北斗卫星导航系统实时定轨与钟差处理策略

目前鲜有对北斗卫星导航系统（BeiDouNavigationSatelliteSystem,BDS）实时精密定轨与钟差确定的研究,文章提出了BDS实时轨道与实时钟差处理策略,包括了观测与动力学模型、实时轨道与实时钟差处理流程与评估方法。尤其对于实时钟差,为了提高计算效率,联合使用两个独立并行的线程估计非差绝对钟差和历元间相对钟差。利用多模全球卫星导航系统试验(MGEX)与全球连续检测评估系统（iGMAS）实测数据进行了北斗实时轨道与钟差解算,BDS实时轨道径向平均精度对于GEO卫星优于20cm,对于IGSO与MEO一般优于10cm;钟差精度对于GEO卫星为0.5~4.5ns,对于IGSO／MEO为0.2~2.0ns。基于目前的轨道与钟差结果,实时精密单点定位（PrecisePointPositioning,PPP）结果可以达到分米量级。     

Time synchronization of new-generation BDS satellites using inter-satellite link measurements

Autonomous satellite navigation is based on the ability of a Global Navigation Satellite System (GNSS), such as Beidou, to estimate orbits and clock parameters onboard satellites using Inter-Satellite Link (ISL) measurements instead of tracking data from a ground monitoring network. This paper focuses on the time synchronization of new-generation Beidou Navigation Satellite System (BDS) satellites equipped with an ISL payload. Two modes of Ka-band ISL measurements, Time Division Multiple Access (TDMA) mode and the continuous link mode, were used onboard these BDS satellites. Using a mathematical formulation for each measurement mode along with a derivation of the satellite clock offsets, geometric ranges from the dual one-way measurements were introduced. Then, pseudoranges and clock offsets were evaluated for the new-generation BDS satellites. The evaluation shows that the ranging accuracies of TDMA ISL and the continuous link are approximately 4?cm and 1?cm (root mean square, RMS), respectively. Both lead to ISL clock offset residuals of less than 0.3?ns (RMS). For further validation, time synchronization between these satellites to a ground control station keeping the systematic time in BDT was conducted using L-band Two-way Satellite Time Frequency Transfer (TWSTFT). System errors in the ISL measurements were calibrated by comparing the derived clock offsets with the TWSTFT. The standard deviations of the estimated ISL system errors are less than 0.3?ns, and the calibrated ISL clock parameters are consistent with that of the L-band TWSTFT. For the regional BDS network, the addition of ISL measurements for medium orbit (MEO) BDS satellites increased the clock tracking coverage by more than 40% for each orbital revolution. As a result, the clock predicting error for the satellite M1S was improved from 3.59 to 0.86?ns (RMS), and the predicting error of the satellite M2S was improved from 1.94 to 0.57?ns (RMS), which is a significant improvement by a factor of 3–4.     

Advanced receiver autonomous integrity monitoring (ARAIM) schemes with GNSS time offsets

Within the current Advanced Receiver Integrity Monitoring (ARAIM) scheme, the time offsets between different Global Navigation Satellite System (GNSS) constellations are estimated along with a position solution and the GNSS receiver clock error. This scheme is called the Time-offsets Estimated ARAIM, or the TOE ARAIM. In order to enhance the interoperability and compatibility between different constellations, the time offsets are expected to be broadcast to users in future multi-GNSS positioning and navigation applications. This paper describes two new ARAIM schemes to make use of the Broadcast Time Offsets (BTOs): Time Offset Observed ARAIM (TOO ARAIM) and Time Offset Synchronized ARAIM (TOS ARAIM). It has been shown that the VPL performances of these two new ARAIM schemes rely strongly on the accuracy of BTOs. By varying the error model of the BTOs, the simulation results also demonstrate that the proposed new TOO ARAIM scheme can outperform the existing TOE ARAIM scheme-even if the accuracy of BTOs for integrity is degraded to 4.5 m and the probability of a BTO fault is relaxed to 10⁻² h⁻¹. In addition, the new Time Offset Synchronized ARAIM scheme (TOS ARAIM) can also perform better than the existing TOE ARAIM scheme if the accuracy of BTOs for integrity can reach 0.75 m. As the TOO ARAIM also has a very relaxed requirement on BTOs and better VPL performance, the TOO ARAIM is regarded as a superior ARAIM scheme for multi-GNSS with BTOs available.     

Autonomous broadcast ephemeris improvement for GNSS using inter-satellite ranging measurements

This paper discusses the concept of using inter-satellite ranging (ISR) measurements of the satellites of a Global Navigation Satellite System (GNSS) for autonomous broadcast ephemeris improvement. Firstly the inter-satellite ranging is modeled to obtain the clock and orbit error observables. The orbit error observable is analyzed and its observation equation is provided. Both least-squares estimation and Kalman Filter approach are proposed to estimate satellite clock errors, while solely the Kalman Filter is used to estimate the orbit errors. All these algorithms are validated using true broadcast ephemeris and precise ephemeris of GPS along with the simulated ranging noise. Based on the settings adopted in the test, the result shows that the orbit accuracy of the precise ephemeris using the proposed method is around 20–50 cm and the accuracy of the satellite clock can reach 20 cm while ranging noise is assumed to be 0.45 m (1σ). The User Ranging Error (URE) is improved from 1.05 m to 0.34 m, which is comparable to other sources of precise ephemeris or even better, while the proposed approach has many advantages such as compatibility and accessibility. It is also noted that the proposed method may provide useful functions in determining inter-constellation coordinate and time differences autonomously for better interoperability and interchangeability in the multi GNSS operation era.     

Analysis of GNSS clock prediction performance with different interrupt intervals and application to real-time kinematic precise point positioning

Continuous and timely real-time satellite orbit and clock products are mandatory for real-time precise point positioning (RT-PPP). Real-time high-precision satellite orbit and clock products should be predicted within a short time in case of communication delay or connection breakdown in practical applications. For prediction, historical data describing the characteristics of the real-time orbit and clock can be used as the basis for performing the prediction. When historical data are scarce, it is difficult for many existing models to perform precise predictions. In this paper, a linear regression model is used to predict clock products. Seven-day GeoForschungsZentrum (GFZ) final clock products sampled at 30 s are used to analyze the characteristics of GNSS clocks. It is shown that the linear regression model can be used as the prediction model for the satellite clock products. In addition, the accuracy of the clock prediction for different satellites are analyzed using historical data with different periods (such as 2 and 10 epochs). Experimental results show that the accuracy of the clock with the linear regression prediction model using historical data with 10 epochs is 1.0 ns within 900 s. This is higher accuracy than that achieved using historical data of 2 epochs. Finally, the performance analysis for real-time kinematic precise point positioning (PPP) is provided using GFZ final clock prediction results and state space representation (SSR) clock prediction results when communication delay or connection breakdown occur. Experimental results show that the positioning accuracy without prediction is better than that with prediction in general, whether using the final clock product or the SSR clock product. For the final clock product, the positioning accuracy in the north (N), east (E), and up (U) directions is better than 10.0 cm with all visible GNSS satellites with prediction. In comparison, the 3D positioning accuracy of N, E, and U directions with visible GNSS satellites whose prediction accuracy is better than 0.1 ns using historical data of 10 epochs is improved from 15.0 cm to 7.0 cm. For the SSR clock product, the positioning accuracy of N, E, and U directions is better than 12.0 cm with visible GNSS satellites with prediction. In comparison, the 3D positioning accuracy of N, E, and U directions with visible GNSS satellites whose prediction accuracy is better than 0.1 ns using historical data of 10 epochs is improved from 12.0 cm to 9.0 cm.     

The GLONASS-M satellite yaw-attitude model

The proper modeling of the satellites’ yaw-attitude is a prerequisite for high-precision Global Navigation Satellite System (GNSS) positioning and poses a particular challenge during periods when the satellite orbital planes are partially eclipsed. Whereas a lot of effort has been put in to examine the yaw-attitude control of GPS satellites that are in eclipsing orbits, hardly anything is known about the yaw-attitude behavior of eclipsing GLONASS-M satellites. However, systematic variations of the carrier phase observation residuals in the vicinity of the orbit’s noon and midnight points of up to ±27 cm indicate significant attitude-related modeling issues. In order to explore the GLONASS-M attitude laws during eclipse seasons, we have studied the evolution of the horizontal satellite antenna offset estimates during orbit noon and orbit midnight using a technique that we refer to as “reverse kinematic precise point positioning”. In this approach, we keep all relevant global geodetic parameters fixed and estimate the satellite clock and antenna phase center positions epoch-by-epoch using 30-second observation and clock data from a global multi-GNSS ground station network. The estimated horizontal antenna phase center offsets implicitly provide the spacecraft’s yaw-attitude. The insights gained from studying the yaw angle behavior have led to the development of the very first yaw-attitude model for eclipsing GLONASS-M satellites. The derived yaw-attitude model proves to be much better than the nominal yaw-attitude model commonly being used by today’s GLONASS-capable GNSS software packages as it reduces the observation residuals of eclipsing satellites down to the normal level of non-eclipsing satellites and thereby prevents a multitude of measurements from being incorrectly identified as outliers. It facilitates continuous satellite clock estimation during eclipse and improves in particular the results of kinematic precise point positioning of ground-based receivers.     

联合北斗导航与星间链路的大椭圆卫星定轨方法

传统的地面测控和GNSS均无法实现HEO卫星全弧段的跟踪观测.在分析北斗导航信号及其星间链路信号对典型HEO的观测几何及覆盖特性的基础上,利用北斗导航及其星间链路对HEO测控支持形成互补的特点,提出了一种卫星导航与星间链路相结合的自主导航方法.对HEO定轨进行分段划分并基于EKF设计了卫星导航与星间链路数据融合定轨的自主导航算法.分析结果表明,本文提出的方法能够从全弧段上改善HEO的观测几何,定轨精度比仅使用卫星导航提高了2个数量级,并且仅需较少的星间链路资源.      

GNSS receiver clock modeling when using high-precision oscillators and its impact on PPP

Processing data from Global Navigation Satellite Systems (GNSS) always requires time synchronization between transmitter and receiver clocks. Due to the limited stability of the receiver’s internal oscillator, the offset of the receiver clock with respect to the system time has to be estimated for every observation epoch or eliminated by processing differences between simultaneous observations. If, in contrast, the internal oscillator of the receiver is replaced by a stable atomic clock one can try to model the receiver clock offset, instead of estimating it on an epoch-by-epoch basis. In view of the progress made in the field of high-precision frequency standards we will investigate the technical requirements for GNSS receiver clock modeling at the carrier phase level and analyze its impact on the precision of the position estimates.     

BeiDou-3 orbit and clock quality of the IGS Multi-GNSS Pilot Project

Within the Multi-GNSS Pilot Project (MGEX) of the International GNSS Service (IGS), precise orbit and clock products for the BeiDou-3 global navigation satellite system (BDS-3) are routinely generated by a total of five analysis centers. The processing standards and specific properties of the individual products are reviewed and the BDS-3 orbit and clock product performance is assessed through direct inter-comparison, satellite laser ranging (SLR) residuals, clock stability analysis, and precise point positioning solutions. The orbit consistency evaluated by the signal-in-space range error is on the level of 4–8 cm for the medium Earth orbit satellites whereas SLR residuals have RMS values between 3 and 9 cm. The clock analysis reveals sytematic effects related to the elevation of the Sun above the orbital plane for all ACs pointing to deficiencies in solar radiation pressure modeling. Nevertheless, precise point positioning with the BDS-3 MGEX orbit and clock products results in 3D RMS values between 7 and 8 mm.     

Early analysis of precise orbit and clock offset determination for the satellites of the global BeiDou-3 system

Eight new-generation BeiDou satellites (BeiDou-3) have been launched into Medium Earth Orbit (MEO), allowing for global coverage since March 2018, and they are equipped with new hydrogen atomic clocks and updated rubidium clocks. Firstly, we analyzed the signals for the carrier-to-noise-density ratio (C/N0) and pseudorange multipath (MP) by using international GNSS (Global Navigation Satellite System) Monitoring and Assessment System (iGMAS) station data, and found that B1C has a lower C/N0, and B2a has the same level of C/N0 as the B1I and B3I signals. For pseudorange multipath, compared with the BeiDou-2 satellites, the obvious systematic variation of MP scatters related to the elevation angle is greatly improved for the BeiDou-3 and BeiDou-3e satellites signals. For the signals of the BeiDou-3 satellites, the order of the Root Mean Square (RMS) values of multipath and noise is B3I?<?B1I?<?B2a?<?B1C. Then, the comparison of the precise orbit determination and clock offset determination for the BeiDou-2, BeiDou-3, and BeiDou-3 experimental (BeiDou-3e) satellites was done by using 10 stations from iGMAS. The 3D precision of the 24?h orbit overlap is 24.55, 25.61, and 23.35?cm for the BeiDou-3, BeiDou-3e, and BeiDou-2 satellites, respectively. BeiDou-3 satellite has a comparable precision to that of the BeiDou-2 satellite. For the precision of clock offset estimation, the Standard Deviation (STD) of the BeiDou-3 MEO satellite is 0.350?ns, which is an improvement of 0.042?ns over that of the BeiDou-2 MEO satellite. The stabilities of the BeiDou-3 and BeiDou-3e onboard clocks are better than those of BeiDou-2 by factors of 2.84 and 1.61 at an averaging time of 1000 and 10,000?s, respectively.     

Performance improvement of real-time PPP ambiguity resolution using a regional integer clock

Obtaining reliable GNSS uncalibrated phase delay (UPD) or integer clock products is the key to achieving ambiguity-fixed solutions for real-time (RT) precise point positioning (PPP) users. However, due to the influence of RT orbit errors, the quality of UPD/integer clock products estimated with a globally distributed GNSS network is difficult to ensure, thereby affecting the ambiguity resolution (AR) performance of RT-PPP. In this contribution, by fully utilising the consistency of orbital errors in regional GNSS network coverage areas, a method is proposed for estimating regional integer clock products to compensate for RT orbit errors. Based on Centre National d’Études Spatiales (CNES) RT precise products, the regional GPS/BDS integer clock was estimated with a CORS network in the west of China. Results showed that the difference between the estimated regional and CNES global integer clock/bias products was generally less than 5 cm for GPS, whereas clock differences of greater than 10 cm were observed for BDS due to the large RT orbit error. Compared with PPP using global integer clock/bias products, the AR performance of PPP using the regional integer clock was obviously improved for four rover stations. For single GPS, the horizontal and vertical accuracies of ambiguity-fixed PPP solutions were improved by 56.2% and 45.3% on average, respectively, whereas improvements of 67.5% and 50.5% in the horizontal and vertical directions, respectively, were observed for the combined GPS/BDS situation. Based on a regional integer clock, the RMS error of a kinematic ambiguity-fixed PPP solution in the horizontal direction could reach 0.5 cm. In terms of initialisation time, the average time to first fix (TTFF) in combined GPS/BDS PPP was shortened from 18.2 min to 12.7 min. In view of the high AR performance realised with the use of regional integer clocks, this method can be applied to scenarios that require high positioning accuracy, such as deformation monitoring.     

一种适用于高轨空间的GNSS矢量跟踪方案设计

高轨空间中全球卫星导航系统（GNSS）信号可用性严重变差，对GNSS接收机的跟踪性能提出更高要求。利用GNSS信号传播链路模型分析了高轨空间GNSS信号特点，对比了标量跟踪和矢量跟踪这2类典型跟踪环路在高轨空间的适用性，进而设计了一种适用于高轨空间的GNSS矢量跟踪方案。该方案通过估计载噪比确定量测噪声方差阵，以对各通道量测信息进行加权处理来获得高精度的导航参数；并根据高轨航天器的动态性能确定过程噪声方差阵，利用轨道动力学模型对导航参数进行一步预测，从而实现了对各通道信号跟踪参数的准确预测及联合跟踪。仿真验证表明:所设计的跟踪方案可实现高轨空间中强信号对弱信号的辅助跟踪，从而提高了高轨空间中弱信号的跟踪性能及可用性，并对中断信号具有一定的桥接能力。      

Galileo real-time orbit determination with multi-frequency raw observations

Real-time GNSS-based applications require corresponding real-time orbit products. While traditional GNSS orbits are generated with the dual-frequency IF (Ionosphere-Free) model, the increase of multi-frequency signal satellites brings new challenges for the data processing. Therefore, real-time orbit determination with the multi-frequency UC (Uncombined) model is introduced in this study considering its flexibility. With the derived mathematical model conforming to IGS (International GNSS Service) dual-frequency clock definition and one-week triple-frequency Galileo observation data from 90 IGS network stations, the convergence and accuracy of real-time orbits is assessed and the characteristics of satellite IFCB (Inter-Frequency Clock Bias) are analyzed. Results indicate that the model differences, including dual-frequency IF model, dual-frequency UC model and triple-frequency UC model, contribute to only cm-level differences with CODE (Center for Orbit Determination in Europe) final orbits after a convergence time of around 12 h. The constellation-mean RMS (Root Mean Square) differences of the converged real-time orbits with the CODE final orbits reaches about 5.0 cm, 7.0 cm and 5.0 cm for the radial, tangential and normal directions. The convergence of satellite IFCB is much faster than that of satellite orbit, which reflects a loose correlation between these two parameters. While the Galileo satellite IFCB are temporally stable, the modeling of satellite IFCB may be unreliable when over constrained and becomes even more unstable with commonly encountered datum changes. In summary, real-time GNSS orbit determination with multi-frequency raw observations is feasible and extendable with proper treatment of IFCB.     

Geosynchronous satellites expanding a future GNSS satellite constellation: A precise orbit determination study

The integration of geosynchronous orbit (GSO) satellites in Global Navigation Satellite Systems (GNSS) is mostly discussed to enable a regional enhancement for tracking. But how do GSO satellites affect the orbit determination of the rest of the constellation? How accurately can these orbits be determined in a future GNSS tracking scenario with optical links? In this simulation study we analyze the benefit of GSO satellites as an expansion of a MEO (Medium Earth Orbit) satellite constellation – we selected the Galileo satellite constellation – for MEO Precise Orbit Determination (POD). We address not only the impact on POD of MEO satellites but also the possibility to precisely determine the GSO satellites – geostationary orbits (GEO) and inclined geosynchronous orbits (IGSO) – in such an expanded MEO constellation. In addition to GNSS microwave observations, we analyze the influence of different optical links between the participating entities: Optical two-way Inter-Satellite Links (OISL) and ground-space oriented Optical Two-Way Links (OTWL). These optical measurements together with the GNSS microwave observations give a remarkable benefit for the POD capability. In the case of GNSS and OTWL, we simulate the measurements with regard to a network of 16 ground stations. We pay great attention to the simulation of systematic effects of all measurement techniques. We discuss the influence on the systematic errors as well as the formal orbit uncertainties. A MEO constellation expanded with GSO satellites as well as the use of optical links together with GNSS observations not only improves the MEO satellite orbits but also the GSOs to a great extent.     

基于高轨航天器的GNSS接收机技术

全球导航卫星系统（GlobalNavigationSatelliteSystem,GNSS）应用于高轨航天器时,因轨道高于导航卫星,可见星数量急剧减少,空间信号功率微弱,信号的快速捕获和跟踪十分困难。文章对高轨地球同步轨道（GeosynchronousEarthOrbit,GEO）接收技术进行了研究。以中国实践十七号卫星为研究对象,采用官方正式发布的发射天线方向图对GEO下GNSS信号特征及可用性开展研究分析,并针对高轨道航天器GNSS信号微弱的特点,采用长时间积分处理的梳状滤波方法、差分相干累加比特同步算法和基于动力学模型补偿的扩展卡尔曼滤波自主定轨算法设计GNSS接收机,并在半物理仿真平台进行了测试验证。试验结果表明：GNSS接收机捕获灵敏度优于-173dBW,跟踪灵敏度优于-175dBW,定轨位置精度优于50m,速度精度优于0.01m/s。     

星载铷原子钟频率特性星地测量技术研究

阐述了借助地面测控站对星载铷钟进行监测,以实现铷钟在轨运行频率特性的四种测量方法:单向时差比对法、双向时差比对法、利用GPS系统时间比对法和激光时差比对法,并对这四种方法的测量原理进行了分析和比较。对育种卫星搭载国产铷钟的试验方案和测量结果进行了介绍。     

基于GNSS测量的天宫二号质心确定

由于轨道机动燃料消耗,科学载荷加载、分离,以及伴飞小卫星在轨释放等原因引起天宫二号空间站质心(COM)发生位移,从而影响天宫二号的动力学质心定轨精度。针对这一问题,提出了基于全球导航卫星系统(GNSS)测量数据的简化动力学质心估计方法。燃料消耗是引起天宫二号质心发生位移的主要原因,质心在本体坐标系X轴方向位移最为显著。利用GNSS测量数据对天宫二号进行质心估计和精密定轨,在三轴对地稳定姿态下,本体坐标系X轴方向与轨道切向重合,定轨结果对本体坐标系X轴方向的质心位移并不敏感。但在连续偏航模式下,本体坐标系X轴在轨道法向上有较大分量,X轴方向的质心位移对基于GNSS测量计算的精密定轨结果有较大影响。定性和定量分析结果表明:偏航姿态模式下天宫二号本体坐标系X轴方向质心位移估计具有可行性。天宫二号实测数据计算结果表明:与未做质心估计的定轨结果进行对比,质心估计后表征轨道动力学建模误差的经验加速度补偿水平在轨道径向、切向和法向上分别降低62%、50%和65%;载波相位后验残差标准差降低0.04 cm;精密轨道与全球激光测距数据比较精度提高0.86 cm。所提方法可以应用于大型低轨航天器在轨质心估计。      

风云三号C星GNOS北斗掩星电离层探测初步结果

利用风云三号卫星C星GNOS掩星探测仪电离层数据,分析了2013年10月FY-3C GNOS探测的北斗掩星电离层廓线分布,将2013年10月1日至2015年10月10日期间FY-3C GNOS观测的F₂层峰值电子密度（N_mF₂）与地面电离层测高仪观测结果进行对比,验证了FY-3C GNOS北斗电离层掩星的探测精度.结果表明,FY3-C GNOS北斗电离层掩星与电离层测高仪探测的N_mF₂数据相关系数为0.96,平均偏差为10.21%,标准差为19.61%.在不同情况下其数据精度有如下特征:白天精度高于夜晚;夏季精度高于分季,分季精度高于冬季;中纬地区精度高于低纬地区,低纬地区精度高于高纬地区; BDS倾斜同步轨道（IGSO）卫星精度高于同步轨道（GEO）卫星和中轨道（MEO）卫星.FY-3C GNOS北斗电离层掩星与国际上其他掩星电离层数据精度的一致性对GNSS掩星探测资料的综合利用具有重大意义.      

An introduction to China FY3 radio occultation mission and its measurement simulation

GNSS (Global Navigation Satellite System) radio occultation mission for remote sensing of the Earth’s atmosphere will be performed by GNOS (GNSS Occultation Sounder) instrument on China FengYun-3 (FY3) 02 series satellites, the first of which FY3-C will be launched in the year 2013. This paper describes the FY3 GNOS mission and presents some results of measurement simulation. The key designed specifications of GNOS are also shown. The main objective of simulation is to provide scientific support for GNOS occultation mission on the FY3-C satellites. We used EGOPS software to simulate occultation measurements according to GNOS designed parameters. We analyzed the accuracy of retrieval profiles based on two typical occultation events occurring in China South–East area among total simulated events. Comparisons between the retrieval atmospheric profiles and background profiles show that GNOS occultation has high accuracy in the troposphere and lower stratosphere. The sensitivities of refractivity to three types of instrumental error, i.e. Doppler biases, clock stability and local multipath, were analyzed. The results indicated that the Doppler biases introduced by along-ray velocity error and GNOS clock error were the primary error sources for FY3-C occultation mission.     

Monitoring atomic clocks on board GNSS satellites

A method for monitoring atomic clocks on board Global Navigation Satellites System (GNSS) satellites is described to address the issue of clock related signal integrity in safety–critical applications of GNSS. The carrier-phase time transfer is employed in the clock monitoring method which enables tight tracking of the satellite onboard clocks and thus improves detectability of clock anomalies. Detecting onboard clock anomalies requires the ability to monitor clocks in real time, and a Kalman filter can then be utilized to estimate the phase offsets between the satellite clocks and ground clocks. This study, using the difference between the measured and predicted phase offset as a test statistic, sets a threshold for clock anomalies based on the prediction interval approach. Finally the validity of the monitoring method is examined by processing a set of real GNSS data that includes two recent incidents of clock anomalies in GNSS satellites.