Quality assessment of GPS rapid static positioning with weighted ionospheric parameters in generalized least squares

Precise GPS positioning requires the processing of carrier-phase observations and fixing integer ambiguities. With increasing distance between receivers, ambiguity fixing becomes more difficult because ionospheric and tropospheric effects do not cancel sufficiently in double differencing. A popular procedure in static positioning is to increase the length of the observing session and/or to apply atmospheric (ionospheric) models and corrections. We investigate the methodology for GPS rapid static positioning that requires just a few minutes of dual-frequency GPS observations for medium-length baselines. Ionospheric corrections are not required, but the ionospheric delays are treated as pseudo-observations having a priori values and respective weights. The tropospheric delays are reduced by using well-established troposphere models, and satellite orbital and clock errors are eliminated by using IGS rapid products. Several numerical tests based on actual GPS data are presented. It is shown that the proposed methodology is suitable for rapid static positioning within 50–70 km from the closest reference network station and that centimeter-level precision in positioning is feasible when using just 1 min of dual-frequency GPS data.     

Performance analysis of integrated GPS/GLONASS carrier phase-based positioning

Due to the different signal frequencies for the GLONASS satellites, the commonly-used double-differencing procedure for carrier phase data processing can not be implemented in its straightforward form, as in the case of GPS. In this paper a novel data processing strategy, involving a three-step procedure, for integrated GPS/GLONASS positioning is proposed. The first is pseudo-range-based positioning, that uses double-differenced (DD) GPS pseudo-range and single-differenced (SD) GLONASS pseudo-range measurements to derive the initial position and receiver clock bias. The second is forming DD measurements (expressed in cycles) in order to estimate the ambiguities, by using the receiver clock bias estimated in the above step. The third is to form DD measurements (expressed in metric units) with the unknown SD integer ambiguity for the GLONASS reference satellite as the only parameter (which is constant before a cycle slip occurs for this satellite). A real-time stochastic model estimated by residual series over previous epochs is proposed for integrated GPS/GLONASS carrier phase and pseudo-range data processing. Other associated issues, such as cycle slip detection, validation criteria and adaptive procedure(s) for ambiguity resolution, is also discussed. The performance of this data processing strategy will be demonstrated through case study examples of rapid static positioning and kinematic positioning. From four experiments carried out to date, the results indicate that rapid static positioning requires 1 minute of single frequency GPS/GLONASS data for 100% positioning success rate. The single epoch positioning solution for kinematic positioning can achieve 94.6% success rate over short baselines (<6 km).     

PERFORMANCE ANALYSIS OF INTEGRATED GPS/GLONASS CARRIER PHASE-BASED POSITIONING

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The stochastic estimation of satellite clock correction information in WADGPS

1 IntroductionChnventional DGPS is limited by the range overwhich the differential corrections are valid due tothe rapid decorrelation of the error sources with in-creasing distance from the reference station to user.In wide area differential GPS (WWPS) errorsources in GPS measurements are medeled sepa-rately,on the basis of a limited number of referencestaitOns, to overcome this drawback. The main er-ror sources are regarded as broadcast ephemeris er-ror,atmospheric refraction and satel…     

Absolute Positioning with Single-Frequency GPS Receivers

The use of precise post-processed satellite orbits and satellite clock corrections in absolute positioning, using one GPS receiver only, has proven to be an accurate alternative to the more commonly used differential techniques for many applications in georeferencing. The absolute approach is capable of centimeter accuracy when using state-of-the-art, dual-frequency GPS receivers. When using observations from single-frequency receivers, however, the accuracy, especially in height, decreases. The obvious reason for this degradation in accuracy is the effect of unmodeled ionospheric delay. This paper discusses the availability of some empirical ionospheric models that are publicly available and quantifies their usefulness for absolute positioning using single-frequency GPS receivers. The Global Ionospheric Model supplied by International GPS Service (IGS) is the most accurate one and is recommended for absolute positioning using single-frequency GPS receivers. Using high-quality single-frequency observations, a horizontal epoch-to-epoch accuracy of better than 1 m and a vertical accuracy of approximately 1 m is demonstrated. ? 2002 Wiley Periodicals, Inc.     

Modelling of differential single difference receiver clock bias for precise positioning

A receiver hardware delay should be seriously considered for time-transfer and determination of ionospheric delay corrections for wide area differential GPS positioning. A receiver hardware delay does not generally effect the common geo-position application, as suitable differences of observations are used, or equivalently, clock error parameters are introduced, epoch-wise, that also absorb the delays. This paper investigates the behavior of inter-frequency (or observation-type) receiver hardware delays by using a single difference (SD) model, which estimates the receiver delay along with the receiver clock error (and SD ambiguities of a reference satellite with carrier phase observations) for zero and short baselines. The purpose of this paper is to model the between-observation-type delays for the purpose of precise positioning, under practical circumstances. The focus is on data series of differential SD receiver clock biases, since they reflect the behavior of receiver hardware delays with time. A simple linear regression of the data series is employed to study the behavior, and test statistics are employed to assess both the significance of the parameters and the observations fit for the linear regression. The statistical analysis results indicate that almost all inter-observation type receiver delays can be modeled as the sum of a constant (offset) and a constant rate of change (slope). The analysis shows that the differential receiver delay is generally at the mm- to cm-level on phase, while at the dm-level on code for the equipment used in the experiments.     

The Southwest Pacific GPS Project: Geodetic results from Burst 1 of the 1990 Field Campaign

The Southwest Pacific GPS Project (SWP) is using the Global Positioning System (GPS) to monitor crustal motion across and within a plate boundary complex between the Australian and Pacific plates. GPS field campaigns were conducted in 1988, 1989 and 1990, to observe networks of increasing size and complexity. The 1990 campaign consisted of two periods, or Bursts, and this paper focuses on the analysis of data collected during the nine day Burst 1 in July, 1990, a period in which GPS Selective Availability was activated. During Burst 1, baselines that spanned the Tonga Trench and the Lau Basin were observed, and only one station (Espiritu Santo, Vanuatu) was located west of Fiji in the network. The lengths of the baselines observed fall mainly between 300 km and 1600 km, but some lines are as long as 3500 km. A total of 78 station-days of field site data and approximately 150 station-days of global fiducial data were processed from predominantly codeless receivers. A global fiducial network of 20 sites was used to provide orbit control and accuracy assessment for the 13 available satellites. The daily solutions for 45 baselines between 10 SWP sites have an RMS scatter in the length of 24 mm plus 6 parts per billion. This scatter provides an estimate of baseline precision for the Burst 1 nominal solution. Experiments were conducted to investigate a variety of possible effects on the SWP Network baseline estimates, including the influence of a reduced global fiducial network for the purpose of assessing the quality of results obtained in 1988 and 1989 in which the fiducial network was smaller than in 1990. These experiments produced results that agreed with the nominal solution at the level of the precision estimate. Furthermore, estimates for selected baselines in Australia, the Central Pacific, North America and Europe, also measured by VLBI and SLR, were used for an external accuracy evaluation. The GPS and VLBI or SLR determinations of length agreed at a level consistent with the nominal solution precision estimate.     

Combined GPS/GLONASS data processing

To obtain the GLONASS satellite position at an epoch other than reference time,the satellite‘s equation of motion has to be integrated with broadcasting ephemerides.The iterative detecting and repairing method of cycle slips based on triple difference residuals for combined GPS/GLONASS positioning and the iterative ambiguity resolution approach suitable for combined post processing positioning are discussed systematically.Experiments show that millimter accuracy can be achieved in short baselines with a few hours‘ dual frequency or even single frequency GPS/GLONASS carrier phase observation,and the precision of dual frequency observations is distinctly higher than that of single frequency observations.     

GPS/GALILEO偏航姿态异常对动态PPP的影响及其改正模型

当GPS、GALILEO卫星运行至与太阳、地球近似共线时,卫星很难维持名义姿态,将出现一段时间的偏航姿态异常。本文基于不同分析中心所提供的精密轨道和钟差产品,在卫星偏航姿态异常时期,设计不同姿态改正策略,选取全球分布的7个MGEX站10 d实测数据,分析了GPS、GALILEO卫星的天线相位中心改正、相位缠绕改正对观测值残差及动态PPP定位结果的影响。研究表明,在卫星偏航姿态异常时期,采用名义偏航姿态对GPS、GALILEO卫星观测值残差的影响可分别达到8和11 cm,在此期间,GPS/GALILEO卫星采用模型偏航姿态,与采用名义偏航姿态相比,动态PPP的E、N、U 3个方向的定位精度可分别提高13.30%、15.77%和12.98%,相较于剔除卫星策略,采用模型偏航姿态的动态PPP定位精度在E、N、U方向可分别提高5.399%、4.430%、5.992%。     

顾及卫星姿态的多系统精密钟差产品综合

国际GNSS服务(IGS)提供的GPS综合产品被广泛应用于各种高精度科学研究中. 随着各国卫星导航系统的发展,亟需研究针对多系统全球卫星导航系统(GNSS)产品的综合策略. 由于卫星姿态与钟差相互耦合,综合钟差时额外考虑姿态改正将进一步提高综合产品精度,因此研究了一种顾及卫星姿态的GNSS钟差综合策略,改正姿态后GPS综合残差最大可减小80%. 对142个IGS测站进行精密单点定位(PPP)解算发现,综合产品比单个分析中心产品更加稳定,东(E)、北(N)、高(U)方向的动态定位精度最大可提升22.7%、16.7%和18.3%. 相对于未顾及姿态改正的综合产品,顾及姿态改正的综合产品的动态定位精度最大可提升65.3%.      

Comparison of baseline results for the TI-4100 and Trimble 4000SDT geodetic GPS receivers

Summary Many GPS networks which were initially surveyed with Texas Instruments TI-4100 receivers have now been resurveyed with mixtures of TI-4100 and Trimble 4000 receivers or exclusively with Trimble receivers. In order to make confident tectonic interpretation of displacements observed between such surveys, it is necessary to understand any biases which may be introduced by using different receiver types or by mixing receivers within a network. Therefore, one of the primary objectives of the Ecuador 1990 GPS campaign (February 1990) was to provide a direct long baseline comparison between the TI-4100 and Trimble 4000SDT GPS receivers. p ]During this campaign, TI and Trimble receivers were co-located at each end of a 1323 kilometer baseline (Jerusalen to Baltra). Solutions for this baseline show no variation with receiver type. Zero-length baseline solutions showed no evidence for any intrinsic bias caused by mixing the two receiver types. Short baseline solutions indicate a bias of -34±10 mm in the baseline vertical component; the sign of the bias indicates that either the assumed phase center location for the TI is too low or the assumed location for the Trimble is too high. The bias is explainable if the phase centers of the Trimble SDT and SST antennas are similarly located. p ]Solutions for baselines measured with codeless receivers (such as the Trimble) should be as precise as those for baselines measured with P-code receivers (such as the TI) as long as it is possible to resolve ambiguities. Resolution of the widelane ambiguity is the limiting factor in ambiguity resolution with any codeless receiver, and in the February 1990 campaigns it was not successful fore baselines longer than 100 km. Without explicit modeling of the ionospheric effect on the widelane, ambiguity resolution with codeless receivers will not be successful for baselines longer than about 100 km, depending on the local ionospheric conditions.     

Performance evaluation of different ionospheric models in single-frequency code-based differential GPS positioning

Differential ionospheric slant delays are obtained from a quiet-time, three-dimensional ionospheric electron density model, called the TaiWan Ionosphere Model (TWIM), to be used in code-based differential GPS positioning. The code observations are acquired from nine continuously operating GPS stations around Taiwan whose baseline ranged from 19 to 340 km. Daily 24-hour epoch-per-epoch positioning obtained for 70 most geomagnetic quiet days (2008–2010) for each of the 72 baselines. The performance of TWIM has been compared with the standard operational Klobuchar model (KLB) used by typical single-frequency receivers and the IGS global ionospheric model (GIM). Generally, TWIM performed well in reducing the differential ionospheric delay especially for long baselines and different levels of low solar activity. It has a much better performance compared to the operational KLB model. TWIM also performed similarly with GIM, though GIM has the best performance overall. GIM has the best ionospheric gradient estimates among the three models whose differential ionospheric delay-to-horizontal error ratio is more than 0.25. This is followed closely by TWIM with about 0.20. KLB only has a ratio of <0.10. The similarity of the performance of TWIM and GIM demonstrates the feasibility of TWIM in correcting for differential ionospheric delays in the C/A code pseudorange that is caused by electron density gradients in the ionosphere. It can provide decimeter-to-centimeter level accuracy in differential GPS positioning for single-frequency receivers during geomagnetic quiet conditions across all seasons and different levels of low solar activities.     

Rapid PPP ambiguity resolution using GPS+GLONASS observations

Integer ambiguity resolution (IAR) in precise point positioning (PPP) using GPS observations has been well studied. The main challenge remaining is that the first ambiguity fixing takes about 30 min. This paper presents improvements made using GPS+GLONASS observations, especially improvements in the initial fixing time and correct fixing rate compared with GPS-only solutions. As a result of the frequency division multiple access strategy of GLONASS, there are two obstacles to GLONASS PPP-IAR: first and most importantly, there is distinct code inter-frequency bias (IFB) between satellites, and second, simultaneously observed satellites have different wavelengths. To overcome the problem resulting from GLONASS code IFB, we used a network of homogeneous receivers for GLONASS wide-lane fractional cycle bias (FCB) estimation and wide-lane ambiguity resolution. The integer satellite clock of the GPS and GLONASS was then estimated with the wide-lane FCB products. The effect of the different wavelengths on FCB estimation and PPP-IAR is discussed in detail. We used a 21-day data set of 67 stations, where data from 26 stations were processed to generate satellite wide-lane FCBs and integer clocks and the other 41 stations were selected as users to perform PPP-IAR. We found that GLONASS FCB estimates are qualitatively similar to GPS FCB estimates. Generally, 98.8% of a posteriori residuals of wide-lane ambiguities are within \(\pm 0.25\) cycles for GPS, and 96.6% for GLONASS. Meanwhile, 94.5 and 94.4% of narrow-lane residuals are within 0.1 cycles for GPS and GLONASS, respectively. For a critical value of 2.0, the correct fixing rate for kinematic PPP is only 75.2% for GPS alone and as large as 98.8% for GPS+GLONASS. The fixing percentage for GPS alone is only 11.70 and 46.80% within 5 and 10 min, respectively, and improves to 73.71 and 95.83% when adding GLONASS. Adding GLONASS thus improves the fixing percentage significantly for a short time span. We also used global ionosphere maps (GIMs) to assist the wide-lane carrier-phase combination to directly fix the wide-lane ambiguity. Employing this method, the effect of the code IFB is eliminated and numerical results show that GLONASS FCB estimation can be performed across heterogeneous receivers. However, because of the relatively low accuracy of GIMs, the fixing percentage of GIM-aided GPS+GLONASS PPP ambiguity resolution is very low. We expect better GIM accuracy to enable rapid GPS+GLONASS PPP-IAR with heterogeneous receivers.     

BDS/GPS实时钟差估计中ISB分析与函数模型设计

实时钟差产品是高精度广域差分位置服务（亚米级、分米级、厘米级）的基础产品,通过研究BDS/GPS融合的ISB,研究了各类型接收机BDS GEO/IGSO/MEO ISB差异,提出了在BDS/GPS联合的实时钟差估计中引入3个ISB参数的函数模型,在此基础上基于非差法实现了BDS/GPS联合的实时钟差估计。采用MGEX和湖南CORS实时观测数据进行了实时钟差解算,利用iGMAS产品综合中心提供的事后精密钟差产品作为基准,对比分析了新方法与原有方法的实时钟差产品的精度差异。结果表明,该方法与原方法估计的GPS钟差精度相当,对BDS实时钟差精度改进显著,尤其对BDS IGSO/MEO卫星,改进幅度在20%以上,验证了算法的有效性。     

基于GPS非差观测值进行精密单点定位研究

介绍了精密单点定位所用的数学模型及解算方案，着重分析了基于GPS非差双频观测值进行精密单点定位的误差模型、数据质量控制方法、卫星钟差的估算和内插、数据和解的一致性及精密单点定位能达到的精度等问题，并和双差结果作了比较。结果表明，利用精密星历及卫星钟改正参数的精密单点定位可达到cm级精度。     

An analysis of carrier phase differential kinematic GPS positioning using DynaPos

A series of activities have been carried out at the University of New Brunswick in an effort to evaluate advances in long-range marine kinematic differential positioning. These activities involved processing and analysis of GPS carrier phase kinematic data sets. Some of the data was collected by UNB and some was provided by The XYZs of GPS Inc. Data were collected using Trimble 5700 and Ashtech Z-12 receivers. The data sets were processed using the software DynaPos provided by the The XYZs of GPS Inc. The best results obtained in our analysis indicate an agreement of 5 cm RMS for the horizontal component and 12 cm RMS for the vertical component between two ionospheric-delay free solutions, in baselines varying from 40 to 100 km.     

BDS/GPS联合定轨的贡献分析

北斗卫星导航系统（BeiDou satellite navigation system,BDS）目前暂未具有全球导航定位能力,卫星轨道的全程跟踪与测站的几何结构还不完善,影响了卫星轨道的测定精度。针对上述问题,根据动力学定轨的原理与方法,推导了多个全球导航卫星系统（global navigation satellite system,GNSS）联合定轨对参数求解精度的解析贡献量,并利用实测数据分析了BDS/GPS联合定轨对轨道和钟差求解精度的统计贡献量。结果表明,联合定轨对系统间公共参数求解精度的贡献显著,除地球静止轨道（geostationary orbit,GEO）卫星外,其余轨道和钟差求解精度均有显著提高。BDS/GPS联合定轨对BDS卫星轨道、卫星钟差均方根误差（root mean square,RMS）以及接收机钟差RMS的统计贡献量分别为36.21%、26.88%和20.88%,其中对可视卫星数较少的区域接收机钟差求解精度的贡献尤为显著,贡献量为45.95%。     

顾及码频间偏差的GPS/GLONASS实时卫星钟差估计

在进行GPS/GLONASS联合卫星钟差估计时,GLONASS码频间偏差（inter-frequency bias,IFB）因卫星频率间的差异而无法被测站接收机钟差参数吸收,其一部分将进入GLONASS卫星钟差估值中。通过引入多个"时频偏差"参数（inter-system and inter-frequency bias,ISFB）及附加基准约束对测站GLONASS码IFB进行函数模型补偿,实现其与待估卫星钟差参数的有效分离,并对所估计实时卫星钟差和实时精度单点定位（real-time precise point positioning,RT-PPP）进行精度评估。结果表明,在卫星钟差估计观测方程中忽略码IFB,会明显降低GLONASS卫星钟差估值精度;新方法能有效避免码IFB对卫星钟差估值的影响,所获得GPS、GLONASS卫星钟差与ESA（European Space Agency）事后精密钟差产品偏差平均均方根值分别小于0.2 ns、0.3 ns。利用实时估计卫星钟差进行静态RT-PPP,当观测时段长为2 h时,GPS单系统、GPS/GLONASS组合系统的3D定位精度优于10 cm,GLONASS单系统3D定位精度约为15 cm;三种模式24 h单天解的3D定位精度均优于5 cm。     

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。     

风云三号D星天基BDS实时定位性能分析

随着北斗三号卫星导航系统(BeiDou navigation satellite system-3, BDS-3)开始向全球提供导航服务,独立使用BDS为在轨运行的卫星提供全球覆盖、全时段的定位服务成为可能。结合风云三号D星(FengYun-3D, FY-3D)全球卫星导航系统掩星探测仪(global navigation satellite system occultation sounder, GNOS)的真实在轨数据对天基BDS的定位性能进行了详细的分析。首先,使用BDS真实广播星历计算了在不同轨道高度下的可见卫星数和定位精度因子（position dilution of precision, PDOP）,并结合精密星历分析了广播星历的轨道误差、时钟误差及空间信号测距误差(signal-in-space range error, SISRE)。仿真结果表明,在95%的置信水平下,从地面到2 000 km的轨道高度,BDS在全球范围内最小可见卫星数为6,最大PDOP小于5,星座可用性已经达到100%,全球平均可见卫星数BDS比GPS(global positioning syste...