A simplified yaw-attitude model for eclipsing GPS satellites

A simplified yaw-attitude modeling, consistent with Bar-Sever (1996), has been implemented and tested in the NRCan PPP software. For Block IIR GPS satellite it is possible to model yaw-attitude control during eclipsing periods by using the constant hardware yaw rate of 0.20°/s. The Block IIR satellites maintain the nominal yaw attitude even during a shadow crossing (Y. E. Bar-Sever, private communication, 2007), except for the noon and shadow midnight turn maneuvers, both of which can be modeled and last up to 15 min. Thus, for Block IIR satellites it is possible to maintain continuous satellite clock estimation even during eclipsing periods. For the Block II/IIA satellites, it is possible to model satisfactorily the noon turns and also shadow crossing, thanks to the permanent positive yaw bias of 0.5°, implemented in November 1995. However, in order to model the Block II/IIA shadow crossings, satellite specific yaw rates should be used, either solved for or averaged yaw-rate solutions. These yaw rates as estimated by the Jet Propulsion Laboratory (JPL) can differ significantly from the nominal hardware values. The Block II/IIA post-shadow recovery periods, which last about 30 min, should be considered uncertain and cannot be properly modeled. Data from post-shadow recovery periods should, therefore, not be used in precise global GPS analyses (Bar-Sever 1996). For high-precision applications, it is essential that users implement a yaw-attitude model, which is consistent with the generation of the satellite clocks. Initial testing and analyses, based on the IGS and AC Final orbits and clocks have revealed that during eclipsing periods, significant inconsistencies in yaw-attitude modeling still exist amongst the IGS Analyses Centers, which contribute to the errors of the IGS Final clock combinations.     

GPS/BDS卫星姿态异常对PPP相位缠绕的影响及其改正模型

在精密单点定位中,相位缠绕是一项不可忽略的误差。相位缠绕的计算严格依赖于卫星姿态的确立,不同的卫星类型产生不同的异常。本文给出了卫星在正常情况下的姿态模型和在异常情况下的姿态改正模型。使用真实数据测试以验证本文所提出模型的正确性。观察滤波收敛后出现异常情况的卫星观测值的残差,结果表明:在异常时期残差最大可能超过20 cm,然而使用本文的改正模型,残差可降低到5 cm以下。使用不同分析中心的精密轨道和钟差产品,效果存在微小差异。II/IIA卫星通过地影区域的时间最长可达1 h,此期间卫星姿态完全受航向角偏差(II/IIA为+0.5°)控制,出了地影区域后30 min,姿态难以模型化,因此这30 min的观测数据不建议采用。     

姿态模式切换期间QZSS卫星轨道及其钟差产品特性分析

导航卫星姿态控制模式切换对精密定轨解算得到的轨道和钟差均有较大影响。本文首先从理论上分析了卫星偏航姿态及其对精密定轨的影响,然后分别以卫星激光测距检核和钟差多项式拟合的方法对IGS MGEX分析中心的QZSS卫星轨道和钟差产品精度进行评价,最后以谱分析方法和改进阿伦方差揭示了卫星钟差的周期特性。基于2014年全年的QZSS卫星轨道和钟差产品的研究表明,一年内有两次长约20 d的地影季,太阳角呈现半年周期的波动;QZSS卫星在低太阳角时有零偏保护,其卫星轨道和钟差精度都与太阳角有显著相关性;卫星钟差具有与轨道周期相近的周期项,且周期项振幅与太阳角的大小也具有相关性,表明现有的定轨策略存在不足。考虑到QZSS与目前北斗星座中IGSO和MEO卫星姿态控制模式的相似性,该结论对于研究我国BDS姿态切换期间的精密定轨有一定参考价值。     

BDS卫星星内多径及其对宽巷FCB解算的影响分析

针对BDS卫星的伪距星内多径(SIMP)问题,提出和强调了在进行SIMP建模时应该采用天底角而非高度角作为自变量,这样获得的模型才能用于不同高程的接收机。收集全球分布的iGMAS和MGEX监测站数据,以天底角为自变量构建了北斗IGSO和MEO两类卫星B1、B2和B3频点的SIMP分段线性模型。利用FY3C星载北斗数据对北斗GEO、IGSO和MEO的SIMP作进一步分析。结果表明,当天底角小于7°时,GEO和IGSO卫星的SIMP非常接近,对B2频点尤其明显。这也许预示着可以将地面数据获得的IGSO卫星的SIMP模型用于GEO卫星。同时还发现在天底角小于12°(MEO)和7°(IGSO)时,所得到的SIMP估值与地面数据获得的模型有非常好的一致性。在此基础上,采用MGEX全球监测网数据进行宽巷小数周偏差(FCB)解算试验,结果表明,经过SIMP改正后,各颗卫星的星端宽巷FCB序列的重复性都有显著提高,改进幅度都超过了60%。具体的,IGSO和MEO的星端FCB重复精度小于0.05周;采用IGSO卫星的SIMP模型对GEO卫星进行改正后,C01和C02星的FCB重复精度分别达到0.023和0.068周。     

北斗卫星ECOM光压模型参数选择策略分析

以ECOM经验光压模型为基础,利用北斗卫星3年的精密星历进行轨道拟合,获得了ECOM光压参数的变化规律,给出了北斗3类卫星的ECOM光压参数选择策略。从北斗卫星姿态控制模式出发,通过卫星星体受照分析,指出在北斗卫星地影期零偏航状态下,由于太阳对卫星帆板的不正照,导致与动态偏航姿态相比,光压摄动力存在与轨道周期相关的分量,需要在ECOM 5参数的基础上增加D向周期分量进行吸收。通过MGEX全球网数据定轨试验,本文提出的方法可使零偏段定轨重叠段位置精度提高50%~80%。     

A new model for GPS yaw attitude

modeling of the GPS satellite yaw attitude is a key element in high-precision geophysical applications. This fact is illustrated here as a new model for the GPS satellite yaw attitude is introduced. The model constitutes a significant improvement over the previously available model in terms of efficiency, flexibility and portability. The model is described in detail and implementation issues, including the proper estimation strategy, are addressed. The performance of the new model is analyzed and an error budget is presented. Finally, the implementation of the yaw bias on the GPS satellites is reviewed from its inception until it reached a steady state in November, 1995.     

FY-3B微波成像仪资料的地理定位误差与订正

风云3号B星(FY-3B)上的微波成像仪(MWRI)通过10.65 GHz,18.7 GHz,23.8GHz,36.5 GHz和189.0 GHz5个频率的双极化通道对地球表面进行监测。自卫星发射至今,MWRI资料的地理定位误差还未进行深入研究。为了提高FY-3B MWRI L1级数据地理定位精度,基于海、陆响应的升、降轨亮温差理论NDM(Node Differential Method),通过卫星位置和速度矢量建立卫星姿态模型、采用非线性最优化方法估计卫星姿态偏差,进而对MWRI 89 GHz通道的地理定位误差进行分析与订正。结果表明,2015年1—9月份俯仰、滚动和偏航角度的平均偏差分别为-0.220°,0.068°和0.062°,对应沿轨误差大约3—4 km,跨轨误差小于1 km。定位误差订正后,地中海、澳大利亚区域海岸线附近的升降轨亮温差明显减小;观测亮温在红海和南美洲东南部区域的分布和海岸线更加吻合,定位精度得到明显提高。     

Improved method for estimating the inter-frequency satellite clock bias of triple-frequency GPS

Considering the contribution of the hardware biases to the estimated clock errors, an improved method for estimating the satellite inter-frequency clock bias (IFCB) is presented, i.e., the difference in the satellite clock error as computed from ionospheric-free pseudorange and carrier phase observations using L1/L2 and P1/P2 versus L1/L5 and P1/P5. The IFCB is composed of a constant and a variable part. The constant part is the inter-frequency hardware bias (IFHB). It contains the satellite and receiver hardware delays and can be expressed as a function of the DCBs [DCB (P1 ? P2) and DCB (P1 ? P5)]. When a reference satellite is selected, the satellite IFHB can be computed but is biased by a reference satellite IFHB. This bias will not affect the utilization of IFCB in positioning since it can be absorbed by the receiver clock error. Triple-frequency observations of 30 IGS stations between June 1, 2013, and May 31, 2014, were processed to show the variations of the IFHB. The IFHB values show a long-term variation with time. When a linear and a fourth-order harmonic function are used to model the estimated IFCB, which contains contributions of the hardware delays and clock errors, the results show that 89 % of the IFCB can be corrected given the current five triple-frequency GPS satellites with the averaged fitting RMS of 1.35 cm. Five days of data are processed to test the estimated satellite clock errors using the strategy presented. The residuals of P1/P5 and L1/L5 have a STD of <0.27 m and 0.97 cm, respectively. In addition, most predicted satellite IFCBs reach an accuracy of centimeter level and its mean accuracy of 5 days is better than 7 cm.     

北斗卫星轨道预报精度分析及改进

针对北斗GEO、IGSO、MEO的3种卫星类型和动态偏航、零偏航两种姿态控制模式,进行了以ECOM光压模型为基础的轨道预报精度分析。确定了北斗3类卫星的短期、中期、长期预报光压参数选择策略。采用光压参数修正法,通过对北斗卫星光压参数长期变化规律建模,有效提升了地影段轨道长期预报精度。研究结果可同时服务于北斗卫星轨道确定及历书参数生成。     

An a priori solar radiation pressure model for the QZSS Michibiki satellite

It has been noted that the satellite laser ranging (SLR) residuals of the Quasi-Zenith Satellite System (QZSS) Michibiki satellite orbits show very marked dependence on the elevation angle of the Sun above the orbital plane (i.e., the \(\beta \) angle). It is well recognized that the systematic error is caused by mismodeling of the solar radiation pressure (SRP). Although the error can be reduced by the updated ECOM SRP model, the orbit error is still very large when the satellite switches to orbit-normal (ON) orientation. In this study, an a priori SRP model was established for the QZSS Michibiki satellite to enhance the ECOM model. This model is expressed in ECOM’s D, Y, and B axes (DYB) using seven parameters for the yaw-steering (YS) mode, and additional three parameters are used to compensate the remaining modeling deficiencies, particularly the perturbations in the Y axis, based on a redefined DYB for the ON mode. With the proposed a priori model, QZSS Michibiki’s precise orbits over 21 months were determined. SLR validation indicated that the systematic \(\beta \)-angle-dependent error was reduced when the satellite was in the YS mode, and better than an 8-cm root mean square (RMS) was achieved. More importantly, the orbit quality was also improved significantly when the satellite was in the ON mode. Relative to ECOM and adjustable box-wing model, the proposed SRP model showed the best performance in the ON mode, and the RMS of the SLR residuals was better than 15 cm, which was a two times improvement over the ECOM without a priori model used, but was still two times worse than the YS mode.     

CODE’s five-system orbit and clock solution—the challenges of multi-GNSS data analysis

This article describes the processing strategy and the validation results of CODE’s MGEX (COM) orbit and satellite clock solution, including the satellite systems GPS, GLONASS, Galileo, BeiDou, and QZSS. The validation with orbit misclosures and SLR residuals shows that the orbits of the new systems Galileo, BeiDou, and QZSS are affected by modelling deficiencies with impact on the orbit scale (e.g., antenna calibration, Earth albedo, and transmitter antenna thrust). Another weakness is the attitude and solar radiation pressure (SRP) modelling of satellites moving in the orbit normal mode—which is not yet correctly considered in the COM solution. Due to these issues, we consider the current state COM solution as preliminary. We, however, use the long-time series of COM products for identifying the challenges and for the assessment of model-improvements. The latter is demonstrated on the example of the solar radiation pressure (SRP) model, which has been replaced by a more generalized model. The SLR validation shows that the new SRP model significantly improves the orbit determination of Galileo and QZSS satellites at times when the satellite’s attitude is maintained by yaw-steering. The impact of this orbit improvement is also visible in the estimated satellite clocks—demonstrating the potential use of the new generation satellite clocks for orbit validation. Finally, we point out further challenges and open issues affecting multi-GNSS data processing that deserves dedicated studies.     

Beidou satellite maneuver thrust force estimation for precise orbit determination

Beidou satellites, especially geostationary earth orbit (GEO) and inclined geosynchronous orbit (IGSO) satellites, need to be frequently maneuvered to keep them in position due to various perturbations. The satellite ephemerides are not available during such maneuver periods. Precise estimation of thrust forces acting on satellites would provide continuous ephemerides during maneuver periods and could significantly improve orbit accuracy immediately after the maneuver. This would increase satellite usability for both real-time and post-processing applications. Using 1 year of observations from the Multi-GNSS Experiment network (MGEX), we estimate the precise maneuver periods for all Beidou satellites and the thrust forces. On average, GEO and IGSO satellites in the Beidou constellation are maneuvered 12 and 2 times, respectively, each year. For GEO satellites, the maneuvers are mainly in-plane, while out-of-plane maneuvers are observed for IGSO satellites and a small number of GEO satellites. In most cases, the Beidou satellite maneuver periods last 15–25 min, but can be as much as 2 h for the few out-of-plane maneuvers of GEO satellites. The thrust forces acting on Beidou satellites are normally in the order of 0.1–0.7 mm/s². This can cause changes in velocity of GEO/IGSO satellites in the order of several decimeters per second. In the extreme cases of GEO out-of-plane maneuvers, very large cross-track velocity changes are observed, namely 28 m/s, induced by 5.4 mm/s² thrust forces. Also, we demonstrate that by applying the estimated thrust forces in orbit integration, the orbit errors can be estimated at decimeter level in along- and cross-track directions during normal maneuver periods, and 1–2 m in all the orbital directions for the enormous GEO out-of-plane maneuver.     

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.     

卫星激光反射器质心改正的概率模型

卫星激光测距通过测量激光脉冲在地面观测站和卫星之间的往返时间来计算卫星到测站的距离。激光反射器位置到卫星质心的距离即质心改正(CoM)需要精确标定,以提高卫星测距精度。卫星激光反射器的质心改正误差主要由角反射器分布效应引起,质心改正与激光束的入射角、角反射器排列结构和地面测距站位置有关。卫星角反射器对光子的反射概率与反射器的有效雷达截面积成正比,本文对角反射器的有效雷达截面面积进行拟合,建立以入射角为随机变量的概率模型,计算了球形LAGEOS-1/2的质心改正值,基于长期观测数据使用不同质心改正值进行了精密定轨,分析了其加权残差变化。同时,对BeiDou-M3的角反射器为平面阵列的情况进行了讨论,计算了质心改正值,用一个月的数据进行精密定轨。试验结果表明,基于概率理论的模型在精密轨道中与国际激光测距服务(ILRS)公布的结果相当,说明概率模型适用于球型卫星或非球型卫星。     

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.     

面向智慧渔船的多功能北斗示位标

为克服传统卫星紧急无线电示位标(EPIRB)定位精度差、功能单一的不足,满足渔船信息化、智能化的需求,设计了一种基于北斗定位和短报文通信技术的新型多功能示位标.首先,进行了示位标的硬件设计;其次,进行了示位标在极端恶劣海况下的偏转角仿真实验和不同姿态下的短报文收发测试,提出了基于示位标姿态的短报文发送机制;最后,进行了实验验证.结果表明:基于示位标姿态的短报文发送机制能够有效提高短报文投递率,设计的多功能北斗示位标在智慧渔船应用中具有良好的推广前景.     

极轨道卫星上测量太阳常数的新方法

该文提出了一种在极轨道太阳同步卫星上，利用指向太阳矢量方向安装的绝对辐射汁，以非跟踪方式测量太阳常数的方法，非跟踪模式下简化模型热力学微分方程解与跟踪模式的解形式相似，微机模拟画出二模式下的能量响应曲线，二曲线在最高点基本重合，表明这种方法同样能够达到太阳进行测量的精度，且结构简单，测量方便。     

Generation of a consistent absolute phase-center correction model for GPS receiver and satellite antennas

The development and numerical values of the new absolute phase-center correction model for GPS receiver and satellite antennas, as adopted by the International GNSS (global navigation satellite systems) Service, are presented. Fixing absolute receiver antenna phase-center corrections to robot-based calibrations, the GeoForschungsZentrum Potsdam (GFZ) and the Technische Universität München reprocessed more than 10 years of GPS data in order to generate a consistent set of nadir-dependent phase-center variations (PCVs) and offsets in the z-direction pointing toward the Earth for all GPS satellites in orbit during that period. The agreement between the two solutions estimated by independent software packages is better than 1 mm for the PCVs and about 4 cm for the z-offsets. In addition, the long time-series facilitates the study of correlations of the satellite antenna corrections with several other parameters such as the global terrestrial scale or the orientation of the orbital planes with respect to the Sun. Finally, completely reprocessed GPS solutions using different phase-center correction models demonstrate the benefits from switching from relative to absolute antenna phase-center corrections. For example, tropospheric zenith delay biases between GPS and very long baseline interferometry (VLBI), as well as the drift of the terrestrial scale, are reduced and the GPS orbit consistency is improved.     

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.     

针对北斗系统的降维快速高精度定向算法

通过分析北斗系统的星座特点及GEO卫星特征,提出了一种针对北斗系统的快速高精度定向方法。该方法利用北斗GEO卫星东西向几何构型好的优势,首先由GEO卫星的观测值结合降维解算理论解算基线向量候选值;然后通过模糊度函数法对候选值进行判决,得到最优基线向量,解出宽巷模糊度;最后在此基础上解算B1模糊度,进行高精度定向。该方法不但可以改善利用北斗定向解算所产生的病态性,而且可以减小模糊度搜索范围,实现单历元整周模糊度快速解算。利用实测北斗星历对算法进行了仿真验证,结果表明在实时动态条件下,该方法解算B1的整周模糊度成功率为99.31%,确定的俯仰角标准差为0.07°,航向角标准差为0.13°,是一种高效快速的定向算法。