Real-time precise point positioning augmented with high-resolution numerical weather prediction model

GPS Solutions - The tropospheric delay is one of the major error sources in precise point positioning (PPP), affecting the accuracy and precision of estimated coordinates and convergence time,...     

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.     

多系统实时精密单点定位及非差模糊度固定

正精密单点定位(precise point positioning,PPP)技术能够在全球区域获取用户在国际地球参考框架下的精确三维坐标,打破了以往只能够使用差分定位技术才能够实现高精度定位的局面,是继RTK/NRTK技术之后出现的又一次技术革命。论文旨在构建实时GNSS PPP服务系统,围绕GNSS卫星钟差估计、多系统融合PPP、卫星姿态、GPS未校准相位延迟(uncalibrated phase delays,UPD)估计、PPP模糊度固定等展开研究,为用户获取实时、高精度和高可靠性的GNSS PPP服务奠定理论和实践基础。本文的主要工作和贡献如下:     

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％.     

双频BDS实时精密单点定位算法和精度分析

为了对BDS实时精密单点定位性能进行评估,该文提出了一种适用于BDS系统的实时精密单点定位算法。采用无电离组合模型作为双频实时精密单点定位的数学模型,采用电离层残差法和Melbourne-Wübbena组合实时探测相位周跳,进而单历元实时估计坐标、模糊度等参数,实现了BDS双频实时精密单点定位算法。基于此算法,采用轨道钟差产品和采样间隔为1s的观测数据,模拟实时BDS双频精密单点定位算法,并评估其定位精度。实验结果表明:BDS双频实时定位的平面精度和三维精度均为0.2m左右。     

Multi-GNSS precise point positioning with raw single-frequency and dual-frequency measurement models

GPS Solutions - The emergence of multiple satellite navigation systems, including BDS, Galileo, modernized GPS, and GLONASS, brings great opportunities and challenges for precise point positioning...     

Enhancing real-time precise point positioning time and frequency transfer with receiver clock modeling

GPS Solutions - In the context of processing global navigation satellite system (GNSS) data by least squares adjustment, one may encounter a mathematical problem when inverting a sum of two...     

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.     

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.     

一种提高精密单点定位实时性的方法

由于要获取PPP需要的精密钟差文件至少有2d的时间延迟,因此通过提取IGS当天发布的超快星历中的卫星钟差数据,并对钟差数据进行插值,将插值结果做成标准格式钟差数据文件应用到PPP中,可以将精密单点定位的实时性提高为3~9h。基于Bernese软件,采用生成的钟差文件以及当天的超快星历文件对大量实测数据进行PPP。结果表明,对于4h的观测数据,该方法解算精度达到厘米级;当观测时间大于6h时,解算精度基本能够稳定在1~5cm。     

Single-frequency precise point positioning with optimal filtering

The accuracy of standalone GPS positioning improved significantly when Selective Availability was turned off in May 2000. With the availability of various public GPS related products including precise satellite orbits and clocks, and ionosphere maps, a single-frequency standalone user can experience even a further improvement of the position accuracy. Next, using carrier phase measurements becomes crucial to smoothen the pseudorange noise. In this contribution, the most critical sources of error in single-frequency standalone positioning will be reviewed and different approaches to mitigate the errors will be considered. An optimal filter (using also carrier phase measurements) will be deployed. The final approach will then be evaluated in a decently long static test with receivers located in different regions of the world. Kinematic experiments have also been performed in various scenarios including a highly dynamic flight trial. The accuracy, in general, can be confirmed at 0.5 m horizontal and 1 m vertical, with static tests. Ultimate results demonstrate an accuracy close to 2 dm (95%) for the horizontal position components and 5 dm (95%) for the vertical in the flight experiment.

Maintaining real-time precise point positioning during outages of orbit and clock corrections

The precise point positioning (PPP) is a popular positioning technique that is dependent on the use of precise orbits and clock corrections. One serious problem for real-time PPP applications such as natural hazard early warning systems and hydrographic surveying is when a sudden communication break takes place resulting in a discontinuity in receiving these orbit and clock corrections for a period that may extend from a few minutes to hours. A method is presented to maintain real-time PPP with 3D accuracy less than a decimeter when such a break takes place. We focus on the open-access International GNSS Service (IGS) real-time service (RTS) products and propose predicting the precise orbit and clock corrections as time series. For a short corrections outage of a few minutes, we predict the IGS-RTS orbits using a high-order polynomial, and for longer outages up to 3 h, the most recent IGS ultra-rapid orbits are used. The IGS-RTS clock corrections are predicted using a second-order polynomial and sinusoidal terms. The model parameters are estimated sequentially using a sliding time window such that they are available when needed. The prediction model of the clock correction is built based on the analysis of their properties, including their temporal behavior and stability. Evaluation of the proposed method in static and kinematic testing shows that positioning precision of less than 10 cm can be maintained for up to 2 h after the break. When PPP re-initialization is needed during the break, the solution convergence time increases; however, positioning precision remains less than a decimeter after convergence.     

星基增强信号的GPS实时精密单点定位算法

针对现有基于网络和数据流量的实时精密单点定位应用中改正信息传播覆盖范围有限及信号延迟等问题,该文提出了一种新的基于GPS增强信号的实时精密单点定位算法。利用增强频段播发精密轨道、钟差产品有效地解决了传统改正信息传递过程中覆盖范围小与信号延迟的问题,极大地提高了实时改正产品的覆盖范围与时效性。基于亚太地区多个测站准实测数据的实验结果表明:基于LEX增强信息的实时动态和静态精密单点定位解算可分别实现分米级和厘米级的定位精度,显示了利用LEX增强信号进行实时高精度定位的可行性。     

基于预报星历和基准站辅助的BDS实时精密单点定位

基于预报星历的常规实时精密单点定位存在相位模糊度难以收敛、定位精度低等问题。文中采用附加基准站改正信息的PPP算法,消除与卫星有关误差影响。依托香港卫星定位参考站网,采用WHU预报星历获取实时卫星轨道和钟差改正,开展基于预报星历和基准站辅助的中国北斗卫星导航系统实时PPP应用研究,并对其定位性能进行分析。试验结果表明,基准站辅助的BDS实时静态PPP单天解的重复测量精度在水平方向优于1 cm,高程方向优于2 cm;基准站辅助的BDS实时动态PPP相位模糊度能够快速收敛,收敛后的定位精度大幅提升,其重复测量精度在水平方向优于4 cm,高程方向优于10 cm,相对于参考坐标的外符合精度在水平方向优于7 cm,高程方向优于15 cm。     

GPS inter-frequency clock bias modeling and prediction for real-time precise point positioning

To ensure the consistent use of the current GPS precise satellite clock products, the inter-frequency clock bias (IFCB) should be carefully considered for triple-frequency precise point positioning (PPP). It is beneficial to investigate the modeling of the IFCB for multi-frequency PPP, especially for real-time users suffering from difficulties in real-time IFCB estimations. Our analysis is based on datasets from 129 stations spanning a whole year. A harmonic analysis is performed for all single-day IFCB time series, and periodic IFCB variations with periods of 12, 8, 6, 4.8, 4 and 3 h are identified. An empirical model composed of a sixth-order harmonic function and a linear function is presented to describe daily variations in the IFCB, and the modeling accuracy is 4 mm. A least squares fit is adopted to estimate the single-day harmonic coefficients phase and amplitude. The prediction accuracy of the IFCB models degrades from 7.2 to 12.3 mm when the time span of prediction is increased from a day to a week. When using IFCB models of the previous day to obtain the IFCB correction values, the positioning accuracy of triple-frequency PPP is improved by 21, 11 and 16% over the triple-frequency PPP neglecting the IFCB in the post-processing mode in the east, north and up directions, respectively. As to the real-time triple-frequency PPP, the corresponding accuracy improvement is 24, 9 and 10% in the three directions, respectively.     

BDS/GPS融合精密定位理论与算法研究

正北斗卫星导航系统是首个异构星座,是目前完全运行的唯一的三频导航系统,集导航定位、授时、用户监测、短报文通信于一体。BDS具有的独特优势,有利于改善DOP(dilution of precision)值、削弱大气误差、缩短模糊度初始化时间等。BDS与GPS融合卫星资源的利用,将成为BDS逐步走向国际卫星导航领域的一个过程。本文分析BDS与GPS在时空参考框架、星座结构、信号内容、数据质量等方面的差异性,研究BDS/GPS融合高精度相对定位关键技术。提出了一套BDS/GPS静态与动态相对定位算法,并开展了大量的试验研究,如铁路CPI控制网静态数据处理,基于相对定位精度因子RPDOP(relative positioning dilution of precision)分析的快速静态定位,不同范围与挑战性环境下RTK(real time kinematic)定位等,验证本文理论算法研究的正确性。本文主要内容如下。     

采用GPS精密单点定位技术实时确定舰船位置与姿态

文章采用静态模拟动态的手段,研究基于精密单点定位技术实时确定海上舰船位置和姿态的方法,并分析实时精密单点定位技术的定位定姿精度.研究表明:用精密单点定位技术进行实时动态定位,一般可获得2cm的平面定位精度和4cm左右的高程精度;在动态精密单点定位技术的定位精度一定的情况下,航向角的精度高于横滚角和俯仰角;真实动态观测值的随机误差比静态模拟的大,定位和定姿精度可能会有所降低.