GNSS星载原子钟性能评估

星载原子钟作为导航卫星上维持时间尺度的关键载荷,其性能会对用户进行导航、定位与授时的精度带来影响。介绍了原子钟评估常用的三个指标（频率准确度、飘移率和稳定度）的定义及计算方法,利用事后卫星精密钟差数据,开展了全球卫星导航系统（global navigation satellite system,GNSS）星载原子钟性能评估,分析了GNSS星载原子钟特性。结果表明,GPS（global position system）BLOCKIIF星载铷钟与Galileo星载氢钟综合性能最优;北斗系统中地球轨道卫星与倾斜同步轨道卫星星载原子钟天稳定度达到2~4×10-14量级,与BLOCK IIR卫星精度相当;频率准确度达到1~4×10-11量级;频率漂移率达到10-14量级。     

Analysis of BDS satellite clocks in orbit

The products of Wuhan University with 5-min sampling are used to analyze the characteristics of BeiDou satellite clocks. Two nanoseconds root-mean-square (RMS) variations are obtained for 1-day quadratic fits in the sub-daily region. The relativistic effects of BDS clocks are also studied. General relativity predicts that linear variation of the semimajor axes of geostationary and inclined geosynchronous satellites causes a quadratic clock drift with a magnitude at the 10^?16/day level. The observed drift is higher than what general relativity theory would produce. Several periodic terms are found in the satellite clock variations through spectrum analysis. In order to identify the origin of the BDS clock harmonics, a correlation analysis between the period or amplitude of the harmonics and properties of the satellite orbits is performed. It is found that the period of the harmonics is not exactly equal to the orbit period, but rather the ratio of the orbit period to clock period is almost the same as that of a sidereal day to solar day. The BDS clocks obey white frequency noise statistics for intervals from 300 s to several thousands seconds. For intervals greater than 10,000 s, all the BDS satellites display more complex, non-power-law behavior due to the effects of periodic clock variations.     

BDS星载原子钟频率稳定性分析

卫星导航系统中星载原子钟作为系统的星上时间基准,其性能直接决定着导航定位的精度。北斗卫星导航系统（BeiDou navigation satellite system,BDS）目前处于全面建设阶段,对系统星载原子钟的性能进行评估非常重要。结合评价星载铷原子钟稳定性的哈达玛（Hadamard）方差、重叠哈达玛方差和哈达玛总方差,分别基于5 min和15 min采样间隔的北斗精密钟差数据,综合三种方差的计算结果对北斗卫星导航系统星载原子钟频率稳定性进行较为全面的评估,得到了一些有益的结论。     

利用不同时间同步体制钟差评估北斗三号星载原子钟性能

全球卫星导航系统(global navigation satellite system,GNSS)星载原子钟性能的优劣直接影响GNSS观测信号质量、测距精度、钟差预报与卫星自主导航能力,从而间接影响整个导航系统的服务性能。结合北斗三号系统独特的星间链路(inter-satellite link, ISL)和星地时间双向比对(two-way time transfer,TWTT)体制以及常用的精密轨道与钟差确定(orbit determination and time synchronization,ODTS)体制所估计的精密钟差数据,分析评估了北斗三号在轨原子钟服务性能。结果表明,3种钟差确定体制评估的频率准确度和漂移率结果基本一致,所有卫星频率准确度在(-4～2)×10^-11范围以内,氢钟频率准确度优于铷钟,ISL钟差评估的频率漂移率精度略优于ODTS。在评估原子钟稳定度方面,3种钟差确定体制各有优势,短期稳定度方面,ODTS钟差评估优于ISL钟差,基于ODTS评估的3 000 s稳定度可达3×10^-14,且氢钟的短期稳定性优于铷钟;中长期...     

BDS星载原子钟长期性能分析

北斗卫星导航系统(BDS)于2012年底开始提供区域服务,进行BDS星载原子钟的长期性能分析,对于系统性能的评估、卫星钟差的确定与预报等具有重要的作用。本文基于3年的多星定轨联合解算的BDS精密卫星钟数据,利用改进的中位数方法进行数据预处理,分析了卫星钟差数据的特点,使用卫星钟差二次多项式拟合模型分析了卫星钟的相位、频率、频漂及钟差模型噪声的长期变化特性,根据频谱分析的方法分析了卫星钟差的周期特性,采用重叠哈达玛方差计算并讨论了卫星钟的频率稳定性。综合上述方法及其试验结果较为全面地分析和评估了BDS星载原子钟的长期性能,得到结论:在噪声特性和钟漂特性方面,MEO卫星钟的性能最好,其次是IGSO卫星钟,最差的是GEO卫星钟,所有卫星钟噪声水平和频漂的均值分别为0.677ns和1.922×10~(-18);多星定轨条件下的北斗卫星钟差存在显著的周期项,其主周期分别近似为对应卫星轨道周期的1/2倍或1倍;BDS星载原子钟频率稳定度的平均值为1.484×10~(-13)。     

北斗新一代试验系统时间及卫星钟精度初步分析

北斗卫星导航系统新一代试验卫星星座由2颗高轨倾斜地球同步轨道卫星（IGSO）和3颗中轨地球轨道卫星(MEO)组成,2016年2月全部发射入轨,其任务是验证北斗系统从目前区域导航定位授时服务走向全球服务的新技术体制设计及指标性能。导航卫星星载原子钟是最重要载荷之一,负责星上时间频率基准信号维持和产生。本文利用星地双向时频传递设备观测的星地钟差数据,评估了试验星配置的新型高精度铷钟和被动型氢钟的实际性能,定量比较了相对于北斗区域系统卫星钟的性能提升。结果表明,新一代试验星与北斗区域系统卫星钟差预报精度相比较有较大提高,IGSO卫星短期预报误差从0.65 ns减小到0.30 ns,MEO卫星短期预报误差从0.78 ns减小到0.32 ns,IGSO／MEO卫星中期预报误差均从2.50 ns减小到约1.50 ns.时频系统是新一代试验系统地面运控的重要组成部分,负责北斗新一代试验系统时间频率信号产生和维持。本文利用试验系统与UTC(BSNC)之间的比对数据,评估了新一代试验系统时间的实际性能,定量比较了相对于北斗区域系统时间的性能提升。结果表明,新一代试验系统时间相对于北斗区域系统时间性能有较大提高,万秒稳和天稳较北斗区域系统提高约半个数量级。时频体制是新一代试验系统的重要技术体制设计之一。本文利用中心节点与末节点的双向时间测量数据,评估了新一代试验系统末节点时频信号的实际性能。结果表明,中心节点与末节点之间具有很好的一致性,时差最大为0.23 ns.      

Benefits of receiver clock modeling in code-based GNSS navigation

Due to the limited frequency stability and poor accuracy of typical quartz oscillators built-in GNSS receivers, an additional receiver clock error has to be estimated in addition to the coordinates. This leads to several drawbacks especially in kinematic applications: At least four satellites in view are needed for navigation, high correlations between the clock estimates and the up-coordinates. This situation can be improved distinctly when connecting atomic clocks to GNSS receivers and modeling their behavior in a physically meaningful way (receiver clock modeling). Recent developments in miniaturizing atomic clocks result in so-called chip-scale atomic clocks and open up the possibility of using stable atomic clocks in GNSS navigation. We present two different methods of receiver clock modeling, namely in an extended Kalman filter and a sequential least-squares adjustment for code-based GNSS navigation using three different miniaturized atomic clocks. Using the data of several kinematic test drives, the benefits of clock modeling for GPS navigation solutions are assessed: decrease in the noise of the up-coordinates by up to 69 % to 20 cm level, decrease in minimal detectable biases by 16 %, and elimination of spikes and subsequently decrease in large position errors (35 %). Hence, a more robust position is obtained. Additionally, artificial partial satellite outages are generated to demonstrate position solutions with only three satellites in view.     

导航卫星原子钟频率漂移特性分析

介绍了原子钟频漂定义，总结了频率漂移率测试评定方法，比较分析了不同噪声情况下的频率漂移率估计方法，并用实验室真空状态铷钟的频率偏差数据和GPS卫星钟的精密星历数据进行了计算分析，表明铷钟都有明显频漂，GPSIIR铷钟的日漂移率在10^-15。量级，而铯钟频漂不是很明显。研究了频漂对原子钟时域稳定性影响规律，还利用模拟数据进行了计算分析。验证了方法的有效性．     

北斗在轨卫星钟中长期钟差特性分析

针对北斗在轨卫星Rb原子钟2013年的实测数据,采用二次多项式拟合得到BDS卫星钟差模型,采用哈达玛总方差公式计算了北斗卫星钟的短期频率稳定度指标,进而分析了北斗在轨卫星钟特性指标的变化规律。通过实例计算,揭示了BDS不同在轨卫星钟的相位、频率、频漂及残差指标的变化规律;计算得出BDS卫星钟万秒频率稳定度维持在10-13量级左右,其中GEO卫星钟的稳定度相对较差,4号和8号卫星在运行期间出现跳变,跳变之后稳定性得到提高,其他在轨卫星钟稳定度变化趋势则相对平稳。     

风云三号D星天基BDS实时定位性能分析

随着北斗三号卫星导航系统(BeiDou navigation satellite system-3, BDS-3)开始向全球提供导航服务,独立使用BDS为在轨运行的卫星提供全球覆盖、全时段的定位服务成为可能。结合风云三号D星(FengYun-3D, FY-3D)全球卫星导航系统掩星探测仪(global navigation satellite system occultation sounder, GNOS)的真实在轨数据对天基BDS的定位性能进行了详细的分析。首先,使用BDS真实广播星历计算了在不同轨道高度下的可见卫星数和定位精度因子（position dilution of precision, PDOP）,并结合精密星历分析了广播星历的轨道误差、时钟误差及空间信号测距误差(signal-in-space range error, SISRE)。仿真结果表明,在95%的置信水平下,从地面到2 000 km的轨道高度,BDS在全球范围内最小可见卫星数为6,最大PDOP小于5,星座可用性已经达到100%,全球平均可见卫星数BDS比GPS(global positioning syste...     

用于GNSS的SpT星载原子钟及时间系统介绍

研究了空间铷钟和被动型氢钟的地面批量和寿命试验测试结果,以及卫星在轨试验所达到的最新性能结果。基于这些星载钟的试验结果,对全球卫星导航系统的地面时间站的关键设备及其相关算法作了简要描述,并介绍了一种新颖的在轨技术,即从星载原子钟组（ONCLE）直接产生高度稳健的时间频率信号。     

Short-term analysis of GNSS clocks

A characterization of the short-term stability of the atomic frequency standards onboard GNSS satellites is presented. Clock performance is evaluated using two different methods. The first method derives the temporal variation of the satellite’s clock from a polynomial fit through 1-way carrier-phase measurements from a receiver directly connected to a high-precision atomic frequency standard. Alternatively, three-way measurements using inter-station single differences of a second satellite from a neighboring station are used if the receiver’s clock stability at the station tracking the satellite of interest is not sufficient. The second method is a Kalman-filter-based clock estimation based on dual-frequency pseudorange and carrier-phase measurements from a small global or regional tracking network. Both methods are introduced and their respective advantages and disadvantages are discussed. The analysis section presents a characterization of GPS, GLONASS, GIOVE, Galileo IOV, QZSS, and COMPASS clocks based on these two methods. Special focus has been set on the frequency standards of new generation satellites like GPS Block IIF, QZSS, and IOV as well as the Chinese COMPASS/BeiDou-2 system. The analysis shows results for the Allan deviation covering averaging intervals from 1 to 1,000 s, which is of special interest for real-time PPP and other high-rate applications like processing of radio-occultation measurements. The clock interpolation errors for different sampling rates are evaluated for different types of clocks and their effect on PPP is discussed.     

北斗卫星导航系统广播星历精度分析

针对系统地评估我国北斗卫星导航系统广播星历精度与保障实时导航定位服务的需求,对BDS广播星历提供的卫星轨道、钟差以及用户测距误差(URE)的精度性能进行分析,统计了2015年连续4周全部BDS在轨健康卫星的广播星历各项精度指标值。分析结果表明:BDS的MEO和IGSO卫星轨道精度优于GEO卫星结果,且径向精度优于法向和切向精度;BDS搭载的国产星载铷钟卫星钟差序列相对比较稳定,其均方根误差优于4ns;GEO/IGSO卫星的用户距离误差(URE)在6m以内,MEO的URE优于20m。研究结果对北斗系统的建设、后期的发展和用户市场的拓展,都具有重要的参考价值。     

北斗在轨卫星钟产品质量分析

星载原子钟是卫星导航系统的星上时间基准,其性能的优劣直接决定了导航定位服务的质量。我国BDS目前处于全面建设阶段,对BDS卫星钟产品进行质量分析以及在轨星载原子钟的性能评估是一项重要的工作。目前,多个GNSS分析中心同时提供BDS卫星钟差产品,但对于不同分析中心的钟差产品特性对比和分析却鲜有报道。因此,本文从连续性指标、一致性指标、拟合精度指标、预报特性指标,对CODE、GFZ和WHU分析中心的北斗卫星钟差不同采样间隔数据进行了对比和分析。同时,基于北斗卫星钟产品对北斗系统星载原子钟短期频率稳定性进行了评估,得出了一些有益的结论。     

In-orbit performance assessment of BeiDou intersatellite link ranging

The introduction of an intersatellite link, also called a crosslink, is considered a promising technique for improving the reliability and integrity of a global navigation satellite system. As one of the most rapidly developing satellite navigation systems, the BeiDou system launched from March 2015 to February 2016 an in-orbit validation constellation that includes two inclined geosynchronous orbit satellites and three medium earth orbit satellites equipped with an intersatellite link in the Ka band. We modeled the intersatellite measurements of BeiDou and evaluated the ranging performance of the intersatellite link based on the analysis of in-orbit measurement data. We used both residual analysis and external data comparison to assess the data. The results show that the ranging precision of the BeiDou intersatellite link is within 10 cm and is determined mainly by the thermal noise of the receiver. Moreover, the drift rate of the group delay of the transceiver channel is within 1 cm per day.     

Joint estimation of GPS/BDS real-time clocks and initial results

We present the joint estimation model for Global Positioning System/BeiDou Navigation Satellite System (GPS/BDS) real-time clocks and present the initial satellite clock solutions determined from 106 stations of the international GNSS service multi-GNSS experiment and the BeiDou experimental tracking stations networks for 1 month in December, 2012. The model is shown to be efficient enough to have no practical computational limit for producing 1-Hz clock updates for real-time applications. The estimated clocks were assessed through the comparison with final clock products and the analysis of post-fit residuals. Using the estimated clocks and corresponding orbit products (GPS ultra-rapid-predicted and BDS final orbits), the root-mean-square (RMS) values of coordinate differences from ground truth values are around 1 and 2–3 cm for GPS-only and BDS-only daily mean static precise point positioning (PPP) solutions, respectively. Accuracy of GPS/BDS combined static PPP solutions falls in between that of GPS-only and BDS-only PPP results, with RMS values approximately 1–2 cm in all three components. For static sites, processed in the kinematic PPP mode, the daily RMS values are normally within 4 and 6 cm after convergence for GPS-only and BDS-only results, respectively. In contrast, the combined GPS/BDS kinematic PPP solutions show higher accuracy and shorter convergence time. Additionally, the BDS-only kinematic PPP solutions using clock products derived from the proposed joint estimation model were superior compared to those computed using the single-system estimation model.     

Apparent clock variations of the Block IIF-1 (SVN62) GPS satellite

The Block IIF satellites feature a new generation of high-quality rubidium clocks for time and frequency keeping and are the first GPS satellites transmitting operational navigation signals on three distinct frequencies. We investigate apparent clock offset variations for the Block IIF-1 (SVN62) spacecraft that have been identified in L1/L2 clock solutions as well as the L1/L5-minus-L1/L2 clock difference. With peak-to-peak amplitudes of 10?C40?cm, these variations are of relevance for future precision point positioning applications and ionospheric analyses. A proper characterization and understanding is required to fully benefit from the quality of the new signals and clocks. The analysis covers a period of 8?months following the routine payload activation and is based on GPS orbit and clock products generated by the CODE analysis center of the International GNSS Service (IGS) as well as triple-frequency observations collected with the CONGO network. Based on a harmonic analysis, empirical models are presented that describe the sub-daily variation of the clock offset and the inter-frequency clock difference. These contribute to a better clock predictability at timescales of several hours and enable a consistent use of L1/L2 clock products in L1/L5-based positioning.     

Orbit and clock analysis of Compass GEO and IGSO satellites

China is currently focussing on the establishment of its own global navigation satellite system called Compass or BeiDou. At present, the Compass constellation provides four usable satellites in geostationary Earth orbit (GEO) and five satellites in inclined geosynchronous orbit (IGSO). Based on a network of six Compass-capable receivers, orbit and clock parameters of these satellites were determined. The orbit consistency is on the 1–2 dm level for the IGSO satellites and on the several decimeter level for the GEO satellites. These values could be confirmed by an independent validation with satellite laser ranging. All Compass clocks show a similar performance but have a slightly lower stability compared to Galileo and the latest generation of GPS satellites. A Compass-only precise point positioning based on the products derived from the six-receiver network provides an accuracy of several centimeters compared to the GPS-only results.     

Galileo status: orbits,clocks, and positioning

The European Global Navigation Satellite System Galileo is close to declaration of initial services. The current constellation comprises a total of 12 active satellites, four of them belonging to the first generation of In-Orbit Validation satellites, while the other eight are Full Operational Capability (FOC) satellites. Although the first pair of FOC satellites suffered from a launch anomaly resulting in an elliptical orbit, these satellites can be used for scientific applications without relevant limitations. The quality of broadcast orbits and clocks has significantly improved since the beginning of routine transmissions and has reached a signal-in-space range error of 30 cm. Precise orbit products generated by the scientific community achieve an accuracy of about 5 cm if appropriate models for the solar radiation pressure are applied. The latter is also important for an assessment of the clock stability as orbit errors are mapped to the apparent clock. Dual-frequency single point positioning with broadcast orbits and clocks of nine Galileo satellites that have so far been declared healthy already enables an accuracy at a few meters. Galileo-only precise point positioning approaches a precision of 2 cm in static mode using daily solutions.     

Estimation of antenna phase center offset for BDS IGSO and MEO satellites

The BeiDou satellite navigation system (BDS) is different from other global navigation satellite systems (GNSSs) because of its special constellation, which consists of satellites in geostationary earth orbit, inclined geosynchronous earth orbit (IGSO), and medium earth orbit (MEO). Compared to MEO satellites, the observations of IGSO satellites cover only a small range of nadir angles. Therefore, the estimation of phase center offsets (PCOs) suffers from high correlation with other estimation parameters. We have estimated the phase center offsets for BeiDou IGSO and MEO satellites with a direct PCO parameters model, and constraints are applied to cope with the correlation between the PCOs and other parameters. Validation shows that the estimated PCO parameters could be used to improve the accuracy of orbit and clock offset overlaps. Compared with the Multi-GNSS Experiment antenna phase center correction model, the average improvements of the proposed method for along-track, cross-track, and radial components are 19 mm (31%), 5 mm (14%), and 2 mm (15%) for MEO satellites, and 13 mm (17%), 12 mm (21%), and 5 mm (19%) for IGSO satellites. For clock offset overlaps, average improvements of standard deviation and root mean square (RMS) are 0.03 ns (20%) and 0.03 ns (12%), respectively. The RMS of precise coordinates in the BDS-only positioning was also improved significantly with a level of 24 mm (30%) in the up-direction. Finally, the overall uncertainty of the estimated results is discussed.