Improvement of orbit determination for geostationary satellites with VLBI tracking

China’s COMPASS satellite navigation system consists of five or more geostationary (GEO) satellites.The roles of GEO satellites are to improve the regional user’s positioning accuracy and provide the continuous Radio Determination Satellite Service.The motion of GEO satellites relative to a ground tracking station is almost fixed,and regular orbit maneuvers are necessary to maintain the satellites’ allocated positions above the equator.These features present difficulties in precise orbit determination (POD).C-band ranging via onboard transponders and the L-band pseudo-ranging technique have been used in the COMPASS system.This paper introduces VLBI tracking,which has been successfully employed in the Chinese lunar exploration programs Chang’E-1 and Chang’E-2,to the POD of GEO satellites.In contrast to ranging,which measures distances between a GEO satellite and an observer,VLBI is an angular measurement technique that constrains the satellite’s position errors perpendicular to the satellite-to-observer direction.As a demonstration,the Chinese VLBI Network organized a tracking and orbit-determination experiment for a GEO navigation satellite lasting 24 h.This paper uses the VLBI delay and delay-rate data,in combination with C-band ranging data,to determine the GEO satellite’s orbit.The accuracies of the VLBI delay and delay rate data are about 3.6 ns and 0.4 ps/s,respectively.Data analysis shows that the VLBI data are able to calibrate systematic errors of the C-band ranging data,and the combination of the two observations improves orbit prediction accuracy with short-arc data,which is important for orbital recovery after maneuvers of GEO satellites.With the implementation of VLBI2010,it is possible for VLBI to be applied in the COMPASS satellite navigation system.     

Precise orbit determination of Haiyang-2 using satellite laser ranging

With the successful launch and official commissioning of China’s first dynamic ocean environment satellite Haiyang-2(HY-2),China’s capabilities for oceanic environment monitoring and oceanic resource detecting have been further improved and enhanced.Precise tracking and orbit determination are not only key technical concerns in the ocean dynamic environment satellite project but also necessary conditions for carrying out related oceanic science research using observational data obtained using spaceborne instruments including radar altimeter.In this study,the current available status of international satellite laser ranging(SLR) monitoring on HY-2 was introduced.Six-months of SLR data from HY-2 were processed to obtain precise satellite orbit information using the dynamic orbit determination method.We carried out a detailed assessment of the SLR orbit accuracy by internal evaluation,comparisons with the orbit derived by the French Doppler orbitography and radio-positioning integrated by satellite(DORIS) system,and station-satellite distance validation.These assessments indicate that the three-dimensional orbital accuracy of HY-2 is about 12.5 cm,and the radial accuracy is better than 3 cm.It provides a good example of the application of international SLR monitoring and precise orbit determination in China’s earth observation satellite project.     

基于着陆器地基测量的火星定向参数确定

火星定向参数的精确测定对约束火星内部结构以及极区干冰变化的建模具有重要意义.基于未来的火星着陆任务,仿真分析了利用双程多普勒与距离测量方法直接跟踪着陆器,解算火星定向参数所能达到的精度.结果表明,通过双程多普勒和双程测距直接跟踪火星着陆器超过200个工作日,将显著提高火星岁差、章动以及日长变化参数的精度,约800个工作日后,岁差参数精度可较目前提高5–10倍,章动参数精度可达到10–30 mas,日长变化与钱德勒摆动参数精度可收敛至5–10 mas,这一精度水平可以满足研究火星内部结构与大气物质交换的需要.通过分析不同纬度着陆器的解算结果,发现高纬度的着陆器有必要进行距离测量,以保持岁差和章动参数的解算精度.此外,研究还发现,当火星星历误差小于75 m时,双程多普勒数据解算火星定向参数的精度不受影响,而对于双程测距数据来说,只有当火星历表精度优于0.15 m时,定向参数的解算结果才具有可信性.     

Precision ERS-2 orbit determination combining multiple tracking techniques

Both of the oceanographic research by using altimetry and the application of InSAR of ERS-2 satellite need the precise ephemerides of the satellite. In this note, the ERS-2 orbit is precisely determined by using SLR and PRARE observations to take advantage of the high accuracy of SLR and the widespread data coverage of PRARE. Based on the software system SODS-VCE established by us, the ERS-2 orbits in 1997 are calculated. The evaluation from tracking data fits, endpoint consistency of orbital arcs and comparison with independent orbit implies an orbit accuracy of 5–6 cm in radial component which can satisfy the requirement of being better than 10 cm in oceanographic research by altimetry, being less than 20 cm in cross-track component which can meet the requirement of InSAR. In orbit computation, the method of variance component estimation is employed to weight the SLR, PRARE range and Doppler measurements properly. The results indicate that the application of the method can improve the computation accuracy efficiently.     

Orbit determination of Chang’E-3 and positioning of the lander and the rover

Chang’E-3 landed on the east of Sinus Iridum area on December 14, 2013, performing China’s first successful soft landing on the lunar surface. We present the results on precision orbit determination and positioning of the lander and the rover. We describe the data, modeling, and methods used to achieve position knowledge over the period December 2–21, 2014. In addition to the radiometric X-band range and Doppler tracking data, delta differential one-way ranging data are also used in the calculation, which show that they strongly improve the accuracy of the orbit reconstruction. Total position overlap differences are about 20 and 30 m for the 100 km × 100 km and 100 km× 15 km lunar orbit, respectively, increased by ~50 % with respect to CE-2 and at the same level as other lunar spacecrafts of recent era such as SELENE and lunar reconnaissance orbiter (LRO). The position error of the soft landing trajectory is less than 100 m. A kinematic statistical method is applied to determine the position of the lander and relative position of the rover with respect to the lander. The position difference of the lander is better than 50 m compared to LRO photograph result. Compared with the delta very long baseline interferometry (VLBI) group delay between the lander and the rover, the delta VLBI phase delay can improve the relative position of the rover from ~1,000 to ~1 m.     

基于同波束VLBI差分相时延的“玉兔”月球车动作监视分析

2013年12月14日嫦娥三号成功在虹湾着陆区软着陆,后续开展两器分离、两器互拍等任务.本文利用同波束VLBI技术同时观测着陆器和月球车发射的信号,解算含整周模糊度的差分相时延(Differential Phase Delay),监视着陆器和月球车两器分离和两器互拍等过程的月球车各种动作.同时,研究和分析月球车行走、转弯、晃动、高程变化等动作导致的差分相时延变化,发现同波束VLBI差分相时延监视月球车动作的灵敏度在50–100 mm之间,后续利用差分相时延变化趋势进行相对定位.同波束VLBI技术在后续的探月三期、火星探测、金星探测等双目标、多目标探测中也将发挥重要作用.     

一点多星轨道计算精度研究

应用理论分析和计算机模拟相结合的方法,讨论了卫星动力学模型中多种误差因素对一点多星轨道计算精度的不同影响,给出了星间相对位置计算的主要误差因素及其限制要求．并在此基础上,对一点多星的轨道计算和跟踪测量方法,提出了一些可行的建议     

Precise positioning of the Chang’E-3 lunar lander using a kinematic statistical method

A kinematic statistical method is proposed to determine the position for Chang’E-3(CE-3) lunar lander.This method uses both ranging and VLBI measurements to the lander for a continuous arc,combing with precise knowledge about the motion of the moon as provided by planetary ephemeris,to estimate the lander’s position on the lunar surface with high accuracy.Accuracy analyses are carried out with simulation data using the software developed at Shanghai Astronomical Observatory in this study to show that measurement errors will dominate the position accuracy.Application of lunar digital elevation model(DEM) as constraints in the lander positioning is also analyzed.Simulations show that combing range/doppler and VLBI data,single epoch positioning accuracy is at several hundred meters level,but with ten minutes data accumulation positioning accuracy is able to be achieved with several meters.Analysis also shows that the information given by DEM can provide constraints in positioning,when DEM data reduce a 3-dimensional positioning problem to 2-dimensional.Considering the Sinus Iridum,CE-3 lander’s planned landing area,has been observed with dedicated details during the CE-1 and CE-2 missions,and its regional DEM model accuracy may be higher than global models,which will certainly support CE-3’s lander positioning.     

Determination of the controlled landing trajectory of Chang’E-1 satellite and the coordinate analysis of the landing point on the Moon

Based on the tracking observations of radio ranges and VLBI delays of Chang’E-1 (CE-1) satellite during the controlled landing on the Moon on March 1, 2009, the landing trajectory and the coordinates of the landing point are determined by positioning analysis. It is shown that the landing epoch (the emission epoch of the last signal) of CE-1 satellite on the Moon was at UTC8h13m6.51s. The lunar longitude, latitude and surface height of the landing point in the lunar primary axes frame are respectively 52.27...     

嫦娥一号绕月卫星对月球重力场模型的优化

月球重力场是揭示月球内部结构和物质组成的重要信息,探测月球重力场仍然是绕月探测任务中的重要科学目标之一．在已有月球重力场模型基础上,利用嫦娥一号探测数据,并结合“月女神”一号探测器、月球勘察者（LP）及早期月球探测器轨道跟踪数据,本文解算得到了高精度月球重力场模型CEGM02（100阶次）,在CEGM01月球重力场模型基础上对模型进行了优化．对新模型的分析结果表明,嫦娥一号卫星轨道跟踪数据的融入,使得对月球重力场长波长部分的解算精度有显著提高,相比于SGMl00h模型在5阶以内精度提高约2倍,在10阶以内有明显贡献,在20阶内都有贡献．初步判断这是由于嫦娥一号卫星轨道动量轮卸载的频度不足“月女神”的1／4,而同时轨道相对较高所导致．文中结合CEGM02和激光测月观测结果解算了月球平均转动惯量0．393446（±0．000006）,对月球内部构造研究提供了更强的约束．     

应用在线整定广义最小方差多项式权值的测头控制方法

在曲面工件的高精度、高效率自动扫描测量过程中,为了提高测头自动跟踪扫瞄控制的精度和平稳性,提出了基于在线整定多项式权值的广义最小方差(OSPW_GMV)控制方法.该方法的主要思想是根据在线估计的被控对象参数及OSPW_GMV的输出,在线调整多项式的权值,实现测头自动跟踪扫瞄的控制.实验结果证明,使用具有高跟踪精度和强鲁棒性的OSPW_GMV控制器,可使测头跟踪过程的误差小于0.1mm的跟踪要求,且每次运算时间与广义最小方差控制器相差不大,因此该控制方法在一些实时性及控制精度要求较高的精密检测场合,有较好的应用价值.     

基于TLE数据的空间目标EDR分类及观测需求计算

根据能量耗散率（EDR）的定义及空间目标的大气阻力摄动加速度公式,推导出一种由卫星两行根数（TLE）数据计算空间目标EDR的方法. 该方法无需计算空间目标弹道系数和大气模型,EDR计算误差可在1%以下,并且运算量极小. 此外,通过空间目标相对轨道的协方差矩阵描述空间目标的定轨精度,并结合扩展卡尔曼滤波方程,提出一种计算平面轨道下不同EDR空间目标的定轨精度-观测需求曲线的方法. 仿真验证了EDR计算方法的有效性,并给出了雷达对不同EDR分类的目标观测时对应的定轨精度-观测需求曲线. 结果表明当观测稀疏时,目标轨道预报误差正比于EDR,而观测较多时,会有观测饱和现象.      

基于多重近似重访周期的火星-太阳同步回归轨道设计

在分析火星-太阳同步回归轨道数学模型的基础上,设计了回归周期的近似重访周期算法.基于对回归要素取整处理,结合回归轨道重访特征函数,通过对重访间隔子间距数的判断,可以得到最优近似重访周期和次优近似重访周期,近似重访周期的设计能以更高的时间分辨率实现对地覆盖.进一步分析了最优回归周期族与火星赤道表面覆盖率的关系,并计算了其对应的轨道参数.为火星探测初期的轨道设计提供了借鉴.      

Satellite orbit determination combining C-band ranging and differenced ranges by transfer

The constraint in the transverse direction of satellite orbit with differenced ranges between master station and slave stations by transfer as an angular observation data is explained in theory. Differenced ranges in combination with C-band ranging by transfer were used in satellite orbit determination. The position error of overlapped orbit differences for combining is less than that for ranging only. The residual of predicted orbit forward 5.5 days for combining is 3.1762 m, while the residual for ranging only with the same duration is 3.5380 m. Both the orbital overlapping and orbit prediction experimentations can testify the constraint in the transverse direction of satellite orbit with differenced ranges, and the results show that the accuracy of orbit determination and orbit prediction is improved by combining differenced ranges and C-band ranging.     

Zero-difference and single-difference precise orbit determination for LEO using GPS

Various methods for precise orbit determination (POD) of low earth orbiters (LEO) are briefly intro-duced in this paper. Based on the software named SHORD-Ⅲ developed by our institute,sin-gle-difference (SD) and zero-difference (ZD) dynamic POD based on LEO carrying an on-board GPS receiver is mainly discussed. The approaches are tested using real GRACE data (November 5―25,2002) and independently validated with Satellite Laser Ranging (SLR) measurements over the same 21 days. Comparisons with the scientific orbits provided by GFZ indicate that the SD POD RMS accuracy can achieve 5,10 and 6 cm in radial,along and cross the track,and the ZD POD RMS accuracy can achieve 4,8 and 4 cm in radial,along and cross the track. SLR validation shows that SD POD accuracy is better than 8 cm in distance,and ZD POD accuracy is better than 6 cm.     

对日本测地卫星的观测和分析

本文介绍了日本发射的测地卫星及广州，上海对它的观测，用本文计算卫星轨道的方法，发现该卫星的轨道比原计划要低得多，而其他轨道根数正常，并对其原因作了探讨，本文认为，该卫星的交光方式可以提高卫生的瞬时亮度，但宜缩小卫星的直径，以减少大气和光压摄动以卫星质心改正，提高激光测距精度。     

Satellite orbit determination by transfer with differenced ranges

The original idea of orbit determination called "determination of satellite orbit by transfer" was proposed by the National Time Service Center,Chinese Academy of Sciences.It shows that the system is very stable and the orbit determination accuracy is improved greatly.A new observation mode called "differenced ranges between master station and slave stations by transfer" is introduced.It is the development of "determination of satellite orbit by transfer".In principle,the differenced ranges between master station and slave stations have a high angular resolution,and strongly constrains in the transverse direction of satellite orbit,perpendicular to the line-of-sight.The principle of "differenced ranges between master station and slave stations by transfer" is discussed in detail.And differenced ranges in combination with ranging data were used to determine satellite’s orbit and orbit prediction under different arc observations.It shows that orbit determination accuracy for orbit prediction can be improved with differenced ranges in combination with ranging data.     

Solar eclipses of Phobos and Deimos observed from the surface of Mars

The small martian satellites Phobos and Deimos orbit in synchronous rotation with inclinations of only 0.01 degrees and 0.92 degrees , respectively, relative to the planet's equatorial plane. Thus, an observer at near-equatorial latitudes on Mars could occasionally observe solar eclipses by these satellites (see ref. 1, for example). Because the apparent angular diameter of the satellites is much smaller than that of the Sun, however, such events are more appropriately referred to as transits. Transit data can be used for correcting and refining the orbital ephemerides of the moons. For example, Phobos is known to exhibit a secular acceleration that is caused by tidal dissipation within Mars. Long-term, accurate measurements are needed to refine the magnitude and origin of this dissipation within the martian interior as well as to refine the predicted orbital evolution of both satellites. Here we present observations of six transits of Phobos and Deimos across the solar disk from cameras on Mars aboard the Mars Exploration Rovers Spirit and Opportunity. These are the first direct imaging observations of satellites transiting the Sun from the surface of another planet.     

轨道根数对极轨气象卫星数据接收的影响

如果轨道根数不准确,由其计算出的地面数据接收站的天线程序控制跟踪数据就存在偏差,会导致天线不能准确跟踪过境卫星从而无法获取卫星数据.以风云三号数据接收为例,给出了轨道根数的计算方法,分析了由错误轨道根数导致的接收卫星数据失败的原因,从理论和实践上指出在极轨卫星数据接收中轨道根数的重要性.提出事先检验轨道根数,并纳入制定极轨卫星数据接收策略的必要性.     

基于电磁定位仪的超声图像中穿刺针实时跟踪软件开发

文中利用高精度电磁定位仪实时跟踪超声探头和穿刺针，开发用于穿刺导引的实时跟踪软件.文中使用NDI Aurora电磁定位仪实时获取穿刺针针尖的三维空间坐标，用PLUS toolkit从电磁定位仪和超声机采集数据，在完成时间以及空间校准（针尖校准、体模校准、探头校准）的基础上，得到从电磁定位坐标系到超声图像坐标系的转换矩阵，进而将由电磁定位器获得的针尖坐标转换到超声图像中，并标注出针尖的位置.为了衡量算法的精确度，文中用人工的方法在图像中选取针尖坐标，多次取样做平均，然后以该坐标作为衡量的标准.文中采集多组数据，计算由转换矩阵得到的针尖坐标与标准之间的均方误差.结果表明，该方法的均方误差MSE为2.456 mm，在可接受范围内.