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.     

Accuracy improvement of zenith tropospheric delay estimation based on GPS precise point positioning algorithm

In the precise point positioning(PPP),some impossible accurately simulated systematic errors still remained in the GPS observations and will inevitably degrade the precision of zenith tropospheric delay(ZTD) estimation.The stochastic models used in the GPS PPP mode are compared.In this paper,the research results show that the precision of PPP-derived ZTD can be obviously improved through selecting a suitable stochastic model for GPS measurements.Low-elevation observations can cover more troposphere informat...     

SHAtrop:基于陆态网GNSS数据的中国大陆区域ZTD模型

对陆态网223个全球导航卫星系统（Global Navigation Satellite System，GNSS）测站6 a实测对流层天顶延迟（zenith total delay，ZTD）的时空特性进行了分析，结果表明，各测站ZTD平均值随大地高指数递减，衰减因子与纬度近似线性关系，其时域变化呈现年周期和半年周期，周期、振幅、初相位与地域分布有关。综合采用周期函数及格网函数，建立了中国大陆区域ZTD经验模型SHAtrop。模型提供区域内分辨率为2.5°×2.0°的格网，用户使用时，先在相应格网内插得到对应参数，再利用三角函数得到椭球面ZTD，最后利用指数函数计算ZTD。实测ZTD的数据验证结果表明，SHAtrop的均方根误差（root mean square，RMS）为3.4 cm，优于常见经验模型。SHAtrop采用较多测站，对高程改正更精细；使用时只需要输入经纬度与时间，使用方便，能满足中国区域GNSS用户实时定位导航的ZTD改正需求。     

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。     

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.     

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。     

一种基于SARIMA的经验对流层延迟模型

为了减弱对流层延迟的影响,提高GNSS定位精度,探讨了在无气象参数的条件下,利用预测模型计算对流层延迟的可能性,并提出了一种经验对流层延迟预测模型,即基于季节性自回归移动平均模型（SARIMA）的对流层延迟预报方法。结合中国长春和上海两个地区的ZTD数据进行预测分析,预测结果表明：基于SARIMA的ZTD预报模型能够满足不同地区不同时段下的ZTD估计需求,是一种较高精度的ZTD预报方法。     

精密单点定位用户自主式完备性监测算法

精密单点定位PPP是当前GNSS高精度定位中的关键技术之一,使用的PPP采用扩展卡尔曼滤波估计,未知参数包括站点坐标,接收机钟差,对流层延迟以及虚拟未知数。在QR奇偶检校法的基础上,重点考察设计矩阵向量间的相关距离,将其作为粗差探测和识别的研究对象。通过向量相关距离时间序列,可以区分单个粗差和多个粗差的粗差集。提出精密单点定位的RAIM算法,解决了精密单点定位中的质量控制问题,使得多个粗差的识别更加清晰和快捷。     

一种区域实时对流层内插模型及其在PPP中的应用

利用反距离加权内插法,对基准站解算的天顶对流层延迟（ZTD）建立了区域实时ZTD模型,评估了该模型内插流动站对流层延迟对PPP定位精度和收敛时间的影响。试验表明：与传统ZTD采用参数估计的处理方法对比,二者解算得到的PPP精度在水平方向上效果相当,但在垂直方向上,模型内插对流层解算的定位精度提高约为5 cm,且能显著提高PPP收敛速度。说明应用本方法建立非气象参数的区域天顶对流层延迟模型能有效加快PPP的收敛速度,且提高定位精度。     

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%。     

京津冀地区GNSS对流层延迟空间插值研究

对流层延迟差异影响合成孔径雷达干涉测量技术(InSAR)形变测量精度;水汽的变化影响天气变化．对流层延迟与水汽具有较好的对应,因此有必要开展全球导航卫星系统(GNSS)对流层延迟的插值研究．以京津冀地区为例,针对GNSS对流层延迟,开展对流层延迟的空间插值研究．首先开展了GNSS对流层延迟与水汽的比较分析,两者存在显著正相关特性,相关性超过91.7％,论证了对流层延迟取代水汽的可行性．然后利用反距离权重法对京津冀地区2016年9月至2017年8月的12组GNSS测站对流层延迟进行空间插值,通过提取插值点对流层延迟与GNSS站点对流层延迟比较验证空间插值精度．全年数据平均偏差最大为1.12 cm,均方根误差最大为0.89 cm;未发生降水过程平均偏差最大为1.25 cm,均方根误差最大为0.82 cm;发生降水过程平均偏差最大为1.08 cm,均方根误差最大为1.38 cm．京津冀平原区域的GNSS对流层延迟空间插值结果精度满足气象等应用要求,可为气象预报和InSAR大气校正提供参考.      

耦合PSO与扩展RBF神经网络估计NWM模型ZTD计算精度EI北大核心CSCD

针对基于数值气象模型获取的对流层天顶延迟精度估计依赖外部基准的问题,本文构建耦合了粒子群算法与扩展径向基函数神经网络的ZTD精度估计模型,模型样本特征集利用NWM自身气象数据和地形特征数据构建,目标集以GNSS ZTD产品为参考值构建,模型规模结构通过层次聚类和模糊C均值聚类确定,模型参数通过粒子群算法优化。以欧洲中期天气预报中心提供的ERA5气压分层产品为NWM特例进行了模型训练和结果验证。结果表明,模型估计精度和泛化能力较好,平均估计精度优于4 mm,可在任意位置实现不依赖于外部参考基准的ZTD精度估计。     

A grid-based tropospheric product for China using a GNSS network

Tropospheric delay accounts for one source of error in global navigation satellite systems (GNSS). To better characterize the tropospheric delays in the temporal and spatial domain and facilitate the safety-critical use of GNSS across China, a method is proposed to generate a grid-based tropospheric product (GTP) using the GNSS network with an empirical tropospheric model, known as IGGtrop. The prototype system generates the GTPs in post-processing and real-time modes and is based on the undifferenced and uncombined precise point positioning (UU-PPP) technique. GTPs are constructed for a grid form (\(2.0{^{\circ }}\times 2.5{^{\circ }}\) latitude–longitude) over China with a time resolution of 5 min. The real-time GTP messages are encoded in a self-defined RTCM3 format and broadcast to users using NTRIP (networked transport of RTCM via internet protocol), which enables efficient and safe transmission to real-time users. Our approach for GTP generation consists of three sequential steps. In the first step, GNSS-derived zenith tropospheric delays (ZTDs) for a network of GNSS stations are estimated using UU-PPP. In the second step, vertical adjustments for the GNSS-derived ZTDs are applied to address the height differences between the GNSS stations and grid points. The ZTD height corrections are provided by the IGGtrop model. Finally, an inverse distance weighting method is used to interpolate the GNSS-derived ZTDs from the surrounding GNSS stations to the location of the grid point. A total of 210 global positioning system (GPS) stations from the crustal movement observation network of China are used to generate the GTPs in both post-processing and real-time modes. The accuracies of the GTPs are assessed against with ERA-Interim-derived ZTDs and the GPS-derived ZTDs at 12 test GPS stations, respectively. The results show that the post-processing and real-time GTPs can provide the ZTDs with accuracies of 1.4 and 1.8 cm, respectively. We also apply the GTPs in real-time kinematic GPS PPP, and the results show that the convergence time of the PPP solutions is shortened. These results confirm that the GTPs can act as an efficient information source to augment GNSS positioning over China.     

单频到五频多系统GNSS精密单点定位参数估计与应用

全球导航卫星系统(GNSS)已发展至多频多系统时代,特别以我国北斗卫星导航系统(BDS)为代表的四大全球导航卫星系统可全天时、全天候播发十几个频率的伪距、相位和多普勒等观测信息。多频多系统GNSS为用户提供更多的观测数据和组合选择,为精密定位、导航和授时(PNT)应用带来了新的机遇,如高精度位置服务、大地测量、空间天气和灾害监测等。但多频多系统GNSS观测为精密单点定位(PPP)组合模型和系统偏差及大气延迟估计等带来诸多问题和挑战。本文给出了单频到五频多系统GNSS精密单点定位(PPP)模型,估计和评估了单频到五频多系统GNSS PPP定位精度、接收机钟差、对流层延迟、卫星和接收机硬件延迟,以及频间偏差。给出了GNSS PPP最新应用进展,包括GNSS气象学、电离层模拟、时间频率传递、建筑物安全和地震监测及其应用。结果表明,多频多系统极大地提高了GNSS PPP参数估计的精度和可靠性,具有重要的应用价值。最后给出了多频多系统GNSS PPP应用前景与展望。     

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...     

Optimum stochastic modeling for GNSS tropospheric delay estimation in real-time

GPS Solutions - In GNSS data processing, the station height, receiver clock and tropospheric delay (ZTD) are highly correlated to each other. Although the zenith hydrostatic delay of the...     

大型桥梁桥塔监测的GNSS相对对流层延迟估计

针对大型桥梁桥塔与基站高程差异较大,残余对流层延迟成为影响全球卫星导航系统(GNSS)监测成功率与精度的主要因素之一。该文基于随机过程理论,对桥梁监测GNSS残余对流层湿延迟进行参数估计,有效地提高了桥梁塔顶监测GNSS模糊度固定率。通过采用对流层经验模型改正对流层干延迟,将基准站和塔顶观测站对流层湿延迟组成相对对流层湿延迟,并联合位置参数和模糊度参数建立双差卡尔曼模型,最后利用最小二乘模糊度降低相关平差法(LAMBDA)对双差模糊度进行固定,并估计位置参数与相对对流层延迟参数。实验结果表明,该方法可以有效估计相对对流层延迟,有效提高GNSS模糊度固定率。     

Impact of tropospheric modelling on GNSS vertical precision: an empirical analysis based on a local active network

The troposphere affects Global Navigation Satellite System (GNSS) signals due to the variability of the refractive index. Tropospheric delay is a function of the satellite elevation angle and the altitude of the GNSS receiver and depends on the atmospheric parameters. If the residual tropospheric delay is not modelled carefully a bias error will occur in the vertical component. In order to analyse the precise altimetric positioning based on a local active network, four scenarios in Southern Spain with different topographical, environmental, and meteorological conditions are presented, considering both favourable and non-favourable conditions. The use of surface meteorological observations allows us to take into account the tropospheric conditions instead of a standard atmosphere, but introduces a residual tropospheric bias which reduces the accuracy of precise GNSS positioning. Thus, with short observation times it is recommended not to estimate troposphere parameters, but to use an a priori model together with the standard atmosphere. The results confirm that it is possible to achieve centimetre-scale vertical accuracy and precision with real time kinematic positioning even with large elevation differences with respect to the nearest reference stations. These numerical results may be taken into consideration for improving the altimetric configuration of the local active network.     

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.     

Comparative analysis of real-time precise point positioning zenith total delay estimates

The continuous evolution of global navigation satellite systems (GNSS) meteorology has led to an increased use of associated observations for operational modern low-latency numerical weather prediction (NWP) models, which assimilate GNSS-derived zenith total delay (ZTD) estimates. The development of NWP models with faster assimilation cycles, e.g., 1-h assimilation cycle in the rapid update cycle NWP model, has increased the interest of the meteorological community toward sub-hour ZTD estimates. The suitability of real-time ZTD estimates obtained from three different precise point positioning software packages has been assessed by comparing them with the state-of-the-art IGS final troposphere product as well as collocated radiosonde (RS) observations. The ZTD estimates obtained by BNC2.7 show a mean bias of 0.21 cm, and those obtained by the G-Nut/Tefnut software library show a mean bias of 1.09 cm to the IGS final troposphere product. In comparison with the RS-based ZTD, the BNC2.7 solutions show mean biases between 1 and 2 cm, whereas the G-Nut/Tefnut solutions show mean biases between 2 and 3 cm with the RS-based ZTD, and the ambiguity float and ambiguity fixed solutions obtained by PPP-Wizard have mean biases between 6 and 7 cm with the references. The large biases in the time series from PPP-Wizard are due to the fact that this software has been developed for kinematic applications and hence does not apply receiver antenna eccentricity and phase center offset (PCO) corrections on the observations. Application of the eccentricity and PCO corrections to the a priori coordinates has resulted in a 66 % reduction of bias in the PPP-Wizard solutions. The biases are found to be stable over the whole period of the comparison, which are criteria (rather than the magnitude of the bias) for the suitability of ZTD estimates for use in NWP nowcasting. A millimeter-level impact on the ZTD estimates has also been observed in relation to ambiguity resolution. As a result of a comparison with the established user requirements for NWP nowcasting, it was found that both the G-Nut/Tefnut solutions and one of the BNC2.7 solutions meet the threshold requirements, whereas one of the BNC2.7 solution and both the PPP-Wizard solutions currently exceed this threshold.