An improvement to ionospheric delay correction for single-frequency GPS users – the APR-I scheme

 For the commonly used GPS wide-area augmentation systems (WAAS) with a grid ionospheric model, the efficient modelling of ionospheric delays in real time, for single-frequency GPS users, is still a crucial issue which needs further research. This is particularly necessary when differential ionospheric delay corrections cannot be broadcast, when users cannot receive them, or when there are ionospheric anomalies. Ionospheric delays have a severe effect on navigation performance of single-frequency receivers. A new scheme is proposed which can efficiently address the above problems. The robust recurrence technique is based on the efficient combination of single-frequency GPS observations by users and the high-precision differential ionospheric delay corrections from WAAS. Its effectiveness is verified with examples. Received: 24 December 1999 / Accepted 21 February 2001     

GPS信号对流层延迟改正新模型研究

为削弱对流层对GPS精密定位的影响，从大气折射率入手将大气分为3层，建立了大气折射率模型，并导出了对流层天顶延迟模型。利用IGS跟踪站的实测数据进行了验证，实验证明了新模型的有效性。     

Quality assessment of GPS rapid static positioning with weighted ionospheric parameters in generalized least squares

Precise GPS positioning requires the processing of carrier-phase observations and fixing integer ambiguities. With increasing distance between receivers, ambiguity fixing becomes more difficult because ionospheric and tropospheric effects do not cancel sufficiently in double differencing. A popular procedure in static positioning is to increase the length of the observing session and/or to apply atmospheric (ionospheric) models and corrections. We investigate the methodology for GPS rapid static positioning that requires just a few minutes of dual-frequency GPS observations for medium-length baselines. Ionospheric corrections are not required, but the ionospheric delays are treated as pseudo-observations having a priori values and respective weights. The tropospheric delays are reduced by using well-established troposphere models, and satellite orbital and clock errors are eliminated by using IGS rapid products. Several numerical tests based on actual GPS data are presented. It is shown that the proposed methodology is suitable for rapid static positioning within 50–70 km from the closest reference network station and that centimeter-level precision in positioning is feasible when using just 1 min of dual-frequency GPS data.     

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 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.     

The TropGrid2 standard tropospheric correction model

TropGrid2 is a new version of a tropospheric model that is based on climatology and provides tropospheric propagation delay corrections for standard positioning users without temperature, pressure and humidity measurements. Zenith hydrostatic and wet delays are modeled as special harmonic functions taking seasonal and diurnal variations into consideration. The grid-point values are height-reduced and can be interpolated horizontally to the user position. The database used to derive this model consists of more than 9 years of 3D numerical weather fields of the NOAA NCEP GDAS weather model. We validated this standard model using 10 years of GPS-derived zenith path delays at 290 International GPS service reference stations. The gridded version is accurate at a level of 3.8 cm (root mean square in zenith direction) on global average; the average long-term bias is ?0.3 cm. The standard deviations computed by the model turn out to be slightly too pessimistic for almost all stations under investigation, in contrast to the site-specific version, which is only marginally (1 mm) more accurate on global scale.     

不同因素下的ZTD端部效应影响分析

任何平滑拟合方法对实际资料处理时均会产生端部效应,即处理结果在资料(弧)段的两端精度较差,端部效应问题,已成为区域GPS气象网准实时PWV(可降水量)解算的重要问题之一。Bernese数据处理软件在解算对流层天顶延迟方面独树一帜,以中国境内和其周边共5个IGS站2012年某天的数据为解算实例,在简要介绍Bernese解算对流层产品的基础上,采用单一变量的原则,研究分析不同截止高度角和时间分辨率对数据处理结果的端部效应影响和误差量级,并给出参考性建议。     

Auto-covariance estimation of variable samples (ACEVS) and its application for monitoring random ionospheric disturbances using GPS

 Ionospheric variation may be considered as a stationary time series under quiet conditions. However, the disturbance of a stationary random process from stationarity results in the bias of corresponding samples from the stationary observations, and in the change of statistical model parameters of the process. From a general mathematical aspect, a new method is presented for monitoring ionospheric variations, based on the characteristic of time-series observation of GPS, and an investigation of the statistical properties of the estimated auto-covariance of the random ionospheric delay when changing the number of samples in the time series is carried out. A preliminary scheme for monitoring ionospheric delays is proposed. Received: 18 August 2000 / Accepted: 12 April 2001     

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 of satellite position,clock and phase bias corrections

Precise point positioning with integer ambiguity resolution requires precise knowledge of satellite position, clock and phase bias corrections. In this paper, a method for the estimation of these parameters with a global network of reference stations is presented. The method processes uncombined and undifferenced measurements of an arbitrary number of frequencies such that the obtained satellite position, clock and bias corrections can be used for any type of differenced and/or combined measurements. We perform a clustering of reference stations. The clustering enables a common satellite visibility within each cluster and an efficient fixing of the double difference ambiguities within each cluster. Additionally, the double difference ambiguities between the reference stations of different clusters are fixed. We use an integer decorrelation for ambiguity fixing in dense global networks. The performance of the proposed method is analysed with both simulated Galileo measurements on E1 and E5a and real GPS measurements of the IGS network. We defined 16 clusters and obtained satellite position, clock and phase bias corrections with a precision of better than 2 cm.     

Precise orbit determination of BeiDou constellation: method comparison

Chinese BeiDou navigation satellite system is in official service as a regional constellation with five geostationary earth orbit (GEO) satellites, five inclined geosynchronous satellite orbit (IGSO) satellites and four medium earth orbit (MEO) satellites. There are mainly two methods for precise orbit determination of the BeiDou constellation found in the current literatures. One is the independent single-system method, where only BeiDou observations are used without help from other GNSS systems. The other is the two-step GPS-assisted method where in the first step, GPS data are used to resolve some common parameters, such as station coordinates, receiver clocks and zenith tropospheric delay parameters, which are then introduced as known quantities in BeiDou processing in the second step. We conduct a thorough performance comparison between the two methods. Observations from the BeiDou experimental tracking stations and the IGS Multi-GNSS Experiment network from January 1 to March 31, 2013, are processed with the Positioning and Navigation Data Analyst (PANDA) software. The results show that for BeiDou IGSO and MEO satellites, the two-step GPS-assisted method outperforms the independent single-system method in both internal orbit overlap precision and external satellite laser ranging validation. For BeiDou GEO satellites, the two methods show close performances. Zenith tropospheric delays estimated from the first method are very close to those estimated from GPS precise point positioning in the second method, with differences of several millimeters. Satellite clock estimates from the two methods show similar performances when assessing the stability of the BeiDou on board clocks.     

确定卫星与接收机信号延迟偏差的新方法及其应用

单频ＧＰＳ接收机用户通常需要进行电离层延迟改正,电离层延迟改正量通常来源于电离层延迟改正模型或双频ＧＰＳ基准站信息,后者即是利用双频ＧＰＳ观测值估计电子含量总数,求解电离层延迟改正量。利用双频ＧＰＳ观测值估计电子含量总数,一个关键总是是去掉卫星与接收信号延迟偏差。     

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.     

On determination of heights by using terrestrial clocks and GPS signals

 Considering a GPS satellite and two terrestrial stations, two types of equations are derived relating the heights of the two stations to the measured data (frequency ratio or clock rate differences) and the coordinates and velocity components of all three participating objects. The potential possibilities of using such relations for the determination of heights (in terms of geopotential numbers or orthometric heights) are discussed. Received: 6 December 2000 / Accepted: 9 July 2001     

GPS-assisted GLONASS orbit determination

 Using 1 week of data from a network of GPS/GLONASS dual-tracking receivers, 15-cm accurate GLONASS orbit determination is demonstrated with an approach that combines GPS and GLONASS data. GPS data are used to define the reference frame, synchronize receiver clocks and determine troposphere delay for the GLONASS tracking network. GLONASS tracking data are then processed separately, with the GPS-defined parameters held fixed, to determine the GLONASS orbit. The quality of the GLONASS orbit determination is currently limited by the size and distribution of the tracking network, and by the unavailability of a sufficiently refined solar pressure model. Temporal variations in the differential clock bias of the dual-tracking receivers are found to have secondary impact on the orbit determination accuracy. Received: 5 January 2000 / Accepted: 15 February 2001     

基于VRS的虚拟观测值生成与质量评定

GPS虚拟参考站(VRS)技术是近些年来发展的一种高精度的快速定位技术。VRS技术的核心是通过用户站周围多个参考站的观测数据融合生成虚拟参考站的观测值,其关键是正确模拟测量区域内的各相关误差项。推导了用于VRS定位的码伪距和载波相位虚拟观测值模型,并对计算结果进行了质量评定,试验采用上海市GPS基准站观测网络收集的数据进行计算分析,证明了所述算法的可行性和有效性。     

How to handle topography in practical geoid determination: three examples

 Three different methods of handling topography in geoid determination were investigated. The first two methods employ the residual terrain model (RTM) remove–restore technique, yielding the quasigeoid, whereas the third method uses the classical Helmert condensation method, yielding the geoid. All three methods were used with the geopotential model Earth Gravity Model (1996) (EGM96) as a reference, and the results were compared to precise global positioning system (GPS) levelling networks in Scandinavia. An investigation of the Helmert method, focusing on the different types of indirect effects and their effects on the geoid, was also carried out. The three different methods used produce almost identical results at the 5-cm level, when compared to the GPS levelling networks. However, small systematic differences existed. Received: 18 March 1999 / Accepted: 21 March 2000     

Regularization of geopotential determination from satellite data by variance components

 Different types of present or future satellite data have to be combined by applying appropriate weighting for the determination of the gravity field of the Earth, for instance GPS observations for CHAMP with satellite to satellite tracking for the coming mission GRACE as well as gradiometer measurements for GOCE. In addition, the estimate of the geopotential has to be smoothed or regularized because of the inversion problem. It is proposed to solve these two tasks by Bayesian inference on variance components. The estimates of the variance components are computed by a stochastic estimator of the traces of matrices connected with the inverse of the matrix of normal equations, thus leading to a new method for determining variance components for large linear systems. The posterior density function for the variance components, weighting factors and regularization parameters are given in order to compute the confidence intervals for these quantities. Test computations with simulated gradiometer observations for GOCE and satellite to satellite tracking for GRACE show the validity of the approach. Received: 5 June 2001 / Accepted: 28 November 2001     

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。     

网络RTK对流层延迟内插模型精度分析

流动站与参考站间双差对流层延迟的精确改正是网络RTK技术的关键。本文采用河南省地基增强系统参考站网7个参考站的观测数据进行试验,选择LIM、LCM、LSM和KRG模型为研究对象,分析了各模型用于不同高差水平流动站对流层延迟改正的效果。试验结果表明：4种常用内插模型中,LIM和KRG模型对流动站对流层延迟改正的精度较优。流动站与主参考站高差达到400 m时,对于低高度角卫星,模型内插精度降低到分米级,不满足用户流动站高精度定位需求。