附有周期项的预报模型及其在GPS卫星钟差预报中的应用研究

为了有效进行GPS卫星钟差预报和更好地反映卫星钟差特性,除了考虑卫星原子钟频移、频漂和频漂率等物理性质外,还应考虑到卫星钟差的周期性变化特点.在二次多项式模型基础上,增加了周期项因素,构造了新的预报模型.选取部分GPS卫星铯钟(Cs.clock)和铷钟(Rb.clock)钟差资料,根据钟差变化趋势分3种情况,按不同时间长度进行钟差预报分析,并与二次多项式模型的预报结果比较分析,大量数据分析表明:附有周期项的二次多项式模型预报精度优于二次多项式模型,铷钟预报精度略优于铯钟.     

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.     

Prediction of Clock Errors of Atomic Clocks Based on Modified Linear Combination Model†

The prediction of the clock errors of atomic clocks plays an important role in the work on time and frequency. Each of the prediction models often used at present has its own merits and shortages. A combination of the predicted results obtained by means of these models can be used to synthesize the characteristics of various kinds of prediction models. In the light of the problem which occurs when the linear combination model is used to make the prediction of clock errors, the concept of learning weight is proposed and the modified combination prediction model is made by taking advantage of various kinds of pieces of accuracy information. For verifying the efficiency of this method the clock error sequences of the IGS (International GNSS Service) of 4 GPS satellites are selected and the predicted results of the quadratic polynomial and grey model are combined. The result shows that the modified model can further improve the stability and accuracy based on the guarantee of the reliability.     

北斗广域增强系统星钟和星历误差改正算法研究

区域北斗星基增强系统提供等效钟差改正数统一修正星历和钟差误差。随着系统的建设发展,新一代北斗星基增强系统将区分星历和钟差误差改正信息,以提高差分改正精度。由于北斗卫星混合星座设计及区域监测网的局限,星历和钟差误差的高精度分离计算面临着新的挑战。对北斗星基增强系统的星历和钟差改正算法进行了研究,分别采用动力学和运动学模式计算了卫星星历和钟差改正数,并基于北斗实测数据,对两种处理模式的差分改正精度进行了对比研究。试验结果表明,采用动力学和运动学差分方法,得到的双频伪距实时定位精度分别为1.76m和1.78m,定位精度与WAAS及EGNOS相当。利用运动学和动力学差分改正数后均可得到分米级的精密单点定位(precise point position,PPP)结果,其中采用动力学广域差分改正数,收敛后定位精度可达到15cm;采用运动学广域差分改正数,收敛后定位精度可达45cm。     

灰色模型用于卫星钟差长期预报的性能研究

利用灰色模型对GPSRb钟和Cs钟进行了长期预报,并与常用的二阶多项式模型预报进行比较,结果表明:灰色模型对GPSCs钟进行长期210d(天)预报时精度高达ns量级,对GPSRb钟的预报精度在10ns量级,明显高于二阶多项式模型的预报精度,满足实际应用中的精度要求。     

Comparison of BDS Station Clock Short-term Prediction Models and their Applications in Precise Orbit Determination

BDS (BeiDou Navigation Satellite System) ground tracking stations are equipped with high accuracy atomic clocks, and they are synchronized with the BDS time scale (BDT) via the Precise Orbit Determination (POD) processing. During the periods of satellite maneuver and post-maneuver, station clocks are kept fixed as known values in the POD processing. To improve the real-time POD capability, station clocks need to be predicted. In this paper, the performance of three clock prediction models is evaluated, including quadratic polynomial model (QP), periodical term model (PM), and grey model (GM). The precision of clock fitting and prediction, as well as the performance of the prediction models in POD are compared. Data of six stations are used for test, and the results show that: the mean fitting accuracy of quadratic polynomial model, periodical term model, and grey model is 0.14 ns, 0.05 ns, 0.27 ns, respectively; the 1 h and 2 h prediction precision of the three models is 1.17 ns, 0.88 ns, 1.28 ns, and 2.72 ns, 2.09 ns, 2.53 ns, respectively. Applying the 1 h and 2 h predicted station clocks in the POD, the 3D orbit accuracy reaches the best using the periodical term model, while the radial accuracy of satellite orbit is rather close for the three models with the difference within 3 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.     

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.     

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.     

Time Transfer Algorithm Using Multi-GNSS PPP with Ambiguity Resolution

With the development of real-time service (RTS) project, timing users can apply the real-time precise point positioning (PPP) technique for time transfer. As a participant in the RTS project, the Centre National d’Etudes Spatiales (CNES) implements the PPPWIZARD (Precise point positioning with Integer and Zero-difference Ambiguity Resolution Demonstrator) project to validate the PPP with ambiguity resolution. In order to analyze the contribution of multiple global navigation satellite system (multi-GNSS) and real-time ambiguity resolution to time transfer, our experiment used the observation from multi-GNSS, including GPS (Global Positioning System), GLONASS (GLObal NAvigation Satellite System), BDS (BeiDou navigation System), and Galileo for data processing. Meanwhile, the real-time products from CNES were utilized to examine the performance of four different PPP processing modes. The experimental results indicated that, of all the processing modes, the time transfer using multi-GNSS PPP with GPS ambiguity resolution had the smallest standard deviations (STDs). The STD value was decreased by 38.1$\%$, compared with the traditional time transfer results using GPS PPP.     

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.     

导航卫星精密定轨与时间同步技术进展

全球卫星导航系统(Global Navigation Satellite System, GNSS)通过播发卫星钟差和精密轨道信息实现时间和空间基准信息向导航用户的传递.随着高精度原子钟等导航卫星载荷、星间链路等天基/地基监测手段以及数据处理方法等技术的不断更新,卫星轨道和钟差产品的精度和实时性也逐步提升. 2018年12月,北斗三号卫星导航系统正式开通,为"一带一路"国家提供实时高精度、高可靠的基本导航定位服务.综述了北斗导航系统从北斗二号区域系统到北斗三号全球系统精密定轨与时间同步处理面临的困难和挑战,针对上述问题,阐述了北斗运行控制系统的解决途径和实现指标.与GPS等其他GNSS系统进行比较,分析了不同导航系统技术特点.最后展望了精密定轨与时间同步技术未来的发展路线图,为更高精度的GNSS导航定位授时服务提供参考.     

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%.     

大气指数模型与探空资料分析的比较─关于广州地区大气层对GPS信号时间延迟问题研究之一

ＧＰＳ系统是现阶段功能最全、精度最高的卫星导航系统，大气层对ＧＰＳ系统定位和定时的影响已成为一个不可忽略的重要因素．本文从广州地区两天各两个时刻的气象探空资料中分析了各个时刻高空中几个已知高度点的折射指数，然后用线性处理的办法得到了１７ｋｍ范围左右高空中折射指数的模型，大气指数模型与此模型相比较，几个点折射指数的均方差很小，最后用这两种模型分别计算两天各两个时刻大气层对ＧＰＳ信号在垂直传播时所引起的附加时间延迟，二者之差最大不大于０．３ｎｓ，用指数模型可基本反映广州地区大气层对ＧＰＳ信号传播时间延迟的影响。     

第三代卫星导航定位系统星载原子钟的新发展

传统铷原子钟和铯原子钟已在卫星导航定位系统中作为星载原子钟获得重要应用.卫星导航定位系统的更新和新发展要求更高精度更小型的新型星载原子钟.该文介绍采用新物理原理和先进技术在下-代卫星导航定位系统有应用前景的新原子钟的产生和发展以及它们目前的进展.     

遗传算法优化的BP神经网络卫星钟差预报

针对BP (Back Propagation)神经网络模型预测卫星钟差中权值和阈值的最优化问题, 提出了基于遗传算法优化的BP神经网络卫星钟差短期预报模型, 给出了遗传算法优化BP神经网络的基本思想、具体方法和实施步骤. 为验证该优化模型的有效性和可行性, 利用北斗卫星导航系统(BeiDou navigation satellite system, BDS)卫星钟差数据进行钟差预报精度分析, 并将其与灰色模型(GM(1,1))和BP神经网络模型预报的结果比较分析. 结果表明: 该模型在短期钟差预报中具有较好的精度, 优于GM(1,1)模型和BP神经网络模型.     

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.     

基于SLR精密轨道的天文定位精度分析

利用全球卫星激光测距服务系统(ILRS,International Laser Ranging Service)标准点资料对Ajisai卫星进行精密定轨,残差均方根(RMS)优于3 cm,得到该星的精密轨道.进而对长春站40 cm空间碎片光电望远镜获得的Ajisai卫星的天文定位资料进行精度分析,外符合精度约3″左右.单独利用天文定位数据进行轨道改进,内符合精度优于3″.改进轨道的x、y、z坐标3分量在观测数据覆盖范围内的精度在100 m之内.同样地对Jason-1卫星作数据分析,结果和Ajisai卫星精度相当.分析各个弧段的精度变化,发现定标星个数减少,会导致天文定位精度下降.据此提出可以把最少定标星比例作为评定数据质量的参考指标之一.     

Analysis of the wide area differential correction for BeiDou global satellite navigation system

The regional BeiDou Satellite System, or BDS2, broadcasts a differential correction as Equivalent Satellite Clock Correction to correct both orbit and satellite clock errors. For the global BDS, or BDS3, satellite orbit and clock corrections conforming with RTCA standards will be broadcast to authorized users. The hybrid constellation and regional monitoring network pose challenges for the high precision separation of orbit and satellite clock corrections. Three correction models of kinematic,dynamic and Two-way Satellite Time Frequency Transfer(TWSTFT)-based dynamic were studied to estimate the satellite orbit and clock corrections. The correction accuracy of the three models is compared and analyzed based on the BDS observation data. Results show that the accuracies(root mean square, RMS) of dual-frequency real-time positioning for the three models are about 1.76 m, 1.78 m and 2.08 m respectively, which are comparable with the performance of WAAS and EGNOS. With dynamic corrections, the precision of Precise Point Positioning(PPP) experiments may reach about 23 cm after convergence.     

北斗星地双向时频传递与广广播钟差精度分析

与其他卫星导航系统不同,北斗卫星导航系统采用星地双向时间比对技术,直接测量卫星钟相对于地面保持的系统时间的钟差,并用于广播电文钟差参数的建模。讨论了电离层延迟误差、卫星相位中心误差等不同误差源对不同类型卫星双向时间同步卫星钟差精度的影响。实测数据分析结果表明,星地双向卫星钟差内符合精度(RMS)优于0.15 ns。利用双向卫星钟差序列,对广播星历钟差参数预报精度进行了分析,统计结果显示广播电文钟差参数预报1 h,精度在2 ns以内,移动卫星刚入境时,钟差参数预报6 h误差可达10 ns。