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.     

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。     

北斗三频精密单点定位模型比较及定位性能分析

在Trip软件的基础上实现了北斗三频无电离层两两组合、三频消电离层组合和三频非组合精密单点定位（precise point positioning,PPP）算法。利用12个陆态网观测站的北斗三频观测数据对3种三频PPP定位模型及传统的双频无电离层组合PPP模型的定位性能进行分析。试验结果表明,对大多数测站,3种三频PPP模型静态定位精度水平方向优于1 cm,高程方向优于2 cm,动态定位精度水平方向优于4 cm,高程方向优于6 cm;3种三频PPP模型静态收敛时间约为120 min,动态收敛时间约180 min;相比于传统的双频PPP模型,三频PPP模型的定位精度有所提高,其中,三频非组合模型静态单天解RMS在水平方向和高程方向分别提高36.1%和6.3%,动态单天解RMS在水平方向和高程方向分别提高9.1%和6.3%。     

基于星载GPS数据的Jason-3卫星简化动力学和运动学法精密定轨

利用Jason-3星载GPS观测数据,采用简化动力学方法和运动学方法对Jason-3卫星进行精密定轨研究. 通过载波相位残差、重叠轨道对比、参考轨道对比和卫星激光测距(SLR)轨道检核四种方式评定轨道精度. 计算相位残差均方根(RMS)值,简化动力学轨道的RMS值在0.7～0.8 cm,运动学轨道的RMS值在0.50～0.55 cm;简化动力学轨道重叠部分径向RMS值达到0.32 cm,运动学轨道重叠部分径向RMS值达到1.12 cm;与国际DORIS服务(IDS)官方提供的参考轨道对比,简化动力学轨道径向精度达到1.47 cm,运动学轨道径向精度达到4.36 cm;利用SLR观测数据进行核验,简化动力学轨道精度整体优于2.1 cm,运动学轨道精度整体优于3.3 cm. 通过实验证明:Jason-3卫星的简化动力学轨道和运动学轨道的精度均达到cm级.      

基于精密单点定位技术的航空测量应用实践

讨论了基于精密单点定位技术来实现无地面基准站的航空测量。计算结果表明，用观测值的验后残差计算得到的实测动态及静态模拟动态进行精密单点定位的三维RMS均优于3cm；用动态数据精密单点定位的结果同多基准站的双差解求较差计算出的RMS．南北分量和东西分量均优于5cm，高程分量优于10cm；用基准站的静态数据模拟动态单点定位解算得到的坐标同已知坐标求较差计算出的RMS，南北分量和东西分量均优于3cm，高程分量优于5cm。     

Precise relative positioning using real tracking data from COMPASS GEO and IGSO satellites

China completed a basic COMPASS navigation network with three Geostationary and three Inclined Geosynchronous satellites in orbit in April 2011. The network has been able to provide preliminary positioning and navigation functions. We first present a quality analysis using 1-week COMPASS measurements collected in Wuhan. Satellite visibility and validity of measurements, carrier-to-noise density ratio and code noise are analyzed. The analysis of multipath combinations shows that the noise level of COMPASS code measurements is higher than that of GPS collected using the same receiver. Second, the results of positioning are presented and analyzed. For the standalone COMPASS solutions, an accuracy of 20 m can be achieved. An accuracy of 3.0 m for the vertical, 1.5 m for the North and about 0.6–0.8 m for the East component is obtained using dual-frequency code only measurements for a short baseline. More importantly, code and phase measurements of the short baseline are processed together to obtain precise relative positioning. Kinematic solutions are then compared with the ground truth. The precision of COMPASS only solutions is better than 2 cm for the North component and 4 cm for the vertical. The standard deviation of the East component is smaller than 1 cm, which is even better than that of the East component of GPS solutions. The accuracy of GPS/COMPASS combination solutions is at least 20 % better than that of GPS alone. Furthermore, the geometry-based residuals of double differenced phase and code measurements are analyzed. The analysis shows that the noise level of un-differenced phase measurements is about 2–4 mm on both B1 and B2 frequencies. For the code measurements, the noise level is less than 0.45 m for B1 CA and about 0.35 m for B2 P code. Many of the COMPASS results presented are very promising and have been obtained for the first time.     

基于星载GPS数据的GRACE卫星动力学法定轨

利用GRACEA卫星的星载GPS观测数据,采用非差动力学低轨卫星定轨方法,解算了2012年1月11日至18日的卫星轨道,将得到的结果与GFZ发布的RSO轨道进行对比分析,并通过SLR观测数据进行轨道的校验。结果表明：定轨精度满足低轨卫星精密定轨的要求,与RSO轨道比较,在X、Y、Z方向的均方根误差的平均值分别为4．7cm、4．3cm和4．9cm;通过SLR观测数据进行校验,残差平均值为-1．6cm,均方根误差为4．7cm．     

Integrating GPS and GLONASS to accelerate convergence and initialization times of precise point positioning

The main challenge of dual-frequency precise point positioning (PPP) is that it requires about 30 min to obtain centimeter-level accuracy or to succeed in the first ambiguity-fixing. Currently, PPP is generally conducted with GPS only using the ionosphere-free combination. We adopt a single-differenced (SD) between-satellite PPP model to combine the GPS and GLONASS raw dual-frequency carrier phase measurements, in which the GPS satellite with the highest elevation is selected as the reference satellite to form the SD between-satellite measurements. We use a 7-day data set from 178 IGS stations to investigate the contribution of GLONASS observations to both ambiguity-float and ambiguity-fixed SD PPP solutions, in both kinematic and static modes. In ambiguity-fixed PPP, we only attempt to fix GPS integer ambiguities, leaving GLONASS ambiguities as float values. Numerous experimental results show that PPP with GLONASS and GPS requires much less convergence time than that of PPP with GPS alone. For ambiguity-float PPP, the average convergence time can be reduced by 45.9 % from 22.9 to 12.4 min in static mode and by 57.9 % from 40.6 to 17.7 min in kinematic mode, respectively. For ambiguity-fixed PPP, the average time to the first-fixed solution can be reduced by 27.4 % from 21.6 to 15.7 min in static mode and by 42.0 % from 34.4 to 20.0 min in kinematic mode, respectively. Experimental results also show that the less the GPS satellites are used in float PPP, the more significant is the reduction in convergence time when adding GLONASS observations. In addition, on average, more than 4 GLONASS satellites can be observed for most 2-h observation sessions. Nearly, the same improvement in convergence time reduction is achieved for those observations.     

BDS/GPS组合精密单点定位精度分析与评价

精密单点定位（precise point positioning,PPP）已经广泛应用于许多领域,如测绘、交通、导航、地震监测等。近些年来,随着卫星数量的增多,多系统组合呈现越来越明显的趋势。利用全球MGEX（Multi-GNSS Experiment）网数据研究了BDS（BeiDou navigation satellite system）/GPS（global positioning system）组合精密单点定位技术,并与BDS单系统和GPS单系统进行了对比。结果表明,在静态定位中,BDS PPP在E、N、U方向的均方根误差分别为4.35 cm、3.01 cm、6.40 cm;GPS PPP在E、N、U方向的均方根误差分别为1.21 cm、0.48 cm、1.79 cm;BDS/GPS组合PPP在E、N、U方向的均方根误差分别为1.21 cm、0.50 cm、1.87 cm。在动态定位中,BDS PPP外符合精度水平方向优于10 cm,高程方向优于15 cm;GPS PPP和BDS/GPS组合PPP的外符合精度水平方向均优于5 cm,高程方向均优于8 cm。另外,无论是在静态还是动态的PPP中,组合系统相对于单系统,能大大缩短收敛时间,减少定位结果抖动,尤其是相对于BDS PPP来说,优势更为明显。     

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。     

HY2A卫星的GPS/DORIS/SLR数据精密定轨

采用HY2A卫星2013年2月的实测数据,研究了GPS、星载多谱勒无线电定轨定位系统(DORIS)及卫星激光测距(SLR)三种观测数据的单独和联合定轨问题。通过与法国CNES的精密轨道数据比较发现:分别采用GPS、DORIS和SLR数据进行单独定轨,GPS数据确定轨道的径向平均精度为1.3cm,三维位置约为6.2cm;DORIS定轨的径向平均精度为1.6cm,比GPS结果略差;SLR确定轨道的径向平均精度为2.3cm。用GPS、DORIS和SLR三种数据联合定轨,确定轨道的径向平均精度为1.2cm,三维位置约为6.5cm。与星载GPS定轨结果比较,三种观测数据的联合定轨在提高卫星轨道确定精度上不明显,但联合定轨有利于保持计算轨道精度相对稳定。用站星间高度角大于60°的SLR数据检验GPS/DORIS联合确定的轨道,两者在测距方向的均方差为2.5cm,可见基于HY2A的观测数据可以实现cm级的定轨需求。     

Generating GPS satellite fractional cycle bias for ambiguity-fixed precise point positioning

With the development of precise point positioning (PPP), the School of Geodesy and Geomatics (SGG) at Wuhan University is now routinely producing GPS satellite fractional cycle bias (FCB) products with open access for worldwide PPP users to conduct ambiguity-fixed PPP solution. We provide a brief theoretical background of PPP and present the strategies and models to compute the FCB products. The practical realization of the two-step (wide-lane and narrow-lane) FCB estimation scheme is described in detail. With GPS measurements taken in various situations, i.e., static, dynamic, and on low earth orbit (LEO) satellites, the quality of FCB estimation and the effectiveness of PPP ambiguity resolution (AR) are evaluated. The comparison with CNES FCBs indicated that our FCBs had a good consistency with the CNES ones. For wide-lane FCB, almost all the differences of the two products were within ±0.05 cycles. For narrow-lane FCB, 87.8 % of the differences were located between ±0.05 cycles, and 97.4 % of them were located between ±0.075 cycles. The experimental results showed that, compared with conventional ambiguity-float PPP, the averaged position RMS of static PPP can be improved from (3.6, 1.4, 3.6) to (2.0, 1.0, 2.7) centimeters for ambiguity-fixed PPP. The average accuracy improvement in the east, north, and up components reached 44.4, 28.6, and 25.0 %, respectively. A kinematic, ambiguity-fixed PPP test with observation of 80 min achieved a position accuracy of better than 5 cm at the one-sigma level in all three coordinate components. Compared with the results of ambiguity-float, kinematic PPP, the positioning biases of ambiguity-fixed PPP were improved by about 78.2, 20.8, and 65.1 % in east, north, and up. The RMS of LEO PPP test was improved by about 23.0, 37.0, and 43.0 % for GRACE-A and GRACE-B in radial, tangential, and normal directions when AR was applied to the same data set. These results demonstrated that the SGG FCB products can be produced with high quality for users anywhere around the world to carry out ambiguity-fixed PPP solutions.     

北斗三频数据的两个无电离层组合轨道钟差估计及其应用

本文针对全球连续监测评估系统（iGMAS）和国际多系统GNSS试验计划（MGEX）两个观测网接收到不同频率北斗卫星数据的情况,提出了一种北斗卫星（BDS）3个频率（B1I、B2I、B3I）的两种无电离层组合（B1/B3和B1/B2）数据精密定轨（POD）和钟差估计（CE）方法。该方法可以统一处理上述两个观测网收到的北斗二代（BDS-2）,北斗三代试验系统（BDS-3e）和北斗三代全球系统（BDS-3g）3个频率的观测数据,并在一次程序运行中对所有北斗卫星进行联合处理,可有效提高一次运行的数据使用率,从而提高参数估计精度。采集了多天iGMAS、MGEX的GPS和BDS数据进行试验。结果表明,对BDS-3e+BDS-2+GPS联合定轨时,采用三频两组合方法后由于增强了观测几何,BDS轨道重叠RMS为15.9 cm,比传统双频法定轨精度提高11.3%。新方法引入了与卫星端3个频率相关的码偏差,该量多天估计结果稳定,证明了模型和方法可靠。将新方法用于BDS-3g+BDS-3e+BDS-2+GPS联合定轨,6颗BDS-3g的MEO卫星轨道重叠RMS为14.5 cm,钟差重叠RMS为0.43 ns,与BDS-3e的15.1 cm和0.49 ns相当。开展了北斗卫星精密单点定位（PPP）试验,结果显示增加了BDS-3g的6颗MEO的精密轨道和钟差后,测站定位精度水平为39.6 mm,天顶为37.8 mm,比仅用BDS-2和BDS-3e卫星定位精度提高了11.1%。     

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。     

Self-consistent treatment of tidal variations in the geocenter for precise orbit determination

We show that the current levels of accuracy being achieved for the precise orbit determination (POD) of low-Earth orbiters demonstrate the need for the self-consistent treatment of tidal variations in the geocenter. Our study uses as an example the POD of the OSTM/Jason-2 satellite altimeter mission based upon Global Positioning System (GPS) tracking data. Current GPS-based POD solutions are demonstrating root-mean-square (RMS) radial orbit accuracy and precision of \({<}1\)  cm and 1 mm, respectively. Meanwhile, we show that the RMS of three-dimensional tidal geocenter variations is \({<}6\)  mm, but can be as large as 15 mm, with the largest component along the Earth’s spin axis. Our results demonstrate that GPS-based POD of Earth orbiters is best performed using GPS satellite orbit positions that are defined in a reference frame whose origin is at the center of mass of the entire Earth system, including the ocean tides. Errors in the GPS-based POD solutions for OSTM/Jason-2 of \({<}4\)  mm (3D RMS) and \({<}2\)  mm (radial RMS) are introduced when tidal geocenter variations are not treated consistently. Nevertheless, inconsistent treatment is measurable in the OSTM/Jason-2 POD solutions and manifests through degraded post-fit tracking data residuals, orbit precision, and relative orbit accuracy. For the latter metric, sea surface height crossover variance is higher by \(6~\hbox {mm}^{2}\) when tidal geocenter variations are treated inconsistently.     

GPS/BDS/Galileo三频精密单点定位模型及性能分析

在精细考虑伪距和载波相位硬件偏差时变特性的基础上,导出了更为严谨的非差非组合观测方程,并给出了非组合模式下两类GNSS偏差的数学表达形式。基于此,本文详细研究了3种常用的三频精密单点定位(PPP),即无电离层两两组合IF1213、单个无电离层组合IF123与非组合UC123函数模型的独立参数化方法,系统分析了3种PPP模型的相互关系以及GPS/BDS/Galileo三频静、动态PPP定位性能。结果表明,静态PPP收敛后定位精度水平方向优于1.0 cm,高程优于1.5 cm;动态PPP水平方向优于2.0 cm,高程优于5.0 cm;三频PPP的定位性能与双频PPP基本相当。     

Reduced dynamic and kinematic precise orbit determination for the Swarm mission from 4 years of GPS tracking

Precise science orbits for the first 4 years of the Swarm mission have been generated from onboard GPS measurements in a systematic reprocessing using refined models and processing techniques. Key enhancements relate to the introduction of macro-models for a more elaborate non-gravitational force modeling (solar radiation pressure, atmospheric drag and lift, earth albedo), as well as carrier phase ambiguity fixing. Validation using satellite laser ranging demonstrates a 30% improvement in the precision of the reduced dynamic orbits with resulting errors at the 0.5–1 cm level (1D RMS). A notable performance improvement is likewise achieved for the kinematic orbits, which benefit most from the ambiguity fixing and show a 50% error reduction in terms of SLR residuals while differences with respect to reduced dynamic ephemerides amount to only 1.7 cm (median of daily 3D RMS). Compared to the past kinematic science orbits based on float-ambiguity estimates, the new kinematic position solutions exhibit a factor of reduction of two to three in Allan deviation at time scales of 1000s and higher, and promise an improved recovery of low-degree and -order gravity field coefficients in Swarm gravity field analyses.     

SBAS orbit and satellite clock corrections for precise point positioning

The quality of real-time GPS positions based on the method of precise point positioning (PPP) heavily depends on the availability and accuracy of GPS satellite orbits and satellite clock corrections. Satellite-based augmentation systems (SBAS) provide such corrections but they are actually intended to be used for wide area differential GPS with positioning results on the 1-m accuracy level. Nevertheless, carrier phase-based PPP is able to achieve much more accurate results with the same correction values. We applied SBAS corrections for dual-frequency PPP and compared the results with PPP obtained using other real-time correction data streams, for example, the GPS broadcast message and precise corrections from the French Centre National d’Etudes Spatiales and the German Deutsches Zentrum für Luft- und Raumfahrt. Among the three existing SBAS, the best results were achieved for the North American wide area augmentation system (WAAS): horizontal and vertical position accuracies were considerably smaller than 10 cm for static 24-h observation data sets and smaller than 30 cm for epoch-by-epoch solutions with 2 h of continuous observations. The European geostationary navigation overlay service and the Japanese multi-functional satellite augmentation system yield positioning results with biases of several tens of centimeters and variations larger by factors of 2–4 as compared to WAAS.     

Initial results of centralized autonomous orbit determination of the new-generation BDS satellites with inter-satellite link measurements

Autonomous orbit determination is the ability of navigation satellites to estimate the orbit parameters on-board using inter-satellite link (ISL) measurements. This study mainly focuses on data processing of the ISL measurements as a new measurement type and its application on the centralized autonomous orbit determination of the new-generation Beidou navigation satellite system satellites for the first time. The ISL measurements are dual one-way measurements that follow a time division multiple access (TDMA) structure. The ranging error of the ISL measurements is less than 0.25 ns. This paper proposes a derivation approach to the satellite clock offsets and the geometric distances from TDMA dual one-way measurements without a loss of accuracy. The derived clock offsets are used for time synchronization, and the derived geometry distances are used for autonomous orbit determination. The clock offsets from the ISL measurements are consistent with the L-band two-way satellite, and time–frequency transfer clock measurements and the detrended residuals vary within 0.5 ns. The centralized autonomous orbit determination is conducted in a batch mode on a ground-capable server for the feasibility study. Constant hardware delays are present in the geometric distances and become the largest source of error in the autonomous orbit determination. Therefore, the hardware delays are estimated simultaneously with the satellite orbits. To avoid uncertainties in the constellation orientation, a ground anchor station that “observes” the satellites with on-board ISL payloads is introduced into the orbit determination. The root-mean-square values of orbit determination residuals are within 10.0 cm, and the standard deviation of the estimated ISL hardware delays is within 0.2 ns. The accuracy of the autonomous orbits is evaluated by analysis of overlap comparison and the satellite laser ranging (SLR) residuals and is compared with the accuracy of the L-band orbits. The results indicate that the radial overlap differences between the autonomous orbits are less than 15.0 cm for the inclined geosynchronous orbit (IGSO) satellites and less than 10.0 cm for the MEO satellites. The SLR residuals are approximately 15.0 cm for the IGSO satellites and approximately 10.0 cm for the MEO satellites, representing an improvement over the L-band orbits.     

Evaluation of CHAMP satellite orbit with SLR measurements

The technique of Evaluating CHAMP satellite orbit with SLR measurements is presented. As an independent evaluation of the orbit solution, SLR data observed from January 1 to 16, 2002 are processed to compute the residuals after fixing the GFZ's post science orbits solutions. The SLR residuals are computed as the differences of the SLR measurements minus the corresponding distances between the SLR station and the GPS-derived orbit positions. On the basis of the SLR residuals analysis, it is found that the accuracy of GFZ' s spost science orbits is better than 10 cm and that there is no systematic error in GFZ's post science orbits.