The optimization of satellite orbit for Space-VLBI observation

By sending one or more telescopes into space,Space-VLBI(SVLBI)is able to achieve even higher angular resolution and is therefore the trend of the VLBI technique.For the SVLBI program,the design of satellite orbits plays an important role for the success of planned observation.In this paper,we present our orbit optimization scheme,so as to facilitate the design of satellite orbits for SVLBI observation.To achieve that,we characterize the uv coverage with a measure index and minimize it by finding out the corresponding orbit configuration.In this way,the design of satellite orbit is converted to an optimization problem.We can prove that,with an appropriate global minimization method,the best orbit configuration can be found within the reasonable time.Besides that,we demonstrate that this scheme can be used for the scheduling of SVLBI observations.     

Orbit determination of satellite “Tance 1” with VLBI data

The satellite “Tance 1” of the “Double-Star Program” is the first truly scientific experimentation satellite of China. Its orbit is the farthest so far launched in China, with a geocentric apogee reaching 78 thousand kilometers. The tracking of “Tance 1” and of more distant space targets, such as the lunar exploration craft, can be realized with the VLBI technique of radio astronomy. In order to test and verify the role which the VLBI technique plays in the lunar exploration program of China, Shanghai Astronomical Observatory organized the only 3 tracking stations in China (located at Shanghai, Urumqi and Kunming), to carry out test tracking of “Tance 1,” and used the time delay data obtained to determine the orbit of “Tance 1” over a two-day period, so providing a preliminary assessment of the possibility of VLBI orbit determination. The fitting error of the orbit so obtained is about 5.5 m in the time delay and about 2 cm/s in the delay rate (this for checking only), much better than is provided by the preliminary orbit (used merely for ensuring tracking) in which the corresponding figures are around 2 km and 15 cm/s. Further, if the orbit is determined by using both the time delay and time delay rate data (with weights according to their internal accuracies), then the residuals are 5.5 m in the time delay and 2 cm/s in the delay rate. For an appreciation of the true accuracy of the VLBI orbit determination, we used simulation data (of the observed two-day VLBI data) and found the results depended greatly on the error in the dynamic model of the satellite which, however, is difficult to assess, while the formal residuals are of the order of 1 kin in the delay and of cm/s in the delay rate. The simulation computation also indicates that a joint determination using both VLBI and USB data will have an improved accuracy.     

利用国内VLBI网跟踪大椭圆轨道卫星

2004年7月,昆明VLBI站经过改造,由上海、乌鲁木齐和昆明站组成的中国VLBI网(CVN)采用统一的MARK4格式编制器和CVN硬盘记录系统,对大椭圆轨道卫星“探测1号”的2圈轨道的共同可视弧段进行了跟踪观测．软件相关处理程序已成功地用于检测卫星遥测信号的干涉条纹和数据相关处理．采用基于条纹幅度的加权最小二乘条纹拟合方法,获得了卫星VLBI观测量及其精度估计,完成了卫星VLBI观测量的3基线闭合误差检验．应用河外射电源校准方法和多频点相位校正信号提取方法,进行了台站钟差和仪器延迟等系统误差改正．经系统差改正后的卫星VLBI观测量序列已用于“探测1号”卫星的轨道确定．     

A pre-launch low frequency VLBI survey for RadioAstron

Preliminary results from two low frequency Very Long Baseline Interferometry (VLBI) observations (EA009 and INTAS1) at 327 MHz are described. Sixty one sources were observed. Twenty five sources are recommended for further detailed investigation. Only two sources (3C345 and 3C309.1) could be mapped. These experiments are part of a long term pre-launch RadioAstron survey at 327 MHz that has two objectives: (i) to establish a suitable list of candidates for low frequency Space VLBI (SVLBI) observations and (ii) to study the limitations on SVLBI due to scattering effects in the interstellar and interplanetary medium.     

利用VLBI数据确定"探测一号"卫星的轨道

双星计划的“探测一号”是中国首颗真正严格意义上的科学实验卫星,其运行轨道为中国迄今所发射的卫星中距地球最远,远地点地心距达7．8万公里．采用射电天文的VLBI技术可以对“探测一号”以及更远的深空目标,如探月飞行器实现跟踪．为了验证VLBI技术在我国探月计划中的作用,上海天文台组织了国内目前仅有的上海、乌鲁木齐和昆明3个台站对“探测一号”进行试跟踪,利用对“探测一号”约两天的VLBI观测数据,确定“探测一号”卫星的轨道,对VLBI的定轨能力做初步的探讨．按照测控部门提供的初轨 (其精度仅保证跟踪)推算的轨道与VLBI时延的拟合误差平均约2 km,时延率的拟合误差平均约15 cm／s．而利用VLBI数据定轨后的拟合程度相对于初轨有了很大的改善,结果表明,单独利用VLBI时延定轨,时延的拟合精度约5．5 m,作为外部检核的VLBI时延率的拟合精度在2 cm／s左右．单独利用VLBI时延率定轨,时延率的拟合精度约为1．3 cm／s,作为外部检核的VLBI时延的拟合精度约为29 m．而若将时延和时延率数据联合定轨,采用其内符精度加权,VLBI时延和时延率的残差分别为5．5 m和 2 cm／s．为了合理地评估VLBI定轨的真实精度,利用模拟数据进行误差协方差分析,结果表明VLBI定轨精度受动力学模型误差的影响较大,由于"探测一号”卫星的动力学模型难以精确确定,所以利用两天弧段的VLBI数据确定“探测一号”卫星轨道的位置误差为km量级,而速度误差可达cm／s量级．模拟计算还表明, VLBI和USB数据联合定轨可以大大提高定轨精度．     

Model of VLBI observation within the relativistic framework

In this paper we derive the post-newtonian expressions for the VLBI time delay and gravitational delay in the barycentric coordinate system of the solar system. We discuss the effect of the various bodies and their range of action. From the transformation between the barycentric and the geocentric systems we then give the VLBI observational model in the geocentric system. Our final results are given by formula (16) for the gravitational delay and by formula (25) for the VLBI time delay.     

Probing the microarcsecond structure of the Circinus megamasers through diffractive interstellar scintillation

We have used the Long Baseline Array to observe the Circinus Galaxy H₂O megamasers on two epochs separated by 49 d. The masers were observed to be highly variable, consistent with previous studies. We observe rapid variations in the linewidth and central velocity of the maser's spectral profile. The characteristics of these spectral variations suggest that the masers have an anisotropic structure, with axial ratios ≲5, and display velocity gradients in their microarcsecond structure. We also find a strong anticorrelation between the linewidth and the modulation index of the maser features and a relationship between the modulation index and characteristic time-scale of the variations. These various phenomena can all be simply explained through a model where the rapid variations in the masers are produced by quenched diffractive scintillation in the presence of modest velocity gradients in the maser emission.
The very long baseline interferometry (VLBI) images are consistent with previous high-resolution observations and show maser emission arising both in a circumnuclear accretion disc, and in a low-velocity outflow. We find no systematic differences in the variability properties of the disc and outflow masers. The VLBI images reveal that there is considerable spectral blending in single-dish spectra of the Circinus megamasers.
In addition to the VLBI imaging we also used these observations to look for a time delay in the intensity variations observed at the different telescopes in the array, as expected for scintillation-induced variability. No time delay was detected, which allows us to place a lower limit on the velocity of the interstellar medium during these observations 22 km s⁻¹ for the second epoch. We conclude that any future attempts to measure a time delay in this source should utilize intercontinental baselines to increase the chances of success.     

基于天文开源软件的卫星干涉测量数据处理系统

VLBI (Very Long Baseline Interferometry)技术观测卫星需要对干涉测量数据进行相关和后处理,通过相关、时延校准、条纹搜索,最终得到卫星的基线几何时延.基于天文开源软件建立起一套卫星干涉测量数据处理系统.该系统可工作在实时和事后两种状态,实现相关、中性大气、电离层、钟模型以及仪器硬件的时延校准、条纹搜索、生成基线时延和时延率序列.使用该系统处理北斗GEO (Geosynchronous Earth Orbit)卫星的干涉测量试验数据,得到了精度在1–2 ns量级的卫星基线时延序列.     

同波束VLBI差分时延率研究

通过分析SELENE的两颗小卫星Rstar和Vstar的同波束VLBI数据,发现两卫星间差分时延率中由中性大气和电离层引起的长周期变化已被去除,且在小角距时,短周期变化也能绝大部分被去除。但角距离越大,去除部分越小。通过将2008年一年中8个台站组成的所有基线的相关相位拟合残差数据分别平滑积分30 s与60 s后,再通过5点直线拟合求得时延率,得出单卫星时延率随机误差分别约为0.32 ps/s RMS与0.20 ps/s RMS,而差分时延率随机误差分别为0.19 ps/s~0.32 ps/s RMS与0.09 ps/s~0.17 ps/s RMS。单卫星的时延率随机误差在秋季最大,春季最小,而差分时延率的随机误差在全年基本稳定。     

Simulation of precise orbit determination of lunar orbiters

Based on the ongoing Chinese lunar exploration mission, i.e. the “Chang'e 1” project, precise orbit determination of lunar orbiters is analyzed for the actual geographical distribution and observational accuracy of the Chinese united S-band (USB) observation and control network as well as the very long baseline interferometry (VLBI) tracking network. The observed data are first simulated, then solutions are found after including the effects of various error sources and finally compared. We use the space data analysis software package, GEODYN, developed at Goddard Space Flight Center, NASA, USA. The primary error source of the flight orbiting the moon is the lunar gravity field. Therefore, the (formal) error of JGL165P1, i.e. the model of the lunar gravity field with the highest accuracy at present, is first discussed. After simulating the data of ranging and velocity measurement as well as the VLBI data of the time delay and time delay rate, precise orbit determination is carried out when the error of the lunar gravity field is added in. When the orbit is determined, the method of reduced dynamics is adopted with the selection of appropriate empirical acceleration parameters to absorb the effect of errors in the lunar gravity field on the orbit determination. The results show that for lunar missions like the “Chang'e 1” project, that do not take the lunar gravity field as their main scientific objective, the method of reduced dynamics is a simple and effective means of improving the accuracy of the orbit determination of the lunar orbiters.     

太阳系天体地面VLBI观测的相对论时延模型

以太阳系质心参考系为基础，根据太阳系的质心参考系和非旋转地球质心参考系的坐标转换关系，推导了太阳系天体地面VLBI观测的相对论时间延迟模型，给出了一个通用的解析表达式．根据这一公式可以得到平劲松博士所采用的公式，以及当地心与源的距离无限大时，可得河外射电源VLBI观测的Zhu—Groten模型、Shapiro模型和IERS(92，96)推荐模型．所推导的公式严格解析且无误差，在实际应用中建议采用这一公式．同时详细地讨论了所推导公式的实用范围和各种舍掉项的量级估计，并详细给出了时间延迟理论模型的计算步骤．     

空间VLBI与天文地球动力学

介绍了空间VLBI的精密定轨及其在天文地球动力学应用研究中的最新进展．指出因为空间VLBI的时延和时延率观测量同时涉及到射电参考系、动力学参考系和地固参考系,所以特别适合于参考系的直接连接工作．对为评价参考系连接的精度而发展的协方差分析理论也作了介绍,还分析了将时延和时延率资料用于精密定轨时遇到的困难及其解决办法．     

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.     

The Experiment and Analysis on VLBI Observations of Space Passive Hydrogen Maser

China plans to establish a lunar orbital VLBI (Very Long Baseline Interferometer) station around 2025, which will carry a space passive hydrogen maser as the time and frequency reference. Since it is the first time to use a space passive hydrogen maser for VLBI observation, its feasibility needs to be studied and verified. Therefore, we carried out VLBI observations using the space passive hydrogen maser as the frequency reference. In the experiment, the active hydrogen atomic clock and space passive hydrogen maser were used as the frequency standard, and the alternate VLBI observations of China’s Mars probe TW1 (Tianwen 1) were carried out using the 25 m radio telescope at Sheshan, Shanghai, and other VLBI stations. The results of data processing and analysis show that the standard deviation of VLBI residual group delay based on both active hydrogen atomic clock and space passive hydrogen maser are within 0.5 ns, which indicates that the space passive hydrogen maser can meet the accuracy requirements of VLBI measurement for deep space exploration, and verify its feasibility as the frequency standard of lunar orbital VLBI stations.     

卡尔曼滤波在VLBI数据处理中的应用

本文探讨卡尔曼滤波技术用于VLBI天体测量和大地测量数据处理的原理和方法;并深入地对Herring等提出的软件系统（SOLVK）进行详细研究,提出一些具体的办法以便应用．然后用1993—1994年的VLBI观测资料,精确计算了几种天文学和地球动力学参数作为例证．     

以基线长度变化率为约束估算VLBI站的垂直形变率

基于NNR-NUVEL-1A地球板块运动模型和ITRF2000地球参考架的三维VLBI站速度矢量,采用实测的VLBI基线长度变化率作为约束,重新估计了部分国际VLBI站的局部或区域性地壳的垂直形变,并与国际地球参考架ITRFs解和VLBI全球解GLB2003,VTRF2003和VTRF2005的结果进行了比较。结果表明,欧亚板块的URUMQI站和太平洋板块的KWAJAL26站,南极OHIGGINS站的垂直形变率、ITRFs解和VLBI全球解存在6-15mm/a的差异,北美YUMA站可能有15-31mm/a 的垂直形变率,而美国西部太平洋板块的San Francisco(PRESIDIO)站的垂直形变率还有待进一步的研究。此外,SC-VLBA,CRIMEA和EFLSBERG站的垂直形变率、ITRFs解和VLBI全球解的差约为1-6mm/a。用不同方法得到的VLBI站的水平形变率解有较好的一致性。     

Tropospheric Delay from VLBI and GNSS Measurements

Using an updated version of the QUASAR software package developed at the Institute of Applied Astronomy of the Russian Academy of Sciences, we have processed the VLBI observations within the international CONT14 program (May 6–20, 2014), in which a global network of 17 stations was involved (a total of ~250 000 observations). The package update concerned the optimization of data structure and the refinement of stochastic models for the random variations in wet tropospheric delay and atomic clock difference. The main goal of this paper is to compare the VLBI determinations of the tropospheric delay with its independent determinations using global navigation satellite systems (GNSS). We show that both these determinations agree well between themselves only in the case of a global analysis of the VLBI observations, where the VLBI station coordinates are also refined, along with the tropospheric delay and the clock synchronization and Earth orientation parameters. If, alternatively, the station coordinates are insufficiently accurate and are not refined from VLBI observations, then it is appropriate not to determine the tropospheric delay from these observations, but to take it from the publicly accessible independent GNSS data. However, this requires that the VLBI and GNSS techniques operate simultaneously at a common observing site. We have established the shortcomings of the universally accepted method of stabilizing the global solution associated with the absence of a criterion for choosing reference stations and radio sources. Two ways of their elimination are proposed: (i) introducing a coordinated list of weight factors for the errors in the coordinates of such stations and sources into the stabilization algorithm and (ii) adopting a coordinated list of stations and sources the refinement of whose coordinates is not required at all for a certain time.     

Two-Component Structure of the Radio Source 0014+813 from VLBI Observations within the CONT14 Program

We consider a method of reconstructing the structure delay of extended radio sources without constructing their radio images. The residuals derived after the adjustment of geodetic VLBI observations are used for this purpose. We show that the simplest model of a radio source consisting of two point components can be represented by four parameters (the angular separation of the components, the mutual orientation relative to the poleward direction, the flux-density ratio, and the spectral index difference) that are determined for each baseline of a multi-baseline VLBI network. The efficiency of this approach is demonstrated by estimating the coordinates of the radio source 0014+813 observed during the two-week CONT14 program organized by the International VLBI Service (IVS) in May 2014. Large systematic deviations have been detected in the residuals of the observations for the radio source 0014+813. The averaged characteristics of the radio structure of 0014+813 at a frequency of 8.4 GHz can be calculated from these deviations. Our modeling using four parameters has confirmed that the source consists of two components at an angular separation of ~0.5 mas in the north–south direction. Using the structure delay when adjusting the CONT14 observations leads to a correction of the average declination estimate for the radio source 0014+813 by 0.070 mas.     

环月飞行器精密定轨的模拟仿真

以中国正在实施的探月计划“嫦娥1号”工程为背景，分析了在中国联合S波段(USB)测控网和甚长基线射电干涉(VLBI)跟踪网的现有空间分布、观测精度水平下的环月飞行器精密定轨．采用的方法是模拟仿真计算，即首先模拟观测数据，然后在计入各误差源的影响后进行求解，并对解算结果进行比较．模拟仿真的工具是美国宇航局哥达德飞行中心的空间数据分析软件系统GEODYN．环月飞行的主要误差源是月球重力场，为此首先讨论了目前精度最高的月球重力场模型JGL165P1的(形式)误差．在模拟了测距、测速以及VLBI的时延、时延率数据后，计入月球重力场的误差进行精密轨道确定．定轨时采用了减缩动力学(reduced dynamic)方法，即选用合适的经验加速度参数吸收重力场误差对定轨的影响．结果表明对于一个不将月球重力场作为主要科学目标的探月计划(如“嫦娥1号”)，减缩动力学方法是一个简单、有效地提高环月飞行器定轨精度的方法．     

月球交会对接VLBI差分时延研究

中国探月3期任务中,月球交会对接技术是任务成功的重要保障.利用嫦娥3号(CE03)绕月飞行的VLBI (Very Long Baseline Interferometry)时延数据,模拟仿真绕月交会对接过程中,同波束VLBI观测模式下,差分群时延的变化情况.仿真结果显示,在远程导引段,轨道器和上升组合体轨道距离保持100 km,持续半小时,差分群时延很好地反映了两者的轨道信息,可以用于定轨定位;自主控制段,上升组合体靠近轨道器,在轨道距离从5 km减小到20 m过程中,上升组合体加速追赶轨道器时,差分群时延快速趋近于0,上升组合体减速远离轨道器时,差分群时延绝对值快速变大.最后,利用嫦娥3号奔月段同时发射两个DOR (Differential One-Ranging)信号的VLBI时延数据,计算差分相时延,初步展示了月球交会对接过程中同波束VLBI差分相时延的误差情况.