Modeling tropospheric wet delays with dense and sparse network configurations for PPP-RTK

GPS Solutions - Precise Point Positioning (PPP) is a well-known technique of positioning by Global Navigation Satellite Systems (GNSS) that provides accurate solutions. With the availability of...     

Ambiguity resolved precise point positioning with GPS and BeiDou

This paper focuses on the contribution of the global positioning system (GPS) and BeiDou navigation satellite system (BDS) observations to precise point positioning (PPP) ambiguity resolution (AR). A GPS + BDS fractional cycle bias (FCB) estimation method and a PPP AR model were developed using integrated GPS and BDS observations. For FCB estimation, the GPS + BDS combined PPP float solutions of the globally distributed IGS MGEX were first performed. When integrating GPS observations, the BDS ambiguities can be precisely estimated with less than four tracked BDS satellites. The FCBs of both GPS and BDS satellites can then be estimated from these precise ambiguities. For the GPS + BDS combined AR, one GPS and one BDS IGSO or MEO satellite were first chosen as the reference satellite for GPS and BDS, respectively, to form inner-system single-differenced ambiguities. The single-differenced GPS and BDS ambiguities were then fused by partial ambiguity resolution to increase the possibility of fixing a subset of decorrelated ambiguities with high confidence. To verify the correctness of the FCB estimation and the effectiveness of the GPS + BDS PPP AR, data recorded from about 75 IGS MGEX stations during the period of DOY 123-151 (May 3 to May 31) in 2015 were used for validation. Data were processed with three strategies: BDS-only AR, GPS-only AR and GPS + BDS AR. Numerous experimental results show that the time to first fix (TTFF) is longer than 6 h for the BDS AR in general and that the fixing rate is usually less than 35 % for both static and kinematic PPP. An average TTFF of 21.7 min and 33.6 min together with a fixing rate of 98.6 and 97.0 % in static and kinematic PPP, respectively, can be achieved for GPS-only ambiguity fixing. For the combined GPS + BDS AR, the average TTFF can be shortened to 16.9 min and 24.6 min and the fixing rate can be increased to 99.5 and 99.0 % in static and kinematic PPP, respectively. Results also show that GPS + BDS PPP AR outperforms single-system PPP AR in terms of convergence time and position accuracy.     

Regional reference network augmented precise point positioning for instantaneous ambiguity resolution

Integer ambiguity fixing can significantly shorten the initialization time and improve the accuracy of precise point positioning (PPP), but it still takes approximate 15 min of time to achieve reliable integer ambiguity solutions. In this contribution, we present a new strategy to augment PPP estimation with a regional reference network, so that instantaneous ambiguity fixing is achievable for users within the network coverage. In the proposed method, precise zero-differenced atmospheric delays are derived from the PPP fixed solution of the reference stations, which are disseminated to, and interpolated at user stations to correct for L1, L2 phase observations or their combinations. With the corrected observations, instantaneous ambiguity resolution can be carried out within the user PPP software, thus achieving the position solutions equivalent to the network real-time kinematic positioning (NRTK). The strategy is validated experimentally. The derived atmospheric delays and the interpolated corrections are investigated. The ambiguity fixing performance and the resulted position accuracy are assessed. The validation confirms that the new strategy can provide comparable service with NRTK. Therefore, with this new processing strategy, it is possible to integrate PPP and NRTK into a seamless positioning service, which can provide an accuracy of about 10 cm anywhere, and upgrade to a few centimeters within a regional network.     

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.     

Modeling and quality control for reliable precise point positioning integer ambiguity resolution with GNSS modernization

Recent research has demonstrated that the undifferenced integer ambiguities can be recovered using products from a network solution. The standard dual-frequency PPP integer ambiguity resolution consists of two aspects: Hatch-Melbourne-Wübbena wide-lane (WL) and ionosphere-free narrow-lane (NL) integer ambiguity resolution. A major issue affecting the performance of dual-frequency PPP applications is the time it takes to fix these two types of integer ambiguities, especially if the WL integer ambiguity resolution suffers from the noisy pseudorange measurements and strong multipath effects. With modernized Global Navigation Satellite Systems, triple-frequency measurements will be available to global users and an extra WL (EWL) model with very long wavelength can be formulated. Then, the easily resolved EWL integer ambiguities can be used to construct linear combinations to accelerate the PPP WL integer ambiguity resolution. Therefore, we propose a new reliable procedure for the modeling and quality control of triple-frequency PPP WL and NL integer ambiguity resolution. First, we analyze a WL integer ambiguity resolution model based on triple-frequency measurements. Then, an optimal pseudorange linear combination which is ionosphere-free and has minimum measurement noise is developed and used as constraint in the WL and the NL integer ambiguity resolution. Based on simulations, we have investigated the inefficiency of dual-frequency WL integer ambiguity resolution and the performance of EWL integer ambiguity resolution. Using almanacs of GPS, Galileo and BeiDou, the performances of the proposed triple-frequency WL and NL models have been evaluated in terms of success rate. Comparing with dual-frequency PPP, numerical results indicate that the proposed triple-frequency models can outperform the dual-frequency PPP WL and NL integer ambiguity resolution. With 1 s sampling rate, generally, only several minutes of data are required for reliable triple-frequency PPP WL and NL integer ambiguity resolution. Under benign observation situations and good geometries, the integer ambiguity can be reliably resolved even within 10 s.     

Analyzing GNSS data in precise point positioning software

This work demonstrates that precise point positioning (PPP) can be used not only for positioning, but for a variety of other tasks, such as signal analysis. The fact that the observation model used for accurate error modeling has to take into consideration the several effects present in GPS signals, and that observations are undifferenced, makes PPP a powerful data analysis tool sensitive to a variety of parameters. The PPP application developed at the University of New Brunswick, which is called GAPS (GPS Analysis and Positioning Software), has been designed and built in order to take advantage of available precise products, resulting in a data analysis tool for determining parameters in addition to position, receiver clock error, and neutral atmosphere delay. These other estimated parameters include ionospheric delays, code biases, satellite clock errors, and code multipath among others. In all cases, the procedures were developed in order to be suitable for real-time as well as post-processing applications. One of the main accomplishments in the development described here is the use of very precise satellite products, coupled with a very complete observation error modeling to make possible a variety of analyses based on GPS data. In this paper, several procedures are described, their innovative aspects are pointed out, and their results are analyzed and compared with other sources. The procedures and software are readily adaptable for using data from other global navigation satellite systems.     

融合对流层模型及其在精密单点定位中的应用

受实测气象参数的限制,使用标准大气参数的传统对流层模型的精度并不高;使用参数估计法的精密对流层模型增加了观测方程的待估参数,影响收敛速度. 针对实测气象参数缺失的情况,提出一种融合对流层模型,使用两种非实测气象参数模型分别计算出平均海平面处和测站处的气象参数,再利用Saastamoinen模型经验公式求解天顶对流层延迟（ZTD）. 利用RTKLIB软件进行精密单点定位（PPP）实验. 提出的融合对流层模型摆脱了实测气象参数的限制,解算结果表明:使用该模型时,在东、北、天方向的定位精度分别比Saastamoinen模型提高16 mm、1 mm、2.2 mm,比MOPS模型提高13.8 mm、0.7 mm、1.6 mm,比GPT/UNB3m+Sa模型提高2.9 mm、0.4 mm、0.7 mm,在天、北方向的定位精度接近参数估计模型,实现了PPP定位精度的提高.      

对流层映射函数对精密单点定位的影响分析

分析对流层映射函数(NMF、VMF1和GMF)对精密单点定位(PPP)精度的影响,对分布于南北半球不同纬度地区的IGS跟踪站的观测数据进行解算。首先比较PPP坐标与IGS发布的日解SNX文件坐标差异和模型间PPP坐标差异,然后分析不同季节对模型差异的影响。实验结果表明,3种映射函数均可提高PPP精度,精度控制在1cm左右。整体而言,VMF1和GMF对PPP精度的影响相当,且优于NMF。在不同季节里,模型差异会发生mm级的变化。     

GPS精密单点定位中对流层延迟处理方法研究

本文首先介绍了GPS精密单点定位技术,采用宽巷组合的方法得到观测方程。然后对精密定位中的误差改正作了简述,主要讨论了处理对流层延迟的Saastamoinen模型和Niell映射函数。提出用扩展卡尔曼滤波参数估计方法来处理对流层延迟,通过实例用Saastamoinen模型、Saastamoinen模型加Niell映射函数和扩展卡尔曼滤波参数估计三种方法对对流层延迟进行改正,结果表明该方法优于Saastamoinen模型。     

基于GNSS精密单点定位的高精度云平台授时

采用GNSS精密单点定位(PPP)技术和时钟驯服技术,构建了基于PPP的云平台高精度授时方案,研制了搭载多系统GNSS接收机板卡、恒温晶振(OCXO)和数字信号处理器(DSP)的授时原理样机。利用协同精密定位平台分析中心(武汉)提供的5 s间隔卫星轨道和钟差产品,采用PPP技术实时解算授时终端坐标和钟差,通过驯服恒温晶振输出亚纳秒精度的1 PPS,实现了长时间高精度的授时能力。本文通过短基线比较和与UTC绝对时间基准比较,验证了精密单点授时精度(RMS)优于1 ns。     

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.     

GNSS多频融合精密单点定位频率间卫星钟偏差研究

全球导航卫星系统(GNSS)提供多频信号,多频融合已经成为一种趋势。在精密钟差估计(PCE)的过程中,卫星钟差参数会吸收卫星端稳定的伪距偏差和时变的相位偏差,这些偏差均与频率相关。因而使用不同的观测值进行PCE时,得到的卫星钟差估值是不同的,它们之间的差值被定义为频率间卫星钟偏差(IFCB)。按组成成分,IFCB可以分成伪距相关的IFCB(CIFCB)和相位相关的IFCB(PIFCB)两部分。国际GNSS服务(IGS)提供的精密卫星钟差产品是基于双频消电离层(IF)组合观测值生成的。由于IFCB的存在,导致IGS卫星钟差产品不能直接应用于多频精密单点定位(PPP)。IFCB的精确考虑已经成为多频PPP的一个关键问题。本研究旨在对IFCB特性和估计方法开展系统深入的研究,并评估其对多频PPP解的影响。     

基于精密单点定位的GNSS时间同步方法研究

高精度时间服务是国家综合PNT(positioning,navigation,timing)体系的重要组成部分,在国防军事、移动通信、天文观测等领域中发挥着重要作用。论文采用全球导航卫星系统GNSS授时的方式,提出了一种基于精密单点定位(PPP)技术的时间同步方法。该方法根据PPP时间传递结果驾驭本地时钟,使本地时钟所表示的本地时间与基准时间同步,可以达到亚纳秒级的时间同步精度,并且具备全天候、全覆盖、高精度、低成本等优点。     

基准站辅助的区域实时精密单点定位

针对常规实时精密单点定位(PPP)精度低、稳定性差的问题,该文采用附加基准站改正信息的精密单点定位算法,开展了基准站辅助的区域实时PPP应用研究.依托山东省卫星定位连续运行综合应用服务系统(SDCORS),采用IGU预报星历和钟差产品获取实时卫星轨道和钟差改正,探讨站间距、不同基准站、单/双基准站等对区域实时PPP的影响.实验结果表明,以事后PPP单天解坐标为参考,基准站辅助的流动站实时PPP坐标分量和点位平均精度均可达到厘米级水平;流动站实时PPP定位精度与站间距没有明显的相关性;基准站的选择对区域实时PPP结果略有影响,附加双基准站改正的PPP相比于单基准站改正PPP的结果更优,点位精度平均提升约8.6％.     

Real-time precise point positioning regional augmentation for large GPS reference networks

An increasing number of GNSS reference stations are installed around the world to provide real-time precise positioning services. In most of the current services, a full network solution is required for the precise determination of biases. Such a network solution is time consuming and difficult to achieve for very large regions such as Europe or China. Therefore, we developed a multi-layer processing scheme for precise point positioning (PPP) regional augmentation to avoid processing large networks. Furthermore, we use L1 and L2 raw observations and estimate atmospheric delays, which were properly constrained to the atmospheric corrections derived from the reference stations. Therefore, inaccurate representation of atmospheric delays due to temporal and/or spatial atmospheric fluctuations in the processing can be compensated. The proposed scheme of PPP regional augmentation was implemented into the operational real-time PPP service system at GFZ for validation. The real-time orbit and clock corrections, the uncalibrated phase delays, and regional augmentation corrections are generated by this system. The augmentation corrections from the regional network are investigated and the positioning performance in terms of positioning accuracy and time for fixed solution is demonstrated in real-time. Our results indicate that a reliable fixing is possible after 5 s on average. The positioning accuracy is about 12, 10, and 25 mm in east, north, and vertical direction, respectively.     

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.     

基于钟差解耦的GNSS精密单点定位模糊度固定模型及效果分析

精密单点定位模糊度固定可以显著提升定位精度,钟差解耦模型作为一种重要的模糊度固定模型,却鲜有文献对其进行研究。本文首先给出了基于钟差解耦模型的用于模糊度固定的产品估计策略,分析了传统的消电离层模型和钟差解耦模型钟差重构形式的差异,导出了提取卫星码偏差的钟差估计模型。然后,深入研究了钟差解耦模型在钟差估计收敛速度等方面的优势。不同于其他模型将宽巷模糊度偏差视为天内常数,钟差解耦模型逐历元估计该偏差项,基于此展开对宽巷模糊度偏差天内时变特性的研究。最后,评价了解耦钟差的精度,并利用解耦钟差产品进行精密单点定位模糊度固定试验。结果表明,相比于提取卫星码偏差的卫星钟差估计模型,钟差解耦模型在钟差估计中的收敛速度更快,钟差产品更加稳定;宽巷模糊度偏差在天内较为稳定;解耦钟差产品具有较高的精度,相比于传统消电离层组合模型,基于该产品的精密单点定位模糊度固定可显著提升定位精度。     

精密单点定位中卫星星历对天顶对流层延迟估计的影响

为了分析不同卫星星历对天顶对流层延迟估计的影响,本文选取不同的卫星星历产品分别进行静态精密单点定位试验,估计天顶对流层延迟,并与IGS发布的天顶对流层延迟产品相比。结果表明,采用最终星历、快速星历和超快星历实测部分时,天顶对流层延迟的平均RMS值分别为4.5mm、4.3mm和4.6mm,估计精度一致。而采用超快星历外推部分时,平均RMS值为6.3mm,估计精度略低。