非差模糊度固定北斗三号实时滤波精密定轨

模糊度固定是全球导航卫星系统（global navigation satellite system,GNSS）高精度数据处理的关键。不同于传统的双差模糊度固定,非差模糊度固定无需构建双差模糊度,更为简单高效。将非差模糊度固定引入北斗三号全球卫星导航系统(BeiDou-3 global navigation satellite system,BDS-3)中地球轨道卫星实时滤波定轨,分析非差模糊度固定对实时滤波轨道收敛速度及精度的影响。利用国际GNSS服务组织全球测站网观测数据进行实时滤波精密定轨实验,以德国地学研究中心的事后快速轨道为参考评定精度。结果表明：非差模糊度固定对收敛速度影响很小,但可以有效提升轨道切向、法向精度;相比浮点解轨道,固定解轨道径向、切向、法向精度分别提高1.0%、18.5%、19.5%,误差均方根分别达到6.0、7.4、6.2 cm;受切向、法向影响,中国空间技术研究院类型卫星轨道精度优于上海微小卫星工程中心类型卫星轨道;顾及窄巷固定率与轨道精度的相关性,窄巷固定率可以作为实时轨道质量的重要指标之一。实时滤波轨道精度的进一步提升有赖于BDS-3数据处理模型的持续精...     

星间单差模糊度固定的低轨卫星精密定轨精度分析

高精度、高可靠性的卫星轨道是实现低轨卫星精密应用的重要前提,而模糊度固定技术是提高卫星定轨精度的关键途径。研究了基于整数钟的星间单差模糊度固定原理和方法,并利用2019年4月—5月的两颗GRACE-FO（gravity recovery and climate experiment follow on）卫星数据（GRACE-C/D）系统评估了固定解对低轨卫星简化动力学和运动学定轨的精度提升效果。结果表明,两颗卫星简化动力学和运动学定轨的宽巷模糊度固定率均达到99%,而窄巷模糊度固定率在95%左右。对于简化动力学定轨,GRACE-C/D固定解轨道的重叠轨道的3D均方根误差（root mean square error, RMSE）分别从7.1 mm和7.4 mm减小到了4.2 mm和3.6 mm;卫星激光测距（satellite laser ranging, SLR）残差标准差（standard deviation, STD）分别从15.9 mm和14.4 mm降低到了10.8 mm和11.0 mm,精度提升了32%和24%;K波段测距残差RMSE从8.0 mm减小到2.9 mm,进一步表明固定解还能有效提升低轨卫星间相对位置精度。对于运动学定轨,与精密科学轨道产品互差3D RMSE,浮点解分别为37.5 mm和36.4 mm,固定解分别为27.7 mm和25.5 mm,精度提升约28%,SLR残差STD也减小了约20%。     

固定模糊度的精密单点定位几何定轨方法及结果分析

传统的基于PPP(precise point positioning)模式的定轨方法采用浮点解,导致其定轨精度及可靠性较双差固定解稍差。为了进一步提高PPP模式事后定轨的精度和可靠性,利用2012年1月2～7日全球IGS跟踪站数据计算出当天所有卫星的宽巷和窄巷FCB产品,实现了GRACE卫星固定PPP整数模糊度的精密定轨。并将定轨结果分别与GFZ事后精密轨道、K波段测距结果进行比较,分析其内外符合精度。实验结果表明:与GFZ提供的事后精密轨道相比,GRACE-A卫星单天轨道固定解的精度为R方向2～3cm,T方向大部分优于2cm,N方向优于2cm,较之浮点解的定轨结果3个方向分别改善了约19%、30%、50%;GRACE-B卫星3个方向精度分别为2～3cm、2cm左右、1～2cm,较之浮点解各方向也有同等程度的改善。与K波段测距结果相比,浮点解的KBR残差STD均值为22.6mm,固定解为16.4mm,比浮点解提高了约28%。可见,PPP模糊度固定解明显改善了低轨卫星的定轨精度,能提供更可靠的轨道服务。     

模糊度固定的北斗卫星多系统融合精密轨道确定

利用全球分布的IGS和MGEX站多模观测数据,研究了北斗卫星多系统融合双差动力学精密定轨方法,提出了适应北斗系统的双差模糊度固定策略。结合实测数据,对比了单系统与多系统融合、模糊度固定解与浮点解的定轨效果。结果表明：相比单系统定轨,多系统融合定轨能有效改进IGSO和MEO卫星轨道精度,但对于GEO卫星,多系统融合定轨并无优势;利用改进的模糊度固定策略对IGSO和MEO卫星双差模糊度进行固定,有效提高了长基线模糊度固定率,整体固定成功率由40%提高到60%以上;模糊度固定对定轨精度改进作用明显,IGSO和MEO卫星三维定轨精度分别提高了48%和36%,达到0.048 m和0.066 m。     

PPP-RTK模糊度快速固定算法研究

将网络RTK（NRTK）与精密单点定位（PPP）技术优势融合的PPP-RTK技术,已经成为目前精密定位研究的热点. 本文提出一种将模糊度快速固定的解决方案,优化了PPP-RTK的模糊度固定解的算法,使得模糊度估计可靠性提高. 在实验中,利用国际GNSS服务（IGS）测站的实测数据进行了PPP-RTK定位解算. 结果统计表明:利用该算法对静态数据进行定位处理,其中数据收敛时间达到厘米级需要20 min,其中在平面位置方向的定位精度优于3 cm,在高程方向上的定位精度优于5 cm.      

非差模糊度整数固定解PPP新方法及实验

研究了观测数据短时失锁或中断情况下的精密单点定位-模糊度解算（precise point positioning-ambiguity resolution,PPP-AR）模糊度快速重收敛方法,给出了合理的观测值精化信息外推时间阈值,从系统端和用户端分别论证了该方法对提升现有非差网络RTK（undifferenced network real time kinematic positioning,URTK）服务可靠性的重要意义,并设计了相应的实时测试方案进行验证分析。测试结果表明,观测值精化信息可有效外推至少30 s,采用PPP-AR模糊度快速重收敛技术后,即使在周跳频繁发生的恶劣观测条件下也能使URTK系统端和用户端保持较高的服务可靠性。用户无需区域增强系统支持即可独立实现模糊度快速重收敛,有效降低了用户从URTK系统端获取区域增强信息时的实时数据通讯负担。     

基于整数钟的PPP非差模糊度固定方法

非差模糊度固定能够有效提高精密单点定位(PPP)的定位精度和收敛速度,是国内外卫星导航定位领域的研究热点。基于整数钟实现了PPP非差模糊度固定,在非差模糊度逐级固定中分别估计接收机宽巷偏差和窄巷偏差;对宽巷和窄巷模糊度进行改正,从而消除了接收机硬件延迟对模糊度的影响;同时采用取整成功率检验和ratio值检验,保证模糊度固定的可靠性。将以上方法应用到动态精密单点定位中,实验结果表明:仿动态条件下,模糊度正确固定后,东、北向定位精度达到mm级、天向定位精度优于5 cm;动态解算条件下,采用1 s采样间隔数据16 min左右即可实现模糊度的首次固定。PPP固定解在东、北、天3个方向的定位精度分别为1.5、2.7和1.3 cm,相比于浮点解分别提升了61%、40%和38%。     

卫星钟差解算及其星间单差模糊度固定

整数相位模糊度解算可以显著提高GNSS精密单点定位（PPP）的精度。本文提出一种解算卫星钟差的方法,通过固定星间单差模糊度恢复出能够支持单台接收机进行整数模糊度解算的卫星钟差,即所谓的“整数”钟差。为了实现星间单差模糊度固定,分别通过卫星端宽巷FCB解算和模糊度基准的选择与固定恢复出宽巷和窄巷模糊度的整数性质。为了证明本文方法的可行性,采用IGS测站的GPS数据进行卫星钟差解算试验。结果表明,在解算钟差时,星间单差模糊度固定的平均成功率为73%。得到的卫星钟差与IGS最终钟差产品相比,平均的RMS和STD分别为0.170和0.012 ns。448个IGS测站的星间单差宽巷和窄巷模糊度小数部分的分布表明本文得到的卫星钟差和FCB产品具备支持PPP用户进行模糊度固定的能力。基于以上产品开展了模拟动态PPP定位试验,结果表明模糊度固定之后,N、E、U和3D的定位精度（RMS）分别达到0.009、0.010、0.023和0.027 m,与不固定模糊度或采用IGS钟差的结果相比,分别提高了30.8%、61.5%、23.3%和37.2%。     

非差模糊度整数固定解PPP新方法及实验

分析了标准模型中非差模糊度无法固定的原因,提出了非差模糊度整数解的小数偏差分离(fractional bias isolating,FBI)模型与方法。实验结果表明,使用30min的静态观测数据,即可达到水平方向mm级、高程cm级的定位精度,相比浮点解水平方向精度提高了一个数量级,高程方向也改善了50%～60%,同时,对流层天顶延迟ZPD的精度也有20%～30%的改善。     

模糊度固定与弧段长度对区域站定轨的影响分析

我国北斗卫星导航系统难以实现境外全球布站,采用区域站观测值是实现高精度定轨的主要手段。本文分析了整网模糊度固定、有效定轨弧段选择对提高区域定轨精度的作用。采用陆态网GPS观测数据进行区域精密定轨仿真验证,首先论证了不同测站分布下,整网模糊度固定对区域定轨精度的效果,结果表明:相同测站条件下,固定解定轨精度比浮点解精度提高30%以上;仅采用国内7个站的固定解三维定轨精度即达到20 cm左右,优于27站的浮点解精度。另外,从星座的构型与地面站分布的可视范围方面,分析了不同观测时长对定轨精度影响,实测数据论证表明:当中国区域站观测时间大于48 h,总能获取不小于24 h的区域有效定轨弧段,并且各卫星最佳的24 h观测弧段三维定轨精度均可达到0.3 m左右。     

多系统实时精密单点定位及非差模糊度固定

正精密单点定位(precise point positioning,PPP)技术能够在全球区域获取用户在国际地球参考框架下的精确三维坐标,打破了以往只能够使用差分定位技术才能够实现高精度定位的局面,是继RTK/NRTK技术之后出现的又一次技术革命。论文旨在构建实时GNSS PPP服务系统,围绕GNSS卫星钟差估计、多系统融合PPP、卫星姿态、GPS未校准相位延迟(uncalibrated phase delays,UPD)估计、PPP模糊度固定等展开研究,为用户获取实时、高精度和高可靠性的GNSS PPP服务奠定理论和实践基础。本文的主要工作和贡献如下:     

Improved method to estimate undifferenced satellite fractional cycle biases using network observations to support PPP ambiguity resolution

GPS Solutions - Fixing ambiguities is beneficial to improve accuracy and convergence time of precise point positioning (PPP). In recent years, several methods have been proposed to estimate...     

Triple-frequency GPS precise point positioning with rapid ambiguity resolution

At present, reliable ambiguity resolution in real-time GPS precise point positioning (PPP) can only be achieved after an initial observation period of a few tens of minutes. In this study, we propose a method where the incoming triple-frequency GPS signals are exploited to enable rapid convergences to ambiguity-fixed solutions in real-time PPP. Specifically, extra-wide-lane ambiguity resolution can be first achieved almost instantaneously with the Melbourne-Wübbena combination observable on L2 and L5. Then the resultant unambiguous extra-wide-lane carrier-phase is combined with the wide-lane carrier-phase on L1 and L2 to form an ionosphere-free observable with a wavelength of about 3.4 m. Although the noise of this observable is around 100 times the raw carrier-phase noise, its wide-lane ambiguity can still be resolved very efficiently, and the resultant ambiguity-fixed observable can assist much better than pseudorange in speeding up succeeding narrow-lane ambiguity resolution. To validate this method, we use an advanced hardware simulator to generate triple-frequency signals and a high-grade receiver to collect 1-Hz data. When the carrier-phase precisions on L1, L2 and L5 are as poor as 1.5, 6.3 and 1.5 mm, respectively, wide-lane ambiguity resolution can still reach a correctness rate of over 99 % within 20 s. As a result, the correctness rate of narrow-lane ambiguity resolution achieves 99 % within 65 s, in contrast to only 64 % within 150 s in dual-frequency PPP. In addition, we also simulate a multipath-contaminated data set and introduce new ambiguities for all satellites every 120 s. We find that when multipath effects are strong, ambiguity-fixed solutions are achieved at 78 % of all epochs in triple-frequency PPP whilst almost no ambiguities are resolved in dual-frequency PPP. Therefore, we demonstrate that triple-frequency PPP has the potential to achieve ambiguity-fixed solutions within a few minutes, or even shorter if raw carrier-phase precisions are around 1 mm. In either case, we conclude that the efficiency of ambiguity resolution in triple-frequency PPP is much higher than that in dual-frequency PPP.     

单频GPS接收机整周模糊度快速动态解算方法研究

本文提出了一种快速动态解算单频GPS接收机整周模糊度的方法,其基本思想是对系数阵进行QR分解,通过矩阵变换使模糊度参数和位置参数分离,降低矩阵维数,并采用了一种残差二次型的快速算法。针对单频GPS接收机数据进行了静态和动态两种实验,本文算法达到静态误差小于1cm、动态误差小于5cm的精度,表明对于动态用户,该方法是快速和有效的,可应用于高精度导航和动态定位。     

The ratio test for future GNSS ambiguity resolution

The performance of the popular ambiguity ratio test is analyzed. Based on experimental and simulated data, it is demonstrated that the current usage of the ratio test with fixed critical value is not sustainable in light of the enhanced variability that future global navigation satellite system (GNSS) ambiguity resolution will bring. As its replacement, the model-driven ratio test with fixed failure rate is proposed. The characteristics of this fixed-failure rate ratio test are described, and a performance analysis is given. The relation between its critical value and various GNSS model parameters is also studied. Finally, a procedure is presented for the creation of fixed failure rate look-up tables for the critical values of the ratio test.     

Undifferenced ionospheric-free ambiguity resolution using GLONASS data from inhomogeneous stations

GLONASS frequency division multiple access signals render ambiguity resolution (AR) rather difficult because: (1) Different wavelengths are used by different satellites, and (2) pseudorange inter-frequency biases (IFBs) cannot be precisely modeled by means of a simple function. In this study, an AR approach based on the ionospheric-free combination with a wavelength of about 5.3 cm is assessed for GLONASS precise point positioning (PPP). This approach simplifies GLONASS AR because pseudorange IFBs do not matter, and PPP-AR can be enabled across inhomogeneous receivers. One month of GLONASS data from 165 European stations were processed for different network size and different durations of observation periods. We find that 89.9% of the fractional parts of ionospheric-free ambiguities agree well within ± 0.15 cycles for a small network (radius = 500 km), while 77.6% for a large network (radius = 2000 km). In case of the 3-hourly GLONASS-only static PPP solutions for the small network, reliable AR can be achieved where the number of fixed GLONASS ambiguities account for 97.6% within all candidate ambiguities. Meanwhile, the RMS of the east, north and up components with respect to daily solutions is improved from 1.0, 0.6, 1.2 cm to 0.4, 0.4, 1.1 cm, respectively. When GPS PPP-AR is carried out simultaneously, the positioning performance can be improved significantly such that the GLONASS ambiguity fixing rate rises from 74.4 to 95.4% in case of hourly solutions. Finally, we introduce ambiguity-fixed GLONASS orbits to re-attempt GLONASS PPP-AR in contrast to the above solutions with ambiguity-float orbits. We find that ambiguity-fixed orbits lead to clearly better agreement among ionospheric-free ambiguity fractional parts in case of the large network, that is 80.5% of fractional parts fall in ± 0.15 cycles in contrast to 74.6% for the ambiguity-float orbits. We conclude that highly efficient GLONASS ionospheric-free PPP-AR is achievable in case of a few hours of data when GPS PPP-AR is also accomplished, and ambiguity-fixed GLONASS orbits will contribute significantly to PPP-AR over wide areas.     

The Null method applied to GNSS three-carrier phase ambiguity resolution

The Null method is a technique to fix the ambiguity in L1 phase measurements of the global positioning system (GPS). The method is adapted to new global navigation satellite systems (GNSS) which offer phase measurements at three frequencies. In order to validate the efficiency of the adapted method, results obtained using a software simulator and an emulator are presented. The results are then compared to those obtained with the least-squares ambiguity decorrelation adjustment (LAMBDA) method. Good performance of the Null method in new GNSS systems is shown.Acknowledgments. The measurements used were provided by the European Space Agency, and were generated by Spectra Precision Terrasat under contract No. 12.406/77/NL/DS. The authors thank Maria Belmontes Rivas for her comments and the reviewers for their suggestions.     

0.99999999 confidence ambiguity resolution with GPS and Galileo

In this short contribution it is demonstrated how integer carrier phase cycle ambiguity resolution will perform in near future, when the US GPS gets modernized and the European Galileo becomes operational. The capability of ambiguity resolution is analyzed in the context of precise differential positioning over short, medium and long distances. Starting from dual-frequency operation with GPS at present, particularly augmenting the number of satellites turns out to have beneficial consequences on the capability of correctly resolving the ambiguities. With a 'double' constellation, on short baselines, the confidence of the integer ambiguity solution increases to a level of 0.99999999 or beyond. Electronic Publication