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.     

Initial results of precise orbit and clock determination for COMPASS navigation satellite system

The development of the COMPASS satellite system is introduced, and the regional tracking network and data availability are described. The precise orbit determination strategy of COMPASS satellites is presented. Data of June 2012 are processed. The obtained orbits are evaluated by analysis of post-fit residuals, orbit overlap comparison and SLR (satellite laser ranging) validation. The RMS (root mean square) values of post-fit residuals for one month’s data are smaller than 2.0 cm for ionosphere-free phase measurements and 2.6 m for ionosphere-free code observations. The 48-h orbit overlap comparison shows that the RMS values of differences in the radial component are much smaller than 10 cm and those of the cross-track component are smaller than 20 cm. The SLR validation shows that the overall RMS of observed minus computed residuals is 68.5 cm for G01 and 10.8 cm for I03. The static and kinematic PPP solutions are produced to further evaluate the accuracy of COMPASS orbit and clock products. The static daily COMPASS PPP solutions achieve an accuracy of better than 1 cm in horizontal and 3 cm in vertical. The accuracy of the COMPASS kinematic PPP solutions is within 1–2 cm in the horizontal and 4–7 cm in the vertical. In addition, we find that the COMPASS kinematic solutions are generally better than the GPS ones for the selected location. Furthermore, the COMPASS/GPS combinations significantly improve the accuracy of GPS only PPP solutions. The RMS values are basically smaller than 1 cm in the horizontal components and 3–4 cm in the vertical component.     

A two-step ionospheric modeling algorithm considering the impact of GLONASS pseudo-range inter-channel biases

The Global Navigation Satellite System presents a plausible and cost-effective way of computing the total electron content (TEC). But TEC estimated value could be seriously affected by the differential code biases (DCB) of frequency-dependent satellites and receivers. Unlike GPS and other satellite systems, GLONASS adopts a frequency-division multiplexing access mode to distinguish different satellites. This strategy leads to different wavelengths and inter-frequency biases (IFBs) for both pseudo-range and carrier phase observations, whose impacts are rarely considered in ionospheric modeling. We obtained observations from four groups of co-stations to analyze the characteristics of the GLONASS receiver P1P2 pseudo-range IFB with a double-difference method. The results showed that the GLONASS P1P2 pseudo-range IFB remained stable for a period of time and could catch up to several meters, which cannot be absorbed by the receiver DCB during ionospheric modeling. Given the characteristics of the GLONASS P1P2 pseudo-range IFB, we proposed a two-step ionosphere modeling method with the priori IFB information. The experimental analysis showed that the new algorithm can effectively eliminate the adverse effects on ionospheric model and hardware delay parameters estimation in different space environments. During high solar activity period, compared to the traditional GPS + GLONASS modeling algorithm, the absolute average deviation of TEC decreased from 2.17 to 2.07 TECu (TEC unit); simultaneously, the average RMS of GPS satellite DCB decreased from 0.225 to 0.219 ns, and the average deviation of GLONASS satellite DCB decreased from 0.253 to 0.113 ns with a great improvement in over 55%.     

由星载GPS相位数据确定地球重力场模型若干问题研究

人造地球卫星在地球引力场中运动,可以探测地球重力场的长波信息。随着GPS技术的发展,星载GPS技术日趋成熟,因此由星载GPS相位数据确定地球重力场模型是当前国际地学研究的热点之一。本文给出了确定地球重力场模型中的星载GPS星地相位双差观测量,阐述了Cowell II数值轨道积分公式,导出了参数估计中星地双差观测量的偏导数,利用分块Bayes最小二乘参数估计地球引力场位系数等有关参数。     

Real-time kinematic positioning of LEO satellites using a single-frequency GPS receiver

Due to their low cost and low power consumption, single-frequency GPS receivers are considered suitable for low-cost space applications such as small satellite missions. Recently, requirements have emerged for real-time accurate orbit determination at sub-meter level in order to carry out onboard geocoding of high-resolution imagery, open-loop operation of altimeters and radio occultation. This study proposes an improved real-time kinematic positioning method for LEO satellites using single-frequency receivers. The C/A code and L1 phase are combined to eliminate ionospheric effects. The epoch-differenced carrier phase measurements are utilized to acquire receiver position changes which are further used to smooth the absolute positions. A kinematic Kalman filter is developed to implement kinematic orbit determination. Actual flight data from China’s small satellite SJ-9A are used to test the navigation performance. Results show that the proposed method outperforms traditional kinematic positioning method in terms of accuracy. A 3D position accuracy of 0.72 and 0.79 m has been achieved using the predicted portion of IGS ultra-rapid products and broadcast ephemerides, respectively.     

Performance comparison of semicodeless GPS receivers for LEO satellites

This report provides a detailed performance analysis of three semicodeless dual-frequency GPS receivers for use in low Earth orbit (LEO). The test set comprises the IGOR receiver, which represents a follow-on of the flight-proven BlackJack receiver, as well as two geodetic receivers (NovAtel OEM4-G2 and Septentrio PolaRx2), which are entirely based on commercial-off-the-shelf technology (COTS). All three receivers are considered for upcoming flight projects or experiments and have undergone at least a preliminary environmental qualification program. Using extensive signal simulator tests, the cold start signal acquisition, tracking sensitivity, differential code biases, raw measurement accuracy, and navigation accuracy of each receiver have been assessed. All tests are based on a common scenario that is representative of an actual space mission and provides a realistic simulation of the signal dynamics and quality on a scientific LEO satellite. Compared to the other receivers, the IGOR instrument exhibits a superior tracking sensitivity and is thus best suited for occultation measurements with low tangent point altitudes. The OEM4-G2 and PolaRx2 receivers are likewise shown to properly track dual-frequency GPS signals and normal signal levels and to provide accurate code and carrier phase measurements. Given their limited resource requirements, these receivers appear well suited for precise orbit determination applications and ionospheric sounding onboard of microsatellites with tight mission budgets.     

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.     

风云3C增强北斗定轨试验结果与分析

首次搭载GPS/BDS双模接收机全球导航卫星掩星探测仪(GNOS)的风云三号C星于2013年9月23日的成功发射,为研究低轨卫星对BDS定轨增强提供了便利。本文首先对低轨卫星GNOS搭载的GPS/BDS双模接收机的观测数据进行统计,并分析了伪距测量精度。然后在全球测站、区域测站两种布局情况下,对无GNOS的BDS单系统定轨、无GNOS的GPS/BDS双系统定轨、有GNOS的BDS单系统定轨增强、有GNOS的GPS/BDS双系统定轨增强4种方案进行北斗轨道及钟差比较分析。结果表明,GNOS对北斗卫星轨道增强在全球测站下,GEO卫星切向精度提升最为显著,提升程度达60%,其次是法向和其他类型卫星切向,部分弧段个别GEO卫星径向精度稍有下降。双系统定轨增强中可视弧段钟差重叠精度RMS值有0.1ns量级改善。7个国内测站区域监测网的定轨试验中对轨道进行了预报,结果表明GNOS对北斗GEO卫星轨道预报精度切向提升达85%,其余方向及卫星有较大改善,平均21.7%。可视弧段钟差重叠精度RMS值有0.5ns量级改善。     

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...     

星载GPS伪距多路径误差与观测噪声对自主定轨的影响分析

对搭载美国BlackJack接收机的CHAMP/GRACE-A/Jason-2卫星和搭载国产接收机的HY2A/ZY3/TH1卫星的星载GPS数据的伪距多路径误差与观测噪声进行了研究,重点分析了国产接收机伪距多路径误差的变化特性,并研究了多路径误差与观测噪声对星载GPS自主定轨的影响。结果表明:国产接收机的C/A码与P1码伪距观测精度要整体差于美国的BlackJack接收机,而P2码伪距观测精度要整体优于BlackJack接收机;国产接收机P1码伪距受多路径效应影响较大,其多路径误差随高度角减小存在单调递增的变化趋势,其中HY2A、ZY3与TH1卫星的多路径误差最大分别可达3.6 m、1.8 m与0.7 m;这种单调递增变化的多路径误差会导致星载GPS自主定轨位置结果在径向与切向产生系统性偏差。     

Is the long-term variation of the estimated GPS differential code biases associated with ionospheric variability?

The global positioning system (GPS) differential code biases (DCB) provided by the International GNSS Service (IGS) show solar-cycle-like variation during 2002–2013. This study is to examine whether this variation of the GPS DCBs is associated with ionospheric variability. The GPS observations from low earth orbit (LEO) satellites including CHAMP, GRACE and Jason-1 are used to address this issue. The GPS DCBs estimated from the LEO-based observations at different orbit altitudes show a similar tendency as the IGS DCBs. However, this solar-cycle-like dependency is eliminated when the DCBs of 13 continuously operating GPS satellites are constrained to zero-mean. Our results thus revealed that ionospheric variation is not responsible for the long-term variation of the GPS DCBs. Instead, it is attributed to the GPS satellite replacement with different satellite types and the zero-mean condition imposed on all satellite DCBs.     

单星模糊度固定的整数相位钟法及在低轨卫星定轨中的应用

单星GPS相位模糊度固定可以显著提升低轨卫星的定轨精度。目前,CNES/CLS、武汉大学和CODE 3家机构都已公开发布用于单星模糊度固定的GPS整数相位钟产品。本文首先利用整数相位钟方法实现单星模糊度固定,并应用于低轨卫星精密定轨中;然后,对比分析了不同机构提供的整数相位钟产品在低轨卫星单星模糊度固定和精密定轨中的应用性能;最后,通过对GRACE-FO编队卫星数据进行处理,发现基于不同机构产品的窄巷模糊度固定成功率都可以达到94%左右。不同机构产品获得的模糊度固定解轨道的SLR(satellite laser ranging)检核残差RMS约为0.9 cm,与模糊度浮点解的定轨结果相比,单星绝对轨道精度提高了约30%。在分别利用CNES/CLS、武汉大学和CODE产品实现单星模糊度固定后,双星相对轨道的KBR(K-band ranging)检核残差RMS分别从5.7、5.4和5.3 mm减小到2.1、2.0和1.5 mm。结果表明,不同整数相位钟产品在GRACE-FO卫星单星模糊度固定和精密定轨中的效果相当。     

An enhanced calibration method of GLONASS inter-channel bias for GNSS RTK

A user of heterogeneous GPS and GLONASS receiver pairs in differential positioning mode will experience ambiguity fixing challenges due to the presence of inter-channel biases. These biases cannot be canceled by differencing GLONASS observations, whether pseudorange or carrier phase. Fortunately, pre-calibration of GLONASS pseudorange and carrier phase observations can make ambiguity fixing for GPS/GLONASS positioning much easier. We propose an effective algorithm that transforms an RTK (real-time kinematic) solution in a mixed receiver baseline from a float to a fixed ambiguity solution. Carrier phase and code inter-channel biases are estimated from a zero baseline. Then, GLONASS both carrier phase and code observations are corrected accordingly. The results show that a mixed baseline can be transformed from a float (~100 %) to a fixed (more than 92 %) solution.     

GPS纯几何法在低轨卫星定轨中的应用

在近地低轨卫星上安装GPS接收机,并同时能捕获到四颗GPS卫星的话,我们就可以直接利用GPS观测值来组成观测方程,解算被求卫星的轨道位置。但由于GPS卫星是为地面上的用户设计的,其主要是满足地面用户的导航定位要求,再加上近地卫星的高动态性、高速度性,有时还不能同时捕获到四颗GPS卫星,这都给近地卫星的定轨带来了不确定的因素。本文主要对这一想法进行了试验,并分析了定轨的精度。     

Swarm低轨卫星星座的GPS接收机差分码偏差估计

差分码偏差(differential code bias,DCB)是指由全球导航卫星系统(global navigation satellite system, GNSS)信号接收和发射硬件导致的频率相关的偏差项,对电离层估计有显著的影响,在利用GNSS观测数据提取电离层总电子含量时需要被精确修正,研究利用低轨卫星的星载GNSS观测数据估计DCB尤为重要。使用Swarm星座3颗卫星GPS接收机2016年1月的双频观测值,设计了独立估计和联合估计两种估计方案,采用附加限制条件的间接平差方法对GPS卫星以及星载接收机的DCB进行估计。以中国科学院和德国宇航中心的DCB产品作为参考,分析了两种估计方案的精度和稳定性,相较于独立估计方案,联合估计方案得到的GPS卫星DCB的稳定性较独立估计方案提高了16.6%,且与参考DCB具有更好的一致性。     

Performance of the L2C civil GPS signal under various ionospheric scintillation effects

As GPS is modernizing, there are currently fourteen satellites transmitting L2C civil code and seven satellites transmitting L5 signal. While the GPS observables are subject to several sources of errors, the ionosphere is one of the largest error sources affecting GPS signals. Small irregularities in the electrons density along the GPS radio signal propagation path cause ionospheric scintillation that is characterized by rapid fluctuations in the signal amplitude and phase. The ionospheric scintillation effects are stronger in equatorial and high-latitude geomagnetic latitude regions and occur mainly due to equatorial anomaly and solar storms. Several researchers have analyzed the L2C signal quality since becoming available in December, 2005. We analyze the performance of L2C using GPS data from stations in the equatorial region of Brazil, which is subject of weak, moderate and strong ionospheric scintillation conditions. The GPS data were collected by Septentrio PolaRxS–PRO receivers as part of the CIGALA/CALIBRA network. The analysis was performed as a function of scintillations indexes S4 and Phi60, lock time (time interval in seconds that the carrier phase is tracked continuously without cycle slips), multipath RMS and position variation of precise point positioning solutions. The analysis shows that L2C code solutions are less affected by multipath effects than that of P2 when data are collected under weak ionospheric scintillation effects. In terms of analysis of positions, the kinematic PPP results using L2C instead P2 codes show accuracy improvements up to 33 % in periods of weak or strong ionospheric scintillation. When combining phase and code collected under weak scintillation effects, the results by applying L2C against P2 provide improvement in accuracy up to 59 %. However, for data under strong scintillation effects, the use of L2C for PPP with code and phase does not provide improvements in the positioning accuracy.     

Precise orbit determination for the FORMOSAT-3/COSMIC satellite mission using GPS

The joint Taiwan–US mission FORMOSAT-3/ COSMIC (COSMIC) was launched on April 17, 2006. Each of the six satellites is equipped with two POD antennas. The orbits of the six satellites are determined from GPS data using zero-difference carrier-phase measurements by the reduced dynamic and kinematic methods. The effects of satellite center of mass (COM) variation, satellite attitude, GPS antenna phase center variation (PCV), and cable delay difference on the COSMIC orbit determination are studied. Nominal attitudes estimated from satellite state vectors deliver a better orbit accuracy when compared to observed attitude. Numerical tests show that the COSMIC COM must be precisely calibrated in order not to corrupt orbit determination. Based on the analyses of the 5 and 6-h orbit overlaps of two 30-h arcs, orbit accuracies from the reduced dynamic and kinematic solutions are nearly identical and are at the 2–3 cm level. The mean RMS difference between the orbits from this paper and those from UCAR (near real-time) and WHU (post-processed) is about 10 cm, which is largely due to different uses of GPS ephemerides, high-rate GPS clocks and force models. The kinematic orbits of COSMIC are expected to be used for recovery of temporal variations in the gravity field.     

顾及码频间偏差的GPS/GLONASS实时卫星钟差估计

在进行GPS/GLONASS联合卫星钟差估计时,GLONASS码频间偏差（inter-frequency bias,IFB）因卫星频率间的差异而无法被测站接收机钟差参数吸收,其一部分将进入GLONASS卫星钟差估值中。通过引入多个"时频偏差"参数（inter-system and inter-frequency bias,ISFB）及附加基准约束对测站GLONASS码IFB进行函数模型补偿,实现其与待估卫星钟差参数的有效分离,并对所估计实时卫星钟差和实时精度单点定位（real-time precise point positioning,RT-PPP）进行精度评估。结果表明,在卫星钟差估计观测方程中忽略码IFB,会明显降低GLONASS卫星钟差估值精度;新方法能有效避免码IFB对卫星钟差估值的影响,所获得GPS、GLONASS卫星钟差与ESA（European Space Agency）事后精密钟差产品偏差平均均方根值分别小于0.2 ns、0.3 ns。利用实时估计卫星钟差进行静态RT-PPP,当观测时段长为2 h时,GPS单系统、GPS/GLONASS组合系统的3D定位精度优于10 cm,GLONASS单系统3D定位精度约为15 cm;三种模式24 h单天解的3D定位精度均优于5 cm。     

An investigation of GNSS atomic clock behavior at short time intervals

A technique for obtaining clock measurements from individual GNSS satellites at short time intervals is presented. The methodology developed in this study allows for accurate satellite clock stability analysis without an ultra-stable clock at the ground receiver. Variations in the carrier phase caused by the satellite clock are isolated using a combination of common GNSS carrier-phase processing techniques. Furthermore, the white phase variations caused by the thermal noise of the collection and processing equipment are statistically modeled and removed, allowing for analysis of clock performance at subsecond intervals. Allan deviation analyses of signals collected from GPS and GLONASS satellites reveal distinct intervals of clock noise for timescales less than 100 s. The clock data collected from GPS Block IIA, IIR, IIR-M, and GLONASS satellites reveal similar stability performance at time periods greater than 20 s. The GLONASS clock stability in the 0.6–10 s range, however, is significantly worse than GPS. Applications that rely on ultra-stable clock behavior from the GLONASS satellites at these timescales may therefore require high-rate corrections to estimate and remove oscillator-based errors in the carrier phase.     

由星载GPS双差相位数据进行CHAMP卫星动力学定轨

为了确定CHAMP卫星的轨道，由星载GPS数据和IGS跟踪站的GPS数据构造星地相位双差观测量，利用EOP、SGO、时间等数据，对GPS数据进行预处理，包括钟差改正、模糊度解算和周跳探测、卫星姿态改正、天线偏差和相位中心改正等，采用CHAMP卫星受力摄动模型，根据动力学原理，对CHAMP卫星进行实际定轨。与德国GFZ定轨结果PSO相比，本方法定轨结果径向精度为0．2857m。对于1d的重叠轨道，径向轨道差异的RMS为0．0958m。对于轨道端点比较，径向轨道差异平均为0．0666m。