基于GNSS基准站网的对流层延迟建模

针对在卫星导航定位中,通常采用对流层模型进行,对流层延迟误差修正的现状,该文研究了一种基于GNSS基准站网的对流层延迟建模方法,并基于此方法利用日本地区GENET参考网约737个站5a的GNSS-ZTD序列建立了区域对流层模型ZTDM-JPN,并将ZTDM-JPN模型应用于GPS及北斗定位实验,分析了其在GPS及北斗定位中的实际应用性能。通过与国际上常用的对流层模型EGNOS、UNB3m作比较,结果表明,ZTDM-JPN模型的模拟精度较相同条件下的EGNOS与UNB3m模型分别提升约26%和21%,从而验证了该建模方法的可行性与优越性。     

A reference station-based GNSS computing mode to support unified precise point positioning and real-time kinematic services

Currently, the GNSS computing modes are of two classes: network-based data processing and user receiver-based processing. A GNSS reference receiver station essentially contributes raw measurement data in either the RINEX file format or as real-time data streams in the RTCM format. Very little computation is carried out by the reference station. The existing network-based processing modes, regardless of whether they are executed in real-time or post-processed modes, are centralised or sequential. This paper describes a distributed GNSS computing framework that incorporates three GNSS modes: reference station-based, user receiver-based and network-based data processing. Raw data streams from each GNSS reference receiver station are processed in a distributed manner, i.e., either at the station itself or at a hosting data server/processor, to generate station-based solutions, or reference receiver-specific parameters. These may include precise receiver clock, zenith tropospheric delay, differential code biases, ambiguity parameters, ionospheric delays, as well as line-of-sight information such as azimuth and elevation angles. Covariance information for estimated parameters may also be optionally provided. In such a mode the nearby precise point positioning (PPP) or real-time kinematic (RTK) users can directly use the corrections from all or some of the stations for real-time precise positioning via a data server. At the user receiver, PPP and RTK techniques are unified under the same observation models, and the distinction is how the user receiver software deals with corrections from the reference station solutions and the ambiguity estimation in the observation equations. Numerical tests demonstrate good convergence behaviour for differential code bias and ambiguity estimates derived individually with single reference stations. With station-based solutions from three reference stations within distances of 22–103 km the user receiver positioning results, with various schemes, show an accuracy improvement of the proposed station-augmented PPP and ambiguity-fixed PPP solutions with respect to the standard float PPP solutions without station augmentation and ambiguity resolutions. Overall, the proposed reference station-based GNSS computing mode can support PPP and RTK positioning services as a simpler alternative to the existing network-based RTK or regionally augmented PPP systems.     

Estimation and evaluation of real-time precipitable water vapor from GLONASS and GPS

The revitalized Russian GLONASS system provides new potential for real-time retrieval of zenith tropospheric delays (ZTD) and precipitable water vapor (PWV) in order to support time-critical meteorological applications such as nowcasting or severe weather event monitoring. In this study, we develop a method of real-time ZTD/PWV retrieval based on GLONASS and/or GPS observations. The performance of ZTD and PWV derived from GLONASS data using real-time precise point positioning (PPP) technique is carefully investigated and evaluated. The potential of combining GLONASS and GPS data for ZTD/PWV retrieving is assessed as well. The GLONASS and GPS observations of about half a year for 80 globally distributed stations from the IGS (International GNSS Service) network are processed. The results show that the real-time GLONASS ZTD series agree quite well with the GPS ZTD series in general: the RMS of ZTD differences is about 8 mm (about 1.2 mm in PWV). Furthermore, for an inter-technique validation, the real-time ZTD estimated from GLONASS-only, GPS-only, and the GPS/GLONASS combined solutions are compared with those derived from very long baseline interferometry (VLBI) at colocated GNSS/VLBI stations. The comparison shows that GLONASS can contribute to real-time meteorological applications, with almost the same accuracy as GPS. More accurate and reliable water vapor values, about 1.5–2.3 mm in PWV, can be achieved when GLONASS observations are combined with the GPS ones in the real-time PPP data processing. The comparison with radiosonde data further confirms the performance of GLONASS-derived real-time PWV and the benefit of adding GLONASS to stand-alone GPS processing.     

Assessment of ZTD derived from ECMWF/NCEP data with GPS ZTD over China

The accuracy and feasibility of computing the zenith tropospheric delays (ZTDs) from data of the European Center for Medium-Range Weather Forecasts (ECMWF) and the United States National Centers for Environmental Prediction (NCEP) are studied. The ZTDs are calculated from ECMWF/NCEP pressure-level data by integration and from the surface data with the Saastamoinen model method and then compared with the solutions measured from 28 global positioning system (GPS) stations of the Crustal Movement Observation Network of China (CMONOC) for 1 year. The results are as follows: (1) the error of the integration method is 1–3 cm less than that of the Saastamoinen model method. The agreement between the ECMWF ZTD and GPS ZTD is better than that between NCEP ZTD and GPS ZTD; (2) the bias and root mean square difference (RMSD), especially the latter, have a seasonal variation, and the RMSD decreases with increasing altitude while the variation with latitude is not obvious; and (3) when using the full horizontal resolution of 0.5° × 0.5° of the ECMWF meteorological data in place of a reduced 2.5° × 2.5° grid, the mean RMSD between GPS and ECMWF ZTD decreases by 4.5 mm. These results illuminated the accuracy and feasibility of computing the tropospheric delays and establishing the ZTD prediction model over China for navigation and positioning with ECMWF and NCEP data.     

Modeling tropospheric wet delays with national GNSS reference network in China for BeiDou precise point positioning

During past decades, precise point positioning (PPP) has been proven to be a well-known positioning technique for centimeter or decimeter level accuracy. However, it needs long convergence time to get high-accuracy positioning, which limits the prospects of PPP, especially in real-time applications. It is expected that the PPP convergence time can be reduced by introducing high-quality external information, such as ionospheric or tropospheric corrections. In this study, several methods for tropospheric wet delays modeling over wide areas are investigated. A new, improved model is developed, applicable in real-time applications in China. Based on the GPT2w model, a modified parameter of zenith wet delay exponential decay wrt. height is introduced in the modeling of the real-time tropospheric delay. The accuracy of this tropospheric model and GPT2w model in different seasons is evaluated with cross-validation, the root mean square of the zenith troposphere delay (ZTD) is 1.2 and 3.6 cm on average, respectively. On the other hand, this new model proves to be better than the tropospheric modeling based on water-vapor scale height; it can accurately express tropospheric delays up to 10 km altitude, which potentially has benefits in many real-time applications. With the high-accuracy ZTD model, the augmented PPP convergence performance for BeiDou navigation satellite system (BDS) and GPS is evaluated. It shows that the contribution of the high-quality ZTD model on PPP convergence performance has relation with the constellation geometry. As BDS constellation geometry is poorer than GPS, the improvement for BDS PPP is more significant than that for GPS PPP. Compared with standard real-time PPP, the convergence time is reduced by 2–7 and 20–50% for the augmented BDS PPP, while GPS PPP only improves about 6 and 18% (on average), in horizontal and vertical directions, respectively. When GPS and BDS are combined, the geometry is greatly improved, which is good enough to get a reliable PPP solution, the augmentation PPP improves insignificantly comparing with standard PPP.     

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。     

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。     

北斗广域实时精密定位服务系统研究与评估分析

采用IGS、MGEX、北斗地基增强网的实时观测数据,研制北斗广域精密定位服务系统,实时生成北斗高精度轨道、钟差、电离层产品,提供厘米级北斗双频PPP、分米级单频PPP、米级单频伪距定位服务。对实时产品评估分析的结果表明:北斗卫星实时轨道与钟差产品URE统计精度约为2.0cm,实时电离层精度优于4.0TECU。采用全国分布的实时测站动态定位精度(95%置信度)评估分析表明:北斗双频PPP精度存在明显的区域特征,高纬度以及西部边缘地区的定位精度平面约0.2m,高程约0.3m;中部地区定位精度平面优于0.1m,高程优于0.2m,接近GPS实时PPP精度水平;北斗与GPS融合可以提高单北斗、单GPS的定位性能,尤其是显著加快了PPP收敛时间,收敛时间缩短到20min内。另外,除边缘地区外,北斗单频PPP实现平面0.5m,高程1.0m;北斗单频伪距单点定位实现平面2.0m,高程3.0m。     

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.     

MSAS系统在中国区域服务性能评估与分析

为了提高GNSS卫星导航系统服务性能,美国、欧洲各国、日本、印度、俄罗斯、韩国、中国已经建立或者即将建立独立的星基增强系统,通过提供广播星历差分与完好性增强信息,满足高精度高完好性用户使用需求。针对日本MSAS系统在中国区域SBAS增强服务性能不稳定的问题,在理解SBAS增强信息内容和处理流程的基础上,对分布在不同位置的日本两个站(GMSD、MIZU)和中国中东部区域3个站(天津、上海、武汉)的数据进行测试,采用GPS单点定位、MSAS增强单点定位和MSAS双频精密单点定位3种模式进行增强效果的评估和分析。结果表明,在中国区域采用MSAS电离层改正参数效果不佳,距离越远,精度改善程度越差。只采用轨道和钟差改正信息,较单点定位可实现10%的精度提升,精密单点定位可实现60%的精度提升,但需数十分钟的收敛时间,本文也给出了多方面的解决方法。     

Improving BeiDou real-time precise point positioning with numerical weather models

Precise positioning with the current Chinese BeiDou Navigation Satellite System is proven to be of comparable accuracy to the Global Positioning System, which is at centimeter level for the horizontal components and sub-decimeter level for the vertical component. But the BeiDou precise point positioning (PPP) shows its limitation in requiring a relatively long convergence time. In this study, we develop a numerical weather model (NWM) augmented PPP processing algorithm to improve BeiDou precise positioning. Tropospheric delay parameters, i.e., zenith delays, mapping functions, and horizontal delay gradients, derived from short-range forecasts from the Global Forecast System of the National Centers for Environmental Prediction (NCEP) are applied into BeiDou real-time PPP. Observational data from stations that are capable of tracking the BeiDou constellation from the International GNSS Service (IGS) Multi-GNSS Experiments network are processed, with the introduced NWM-augmented PPP and the standard PPP processing. The accuracy of tropospheric delays derived from NCEP is assessed against with the IGS final tropospheric delay products. The positioning results show that an improvement in convergence time up to 60.0 and 66.7% for the east and vertical components, respectively, can be achieved with the NWM-augmented PPP solution compared to the standard PPP solutions, while only slight improvement in the solution convergence can be found for the north component. A positioning accuracy of 5.7 and 5.9 cm for the east component is achieved with the standard PPP that estimates gradients and the one that estimates no gradients, respectively, in comparison to 3.5 cm of the NWM-augmented PPP, showing an improvement of 38.6 and 40.1%. Compared to the accuracy of 3.7 and 4.1 cm for the north component derived from the two standard PPP solutions, the one of the NWM-augmented PPP solution is improved to 2.0 cm, by about 45.9 and 51.2%. The positioning accuracy for the up component improves from 11.4 and 13.2 cm with the two standard PPP solutions to 8.0 cm with the NWM-augmented PPP solution, an improvement of 29.8 and 39.4%, respectively.     

利用GPS/BDS/GLONASS/Galileo组合PPP反演大气可降水量

为进一步改善精密单点定位（PPP）探测大气可降水量（PWV）的性能，本文提出采用GPS/BDS/GLONASS/Galileo组合PPP进行PWV反演的方法，并利用国内3个MGEX（multi-GNSS experiment）观测站的实测数据，对GPS/BDS/GLONASS/Galileo组合PPP在大气水汽探测方面的性能进行了评估。试验结果表明：相较于GPS PPP、GPS/BDS组合PPP和GPS/GLONASS组合PPP，GPS/BDS/GLONASS/Galileo组合PPP估计天顶对流层延迟（ZTD）的初始化时间分别缩短了33%、26%、20%，且能获得更高精度的ZTD估值和PWV信息，在大气水汽探测方面的性能更优。     

Tropospheric refractivity and zenith path delays from least-squares collocation of meteorological and GNSS data

Precise positioning requires an accurate a priori troposphere model to enhance the solution quality. Several empirical models are available, but they may not properly characterize the state of troposphere, especially in severe weather conditions. Another possible solution is to use regional troposphere models based on real-time or near-real time measurements. In this study, we present the total refractivity and zenith total delay (ZTD) models based on a numerical weather prediction (NWP) model, Global Navigation Satellite System (GNSS) data and ground-based meteorological observations. We reconstruct the total refractivity profiles over the western part of Switzerland and the total refractivity profiles as well as ZTDs over Poland using the least-squares collocation software COMEDIE (Collocation of Meteorological Data for Interpretation and Estimation of Tropospheric Pathdelays) developed at ETH Zürich. In these two case studies, profiles of the total refractivity and ZTDs are calculated from different data sets. For Switzerland, the data set with the best agreement with the reference radiosonde (RS) measurements is the combination of ground-based meteorological observations and GNSS ZTDs. Introducing the horizontal gradients does not improve the vertical interpolation, and results in slightly larger biases and standard deviations. For Poland, the data set based on meteorological parameters from the NWP Weather Research and Forecasting (WRF) model and from a combination of the NWP model and GNSS ZTDs shows the best agreement with the reference RS data. In terms of ZTD, the combined NWP-GNSS observations and GNSS-only data set exhibit the best accuracy with an average bias (from all stations) of 3.7 mm and average standard deviations of 17.0 mm w.r.t. the reference GNSS stations.     

PPP/PPP-RTK新进展与北斗/GNSS PPP定位性能比较

首先简要回顾了精密单点定位（PPP）技术在最近几年的发展现状,重点总结了高采样率钟差实时快速估计、多系统组合PPP模糊度固定、多频GNSS PPP模型及其模糊度固定、PPP快速初始化、PPP-RTK等若干热点方向的最新研究进展。在此基础上,利用目前四大卫星导航系统（GPS、GLONASS、Galileo、北斗）最新的实际观测数据,全面比较分析了各系统及多系统组合PPP定位性能,重点给出了北斗二号+北斗三号PPP浮点解和固定解的定位精度、收敛时间和首次固定时间。结果表明：我国北斗导航卫星系统已经可以实现与其他导航卫星系统基本相当的PPP定位性能。北斗二号+北斗三号组合PPP的收敛时间/首次固定时间20~30 min;静态解的东、北、天方向定位精度在毫米到厘米级;动态解水平方向约5 cm,高程方向约7 cm;多系统组合可显著提高PPP定位精度、收敛时间和首次固定时间：固定解定位精度比浮点解在东、北、天方向分别提升了14.8%、12.0%和12.8%;相比单GPS,多系统组合PPP浮点解的收敛时间和固定解首次固定时间分别缩短了36.5%和40.4%。     

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。     

非校正相位延迟参数在复杂铁路场景下GPS精密单点定位应用研究

在复杂艰险地区的铁路沿线上全球卫星导航系统(GNSS)基准站相对较少且稀疏,如何获得该场景下测站点的高精度位置信息是亟待解决的重大问题. 论文以GPS系统为例,利用铁路沿线上7个GNSS测站点(14个观测时段)分别开展了卫星跟踪数和位置精度因子(PDOP)评估,观测数据的可靠性、高精度性验证以及固定解精密单点定位(PPP)技术研究. 试验结果表明:1) 在所有时间段内卫星平均跟踪数约分布在5.14～9.07颗,PDOP平均值约分布在2.19～5.72 cm,具有较高地定位可用性;2) 模糊度固定的PPP可进一步改善铁路环境下的单点定位精度. 当观测时间约为90 min时,其在水平方向和高程方向上可分别实现优于10 cm和15 cm的解算精度,且相对于浮点解,三维方向上的定位精度可提升约35.43%. 该研究可为复杂铁路场景下的勘测和施工阶段提供高精度的测站位置信息.      

GPS/VRS 参考站网络的对流层误差建模技术研究

在虚拟参考站(VRS)技术中,参考站与流动站间的高程差异会引起对流层误差改正数中存在系统偏差影响,使对流层改正精度降低。在常规网络内插改正模型的基础上,借助先验对流层模型,提出了一种能自主修正高程偏差的距离相关对流层网络内插模型(MHDIM)。基于四川GPS连续运行参考站网络(Sichuan GPS Reference Station Network-SGRSN)实际测试数据的分析表明,对于地形变化较大的中长距离稀疏GPS/VRS参考站网络(如流动站与参考站间高程差异大于500m),应用MHDIM模型可使对流层延迟误差改正精度提高到2到3cm并实现cm级网络RTK定位结果,适用于GPS/VRS参考站网络cm级实时动态定位要求。     

A modified mix-differenced approach for estimating multi-GNSS real-time satellite clock offsets

A modified mixed-differenced approach for estimating multi-GNSS real-time clock offsets is presented. This approach, as compared to the earlier presented mixed-differenced approach which uses epoch-differenced and undifferenced observations, further adds a satellite-differenced process. The proposed approach, based on real-time orbit products and a mix of epoch-differenced and satellite-differenced observations to estimate only satellite clock offsets and tropospheric zenith wet delays, has fewer estimated parameters than other approaches, and thus its implementing procedure is efficient and can be performed and extended easily. To obtain high accuracy, the approach involves three steps. First, the high-accuracy tropospheric zenith wet delay of each station is estimated using mixed-differenced carrier phase observations. Second, satellite clock offset changes between adjacent epochs are estimated using also mixed-differenced carrier phase observations. Third, the satellite clock offsets at the initial epoch are estimated using satellite-differenced pseudorange observations. Finally, the initial epoch clock results and clock offset changes are concatenated to obtain the clock results of the current epoch. To validate the real-time satellite clock results, multi-GNSS post-processing clock products from IGS ACs were selected for comparison. From the comparison, the standard deviations of the GPS, GLONASS, BeiDou and Galileo systems clock results are approximately 0.1–0.4 ns, except for the BeiDou GEO satellites. The root mean squares are about 0.4–2.3 ns, which are similar to those of other international real-time products. When the clock estimates were assessed based on a pseudo-kinematic PPP procedure, the positioning accuracies in the East, North and Up components reach 5.6, 5.5 and 7.6 cm, respectively, which meet the centimeter level and are comparable to the application of other products.     

同时估计电离层延迟的单频精密单点定位方法

提出一种基于单频码和相位观测量的单频精密单点定位方法,将每个观测量的电离层延迟量与接收机钟差、对流层天顶延迟、接收机位置、相位模糊度一起作为未知参数。采用约化参数的平方根信息滤波与平滑算法进行参数解算。该方法适用于实时定位和事后处理,且不需要外部的电离层模型。采用全球分布的32个IGS监测站16 d实测数据进行静态解算试验,结果表明E、N、U方向的RMS分别为0.023 m、0.018 m、0.059 m;基于一组机载GPS数据进行动态解算试验,得到E、N、U方向的RMS(与载波相位动态相对定位结果比较)分别为0.168 m、0.151 m、0.172 m。     

Multi-GNSS phase delay estimation and PPP ambiguity resolution: GPS,BDS, GLONASS,Galileo

This paper focuses on the precise point positioning (PPP) ambiguity resolution (AR) using the observations acquired from four systems: GPS, BDS, GLONASS, and Galileo (GCRE). A GCRE four-system uncalibrated phase delay (UPD) estimation model and multi-GNSS undifferenced PPP AR method were developed in order to utilize the observations from all systems. For UPD estimation, the GCRE-combined PPP solutions of the globally distributed MGEX and IGS stations are performed to obtain four-system float ambiguities and then UPDs of GCRE satellites can be precisely estimated from these ambiguities. The quality of UPD products in terms of temporal stability and residual distributions is investigated for GPS, BDS, GLONASS, and Galileo satellites, respectively. The BDS satellite-induced code biases were corrected for GEO, IGSO, and MEO satellites before the UPD estimation. The UPD results of global and regional networks were also evaluated for Galileo and BDS, respectively. As a result of the frequency-division multiple-access strategy of GLONASS, the UPD estimation was performed using a network of homogeneous receivers including three commonly used GNSS receivers (TRIMBLE NETR9, JAVAD TRE_G3TH DELTA, and LEICA). Data recorded from 140 MGEX and IGS stations for a 30-day period in January in 2017 were used to validate the proposed GCRE UPD estimation and multi-GNSS dual-frequency PPP AR. Our results show that GCRE four-system PPP AR enables the fastest time to first fix (TTFF) solutions and the highest accuracy for all three coordinate components compared to the single and dual system. An average TTFF of 9.21 min with \(7{^{\circ }}\) cutoff elevation angle can be achieved for GCRE PPP AR, which is much shorter than that of GPS (18.07 min), GR (12.10 min), GE (15.36 min) and GC (13.21 min). With observations length of 10 min, the positioning accuracy of the GCRE fixed solution is 1.84, 1.11, and 1.53 cm, while the GPS-only result is 2.25, 1.29, and 9.73 cm for the east, north, and vertical components, respectively. When the cutoff elevation angle is increased to \(30{^{\circ }}\), the GPS-only PPP AR results are very unreliable, while 13.44 min of TTFF is still achievable for GCRE four-system solutions.