Lunar gravity field determination using SELENE same-beam differential VLBI tracking data

A lunar gravity field model up to degree and order 100 in spherical harmonics, named SGM100i, has been determined from SELENE and historical tracking data, with an emphasis on using same-beam S-band differential VLBI data obtained in the SELENE mission between January 2008 and February 2009. Orbit consistency throughout the entire mission period of SELENE as determined from orbit overlaps for the two sub-satellites of SELENE involved in the VLBI tracking improved consistently from several hundreds of metres to several tens of metres by including differential VLBI data. Through orbits that are better determined, the gravity field model is also improved by including these data. Orbit determination performance for the new model shows improvements over earlier 100th degree and order models, especially for edge-on orbits over the deep far side. Lunar Prospector orbit determination shows an improvement of orbit consistency from 1-day predictions for 2-day arcs of 6 m in a total sense, with most improvement in the along and cross-track directions. Data fit for the types and satellites involved is also improved. Formal errors for the lower degrees are smaller, and the new model also shows increased correlations with topography over the far side. The estimated value for the lunar GM for this model equals 4902.80080±0.0009 km³/s² (10 sigma). The lunar degree 2 potential Love number k ₂ was also estimated, and has a value of 0.0255 ± 0.0016 (10 sigma as well).     

由SGM100i质量分析看SELENE的贡献

月球重力场是研究月球演化和深部构造的基本物理量,也是低轨月球卫星精密定轨的关键。SELENE以高-低卫星跟踪卫星模式历史上首次获得了月球背面重力场直接观测数据。与GLGM-3相比,增加了SELENE跟踪数据的SGM100i在各方面表现出较高的精度:其位系数误差阶方差在15～30阶减小超过10倍,最大达到66倍(15阶);位系数与地形的相关性系数在50～70阶高达0.9,而GLGM-3只有0.6～0.7;基于SGM100i计算的重力异常和月球大地水准面起伏也更好地揭示了月球背面与环形地形相关的重力场特征,从而验证了SELENE 4程Doppler数据对于月球重力场解算的贡献。     

BDS/GPS联合定轨的贡献分析

北斗卫星导航系统（BeiDou satellite navigation system,BDS）目前暂未具有全球导航定位能力,卫星轨道的全程跟踪与测站的几何结构还不完善,影响了卫星轨道的测定精度。针对上述问题,根据动力学定轨的原理与方法,推导了多个全球导航卫星系统（global navigation satellite system,GNSS）联合定轨对参数求解精度的解析贡献量,并利用实测数据分析了BDS/GPS联合定轨对轨道和钟差求解精度的统计贡献量。结果表明,联合定轨对系统间公共参数求解精度的贡献显著,除地球静止轨道（geostationary orbit,GEO）卫星外,其余轨道和钟差求解精度均有显著提高。BDS/GPS联合定轨对BDS卫星轨道、卫星钟差均方根误差（root mean square,RMS）以及接收机钟差RMS的统计贡献量分别为36.21%、26.88%和20.88%,其中对可视卫星数较少的区域接收机钟差求解精度的贡献尤为显著,贡献量为45.95%。     

星地跟踪网的导航卫星精密轨道确定及预报

针对区域跟踪网不能覆盖导航卫星全弧段从而导致卫星定轨精度低的问题,简述了导航卫星和低轨卫星联合定轨模型,然后利用星地跟踪网观测数据同时确定了低轨卫星和导航卫星精密轨道,并根据实验结果详细分析了低轨卫星在联合定轨中所起到的作用。计算结果表明,引入低轨卫星之后,全球网和区域网定轨精度分别平均提高了20.0%和44.3%,区域网6h和24h的轨道预报精度分别优于10cm、13cm,利用星地跟踪网观测数据联合定轨方案是一种提高定轨精度并削弱对地面站依赖性的有效方法。     

VLBI在GEO卫星精密定轨中的应用

影响GEO轨道确定精度的原因主要有两方面:一是高轨卫星的几何跟踪条件受到局部测轨网的限制;二是卫星相对于地面的动力学约束信息较弱。利用一个针对GEO卫星的简化动力法定轨的协方差分析模型,研究了联合测距跟踪网和甚长基线干涉测量(VLBI)对定轨精度的改善情况。指出测距系统的校正误差是常规测距跟踪网定轨精度的主要误差源;当附加一条东西向VLBI基线时,仅利用不定期的少量VLBI高精度数据就能够显著改善测距偏差对轨道的影响,从而保证了卫星的整体位置解算精度。     

Long-wavelength global gravity field models: GRIM4-S4, GRIM4-C4

Summary.  GFZ Potsdam and GRGS Toulouse/Grasse jointly developed a new pair of global models of the Earth's gravity field to satisfy the requirements of the recent and future geodetic and altimeter satellite missions. A precise gravity model is a prerequisite for precise satellite orbit restitution, tracking station positioning and altimeter data reduction. According to different applications envisaged, the new model exists in two parallel versions: the first one being derived exclusively from satellite tracking data acquired on 34 satellites, the second one further incorporating satellite altimeter data over the oceans and terrestrial gravity data. The most recent “satellite-only” gravity model is labelled GRIM4-S4 and the “combined” gravity model GRIM4-C4. The models are solutions in spherical harmonics and have a resolution up to degree and order 60 plus a few resonance terms in the case of GRIM4-S4, and up to degree/order 72 in the case of GRIM4-C4, corresponding to a spatial resolution of 555 km at the Earth's surface. The gravitational coefficients were estimated in a rigorous least squares adjustment simultaneously with ocean tidal terms and tracking station position parameters, so that each gravity model is associated with a consistent ocean tide model and a terrestrial reference frame built up by over 300 optical, laser and Doppler tracking stations. Comprehensive quality tests with external data and models, and test arc computations over a wide range of satellites have demonstrated the state-of-the-art capabilities of both solutions in long-wavelength geoid representation and in precise orbit computation. Received 1 February 1996; Accepted 17 July 1996     

TJS-2 geostationary satellite orbit determination using onboard GPS measurements

This study analyzes the quality of onboard data of tracking signals from GPS satellites on the far side of the earth and determines the orbit of the geostationary satellite using code and carrier phase observations with 30-h and 3-day orbit arc length. According to the analysis results, the onboard receiver can track 6–8 GPS satellites, and the minimum and maximum carrier to noise spectral densities were 24 and 45 dB-Hz, respectively. For a GPS receiver on a high-altitude platform above the navigation constellations, the blocking of the earth and a weak signal strength usually cause a piece-wise GPS signal tracking and an increase in the number of ambiguity parameters. Individual GPS satellites may be continuously tracked for as little as several minutes and as long as 3 h. Moreover, considering the negative sign of elevation angles reflects the fact that GPS satellites are tracked below the receiver in the study. GPS satellites appear mainly in the elevation angle range of ??53° to ??83°, and dilution of precision values could reach ten or one hundred and more. Also, it is observed that when a signal suffers from atmospheric refraction, other GPS signals tracked simultaneously by the receiver experience strong systematic errors in the code observations. Based on single-frequency code and carrier phase measurements, the mean 3D root mean square (RMS) value of the overlap comparisons between 30-h orbit determination arcs is 2.14 m. However, we found that there were also some biases in the carrier phase residuals, which contributed to poor orbit accuracy. To eliminate the effects of the biases, we established a correction sequence for each GPS satellite. After corrections, the mean 3D RMS was reduced to 0.99 m, representing a 53% improvement.     

USB-VLBI综合确定SMART-1环月探测器轨道

我国绕月探测工程中"嫦娥一号"(CE-1)卫星将综合使用统一S波段系统(USB)和甚长基线干涉仪(VLBI)完成测定轨任务。为了检验USB-VLBI综合测定轨精度,测控系统于2006年5月利用欧空局(ESA)的SMART-1环月探测器进行了USB-VLBI综合测定轨试验。本文对这次试验的测轨数据进行了分析,研究了不同观测弧长和不同类型观测数据组合情况下的定轨和预报精度,得出了一些结论。     

Improving BeiDou precise orbit determination using observations of onboard MEO satellite receivers

In recent years, the precise orbit determination (POD) of the regional Chinese BeiDou Navigation Satellite System (BDS) has been a hot spot because of its special constellation consisting of five geostationary earth orbit (GEO) satellites and five inclined geosynchronous satellite orbit (IGSO) satellites besides four medium earth orbit (MEO) satellites since the end of 2012. GEO and IGSO satellites play an important role in regional BDS applications. However, this brings a great challenge to the POD, especially for the GEO satellites due to their geostationary orbiting. Though a number of studies have been carried out to improve the POD performance of GEO satellites, the result is still much worse than that of IGSO and MEO, particularly in the along-track direction. The major reason is that the geostationary characteristic of a GEO satellite results in a bad geometry with respect to the ground tracking network. In order to improve the tracking geometry of the GEO satellites, a possible strategy is to mount global navigation satellite system (GNSS) receivers on MEO satellites to collect the signals from GEO/IGSO GNSS satellites so as that these observations can be used to improve GEO/IGSO POD. We extended our POD software package to simulate all the related observations and to assimilate the MEO-onboard GNSS observations in orbit determination. Based on GPS and BDS constellations, simulated studies are undertaken for various tracking scenarios. The impact of the onboard GNSS observations is investigated carefully and presented in detail. The results show that MEO-onboard observations can significantly improve the orbit precision of GEO satellites from metres to decimetres, especially in the along-track direction. The POD results of IGSO satellites also benefit from the MEO-onboard data and the precision can be improved by more than 50% in 3D direction.     

Precise orbit determination of BeiDou constellation: method comparison

Chinese BeiDou navigation satellite system is in official service as a regional constellation with five geostationary earth orbit (GEO) satellites, five inclined geosynchronous satellite orbit (IGSO) satellites and four medium earth orbit (MEO) satellites. There are mainly two methods for precise orbit determination of the BeiDou constellation found in the current literatures. One is the independent single-system method, where only BeiDou observations are used without help from other GNSS systems. The other is the two-step GPS-assisted method where in the first step, GPS data are used to resolve some common parameters, such as station coordinates, receiver clocks and zenith tropospheric delay parameters, which are then introduced as known quantities in BeiDou processing in the second step. We conduct a thorough performance comparison between the two methods. Observations from the BeiDou experimental tracking stations and the IGS Multi-GNSS Experiment network from January 1 to March 31, 2013, are processed with the Positioning and Navigation Data Analyst (PANDA) software. The results show that for BeiDou IGSO and MEO satellites, the two-step GPS-assisted method outperforms the independent single-system method in both internal orbit overlap precision and external satellite laser ranging validation. For BeiDou GEO satellites, the two methods show close performances. Zenith tropospheric delays estimated from the first method are very close to those estimated from GPS precise point positioning in the second method, with differences of several millimeters. Satellite clock estimates from the two methods show similar performances when assessing the stability of the BeiDou on board clocks.     

VLBI在探月卫星定位中的应用分析

中国实施的"嫦娥"探月工程中,探月卫星的定轨测控系统由我国现有的S频段航天测控网(USB)和甚长基线干涉测量(VLBI)系统组成。系统中,VLBI技术主要为绕月卫星定轨提供卫星的角位置。本文分析了在探月项目中,VLBI单点定位的必要性。探讨了VLBI技术用于探月卫星单点定位的基本原理及其实现方法。通过算例对模拟数据进行处理,检验了方法的正确性。对结果进行分析,得出一些结论。     

CEI对静止轨道共位卫星的轨道确定

主要考察了CEI对静止轨道共位卫星的轨道确定能力。仿真结果表明,利用CEI对共位卫星进行定轨时,需采用基线阵列。对于110°E共位卫星采用三亚-昆明基线阵列、10 km基线和2 d的数据,可使绝对轨道精度达百米级;外推至14 d时,相对轨道精度保持在m级。同样,要使绝对和相对轨道精度达到相同的量级,对于80°E共位卫星,需选用昆明-三亚基线阵列、100 km基线和1 d的观测弧段;对于140°E共位卫星,需选用上海-三亚基线阵列5、0 km基线和2 d的观测弧段。     

Precise orbit determination of the Fengyun-3C satellite using onboard GPS and BDS observations

The GNSS Occultation Sounder instrument onboard the Chinese meteorological satellite Fengyun-3C (FY-3C) tracks both GPS and BDS signals for orbit determination. One month’s worth of the onboard dual-frequency GPS and BDS data during March 2015 from the FY-3C satellite is analyzed in this study. The onboard BDS and GPS measurement quality is evaluated in terms of data quantity as well as code multipath error. Severe multipath errors for BDS code ranges are observed especially for high elevations for BDS medium earth orbit satellites (MEOs). The code multipath errors are estimated as piecewise linear model in \(2{^{\circ }}\times 2{^{\circ }}\) grid and applied in precise orbit determination (POD) calculations. POD of FY-3C is firstly performed with GPS data, which shows orbit consistency of approximate 2.7 cm in 3D RMS (root mean square) by overlap comparisons; the estimated orbits are then used as reference orbits for evaluating the orbit precision of GPS and BDS combined POD as well as BDS-based POD. It is indicated that inclusion of BDS geosynchronous orbit satellites (GEOs) could degrade POD precision seriously. The precisions of orbit estimates by combined POD and BDS-based POD are 3.4 and 30.1 cm in 3D RMS when GEOs are involved, respectively. However, if BDS GEOs are excluded, the combined POD can reach similar precision with respect to GPS POD, showing orbit differences about 0.8 cm, while the orbit precision of BDS-based POD can be improved to 8.4 cm. These results indicate that the POD performance with onboard BDS data alone can reach precision better than 10 cm with only five BDS inclined geosynchronous satellite orbit satellites and three MEOs. As the GNOS receiver can only track six BDS satellites for orbit positioning at its maximum channel, it can be expected that the performance of POD with onboard BDS data can be further improved if more observations are generated without such restrictions.     

单中继星单低轨卫星的联合定轨精度分析

针对由单中继星和单低轨卫星组成的联合定轨系统,给出了系统内不同轨道卫星摄动项的选取方案和卫星间的可见性判别模型。在模拟出含有白噪声的四程测距观测数据文件的基础上,研究了测距精度和采样弧段对联合定轨中高、低轨卫星定轨精度的影响。得出如下结论:联合定轨更有利于对低轨卫星的轨道改进;同样的采样时间条件下,测距噪声越小定轨精度越高,并且采样时间越短它的影响越明显;同样的测距噪声条件下,所用资料的采样时间越长精度越高,但当测距精度很高时,TDRS达到最好定轨精度所需的采样时间相应有所缩短。并在定出轨道后进行了轨道预报,分析了轨道预报的趋势及精度。     

火星探测器精密定轨软件研制及实测数据处理

研发了一套具有自主知识产权的火星探测器精密定轨及动力学参数解算软件系统,介绍了软件的设计思路与基本结构。对2009年8月中国甚长基线干涉测量网跟踪的火星快车号三程多谱勒数据和相同弧段欧洲空间局的双程多谱勒数据进行了处理。结果表明,对于三程多谱勒数据,精密定轨后的残差处于0.079 mm/s的水平,轨道与比利时皇家天文台发布的火星快车精密轨道（精度20~25 m）最大差距小于100 m;对于欧洲空间局双程多谱勒数据,精密定轨后的残差处于0.067 mm/s的水平,轨道与精密轨道最大差距小于10 m。对火星快车跟踪数据的处理结果表明该软件可靠。     

Orbit determination of the Lunar Reconnaissance Orbiter

We present the results on precision orbit determination from the radio science investigation of the Lunar Reconnaissance Orbiter (LRO) spacecraft. We describe the data, modeling and methods used to achieve position knowledge several times better than the required 50–100 m (in total position), over the period from 13 July 2009 to 31 January 2011. In addition to the near-continuous radiometric tracking data, we include altimetric data from the Lunar Orbiter Laser Altimeter (LOLA) in the form of crossover measurements, and show that they strongly improve the accuracy of the orbit reconstruction (total position overlap differences decrease from ~70 m to ~23 m). To refine the spacecraft trajectory further, we develop a lunar gravity field by combining the newly acquired LRO data with the historical data. The reprocessing of the spacecraft trajectory with that model shows significantly increased accuracy (~20 m with only the radiometric data, and ~14 m with the addition of the altimetric crossovers). LOLA topographic maps and calibration data from the Lunar Reconnaissance Orbiter Camera were used to supplement the results of the overlap analysis and demonstrate the trajectory accuracy.     

Initial results of centralized autonomous orbit determination of the new-generation BDS satellites with inter-satellite link measurements

Autonomous orbit determination is the ability of navigation satellites to estimate the orbit parameters on-board using inter-satellite link (ISL) measurements. This study mainly focuses on data processing of the ISL measurements as a new measurement type and its application on the centralized autonomous orbit determination of the new-generation Beidou navigation satellite system satellites for the first time. The ISL measurements are dual one-way measurements that follow a time division multiple access (TDMA) structure. The ranging error of the ISL measurements is less than 0.25 ns. This paper proposes a derivation approach to the satellite clock offsets and the geometric distances from TDMA dual one-way measurements without a loss of accuracy. The derived clock offsets are used for time synchronization, and the derived geometry distances are used for autonomous orbit determination. The clock offsets from the ISL measurements are consistent with the L-band two-way satellite, and time–frequency transfer clock measurements and the detrended residuals vary within 0.5 ns. The centralized autonomous orbit determination is conducted in a batch mode on a ground-capable server for the feasibility study. Constant hardware delays are present in the geometric distances and become the largest source of error in the autonomous orbit determination. Therefore, the hardware delays are estimated simultaneously with the satellite orbits. To avoid uncertainties in the constellation orientation, a ground anchor station that “observes” the satellites with on-board ISL payloads is introduced into the orbit determination. The root-mean-square values of orbit determination residuals are within 10.0 cm, and the standard deviation of the estimated ISL hardware delays is within 0.2 ns. The accuracy of the autonomous orbits is evaluated by analysis of overlap comparison and the satellite laser ranging (SLR) residuals and is compared with the accuracy of the L-band orbits. The results indicate that the radial overlap differences between the autonomous orbits are less than 15.0 cm for the inclined geosynchronous orbit (IGSO) satellites and less than 10.0 cm for the MEO satellites. The SLR residuals are approximately 15.0 cm for the IGSO satellites and approximately 10.0 cm for the MEO satellites, representing an improvement over the L-band orbits.     

GNSS卫星精密定轨全球地面基准站网随机优化算法

为确保GNSS精密定轨精度和可靠性,需要顾及站点稳定性和观测质量等信息,在全球范围内均匀选取一定数目的地面基准站。在探讨测站数量和分布对导航卫星精密定轨影响的基础上,针对GNSS定轨地面跟踪站在全球分布不均匀的现状,综合考虑站点几何分布、站点稳定性和观测质量信息,提出基于格网控制概率下的全球测站随机优选方法。该方法综合利用格网方法和随机优化方法,通过全球测站分配一定的概率,进而随机抽样和筛选得到全球均匀分布的测站构型。实验结果显示,该方法在全球范围内选取30个测站时,GPS精密定轨的精度能达到2.15 cm,60个测站时,定轨精度优于1.26 cm;90个测站时,定轨精度可提高到1 cm以内。     

USB-VLBI综合快速确定环月飞行器短弧轨道

2006-05-29~2006-06-02,有关单位利用欧空局(ESA)的SMART-1环月飞行器进行了USB-VLBI综合测定轨试验,其中一个重要目标就是考察环月飞行器的短弧快速轨道确定能力。这里对综合测轨数据的精度进行了评估,分析了不同类型测轨数据组合和定轨弧长对短弧定轨和预报的影响。利用5 d测量数据进行统计:VLBI时延的RMS约为1 m,时延率的RMS约为0.25 cm/s,USB测速的RMS约为3~6 cm/s,测距的RMS约为1~3 m。30 min定轨及预报一个环月轨道周期(5 h)位置的RMS约为250 m,速度的RMS约为15 cm/s。     

基于星载GPS的CHAMP卫星精密简动力定轨

定轨是地球探测卫星任务顺利执行的关键。星载GPS技术提供了大量、连续的高低卫星跟踪观测,为低轨卫星精密定轨提供了技术支撑。为了确定CHAMP卫星的轨道,并分析定轨精度,利用CHAMP卫星星载GPS数据,运用零差简动力法进行精密定轨,给出了精密定轨流程。利用实际数据进行了精密定轨实验,结果与德国地学研究中心（GFZ）公布的CHAMP卫星快速轨道（RSO）进行了对比,结果显示：求解轨道可以达到厘米量级。