phase plane analysis. Using the traveling wave transformation, the plasma system is reduced to a planar autonomous dynamical system. Utilizing phase plane analysis of planar dynamical systems, all possible phase portraits including nonlinear homoclinic orbit, nonlinear periodic orbit, supernonlinear homoclinic orbit and supernonlinear periodic orbit are presented depending on physical parameters $q,\alpha ,\sigma$ and V. Using numerical simulations, nonlinear and supernonlinear ion-acoustic periodic waves are shown for different conditions. It is found that the nonextensive parameter q plays a crucial role in the bifurcations of nonlinear and supernonlinear ion-acoustic periodic waves. Our study may be applicable to understand the nonlinear and supernonlinear periodic features in auroral plasma.