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.     

BDS/GPS精密单点定位收敛时间与定位精度的比较

采用武汉大学卫星导航定位技术研究中心发布的北斗精密卫星轨道和钟差,在TriP 2.0软件的基础上实现了BDS PPP定位算法,并利用大量实测数据进行了BDS/GPS静态PPP和动态PPP浮点解试验。结果表明,BDS静态PPP的收敛时间约为80min,动态PPP的收敛时间为100min;对于3h的观测数据,静态PPP收敛后定位精度优于5cm,动态PPP收敛后水平方向优于8cm,高程方向约12cm;与GPS PPP类似,东分量上定位精度较北分量稍差。当前由于BDS的全球跟踪站有限,精密轨道和钟差精度不如GPS,因此BDS PPP的收敛时间较GPS长,但收敛后可实现厘米至分米级的绝对定位。     

Zero-difference GPS ambiguity resolution at CNES–CLS IGS Analysis Center

CNES (Centre National d’Etudes Spatiales) and CLS (Collecte Localisation Satellites) became an International GNSS Service (IGS) Analysis Center (AC) the 20th of May 2010. Since 2009, we are using the integer ambiguity fixing at the zero-difference level strategy in our software package (GINS/Dynamo) as an alternative to classical differential approaches. This method played a key role among all the improvements in the GPS processing we made during this period. This paper provides to the users the theoretical background, the strategies and the models used to compute the products (GPS orbits and clocks, weekly station coordinate estimates and Earth orientation parameters) that are submitted weekly to the IGS. The practical realization of the two-step, ambiguity-fixing scheme (wide-lane and narrow-lane) is described in detail. The ambiguity fixing improved our orbit overlaps from 6 to 3?cm WRMS in the tangential and normal directions. Since 2008, our products have been also regularly compared to the IGS final solutions by the IGS Analysis Center Coordinator. The joint effects of ambiguity fixing and dynamical model changes (satellite solar radiation pressure and albedo force) improved the consistency with IGS orbits from 35 to 18?mm 3D-WRMS. Our innovative strategy also gives additional powerful properties to the GPS satellite phase clock solutions. Single receiver (zero-difference) ambiguity resolution becomes possible. An overview of the applications is given.     

利用改进的动态PPP技术建立中国香港区域海潮负荷位移模型

利用GPS技术反演海潮负荷信息，相比传统重力及甚长基线干涉测量，有着全球覆盖、测站数多、全天候、成本低等诸多优势，为海潮模型的建立提供了有效的技术手段，也对海潮负荷效应的研究有着重要的理论意义和参考价值。利用动态精密单点定位技术（precise point positioning，PPP）反演海潮负荷位移，同时构建了区域海潮负荷位移模型。利用香港连续运行参考站8 a的GPS观测数据，精密测定了11个测站的三维海潮负荷位移参数，与高精度海潮模型提供的海潮负荷位移参数进行比较，发现除K₂、K₁潮波外，其他潮波的均方根误差均小于2 mm。与已有的动态PPP及静态PPP结果对比发现，采用改进的重叠时段动态PPP算法可有效改善K₁潮波的反演精度；该方法反演的海潮负荷位移精度可达到静态PPP反演海潮负荷位移的精度，且对于K₁潮波，在东西方向，动态PPP算法的反演精度较静态PPP略有改善。利用最小二乘曲面拟合法可有效建立中国香港地区GPS区域海潮负荷位移模型，可有效弥补沿海地区因验潮站稀少而导致的海潮模型适应性差的问题。     

基于非差观测量的BDS+GPS近实时钟差估计

卫星钟差的难预测性是影响实时高精度定位的重要因素之一。为快速获得高精度位置或对流层等信息，在非差观测模型的基础上，本文提出了一种延迟量约1 h的近实时钟差估计策略，该策略主要包含超快速轨道解算和钟差估计两部分。经验证，预报部分第2~5 h的GPS轨道三维平均精度为3.85 cm，BDS GEO和IGSO+MEO轨道三维平均精度分别为81.4和21.74 cm。基于超快速轨道可获得近实时钟差精度GPS为0.054 ns，BDS为0.12 ns。最后通过BDS+GPS静态PPP试验验证了轨道和钟差的可用性。     

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.     

利用GPS动态PPP技术求解海潮负荷位移

受特殊海岸线及复杂海底地形的影响,目前发布的全球海潮模型在局部沿海地区差异较大,需利用其他大地测量手段直接测定沿海地区的海潮负荷位移参数。GPS技术因具有全天候、精度高、成本低等优势,已成为获取海潮负荷位移参数的有效手段。本文基于GPS技术监测测站三维位移变化的灵敏度高于监测48个海潮参数的灵敏度这一基本思想,改进了利用GPS精密单点定位(PPP)技术估计48个海潮调和参数的方法,直接逐历元求解三维海潮负荷位移变化,再利用调和分析方法提取主要潮波(M2、S2、N2、K2、K1、O1、P1、Q1)的海潮负荷位移建模参数(振幅与相位)。利用12个香港连续运行参考站(CORS)8年的GPS观测数据,计算各测站的海潮负荷位移建模参数。与传统方法比较,本文方法可有效加速K1潮波在东西方向的收敛。将GPS海潮负荷位移建模参数估值与中国近海海潮模型值比较,发现除S2、K2和K1潮波的均方根误差较大外,其他潮波的均方根误差均小于1.5mm。将香港2008—2014年验潮站数据反演的潮波参数与海潮模型值比较,结果表明:GPS与验潮站数据反演的潮波参数均与中国近海海潮模型及HAMTIDE2011.11A全球海潮模型符合较好,验证了GPS PPP反演海潮负荷位移的有效性。采用GPS PPP估计的8个潮波的振幅与相位值替换全球海潮模型中对应的潮波值,进行海潮负荷效应改正,可减弱GPS长时间序列中的半周年信号。     

不同海潮模型对东南极沿海地区GPS基线解算的影响

在高精度GPS数据处理中,海潮的影响是一个不可忽略的因素。利用GAMIT软件解算2011年东南极沿海地区中国中山站及其周边6个IGS站的GPS数据,对比分析了FES2004、DTU10、EOT11a、GOT4.7、HAMTIDE11a、OSU12以及TPXO7.2等7个全球海潮模型在不同测站的海潮负荷差异,比较了海潮负荷对于GPS基线解的影响。结果表明,海潮负荷对GPS基线解的影响与测站所处位置及基线方位有关,达到cm级,相对影响达到10-8,因此,在高精度的GPS基线解算中必须考虑海潮的影响;但选用不同海潮模型对东南极沿海地区GPS基线解算的差异可忽略不计。     

Swarm系列卫星非差运动学厘米级精密定轨

采用2015年5月24日—30日的Swarm星载GPS双频观测数据,基于Melbourne-Wübbena(MW)和消电离层线性组合,在精密单点定位技术的基础上,采用批处理最小二乘估计法对不同轨道高度的Swarm系列卫星进行非差运动学精密定轨。利用星载GPS相位观测值残差、与欧空局发布的简化动力学轨道对比,以及SLR检核3种方法对Swarm系列卫星非差运动学定轨结果进行精度评估。结果表明:①Swarm系列卫星星载GPS相位观测值残差RMS为6~7 mm;②与欧空局发布的简化动力学轨道进行求差,径向、切向及法向轨道差值RMS为2~4 cm;③与欧空局发布的运动学轨道进行求差,径向、切向及法向轨道差值RMS为1~2 cm;④SLR检核结果表明Swarm-A/B/C卫星轨道精度为3~4 cm。因此,采用非差运动学定轨方法与本文提供的定轨策略进行Swarm系列卫星精密定轨是切实可行的,定轨精度为厘米级。     

GPS satellite clock determination in case of inter-frequency clock biases for triple-frequency precise point positioning

Significant time-varying inter-frequency clock biases (IFCBs) within GPS observations prevent the application of the legacy L1/L2 ionosphere-free clock products on L5 signals. Conventional approaches overcoming this problem are to estimate L1/L5 ionosphere-free clocks in addition to their L1/L2 counterparts or to compute IFCBs between the L1/L2 and L1/L5 clocks which are later modeled through a harmonic analysis. In contrast, we start from the undifferenced uncombined GNSS model and propose an alternative approach where a second satellite clock parameter dedicated to the L5 signals is estimated along with the legacy L1/L2 clock. In this manner, we do not need to rely on the correlated L1/L2 and L1/L5 ionosphere-free observables which complicates triple-frequency GPS stochastic models, or account for the unfavorable time-varying hardware biases in undifferenced GPS functional models since they can be absorbed by the L5 clocks. An extra advantage over the ionosphere-free model is that external ionosphere constraints can potentially be introduced to improve PPP. With 27 days of triple-frequency GPS data from globally distributed stations, we find that the RMS of the positioning differences between our GPS model and all conventional models is below 1 mm for all east, north and up components, demonstrating the effectiveness of our model in addressing triple-frequency observations and time-varying IFCBs. Moreover, we can combine the L1/L2 and L5 clocks derived from our model to calculate precisely the L1/L5 clocks which in practice only depart from their legacy counterparts by less than 0.006 ns in RMS. Our triple-frequency GPS model proves convenient and efficient in combating time-varying IFCBs and can be generalized to more than three frequency signals for satellite clock determination.     

GPS非差相位精密单点定位技术探讨

探讨了精密单点定位的基本原理，处理方法，所涉及的误差改正及数据处理中的一些关键技术；采用直接内插IGS卫星精密星历的方法代替利用IGS跟踪站进行轨道精化方法计算卫星轨道参数，对现有精密单点定位计算方法进行了简化，使之更具有实用性。最后利用自主研发的精密非差单点定位软件计算和分析了实测数据。计算结果表明，经过大约15min的初始化后，非差相位单历元的定位结果精确度在X，Y，Z方向上均优于20cm。     

GPS非差相位精密单点定位方法与实现

探讨了精密单点定位的基本原理、处理方法、所涉及的误差改正及数据处理中的一些关键技术;采用直接内插IGS卫星精密星历的方法代替利用IGS跟踪站进行轨道精化方法计算卫星轨道参数,对现有精密单点定位计算方法进行了简化,使之更具有实用性。最后利用自主研发的精密非差单点定位软件计算和分析了实测数据。计算结果表明,经过大约15 min的初始化后,非差相位单历元的定位结果精确度在X,Y,Z方向上均优于20 cm。     

广域实时精密定位与时间服务系统

广域实时精密定位与时间服务已成为GNSS应用领域研究热点,目前国内外学者围绕其模型算法已展开大量的研究。本文重点论述广域实时精密定位与时间服务数据的处理方法和服务系统,给出了基于不同基准约束的卫星钟差解算数学模型,提出通过引入外接原子钟测站、标准时间源(UTC/BDT)等不同时间基准,构建卫星拟稳基准、外接原子钟跟踪站拟稳基准及标准时间源等约束下的钟差解算模型,分析了时间基准对精密单点定位和精密单点授时的影响。本文采用实时卫星轨道、钟差、相位偏差、电离层延迟等服务产品及跟踪站实时数据,验证了系统产品可靠性及终端定位与时间服务性能。实测结果表明:GPS轨道径向精度1.8 cm,钟差STD精度约0.05 ns;BDS-3轨道径向精度6.7 cm,钟差STD精度优于0.1 ns;GPS和BDS-2电离层改正精度分别为0.74 TECU与1.03 TECU。基于该产品实现了用户端PPP、PPP-RTK及PPT、PPT-RTK服务,满足了用户实时厘米级定位和优于0.5 ns的单站时间传递服务,当采用GPS+BDS-2 PPP-RTK解算时,平面收敛至5 cm约需要12 min。     

Single receiver phase ambiguity resolution with GPS data

Global positioning system (GPS) data processing algorithms typically improve positioning solution accuracy by fixing double-differenced phase bias ambiguities to integer values. These “double-difference ambiguity resolution” methods usually invoke linear combinations of GPS carrier phase bias estimates from pairs of transmitters and pairs of receivers, and traditionally require simultaneous measurements from at least two receivers. However, many GPS users point position a single local receiver, based on publicly available solutions for GPS orbits and clocks. These users cannot form double differences. We present an ambiguity resolution algorithm that improves solution accuracy for single receiver point-positioning users. The algorithm processes dual- frequency GPS data from a single receiver together with wide-lane and phase bias estimates from the global network of GPS receivers that were used to generate the orbit and clock solutions for the GPS satellites. We constrain (rather than fix) linear combinations of local phase biases to improve compatibility with global phase bias estimates. For this precise point positioning, no other receiver data are required. When tested, our algorithm significantly improved repeatability of daily estimates of ground receiver positions, most notably in the east component by approximately 30% with respect to the nominal case wherein the carrier biases are estimated as real values. In this “static” test for terrestrial receiver positions, we achieved daily repeatability of 1.9, 2.1 and 6.0 mm in the east, north and vertical (ENV) components, respectively. For kinematic solutions, ENV repeatability is 7.7, 8.4, and 11.7 mm, respectively, representing improvements of 22, 8, and 14% with respect to the nominal. Results from precise orbit determination of the twin GRACE satellites demonstrated that the inter-satellite baseline accuracy improved by a factor of three, from 6 to 2 mm up to a long-term bias. Jason-2/Ocean Surface Topography Mission precise orbit determination tests results implied radial orbit accuracy significantly below the 10 mm level. Stability of time transfer, in low-Earth orbit, improved from 40 to 7 ps. We produced these results by applying this algorithm within the Jet Propulsion Laboratory’s (JPL’s) GIPSY/OASIS software package and using JPL’s orbit and clock products for the GPS constellation. These products now include a record of the wide-lane and phase bias estimates from the underlying global network of GPS stations. This implies that all GIPSY–OASIS positioning users can now benefit from this capability to perform single-receiver ambiguity resolution.     

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.     

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.     

Estimates of ocean tide loading displacements and its impact on position time series in Hong Kong using a dense continuous GPS network

Three-dimensional ocean tide loading (OTL) displacements of eight diurnal and semidiurnal constituents at 12 sites in Hong Kong were estimated using 3–7 years of continuous global positioning system (GPS) observations. OTL displacements were estimated using the precise point positioning (PPP) technique on a daily basis and then combined. The OTL displacements obtained by GPS were compared with predictions using seven recent global ocean tide models. The effect of OTL displacements on GPS position time series was also investigated. The study shows that the GPS-derived OTL displacements (excluding K1 and K2 constituents) agree best with those predicted by the GOT4.7 and NAO99b models. The GPS/model agreement is generally at the sub-millimeter level, except for S2, K1, and K2 constituents with relatively large errors. After systematic biases between the GPS and model values are removed, the misfits of all sites for M2, S2, N2, O1, P1, and Q1 are less than 0.5 and 1.0 mm in the horizontal and vertical components, respectively, while larger misfits (within 2.5 mm) are observed for K1 and K2. Integer ambiguity fixing slightly improves the east component of OTL displacement estimates. The study also finds that GPS-derived OTL corrections, instead of model predicts, can be used in daily data processing with the exception of K1 and K2. Including K2 corrections, a secular vertical rate of up to 1 mm/year in position time series can be induced, which needs to be confirmed by further studies.     

北斗/GPS实时精密卫星钟差融合解算模型及精度分析

实时GNSS精密单点定位(PPP)技术必须使用实时的高精度卫星精密轨道和钟差。本文研究了精密卫星钟差融合解算模型及策略,并利用滤波算法实现了北斗/GPS实时精密卫星钟差融合估计算法。仿真实时试验结果显示:获得的北斗/GPS实时钟差与GFZ事后多GNSS精密钟差(GBM)的标准差在0.15 ns左右;使用该钟差进行GPS动态PPP试验,收敛后水平精度优于5 cm,高程精度优于10 cm;使用仿真实时钟差进行的北斗动态PPP与使用GFZ事后多GNSS精密钟差开展的试验相比精度相当,可实现分米级定位。     

MADOCA-LEX高频GPS卫星钟差 短期预测精度分析

日本准天顶卫星系统（QZSS）卫星通过L波段实时播发高频全球卫星导航系统（GNSS）精密轨道和钟差产品,为GNSS导航用户提供实时精密单点定位（PPP）服务. 本文以JAXA MADOCA数据中心提供的1 s采样率GPS卫星钟差数据为研究对象,首先采用阿伦方差对卫星钟差的短期稳定性进行评估;然后分别采用一阶多项式、二阶多项式和灰色模型对高频钟差产品进行建模,在5 s,10 s和30 s的拟合窗口内预报后续10 s内钟差,并基于预报残差的均方根误差（RMS）评定不同类型GPS卫星钟差产品的短期预报精度. 基于2020年1月1日-21日连续21天的实时高频钟差统计分析结果表明,不同型号的GPS卫星钟差1 s,5 s和10 s的短期稳定性均能达到10-12量级;对比预报精度显示,10 s以内的拟合窗口采用最简单的一阶多项式最为稳定可靠,10 s延迟预报RMS精度可控制在0.1 ns以内;若采用30 s的拟合窗口,考虑钟差频漂特性的二阶多项式则更为稳定可靠,预报钟差的RMS精度能达到0.15 ns以内．由此可见,本文基于MADOCA-LEX钟差产品的实时预报精度可以满足厘米级PPP的需求．      

Implementation and testing of the gridded Vienna Mapping Function 1 (VMF1)

The new gridded Vienna Mapping Function (VMF1) was implemented and compared to the well-established site-dependent VMF1, directly and by using precise point positioning (PPP) with International GNSS Service (IGS) Final orbits/clocks for a 1.5-year GPS data set of 11 globally distributed IGS stations. The gridded VMF1 data can be interpolated for any location and for any time after 1994, whereas the site-dependent VMF1 data are only available at selected IGS stations and only after 2004. Both gridded and site-dependent VMF1 PPP solutions agree within 1 and 2 mm for the horizontal and vertical position components, respectively, provided that respective VMF1 hydrostatic zenith path delays (ZPD) are used for hydrostatic ZPD mapping to slant delays. The total ZPD of the gridded and site-dependent VMF1 data agree with PPP ZPD solutions with RMS of 1.5 and 1.8 cm, respectively. Such precise total ZPDs could provide useful initial a priori ZPD estimates for kinematic PPP and regional static GPS solutions. The hydrostatic ZPDs of the gridded VMF1 compare with the site-dependent VMF1 ZPDs with RMS of 0.3 cm, subject to some biases and discontinuities of up to 4 cm, which are likely due to different strategies used in the generation of the site-dependent VMF1 data. The precision of gridded hydrostatic ZPD should be sufficient for accurate a priori hydrostatic ZPD mapping in all precise GPS and very long baseline interferometry (VLBI) solutions. Conversely, precise and globally distributed geodetic solutions of total ZPDs, which need to be linked to VLBI to control biases and stability, should also provide a consistent and stable reference frame for long-term and state-of-the-art numerical weather modeling.