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.     

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.     

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.      

基于多传感器的卫星自主导航信息融合算法

通常卫星上装有较多的自主导航传感器,如何将其信息有效的组织并充分利用,是卫星自主导航的关键问题。采用信息融合技术把两种或多种导航系统组合起来,应用最优估计理论,形成最优组合导航系统,有利于充分运用各导航系统的信息进行信息互补和信息合作,已逐渐成为了导航定位技术的发展方向。文章针对星敏感器、红外地平仪、雷达高度计、紫外敏感器组成的卫星自主导航系统的特点,提出了一种基于联邦卡尔曼滤波技术进行轨道确定的信息融合算法。仿真结果表明,该方案能够获得较高的定轨精度,有效抑制滤波发散,整个系统的运算速度和收敛速度也有所提高。     

近地卫星利用光学敏感器的自主导航方法

基于光学敏感器的卫星自主导航技术是利用红外地球敏感器（IRES）和星敏感器（ST）等姿态测量部件提供的测量信息,通过计算含有轨道信息的星光角距和地球视半径角,修正由轨道动力学模型递推得到的轨道参数。通过系统状态模型和观测模型的离散化和线性化,得到扩展卡尔曼滤波算法的递推关系,并在此基础上进行数学仿真。仿真结果表明,该方法的收敛速度和收敛精度都比较好。由于该方法不需要增加额外的星载敏感器,因此具有很好的应用前景。     

航天器天文导航中星敏感器最佳安装方位研究

航天器自主天文导航中,通常用星敏感器和地平仪测量的星光角距作为观测量,星敏感器安装方位角是影响导航精度的一个重要因素.针对星光角距作为观测量的自主天文导航方法,分别采用扩展卡尔曼滤波EKF(Extended Kalman Filter)和Unscented卡尔曼滤波UKF(Unscented Kalman Filter)2种滤波方法进行仿真计算,研究了星敏感器安装方位角对导航精度的影响规律,得出星敏感器的最佳安装方位角,并考察了其在不同轨道参数下的适用性,为星敏感器的安装和星敏感器视场内观测星的选取提供了依据.仿真计算表明,本结论对其它利用"星光+地平"的自主导航方法也适用.      

基于正弦拟合的空间目标短弧关联算法

星敏感器是一种高精度姿态传感器，具有断续拍摄空间目标的能力，可作为空间目标监视平台。将星敏感器断续观测的短弧准确关联是实现空间目标精确定轨的前提。通过对空间目标的大量观测数据统计发现，空间目标的赤纬随赤经的变化始终满足一条周期为360°的正弦曲线且峰值与轨道倾角有关。对新旧航迹的赤经赤纬变化规律进行研究，提出一种基于正弦拟合的空间目标短弧关联算法，避免了空间目标初定轨的步骤，节约了算法运行时间。仿真中观测时长最短为50s，通过对目标密集的GEO带增加额外约束，可区分倾角相差0.01°的轨道。当航迹段间隔3h时，3组噪声水平目标关联的准确率均达90%以上。     

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.     

星敏感器低频误差分析

介绍星敏感器的误差分类、低频误差定义、误差产生原因及其测试标定方法等.星敏感器输出姿态周期性误差的主要原因为视场空间误差和热弹性变形误差,典型星敏感器采取相应的解决措施后,低频误差可控制在0.8″以内.     

星敏感器姿态测量相对基准偏差在轨标校方法研究

摘要： 对航天器星敏感间姿态测量基准偏差在轨标校及性能评估问题进行研究.建立包含敏感器安装误差与测量误差的星敏感器模型,针对两种不同形式的安装误差模型,推导出相应的观测方程,基于卡尔曼滤波方法设计相对基准偏差估计器,并比较分析两种估计器实际应用特点.然后针对在轨实际应用,给出一种基于敏感器光轴夹角的标校性能评估方法,通过数学仿真验证星敏感器相对基准偏差的标校的有效性,并基于在轨数据的标校应用获取相对基准偏差在轨特性.     

新型复合多视场光学敏感器及其导航方法

基于利用四面镜结构实现的复合多视场光学敏感器,给出了一种高精度天文导航方法,即通过四面镜同时观测地球、导航星和折射星,利用卫星、地球、恒星之间的位置关系,实现自主导航。通过研究导航量测信息的获取途径,给出了复合多视场光学敏感器的5种实用工作方式。结合卡尔曼滤波算法,建立了自主天文导航的仿真模型,并对5种工作方式进行了仿真与比较。仿真结果表明:双组直接敏感地平与单组间接敏感地平结合的导航方式精度最高,位置精度达到了10 m量级。      

一种利用星敏感器的航天器自主定位方法

提出用星敏感器和地平仪测量星光与地平之间的“星光仰角”为观测量，用推广卡尔曼滤波方法来实时估计航天器的最佳位置的自主定位方法。分析比较了同时瞄准恒星的个数、星敏感器的精度以及改变采样周期对航天器定位误差的影响。     

Autonomous satellite navigation using starlight refraction angle measurements

An on-board autonomous navigation capability is required to reduce the operation costs and enhance the navigation performance of future satellites. Autonomous navigation by stellar refraction is a type of autonomous celestial navigation method that uses high-accuracy star sensors instead of Earth sensors to provide information regarding Earth’s horizon. In previous studies, the refraction apparent height has typically been used for such navigation. However, the apparent height cannot be measured directly by a star sensor and can only be calculated by the refraction angle and an atmospheric refraction model. Therefore, additional errors are introduced by the uncertainty and nonlinearity of atmospheric refraction models, which result in reduced navigation accuracy and reliability. A new navigation method based on the direct measurement of the refraction angle is proposed to solve this problem. Techniques for the determination of the refraction angle are introduced, and a measurement model for the refraction angle is established. The method is tested and validated by simulations. When the starlight refraction height ranges from 20 to 50 km, a positioning accuracy of better than 100 m can be achieved for a low-Earth-orbit (LEO) satellite using the refraction angle, while the positioning accuracy of the traditional method using the apparent height is worse than 500 m under the same conditions. Furthermore, an analysis of the factors that affect navigation accuracy, including the measurement accuracy of the refraction angle, the number of visible refracted stars per orbit and the installation azimuth of star sensor, is presented. This method is highly recommended for small satellites in particular, as no additional hardware besides two star sensors is required.     

基于资源一号02B卫星红外地球敏感器和星敏感器的自主导航

 本文阐述了利用星敏感器和红外地球敏感器进行自主导航的原理。以资源一号02B卫星的飞行数据为基础,进行了自主导航的研究,结果表明采用国产红外地球敏感器和星敏感器的资源一号02B卫星可以实现较高精度的自主导航,说明了该方案的可行性。     

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.     

航天器轨道机动过程中的自主导航方法

典型的航天器自主天文导航方法利用地球敏感器和星敏感器的观测信息,根据轨道动力学模型和测量信息,采用扩展卡尔曼滤波算法（EKF）估计航天器位置矢量。为了在航天器轨道机动过程中减小滤波器的估计误差,设计了用于航天器自主导航的自适应鲁棒扩展卡尔曼滤波（AREKF）算法。仿真结果表明,采用AREKF算法能够有效地减小推力不确定性的不利影响,在不增加导航敏感器的前提下改善系统的导航性能,取得优于传统EKF算法和自适应扩展卡尔曼滤波（AEKF）的估计精度。     

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.     

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.     

基于地标信息的星敏感器低频误差标定方法

针对星敏感器及其安装结构热变形等因素引起的星敏感器低频误差(LFE)影响卫星姿态确定精度的问题,提出了根据有效载荷提供的地标信息,采用最小二乘算法标定星敏感器低频误差的方法.考虑到卫星姿态确定系统是为有效载荷服务的,为了使卫星姿态确定系统输出的姿态信息与有效载荷相一致,从而准确反映有效载荷的指向变化情况,星敏感器低频误差的标定以有效载荷提供的地标信息为观测量进行.仿真结果表明,所提方法能够有效减弱星敏感器低频误差对卫星姿态确定精度的影响,从而提高卫星姿态确定精度.     

Design and performances of laser retro-reflector arrays for Beidou navigation satellites and SLR observations

Beidou is the regional satellite navigation system in China, consisting of three kinds of orbiting satellites, MEO, GEO and IGSO, with the orbital altitudes of 21500–36000 km. For improving the accuracy of satellites orbit determination, calibrating microwave measuring techniques and providing better navigation service, all Beidou satellites are equipped with laser retro-reflector arrays (LRAs) to implement high precision laser ranging. The paper presents the design of LRAs for Beidou navigation satellites and the method of inclined installation of LRAs for GEO satellites to increase the effective reflective areas for the regional ground stations. By using the SLR system, the observations for Beidou satellites demonstrated a precision of centimeters. The performances of these LRAs on Beidou satellites are very excellent.