Estimation and evaluation of hourly updated global GPS Zenith Total Delays over ten months

The EUMETNET EIG GNSS Water Vapour Programme (E-GVAP) is responsible for the coordination of near real time GPS Zenith Total Delay (ZTD) production in Europe and for aiding the development of ZTD assimilation into Numerical Weather Prediction (NWP) models. Since 2000, the Geodetic Observatory Pecný (GOP) has been routinely estimating regional ZTDs in near real time. In 2010, GOP developed a modified processing system in order to provide the first optimal and robust ZTD solution with a global scope and hourly upgrade, fulfilling the requirements for assimilation into operational NWP models. Since July 2010, the GOP global tropospheric product has consisted of about 90 sites and has contributed routinely in a testing mode into the E-GVAP database. Global near real time ZTDs generated over ten months have been evaluated with respect to IGS and EUREF routine post-processed ZTD products, ZTDs integrated from radiosonde profiles, and ZTDs calculated from the Met Office global NWP model. Comparison with the GNSS post-processed solutions gives standard deviations of 3–6 mm in ZTD and biases of 1–2 mm, which is comparable to GOP regional near real time solution, however, for some isolated or low data quality stations up to 20 % quality decrease can be found. Comparison with NWP shows a latitudinal trend in the standard deviation with values as low as 4 mm at high latitudes, increasing to almost 20 mm in the tropics, and a lack of variability in the model background ZTD in the tropics. The evaluation with global radiosondes gives ZTD standard deviation of 5–16 mm, which is comparable with previous studies in European scope. Since the 10-month comparison gave satisfactory results, GOP was asked by UK Met Office to disseminate the global product to the end users via the Global Telecommunications System. Since 10 October 2011, the GOP global ZTD product configuration has been extended to about 164 global stations and still processed within 10 min. However, in GOP routine contribution to E-GVAP, about 124 stations are available in general due to hourly data latency above 30 min or data gaps.     

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.     

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.     

Using external tropospheric corrections to improve GNSS positioning of hot-air balloon

High accurate global navigation satellite systems (GNSS) require to correct a signal delay caused by the troposphere. The delay can be estimated along with other unknowns or introduced from external models. We assess the impact of the recently developed augmentation tropospheric model on real-time kinematic precise point positioning (PPP). The model is based on numerical weather forecast and thus reflects the actual state of weather conditions. Using the G-Nut/Geb software, we processed GNSS and meteorological data collected during the experiment using a hot-air balloon flying up to an altitude of 2000 m. We studied the impacts of random walk noise setting of zenith total delay (ZTD) on estimated parameters and the mutual correlations, the use of external tropospheric corrections, the use of data from a single or dual GNSS constellation and the use of Kalman filter and backward smoothing processing methods. We observed a significant negative correlation of the estimated rover height and ZTD which depends on constraining ZTD estimates. Such correlation caused a degraded performance of both parameters when estimated simultaneously, in particular for a single GNSS constellation. The impact of ZTD constraining reached up to 50-cm differences in the rover height. Introducing external tropospheric corrections improved the PPP solution regarding: (1) shortened convergence, (2) better overall robustness, particularly, in case of degraded satellite geometry, (3) less adjusted parameters with lower correlations. The numerical weather model-driven PPP resulted in 9–12- and 5–6-cm uncertainties in the rover altitude using the Kalman filter and the backward smoothing, respectively. Compared to standard PPP, it indicates better performance by a factor of 1–2 depending on the availability of GNSS constellations, the troposphere constraining and the processing strategy.     

Multi-technique comparison of troposphere zenith delays and gradients during CONT08

CONT08 was a 15 days campaign of continuous Very Long Baseline Interferometry (VLBI) sessions during the second half of August 2008 carried out by the International VLBI Service for Geodesy and Astrometry (IVS). In this study, VLBI estimates of troposphere zenith total delays (ZTD) and gradients during CONT08 were compared with those derived from observations with the Global Positioning System (GPS), Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS), and water vapor radiometers (WVR) co-located with the VLBI radio telescopes. Similar geophysical models were used for the analysis of the space geodetic data, whereas the parameterization for the least-squares adjustment of the space geodetic techniques was optimized for each technique. In addition to space geodetic techniques and WVR, ZTD and gradients from numerical weather models (NWM) were used from the European Centre for Medium-Range Weather Forecasts (ECMWF) (all sites), the Japan Meteorological Agency (JMA) and Cloud Resolving Storm Simulator (CReSS) (Tsukuba), and the High Resolution Limited Area Model (HIRLAM) (European sites). Biases, standard deviations, and correlation coefficients were computed between the troposphere estimates of the various techniques for all eleven CONT08 co-located sites. ZTD from space geodetic techniques generally agree at the sub-centimetre level during CONT08, and??as expected??the best agreement is found for intra-technique comparisons: between the Vienna VLBI Software and the combined IVS solutions as well as between the Center for Orbit Determination (CODE) solution and an IGS PPP time series; both intra-technique comparisons are with standard deviations of about 3?C6?mm. The best inter space geodetic technique agreement of ZTD during CONT08 is found between the combined IVS and the IGS solutions with a mean standard deviation of about 6?mm over all sites, whereas the agreement with numerical weather models is between 6 and 20?mm. The standard deviations are generally larger at low latitude sites because of higher humidity, and the latter is also the reason why the standard deviations are larger at northern hemisphere stations during CONT08 in comparison to CONT02 which was observed in October 2002. The assessment of the troposphere gradients from the different techniques is not as clear because of different time intervals, different estimation properties, or different observables. However, the best inter-technique agreement is found between the IVS combined gradients and the GPS solutions with standard deviations between 0.2 and 0.7?mm.     

GGOS对流层延迟产品精度分析及在PPP中的应用

对流层延迟是卫星导航定位的主要误差源,GNSS广域增强需要高精度的对流层延迟产品进行误差修正。对流层延迟可通过GNSS进行实时估计,也可通过融合多源数据的数值气象预报模型获取。IGS发布的全球对流层天顶延迟产品由GNSS解算,其精度可达4mm,时间分辨率为5min,但其分布不均匀,在广袤的海洋区域无数据覆盖。GGOS Atmosphere基于ECMWF 40年再分析资料,可提供1979年以来时间分辨率为6h、空间分辨率为2.5°×2°的全球天顶对流层总延迟格网数据。本文通过2015年全球IGS测站的ZTD资料对GGOS的ZTD产品进行了评估,研究了GGOS Atmosphere对流层延迟产品与IGS发布ZTD资料之间的系统差,通过线性拟合估计出每个测站GGOS-ZTD与IGSZTD系统差系数(包括比例误差a和固定误差b),然后对比例误差a、固定误差b进行球谐展开,建立了两种ZTD数据源之间的系统差模型。选取IGS测站和陆态网测站,对附加系统偏差改正后的GGOSZTD产品对PPP的收敛速度的影响进行研究。本文研究结果表明:GGOS-ZTD与IGS-ZTD间存在系统偏差,其bias平均为-0.54cm;两者之间较差的RMS平均为1.31cm,说明GGOS-ZTD产品足以满足广大GNSS导航定位用户对对流层延迟改正的需要。将改正了系统差后的GGOS-ZTD产品用于ALBH、DEAR、ISPA测站、PALM测站、ADIS测站、YNMH测站、WUHN测站进行PPP试验,发现可明显提高定位收敛速度,尤其是在U方向上,收敛速度分别提高10.58%、31.68%、15.96%、43.89%、51.46%、14.69%、18.40%。     

一种优化的对流层天顶延迟融合模型FZTD

对流层延迟是影响全球卫星导航系统(GNSS)定位精度的主要误差源之一,模型修正法是目前削弱对流层延迟影响的主要方法. 以简单易用的角度为切入点,综合UNB3模型的简易性和GPT2w模型的高精度特点,构建一种简易且精度较高的对流层天顶延迟融合模型(FZTD). 并利用多年的国际GNSS服务(IGS) 对流层天顶延迟(ZTD)数据对该模型精度进行了验证. 结果表明FZTD模型的均方根(RMS)与平均偏差(bias)值分别为4.4 cm和?0.3 cm,均小于传统模型UNB3m(RMS:5.1 cm,bias:1.1 cm)和EGNOS(RMS:5.1 cm,bias:0.3 cm),定位精度提高了14%,而且在南半球提高尤为明显,特别在南极地区,精度提高了近3倍,弥补了传统模型在南北半球精度差异大的不足. 新模型总气象参数仅为120个比GPT2w模型急剧减少,与传统模型相当,为GNSS实时导航定位终端的预定义对流层延迟改正提供了更优的选择.      

The IGS-combined station coordinates, earth rotation parameters and apparent geocenter

The International GNSS Service (IGS) routinely generates a number of weekly, daily and sub-daily products. Station coordinates and velocities, earth rotation parameters (ERPs) and apparent geocenter are among these products generated weekly by the IGS Reference Frame Coordinator. They have been determined since 1999 by combining independent estimates from at least seven IGS Analysis Centers (ACs). Two Global Network Associate Analysis Centers (GNAACs) also provide independent combinations using the same AC weekly solutions and they are currently used to quality control the IGS combination. The combined solutions are aligned to an IGS realization (IGS05) of the ITRF2005 using a carefully selected set of the IGS Reference Frame (RF) stations (nominally 132). During the combination process, the contributing solutions are compared and outliers are removed to ensure a high level of consistency of the estimated parameters. The ACs and the weekly combined solution are consistent at the 1–2 and 3–4 mm levels for the horizontal and vertical components. Similarly, the excess Length of Day (LOD), the pole positions and pole rates are consistent at the 10μs, 0.03–0.05 mas and 0.10–0.20 mas/day levels, respectively. The consistency of the apparent geocenter estimate is about 5 mm in the X and Y components and 10 mm in the Z component. Comparison of the IGS-combined ERP estimates with the IERS Bulletin A suggests a small bias of the order of ?0.04 mas and + 0.05 mas (both ±0.05 mas) in the x and y components.     

The impact of errors in predicted GPS orbits on zenith troposphere delay estimation

The impact of precise GPS ephemeris errors on estimated zenith tropospheric delays (ZTD) is studied for applications in meteorology. First, the status of IGS ultra-rapid orbit prediction is presented and specific problems are outlined. Second, a simplified analytical solution of the impact of ephemeris errors on estimated ZTDs is presented. Two widely used methods are studied—the precise point positioning technique (PPP) and the double-difference network approach. A simulation experiment is additionally conducted for the network approach to assess the capability of ephemeris error compensation by the ambiguities. An example of marginal requirements for ephemeris accuracy is presented, assuming the compensation by ZTD only and admitting the error of 1 cm in ZTD. The requirement for the maximum orbit error 1 cm for radial and 8 cm for tangential position components using PPP approach, versus 217 cm (radial) and 19 cm (tangential) using network solution. Furthermore, an assessment of possible compensations of ephemeris errors by other estimated parameters was considered. In radial orbit position, an error of a few meters can be still absorbed by satellite clocks (96%) and phase ambiguities (96%) even for the PPP technique. A tangential orbit position error up to 16 cm for PPP and 38 cm for network solutions should not bias ZTD by more than 1 cm, but any bigger error could, in general. The error impact on ZTD in such cases depends on the compensation ability of ambiguities and clocks (PPP).     

GPS静态精密单点定位算法精度分析

采用精密轨道和钟差，利用Bernese软件解算得到亚洲地区13个IGS跟踪站的站坐标、对流层ZTD和接收机钟差，将解算的结果与CODE发布的结果对比发现：静态PPP算法解算的N方向收敛精度明显优于E方向和U方向，4~6 h后，坐标偏差在1 cm左右；NEU RMS均值分别为0.45、0.29、0.69 cm，ZTD RMS均值为0.85 cm，接收机钟差RMS均值为0.14 ns。试验表明：精密单点定位算法具有较高的精度和可靠性，可为实际工程测量及相关地球物理信号研究提供理论依据。     

不同对流层改正方法对 PPP 定位效果影响的对比分析

对流层延迟是影响精密单点定位效果的一项重要误差源,不同的对流层改正方法直接影响PPP的定位结果。对比分析采用UNB3模型、Saastamoinen模型、ZTD参数估计3种方法对PPP定位精度和收敛时间的影响。实验结果表明:3种模型平面改正精度和收敛时间基本一致。天顶方向改正精度UNB3模型与ZTD参数估计法基本相当,但两者优于Saastamoinen模型;收敛速度UNB3模型与Saastamoinen模型基本一致,ZTD参数估计法收敛速度较慢。     

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.     

利用中国区域MERRA-2资料计算ZTD和ZWD的精度分析

对流层延迟是影响高精度定位与导航的主要误差之一,也是全球导航卫星系统（global navigation satellite system,GNSS）水汽探测的关键参数。美国航空航天局发布了最新一代的大气再分析资料（MERRA-2资料）,其可用于计算高时空分辨率的对流层延迟产品,但是目前尚无文献对利用MERRA-2资料计算天顶对流层延迟（zenith tropospheric delay,ZTD）和天顶湿延迟（zenith wet delay,ZWD）的精度进行分析。因此,联合2015年中国陆态网214个GNSS站ZTD产品和分布于中国区域的87个探空站资料,对利用MERRA-2资料在中国区域计算ZTD/ZWD的精度进行评估。结果表明：（1）以陆态网ZTD为参考值,利用MERRA-2资料积分计算ZTD的年均偏差和均方根误差（root mean square error,RMSE）分别为0.32 cm和1.21 cm,且偏差和RMSE均表现出一定的季节变化,总体上呈现为夏季精度低、冬季精度高;在空间分布上,偏差随纬度和高程的变化趋势并不明显,但RMSE随纬度和高程的增加总体上呈现递减的趋...     

Using a regional numerical weather prediction model for GNSS positioning over Brazil

The global navigation satellite system (GNSS) can provide centimeter positioning accuracy at low costs. However, in order to obtain the desired high accuracy, it is necessary to use high-quality atmospheric models. We focus on the troposphere, which is an important topic of research in Brazil where the tropospheric characteristics are unique, both spatially and temporally. There are dry regions, which lie mainly in the central part of the country. However, the most interesting area for the investigation of tropospheric models is the wet region which is located in the Amazon forest. This region substantially affects the variability of humidity over other regions of Brazil. It provides a large quantity of water vapor through the humidity convergence zone, especially for the southeast region. The interconnection and large fluxes of water vapor can generate serious deficiencies in tropospheric modeling. The CPTEC/INPE (Center for Weather Forecasting and Climate Studies/Brazilian Institute for Space Research) has been providing since July 2012 a numerical weather prediction (NWP) model for South America, known as Eta. It has yield excellent results in weather prediction but has not been used in GNSS positioning. This NWP model was evaluated in precise point positioning (PPP) and network-based positioning. Concerning PPP, the best positioning results were obtained for the station SAGA, located in Amazon region. Using the NWP model, the 3D RMS are less than 10 cm for all 24 h of data, whereas the values reach approximately 60 cm for the Hopfield model. For network-based positioning, the best results were obtained mainly when the tropospheric characteristics are critical, in which case an improvement of up to 7.2 % was obtained in 3D RMS using NWP models.     

Multi-GNSS precise point positioning (MGPPP) using raw observations

A joint-processing model for multi-GNSS (GPS, GLONASS, BDS and GALILEO) precise point positioning (PPP) is proposed, in which raw code and phase observations are used. In the proposed model, inter-system biases (ISBs) and GLONASS code inter-frequency biases (IFBs) are carefully considered, among which GLONASS code IFBs are modeled as a linear function of frequency numbers. To get the full rank function model, the unknowns are re-parameterized and the estimable slant ionospheric delays and ISBs/IFBs are derived and estimated simultaneously. One month of data in April, 2015 from 32 stations of the International GNSS Service (IGS) Multi-GNSS Experiment (MGEX) tracking network have been used to validate the proposed model. Preliminary results show that RMS values of the positioning errors (with respect to external double-difference solutions) for static/kinematic solutions (four systems) are 6.2 mm/2.1 cm (north), 6.0 mm/2.2 cm (east) and 9.3 mm/4.9 cm (up). One-day stabilities of the estimated ISBs described by STD values are 0.36 and 0.38 ns, for GLONASS and BDS, respectively. Significant ISB jumps are identified between adjacent days for all stations, which are caused by the different satellite clock datums in different days and for different systems. Unlike ISBs, the estimated GLONASS code IFBs are quite stable for all stations, with an average STD of 0.04 ns over a month. Single-difference experiment of short baseline shows that PPP ionospheric delays are more precise than traditional leveling ionospheric delays.     

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.     

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.     

天线相位中心改正模型对PPP参数估计的影响

比较了IGS发布的相对天线相位中心改正模型与绝对天线相位中心改正模型,分析了两种不同模型对精密单点定位（PPP）参数估计的影响。结果表明,采用不同的天线相位中心改正模型,天顶对流层延迟（ZPD）的估值存在5mm左右的差异,接收机钟差参数存在3ns左右的差异,估计的测站坐标高程方向有1cm左右的差异。使用绝对天线相位中心模型估计得到的ZPD精度优于5mm,高程方向定位精度约为1cm,接收机钟差估计的精度达0.1ns。     

高纬度BDS/GPS PPP中的对流层延迟改正模型优选

由于高纬度地区气温气压值及变化率与中低纬度地区有较大差异,因此目前发布的多种对流层延迟模型在高纬度地区使用的精度会不同。为了给高纬度地区BDS/GPS用户提供更好的对流层延迟模型选择,文中采用UNB3,EGNOS和GPT2模型,以IGS发布的ZPD产品和SINEX文件作为参考,对比基于这三种对流层延迟模型计算的天顶对流层总延迟量以及精密单点定位精度,可知GPT2较UNB3和EGNOS在高纬度地区定位中有更好的精度表现。     

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.