北斗系统测站钟差短期预报模型比较及其在单星定轨中的应用

北斗卫星导航系统(BDS)地面跟踪站都配置有高精度的氢原子钟,并基于精密定轨数据处理与主站的时间基准进行同步.在卫星轨道机动以及机动恢复期间,通常采用几何法定轨以及单星定轨确定卫星的轨道.而在这两种定轨模式中,需要提供精确的测站钟差作为输入.为提高定轨的实时性,需要对测站钟差进行预报处理.分析了2次多项式模型、附加周期项模型、灰色模型3种模型对北斗地面跟踪站钟差短期拟合和预报的性能,并将钟差预报结果应用于单星定轨,同时还分析了不同预报钟差用于定轨的精度.试验发现,以上3种模型对6个测站钟差的平均拟合精度分别为0.14 ns、0.05 ns、0.27 ns,预报1 h的平均精度分别为1.17 ns、0.88 ns、1.28 ns,预报2 h的平均精度分别为2.72 ns、2.09 ns、2.53 ns.采用3种模型对测站钟差进行预报并用于单星定轨,采用附加周期项的钟差预报模型轨道3维误差最小,不同模型轨道径向精度差异在3 cm以内.以上结果表明,附加周期项的站钟拟合及预报模型在北斗系统机动期间的轨道恢复数据处理具有最好的效果.     

双行根数编目体系轨道误差研究

大量空间目标的真实轨道无法精确知道,目前只能通过跟踪观测的数据进行定轨来得到估计轨道,而估计的轨道就会有误差.双行根数(TLE)是广泛使用的一种特殊编目轨道根数,其配套的轨道模型为Simplified General Perturbations 4(SGP4)/Simplified Deep-space Perturbations 4(SDP4)模型.编目轨道的精度主要依赖于相应的观测模型和动力学模型,这些模型一般都不会非常准确,往往会有误差,有些误差可能直接导致编目定轨结果在局部为有偏估计.通过理论研究和仿真模拟,分析了动力学模型中地球非球形引力位田谐摄动项对编目轨道精度的影响,发现TLE编目轨道中存在随时间周期变化的系统差,该系统误差甚至可以达到千米量级.几何构型较好的测站分布在一定程度上可以削弱编目定轨中产生的系统误差,由于力学模型的限制,无法彻底消除.     

星载氢钟VLBI观测实验及分析

中国计划于2025年左右建立月球轨道VLBI (Very Long Baseline Interferometer)测站,将会搭载被动型星载氢钟作为时间频率标准.由于是首次在VLBI观测中使用星载氢钟,需要研究和验证其可行性.因此,利用星载氢钟作为频率基准开展了VLBI观测.实验时,分别使用主动型地面氢钟和被动型星载氢钟作为频率基准,利用上海天文台佘山25 m射电望远镜和其他测站对我国火星探测器天问一号进行了交替VLBI观测.数据处理分析结果表明,基于地面氢钟与星载氢钟的VLBI残余群时延标准差均在0.5 ns以内,表明星载氢钟可满足深空探测VLBI测定轨的精度要求,验证了其作为月球VLBI测站频率基准的可行性.     

BDS/GPS接收机系统间偏差稳定性分析

接收机系统间偏差(Inter-System Bias,ISB)稳定性分析对于了解ISB误差特性和建模预报具有重要意义.为了分析ISB的长期稳定性,选择MGEX(Multiple Global Navigation Satellite System Experiment)网2014—2016年每年各1周的数据,分别采用武汉大学和德国地学研究中心提供的精密钟差和轨道产品,利用BDS(Bei Dou Navigation Satellite System)/GPS(Global Positioning System)组合精密单点定位(Precise Point Positioning,PPP)计算测站的ISB值,并对ISB的日稳定性和周稳定性进行了深入分析.实验结果表明:ISB的日变化比较稳定,日标准差平均值约为0.5 ns.不同年份数据的ISB周平均值和周标准差的差异较大,并且ISB周平均值与测站的接收机类型有关.采用不同精密产品计算得到的ISB之间存在系统性偏差,对于同一周不同测站的ISB周平均值,该系统性偏差一致性较好.     

同波束VLBI双差分电离层电子总量抖动天顶方向统计特性研究

深空探测器和射电源的信号通过地球大气和电离层时相位发生抖动,对地面观测系统如VLBI(Very Long Baseline Interferometry)的测量精度产生极大影响.基于日本SELENE工程的两颗小卫星Rstar和Vstar 4测站长达1 yr的同波束VLBI观测数据,考虑视线方向不同仰角的影响并利用投影函数进行归一化处理,首次得到天顶方向的双差分电离层电子总量抖动统计数据.利用结构函数分析研究了6条基线的双差分电离层电子总量抖动的统计特性,并反演得到4个测站的统计特性.首次解算出天顶方向双差分电离层电子总量抖动的均方根与角距离的关系模型.6条基线天顶方向的双差分电离层电子总量抖动的均方根σ(单位为TECU)和角距离θ(单位为?)的关系模型为:σ=0.50928θ+0.39534,由基线反演出4个测站天顶方向的关系模型为:σ=0.36595θ+0.27974.     

北斗卫星导航系统服务精度评估

精度是北斗卫星导航系统(Beidou Navigation Satellite System,BDS)服务指标体系的重要内容.给出了北斗卫星导航系统精度指标的含义及精度指标的评估方法,利用实测数据分析了北斗系统实际实现的精度指标,并将其与GPS系统实际实现的精度指标作比较分析.DOP(几何精度因子)值由卫星导航系统空间星座分布决定,是影响用户定位授时精度的重要因素,比较了北斗与GPS在中国区域DOP值分布的差异.GPS系统PDOP(定位几何精度因子)分布均匀,随用户经度和纬度变化不大,在1.0–2.0之间.而受混合星座影响,北斗系统PDOP分布随着测站经度和纬度变化较大,变化范围为1.5–5.0;且随测站纬度增加而变大,由中心经度(东经118?)向两侧不断变大.对于影响用户等效距离误差的空间信号精度进行了比较分析.利用IGS(国际GNSS服务组织)提供的事后精密轨道、激光跟踪数据和北斗双向时频传递测量的卫星钟差评估了北斗基本导航电文的精度.结果表明:北斗IGSO(倾斜地球同步轨道)卫星和MEO(中轨道)卫星轨道径向误差约为0.5 m,大于GPS卫星轨道小于0.2 m的径向误差.北斗GEO(地球同步轨道)卫星激光残差约为65 cm,IGSO卫星和MEO卫星激光残差约为50 cm.受卫星钟差数据龄期影响,MEO卫星钟差参数误差明显大于IGSO卫星和GEO卫星,约为0.80 m.最后,采用MGEX(多GNSS系统试验项目)多模接收机进行了定位试验,分析了北斗系统和GPS在定位精度上的差异.结果表明:受星座构型影响,北斗卫星导航系统定位精度与GPS系统定位精度相比有所差异,但满足水平定位精度优于10 m、高程定位精度优于10 m的设计要求,双系统组合定位精度好于单一系统定位精度.     

地月系L_2点中继星激光测距成功率的估算

为了模拟位于地月系L2点的中继星"鹊桥"与月球的位置关系,进而估算中继星激光测距的成功率,按照轨道周期约为14天的要求对中继星所在的晕轨道进行计算,建立了一个综合考虑望远镜抖动、大气抖动和预报轨道横向偏离的模型。从数值上给出了一条轨道周期为14. 78天,X方向(地月连线方向)振幅为12 493 km,Y方向为34 596 km,Z方向(垂直于地月轨道平面方向)为11 916 km的周期轨道。由于晕轨道的最小振幅远大于月球遮挡的临界振幅4 000 km,因此月球对中继星不存在遮挡问题。基于建立的测距成功率模型,根据昆明站(国际编号:7820)的激光测距系统对运行在该轨道上的中继星进行测距成功率分析,结果表明:测距成功率随着中继星横向轨道标准差的增大呈快速降低的趋势。对于中继星到测站的平均距离而言,当中继星没有横向偏离时,探测器产生的光电子数为0. 151,成功率为14. 07%;横向偏离2 km时,光电子数降为0. 035,成功率降为3. 46%。对比最近距离与最远距离的情况,无横向偏离的情况下,探测器产生的光电子数从0. 174降为0. 139,成功率从16. 01%降为13. 02%。该计算结果可为云南天文台1. 2 m望远镜实现中继星激光测距提供参考。     

GNSS精密轨道产品不连续性分析及评估

按照目前的国际规范, 高精度GNSS (Global Navigation Satellite System)轨道产品一般以天为周期进行发布, 提供给用户使用. 连续使用多天的产品存在不同天间的跳变问题. 利用德国地学研究中心(GFZ)、欧洲定轨中心(COD)、欧空局(ESA)、美国喷气试验室(JPL)以及上海天文台(SHA)共5个GNSS分析中心2013---2017年的轨道产品, 分析了轨道跳变的特性. 计算结果表明: GFZ、COD、ESA、SHA和JPL的3维轨道跳变平均分别为7.79cm、1.51cm、7.77cm、11.75cm和2.51cm. 轨道跳变序列的周期特性分析表明: 序列存在90d、120d、340d左右的显著周期项, 对应于海潮对地球自转的影响, 其振幅为数毫米至1cm左右. 表明精密轨道确定需要进一步精化该项模型; GPS的跳变序列还存在与卫星星座相关的175d和352d左右的交点年显著周期项. 此外, 针对COD产品外推轨道的分析, 验证了地球反照辐射压和太阳光压模型等动力学模型对轨道的差异.     

微分多普勒单站定位

本文给出了地固坐标系中含二阶项(包括相对论效应项)的卫星多普勒测速实用公式,导出以测站坐标三分量、频偏、卫星位置沿径向、切向和轨道面法向计七个未知量的观测方程。利用JSZ—4型接收机的48圈观测资料,按线性最小方差估计式逐圈进行单站定位计算,所得站坐标的均方差为8.44米,与测站坐标在DX—1坐标系中的值相比较的误差为±6.93米。     

北斗三号卫星精密定轨中的光压模型研究

对于在轨运行的BDS (BeiDou Navigation Satellite System)卫星, 太阳光压是作用在卫星上主要的非引力摄动. 受多种因素的影响, 太阳光压摄动力难以精确建模, 是BDS卫星精密定轨和轨道预报过程中重要的误差来源. 由于ECOMC (Empirical CODE Orbit Model 1 and 2 Combined)模型兼顾了ECOM1 (Empirical CODE Orbit Model 1)和ECOM2 (Empirical CODE Orbit Model 2)模型的特点, 在模型中引入了较多的待估参数, 使得参数之间存在强相关性. 针对ECOMC模型的这一缺陷, 文中收集了2019年1月至2022年4月武汉大学分析中心提供的BDS-3卫星精密星历, 采用动力学轨道拟合方法得到了ECOMC模型的13个光压参数. 通过对该模型的光压参数进行时间序列分析, 分别给出了BDS-3 IGSO (Inclined Geosynchronous Orbit)和MEO (Medium Earth Orbit)卫星光压模型的参数选择策略. 并利用轨道拟合和轨道预报试验, 验证了光压模型参数选择策略的合理性. 结果表明, 采用改进型ECOMC模型进行BDS-3 IGSO和MEO卫星轨道拟合的效果最佳, 同时, 也能够提升BDS-3 IGSO和MEO卫星中长期轨道预报的精度.     

星载GPS相位观测值非差运动学定轨探讨

在几何法、动力学法和减缩动力学法定轨基础上，探讨了星载GPS相位观测值非差运动学定轨方法及其实现程序。该方法无需复杂的力学模型和地面资料，只需LEO(Low Earth Orbit)卫星上的GPS数据和IGS的GPS精密星历产品，它计算简单、方便，能快速、高精度地确定轨道，同时，还能确定一些动力学参数，但没有轨道预报功能；针对法方程系数矩阵比较庞大，提出了矩阵分块、上三角化的参数解算方法，并用CHAMP卫星资料分析了上述方法的定轨精度。     

Dynamics of Saturn's magnetodisk near Titan's orbit: Comparison of Cassini magnetometer observations from real and virtual Titan flybys

We analyze the variability of the ambient magnetospheric field along Titan's orbit at 20.3 Saturn radii. However, while our preceding study (Simon et al., 2010) focused on Cassini magnetometer observations from the 62 Titan flybys (TA-T62) between October 2004 and October 2009, the present work discusses magnetic field data that were collected near Titan's orbit when the moon was far away. In analogy to the observations during TA-T62, the magnetospheric fields detected during these 79 “virtual” Titan flybys are strongly affected by the presence of Saturn's bowl-shaped and highly dynamic magnetodisk current sheet. We therefore provide a systematic classification of the magnetic field observations as magnetodisk current sheet or lobe-type scenarios. Among the 141 (62 real+79 virtual) crossings of Titan's orbit between July 2004 and December 2009, only 17 encounters (9 real+8 virtual) took place within quiet, magnetodisk lobe-type fields. During another 50 encounters (21 real+29 virtual), rapid transitions between current sheet and lobe fields were observed around the moon's orbital plane. Most of the encounters (54=22 real+32 virtual) occurred when Titan's orbit was embedded in highly distorted current sheet fields, thereby invalidating the frequently applied idealized picture of Titan interacting with a homogeneous and stationary magnetospheric background field. The locations of real and virtual Titan flybys are correlated to each other. Each of the 62 real Titan flybys possesses at least one virtual counterpart that occurred shortly before or after the real encounter and at nearly the same orbital position. A systematic comparison between Cassini magnetometer observations from the real Titan flybys and their virtual companions suggests that there is no clear evidence of Titan exerting a significant level of control on the vertical oscillatory motion of the magnetodisk near its orbit.     

Collisional spreading of Enceladus’ neutral cloud

We describe a direct simulation Monte Carlo (DSMC) model of Enceladus’ neutral cloud and compare its results to observations of OH and O orbiting Saturn. The OH and O are observed far from Enceladus (at 3.95 R_S), as far out as 25 R_S for O. Previous DSMC models attributed this breadth primarily to ion/neutral scattering (including charge exchange) and molecular dissociation. However, the newly reported O observations and a reinterpretation of the OH observations (Melin, H., Shemansky, D.E., Liu, X. [2009] Planet. Space Sci., 57, 1743-1753, PS&S) showed that the cloud is broader than previously thought. We conclude that the addition of neutral/neutral scattering (Farmer, A.J. [2009] Icarus, 202, 280-286), which was underestimated by previous models, brings the model results in line with the new observations. Neutral/neutral collisions primarily happen in the densest part of the cloud, near Enceladus’ orbit, but contribute to the spreading by pumping up orbital eccentricity. Based on the cloud model presented here Enceladus maybe the ultimate source of oxygen for the upper atmospheres of Titan and Saturn. We also predict that large quantities of OH, O and H₂O bombard Saturn’s icy satellites.     

Possible Alternatives to the Supermassive Black Hole at the Galactic Center

Now there are two basic observational techniques to investigate a gravitational potential at the Galactic Center, namely, (a) monitoring the orbits of bright stars near the Galactic Center to reconstruct a gravitational potential; (b) measuring the size and shape of shadows around black hole giving an alternative possibility to evaluate black hole parameters in mm-band with VLBI-technique. At the moment, one can use a small relativistic correction approach for stellar orbit analysis (however, in the future the approximation will not be precise enough due to enormous progress of observational facilities) while for smallest structure analysis in VLBI observations one really needs a strong gravitational field approximation. We discuss results of observations, their conventional interpretations, tensions between observations and models and possible hints for a new physics from the observational data and tensions between observations and interpretations. We discuss an opportunity to use a Schwarzschild metric for data interpretation or we have to use more exotic models such as Reissner–Nordstrom or Schwarzschild–de-Sitter metrics for better fits.     

TV Observation of the Daytime Meteor Shower; The Arietids

We have carried out multi-station TV observations since 1994 in order to determine the orbit of the Arietid daytime meteor stream. In 1999, one possible Arietid meteor was recorded by our simultaneous observations and its orbit was determined. In 2003, two Arietid meteors were observed from two stations of our observing site, those orbits were determined precisely, the orbital elements were in good agreement with each other. This is the first time that determination of the precise orbit of the Arietids has been made from optical observations. The orbit of these Arietid meteors, and comparison with the orbit obtained from radar observations are discussed.     

The Millennium Galaxy Catalogue: bulge–disc decomposition of 10 095 nearby galaxies

We present near-infrared (NIR) adaptive optics-assisted spectroscopic observations of the  CO (Δμ= 2)  absorption bands towards the centre of the giant elliptical galaxy NGC 1399. The observations were made with NAOS-CONICA (on the European Southern Observatory's Very Large Telescope) and have a full width at half-maximum resolution of 0.15 arcsec (14 pc). Kinematic analysis of the observations reveals a decoupled core and strongly non-Gaussian line-of-sight velocity profiles in the central 0.2 arcsec (19 pc). NIR imaging also indicates an asymmetric elongation of the central isophotes in the same region.
We use spherical orbit-superposition models to interpret the kinematics, using a set of orthogonal 'eigen-velocity profiles' that allow us to fit models directly to spectra. The models require a central black hole of mass  1.2^+0.5_−0.6× 10⁹ M_⊙  , with a strongly tangentially biased orbit distribution in the inner 40 pc.     

两行根数辅助的SLR单站定轨

单站测距资料定轨的困难限制了漫反射SLR(Satellite Laser Ranging)测距资料的应用.为此,提出利用两行根数模拟多站SLR测距资料作为辅助,实现单站SLR测距资料定轨的方法.该方法对卫星Ajisai单站SLR测距资料定轨并生成5 d预报轨道,误差小于40 m,实现利用单站测距资料的轨道改进,验证了方法的可行性.     

Topocentric orbit determination: Algorithms for the next generation surveys

The process of calculating a good orbit from astrometric observations of the same object involves three main steps: preliminary orbit determination, least squares orbit fitting, and quality control assessing the orbit's uncertainty and reliability. For the next generation sky surveys, with much larger number density of observations, new algorithms, or at least substantial revisions of the classical ones, are needed. The classical theory of preliminary orbit algorithms was incomplete in that the consequences of the topocentric correction had not been fully studied. We show that it is possible to rigorously account for topocentric observations and that this correction may increase the number of alternate preliminary orbits without impairing the overall performance. We have developed modified least squares algorithms including the capability of fitting the orbit to a reduced number of parameters. The restricted fitting techniques can be used to improve the reliability of the orbit computing procedure when the observed arcs have small curvature. False identification (where observations of different objects are incorrectly linked together) can be discarded with a quality control on the residuals and a ‘normalization’ procedure removing duplications and contradictions. We have tested our algorithms on two simulations based on the expected performance of Pan-STARRS—one of the next generation all-sky surveys. The results confirm that large sets of discoveries can be handled very efficiently resulting in good quality orbits. In these tests we lost only 0.6 to 1.3% of the possible objects, with a false identification rate in the range 0.02 to 0.06%.     

Orbit determination of space debris: admissible regions

The main problem in the orbit determination of the space debris population orbiting our planet is identifying which separate sets of data belong to the same physical object. The observations of a given object during a passage above an observing station are collectively called a Too Short Arc (TSA): data from a TSA cannot allow for a complete determination of an orbit. Therefore, we have to solve first the identification problem, finding two or more TSAs belonging to the same physical object and an orbit fitting all the observations. This problem is well known for the determination of orbits of asteroids: we shall show how to apply the methods developed for preliminary orbit determination of heliocentric objects to geocentric objects. We shall focus on the definition of an admissible region for space debris, both in the case of optical observations and radar observations; then we shall outline a strategy to perform a full orbit determination.     

Innovative methods of correlation and orbit determination for space debris

We propose two algorithms to provide a full preliminary orbit of an Earth-orbiting object with a number of observations lower than the classical methods, such as those by Laplace and Gauss. The first one is the Virtual debris algorithm, based upon the admissible region, that is the set of the unknown quantities corresponding to possible orbits for a given observation for objects in Earth orbit (as opposed to both interplanetary orbits and ballistic ones). A similar method has already been successfully used in recent years for the asteroidal case. The second algorithm uses the integrals of the geocentric 2-body motion, which must have the same values at the times of the different observations for a common orbit to exist. We also discuss how to account for the perturbations of the 2-body motion, e.g., the J ₂ effect.