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.     

区域导航卫星精密定轨研究

区域卫星导航系统采用混合星座设计,GEO(地球同步轨道)卫星是系统的重要组成部分,其精密定轨技术也是导航系统的关键技术之一。GEO卫星的高轨特性致使地面跟踪基线长度有限,定轨几何条件不佳;其静地特性致使卫星轨道与钟差存在强相关特性,对于基于伪距的GEO卫星定轨模式,需要星地与站间时间同步技术的支持。因此,如何利用区域卫星导航系统的多种测量技术实现多模式、多层次的导航卫星精密定轨,是一项值得深入研究的课题。     

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.     

基于iGMAS的北斗三号组网星数据初步分析

北斗卫星导航系统目前已经完成北斗卫星导航试验验证系统和北斗区域卫星导航系统,正在建设北斗全球卫星导航系统,简称北斗三号系统.截至2018年11月,北斗三号系统已经发射19颗组网星.为了了解新发射组网星的信号、数据质量和目前能达到的定轨精度,基于2018年5月18日至28日22个国际GNSS (Global Navigation Satellite System)监测评估系统(iGMAS)跟踪站的数据,从观测噪声和伪距多路径两方面分析比较了最早发射的8颗北斗三号组网星新旧信号的数据质量,分别用旧信号B1I、B3I和新信号B1C、B2a对北斗三号组网星和GPS进行联合定轨实验.实验结果表明,新信号B2a的数据质量与旧信号相当, B1C的数据质量略差于老信号;比较3 d解重叠弧段(48 h)轨道和钟差结果,新旧信号的结果相当, B1I/B3I和B1C/B2a定轨的3维位置精度(3D-RMS)都在35 cm左右,钟差结果基本在0.5 ns以内.     

北斗卫星导航系统SISURE初步评估

北斗导航系统自2018年12月27日提供全球服务以来,其服务性能受到了极大关注.以上海天文台iGMAS (International GNSS MonitoringAssessment System)分析中心发布的精密轨道、钟差产品作为基准,评估了2019年年积日3–12 d的北斗二号、北斗三号以及GPS广播星历的轨道、钟差和空间信号用户测距误差(Signal in Space User Ranging Error, SISURE,简称为URE),并且对北斗卫星导航系统结果进行了详细的分析.结果表明:在评估时间段内,北斗三号广播星历轨道精度、URE均明显优于北斗二号,且部分结果优于GPS.北斗三号广播星历轨道径向精度最高,优于0.2 m.北斗三号全部卫星URE均值优于0.4 m, URE RMS (root mean square)优于0.5 m.北斗二号每颗卫星URE均值、95%URE (置信度为95%的URE)、URE RMS小于2 m,北斗三号每颗卫星URE均值、95%URE、URE RMS小于1 m,均达到了系统公开承诺的服务性能标准.     

用非差分方法确定单颗导航卫星的轨道

在导航系统中有时需要对单颗导航卫星进行定轨.此时由于无法组成常用的同历元单差或双差以消除卫星钟差或接收机钟差,有必要发展新的定轨策略和精度分析.该文以GPS为例,讨论在不依赖于星站间时间同步的情况下,对单颗导航卫星进行精密定轨.首先分析了GPS卫星钟差以及GPS接收机钟差的特性,发现在一定间隔内钟差主要表现为线性变化,而在去除这一线性项后,非线性钟差在3 m以内.利用GPS的伪距对单颗卫星定轨,在将钟差的主要部分作为测距的偏差和偏差变化率后,伪距测量量等价于常见的测距测量量.在利用等价的测距测量量定轨时可同时解算出偏差和偏差变化率参数.为验证该方案的可行性及其定轨精度,利用实测GPS观测数据进行了试验.结果表明,此种定轨方案定轨的径向精度优于4 m.考虑到GPS接收机的频率信号是由普通的晶振产生的,如果地面接收机采用原子钟提供的频率标准,其钟差的非线性部分将更小.模拟计算表明,采用本方案可以期望得到更高的定轨精度.     

利用Bernese5.0软件实现LEO卫星精密定轨

越来越多的LEO卫星装载了高精度的星载GPS接收机,星载GPS定轨已成为LEO卫星精密定轨的重要手段之一。星载GPS精密定轨精度依赖于GPS星历及钟差精度,采用CODE(Center for Orbit Determination in Europe)官方网站提供的GPS精密星历及钟差数据,基于瑞士伯尼尔大学开发的Bernese 5.0软件,采用非差减缩动力学定轨方法,解算了60天的CHAMP卫星和SAC-C卫星轨道,并将所得轨道与JPL和GFZ事后科学轨道比较,得出的轨道位置三维精度优于20 cm量级,速度三维精度约为0.20 mm/s。     

北斗三号试验卫星的钟差评估及预报

目前,在轨的5颗新一代北斗卫星(北斗三号)可同时向用户播发北斗二号信号与新的卫星信号,而且北斗三号搭载了高精度的铷钟或被动氢钟.因北斗三号的星钟作为卫星导航、定位和授时服务的主要载荷组成部分,为分析北斗三号卫星钟的时频性能,采用北斗数据处理与分析中心估计的卫星钟差产品评估北斗三号卫星钟的频率稳定度、漂移率和准确度.同时,考虑到北斗三号卫星钟精度较差且存在频繁的相位跳变以及数据中断等问题,筛选出了一种最优的钟差预报模型,即对频率数据进行建模并采用抗差估计的方法进行参数估计.实验结果显示北斗三号钟差预报精度相对传统预报模型提升1.6%–61.9%.     

GPS星历对LEO星载GPS精密定轨精度的影响

目前,越来越多的低轨卫星上都搭载了用于精密定轨的星载GPs接收机,星载GPS已成为低轨卫星精密定轨的主要手段之一.星载GPS精密定轨精度依赖于GPS星历及钟差精度.基于SHORDE-Ⅲ非差动力学定轨功能,以2005年8月1日至8月7日一周的GRACE卫星实测数据为例,采用事后精密轨道(igs)、快速轨道(igr)和超快速轨道(igu)三种GPS星历在同等条件下定轨,估计GPS星历精度对低轨卫星定轨精度的影响,实际计算结果表明igs和igr两类GPS星历定轨精度相当,约为9.5 cm,igu星历定轨精度略低于igs和igr星历,约为10.5cm:高频GPS卫星钟差数据对定轨精度会产生1-6cm影响.     

北斗亚欧全视时间比对试验

基于卫星导航双频时间传递型接收机的伪码观测量,利用国际全球卫星导航系统服务组织(International Global Navigation Satellite System (GNSS) Service, IGS)提供的高精度卫星轨道和钟差产品,实现了北斗全视法时间比对.以IGS提供的时间尺度为两个待比对站的公共参考时间,首先使用双频组合法消除电离层对伪距观测的影响,然后将对流层和地球自转效应带来的时延利用理论模型在伪码观测量中进行扣除,分别获得两个比对站时间与公共参考时间之差后,将2者再做差,便得到了北斗全视时间比对结果.以中国科学院国家授时中心(NTSC)、德国物理技术研究院(PTB)和西班牙海军天文台(ROA)所保持的国家标准时间作为比对对象,开展了长基线北斗全视时间比对试验,获得北斗全视时间传递结果,最后利用阿伦方差和时间方差两项关键性能指标以及卫星双向时间比对对其进行性能评估.结果表明:北斗全视时间比对的天稳为10-14量级,可以满足国际时间比对需求.     

Status of Satellite Orbit Determination and Time Synchronization Technology for Global Navigation Satellite System

In the form of satellite ephemerides and clock parameters, the information of space datum and system time of one global navigation satellite system (GNSS) is transferred to users. With continuously updating of satellite payload such as high precision atomic clocks, monitoring and tracking techniques such as inter-satellite links, and data processing techniques, the accuracy and real-time performance of satellite ephemerides and clock products are steadily improved. Starting from December 27th, 2018, BeiDou Navigation System 3, or BDS-3 has been providing accurate and reliable basic positioning, navigation, and timing (PNT) services to users in the countries within the “one belt and one road”. This paper summarizes the challenges of precise orbit determination and time synchronization faced and specific solutions sought from the regional BDS-2 system to BDS-3 global system at the control segment. It is interesting to compare BDS with other GNSS systems in terms of technical characteristics. Finally, aiming at higher accuracy and more reliable PNT services, a road map of precise orbit determination and time synchronization technique for next generation navigation systems is discussed, which will lead to better and better global navigation satellite systems.     

Status of Satellite Orbit Determination and Time Synchronization Technology for Global Navigation Satellite Systems

In the form of satellite ephemerides and clock parameters, the space datum and system time information of one global navigation satellite system (GNSS) is transferred to users. With the continuous updating in the satellite payload such as the high-precision atomic clock, the monitoring and tracking technique such as the inter-satellite link, and in the data processing technique, the accuracy and real-time performance of the satellite ephemeris and clock error products are steadily improved. Starting from December 27th, 2018, the BeiDou Navigation System 3, or BDS-3, has provided the accurate and reliable basic positioning, navigation, and timing (PNT) service for the users in the countries within the “one belt and one road”. This paper has summarized the faced challenges of the precise orbit determination and time synchronization from the regional BDS-2 system to the BDS-3 global system, and the specific solutions at the control segment. In addition, this paper has compared the BDS with other GNSS systems in terms of technical characteristics. Finally, aiming at a higher accuracy and more reliable PNT service, the road map of precise orbit determination and time synchronization technique for the next generation navigation systems is discussed, which will provide a reference for developing the global navigation satellite systems with an even higher accuracy.     

The Effect of GPS Ephemeris on the Accuracy of Precise Orbit Determination of LEO Satellite-borne GPS

The satellite-borne GPS receivers dedicated to precise orbit determination are now being carried by more and more low earth orbit (LEO) satellites and the satellite-borne GPS has become one of the main means for the precise orbit determination of low earth orbit satellites. The accuracy of satellite-borne GPS precise orbit determination depends on the accuracies of the GPS ephemeris and the clock error. Based on the orbit determination function of SHORDEIII zero-difference dynamics and using the observational data obtained by the GRACE satellites for the week from 2005 August 1 to 7 as an example, three versions of GPS ephemerides (igs, igr and igu) are used to carry out orbit determination under the same conditions and to estimate the effect of the GPS ephemeris accuracy on the accuracy of orbit determination of low earth orbit satellites. Our calculated results show that the two ephemerides, igs and igr, are equivalent to each other in orbit determination accuracy (about 9.5 cm), while igu is slightly less accurate, at about 10.5 cm. The effect produced by the data of the high frequency GPS satellite clock error on the accuracy of orbit determination is 1–6 cm.     

Long-term Clock Bias Prediction Based on An ARMA Model

The long-term and reliable prediction of satellite clock bias (SCB) is an important prerequisite for realizing the satellite autonomous navigation and orbit determination. Considering the shortcomings of the quadratic polynomial model (PM) and gray system model (GM) in the long-term prediction of SCB, a new prediction method of SCB based on an ARMA (Auto-Regressive Moving Average) model is proposed to represent the variation characteristics of SCB more accurately. In this paper, a careful precision analysis of the 90-day SCB prediction is made to verify the feasibility and validity of this proposed method by using the IGS (International GNSS Service) clock data. According to the variation characteristics of each satellite clock, the pattern recognition, modeling and prediction of SCB are conducted, and the detailed comparison is made with the other three models at the same time. The results show that adopting the ARMA model can effectively improve the accuracy of long-term SCB prediction.     

Future Satellite Gravimetry for Geodesy

After GRACE and GOCE there will still be need and room for improvement of the knowledge (1) of the static gravity field at spatial scales between 40 km and 100 km, and (2) of the time varying gravity field at scales smaller than 500 km. This is shown based on the analysis of spectral signal power of various gravity field components and on the comparison with current knowledge and expected performance of GRACE and GOCE. Both, accuracy and resolution can be improved by future dedicated gravity satellite missions. For applications in geodesy, the spectral omission error due to the limited spatial resolution of a gravity satellite mission is a limiting factor. The recommended strategy is to extend as far as possible the spatial resolution of future missions, and to improve at the same time the modelling of the very small scale components using terrestrial gravity information and topographic models.We discuss the geodetic needs in improved gravity models in the areas of precise height systems, GNSS levelling, inertial navigation and precise orbit determination. Today global height systems with a 1 cm accuracy are required for sea level and ocean circulation studies. This can be achieved by a future satellite mission with higher spatial resolution in combination with improved local and regional gravity field modelling. A similar strategy could improve the very economic method of determination of physical heights by GNSS levelling from the decimeter to the centimeter level. In inertial vehicle navigation, in particular in sub-marine, aircraft and missile guidance, any improvement of global gravity field models would help to improve reliability and the radius of operation.     

BDS-3新频点信号双频精密单点定位精度分析

北斗卫星导航系统(BeiDou navigation satellite System, BDS)已于2020年7月正式建成并开通, 北斗三号(BDS-3)在旧信号B1I和B3I的基础上, 增加了B1C、B2a新信号. 为了全面评估BDS-3的新信号B1C、B2a的定位性能, 试验了GPS (Global Positioning System)、BDS-3、BDS-2/BDS-3新旧信号的定位性能和BDS系统不同频点与GPS组合定位性能, 对BDS (B1I+B3I、B1C/B2a)+GPS (L1+L2)组合静态PPP (Precise Point Positioning)定位性能进行分析, 并与单卫星系统对比分析. 试验结果表明: BDS-3 (B1C/B2a)在East (E)、\lk North (N)、Up (U)方向的定位精度优于1.25cm、0.89cm、1.67cm, BDS-3新旧频点在E、N方向上定位精度与GPS L1/L2在同一水平上, U方向上新频点定位精度高于GPS L1/L2和BDS-3旧频点, 较旧频点定位精度提升了34.2%, 新频点收敛时间25.9min比旧频点提升了12.7%; 相较于BDS、GPS单系统, 组合系统BDS/GPS定位精度和收敛时间有了明显的提高, BDS-3 (B1C/B2a)+GPS在E、N方向上与BDS-3 (B1I/B3I)+GPS定位精度相当, 在U方向上定位精度前者较后者有了明显的提升, 提升了17.2%, 组合系统新频点收敛时间20.1min比旧频点提升了17.6%.     

The Model of Radio Two-way Time Comparison between Satellite and Station and Experimental Analysis

Time synchronization between satellite and station is the key technique of satellite navigation system and the foundation of realization of satellite navigation and positioning. Aiming at solving the problems of time synchronization, we have discussed a new method of radio two-way time comparison between satellite and station, deduced in detail the reduction model of up- and down-link pseudo ranges between satellite and station, and provided a practical calculation model of clock error between satellite and station. By calculating the differences between up- and down-link pseudo ranges, this method has eliminated the influences of common errors, such as the tropospheric delay, satellite ephemeris errors, ground station coordinates errors and so on. The ionospheric delay relevant to signal frequency is also weakened largely, thus this improves the accuracy of time comparison greatly. Finally, experimental analysis is conducted by using observational data, and the results show that the accuracy of radio two-way time comparison between satellite and station can attain about 0.34 ns, which validates the correctness of theoretical method and model.     

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.     

两种观测技术综合精密定轨的探讨

利用T／P卫星的SLR和DORIS实测资料,对两种观测技术综合精密定轨中的加权及其对定轨影响的问题作了初步的探讨。根据所提出的一种经验性的加权方法进行了综合定轨计算,结果表明：对于两种不同技术的观测,相对权选取的恰当与否将影响综合定轨的精度;综合定轨的最优加权不仅依赖于观测资料的精度,还与观测资料的多少和几何分布有关;通过选用最优加权,可使得综合轨的精度优于仅用其中一种技术的定轨精度,综合定轨能有效地提高定轨精度。