Using DORIS measurements for modeling the vertical total electron content of the Earth’s ionosphere

The Doppler orbitography and radiopositioning integrated by satellite (DORIS) system was originally developed for precise orbit determination of low Earth orbiting (LEO) satellites. Beyond that, it is highly qualified for modeling the distribution of electrons within the Earth’s ionosphere. It measures with two frequencies in L-band with a relative frequency ratio close to 5. Since the terrestrial ground beacons are distributed quite homogeneously and several LEOs are equipped with modern receivers, a good applicability for global vertical total electron content (VTEC) modeling can be expected. This paper investigates the capability of DORIS dual-frequency phase observations for deriving VTEC and the contribution of these data to global VTEC modeling. The DORIS preprocessing is performed similar to commonly used global navigation satellite systems (GNSS) preprocessing. However, the absolute DORIS VTEC level is taken from global ionospheric maps (GIM) provided by the International GNSS Service (IGS) as the DORIS data contain no absolute information. DORIS-derived VTEC values show good consistency with IGS GIMs with a RMS between 2 and 3 total electron content units (TECU) depending on solar activity which can be reduced to less than 2 TECU when using only observations with elevation angles higher than \(50^\circ \) . The combination of DORIS VTEC with data from other space-geodetic measurement techniques improves the accuracy of global VTEC models significantly. If DORIS VTEC data is used to update IGS GIMs, an improvement of up to 12  % can be achieved. The accuracy directly beneath the DORIS satellites’ ground-tracks ranges between 1.5 and 3.5 TECU assuming a precision of 2.5 TECU for altimeter-derived VTEC values which have been used for validation purposes.     

Global Ionosphere Maps of VTEC from GNSS,satellite altimetry,and formosat-3/COSMIC data

For space geodetic techniques, operating in microwave band, ionosphere is a dispersive medium; thus signals traveling through this medium are in the first approximation affected proportional to inverse of the square of their frequencies. This effect allows gaining information about the parameters of the ionosphere in terms of Total Electron Content (TEC) or the electron density (N _e ). TEC or electron density can then be expressed by means of spherical harmonic base functions to provide a Global Ionosphere Map (GIM). The classical input data for development of GIMs are obtained from dual-frequency observations carried out at Global Navigation Satellite Systems (GNSS) stations. However, GNSS stations are in-homogeneously distributed around the world, with large gaps particularly over the oceans; this fact reduces the precision of the GIM over these areas. On the other hand, dual-frequency satellite altimetry missions such as Jason-1 provide information about the ionosphere precisely above the oceans; and furthermore Low Earth Orbiting (LEO) satellites, such as Formosat-3/COSMIC (F/C) provide well-distributed information of ionosphere globally. This study investigates on global modeling of TEC through combining GNSS and satellite altimetry data with global TEC data derived from the occultation measurements of the F/C mission. The combined GIMs of vertical TEC (VTEC) show a maximum difference of 1.3–1.7 TEC units (TECU) with respect to the GNSS-only GIMs in the whole day. The root mean square error (RMS) maps of combined solution show a reduction of about 0.1 TECU in the whole day. This decrease of RMS can reach up to 0.5 TECU in areas where no or few GNSS observations are available, but high number of F/C measurement is carried out. This proves that the combined GIMs provide a more homogeneous global coverage and higher reliability than results of each single method. All comparisons and validations made within this study provide vital information regarding combination and integration of various observation techniques in the Global Geodetic Observing System of the International Association of Geodesy.     

A preliminary evaluation of the performance of multiple ionospheric models in low- and mid-latitude regions of China in 2010–2011

Ionospheric delay is a dominant error source in Global Navigation Satellite System (GNSS). Single-frequency GNSS applications require ionospheric correction of signal delay caused by the charged particles in the earth’s ionosphere. The Chinese Beidou system is developing its own ionospheric model for single-frequency users. The number of single-frequency GNSS users and applications is expected to grow fast in the next years in China. Thus, developing an appropriate ionospheric model is crucially important for the Chinese Beidou system and worldwide single-frequency Beidou users. We study the performance of five globally accessible ionospheric models Global Ionospheric Map (GIM), International Reference Ionosphere (IRI), Parameterized Ionospheric Model (PIM), Klobuchar and NeQuick in low- and mid-latitude regions of China under mid-solar activity condition. Generally, all ionospheric models can reproduce the trend of diurnal ionosphere variations. It is found that all the models have better performances in mid-latitude than in low-latitude regions. When all the models are compared to the observed total electron content (TEC) data derived from GIM model, the IRI model (2012 version) has the best agreement with GIM model and the NeQuick has the poorest agreement. The RMS errors of the IRI model using the GIM TEC as reference truth are about 3.0–10.0 TECU in low-latitude regions and 3.0–8.0 TECU in mid-latitude regions, as observed during a period of 1 year with medium level of solar activity. When all the ionospheric models are ingested into single-frequency precise point positioning (PPP) to correct the ionospheric delays in GPS observations, the PIM model performs the best in both low and mid-latitudes in China. In mid-latitude, the daily single-frequency PPP accuracy using PIM model is ~10 cm in horizontal and ~20 cm in up direction. At low-latitude regions, the PPP error using PIM model is 10–20 cm in north, 30–40 cm in east and ~60 cm in up component. The single-frequency PPP solutions indicate that NeQuick model has the lowest accuracy among all the models in both low- and mid-latitude regions of China. This study suggests that the PIM model may be considered for single-frequency GNSS users in China to achieve a good positioning accuracy in both low- and mid-latitude regions.     

Evaluation of NTCM-BC and a proposed modification for single-frequency positioning

Ionospheric delay is a dominant factor that affects the accuracy of single-frequency positioning. Thus, an empirical ionospheric model with high accuracy is very important for single-frequency users. This study proposes a modified empirical broadcast ionospheric model, called MNTCM-BC, based on the Neustrelitz Total Electron Content (TEC) broadcast model NTCM-BC. Nine daily ionospheric coefficients of these models are estimated using datasets of the previous day from 30 globally distributed Global Navigation Satellite System monitor stations, and the prediction performance of the MNTCM-BC is evaluated with the datasets of the current day from all 300 verification stations. The results show that the complex behavior of the ionosphere is well described by the MNTCM-BC, including the visibility of two ionization crests on both sides of the geomagnetic equator and the TEC variations that depend on the local time and geomagnetic latitude. In terms of the prediction accuracy, compared with the NTCM-BC, the main improvement in the MNTCM-BC is achieved in summer, whereas the accuracy is comparable in other seasons. Hence, the following analyses are focused on summer. In the low-solar activity year of 2009, the prediction accuracy of the MNTCM-BC is improved by 0.11 TECU compared with that of the NTCM-BC. As to the high-solar activity year of 2014, the corresponding improvement is 0.35 TECU. In addition, when the number of monitor stations is increased from 30 to 300, the prediction accuracy of two models can be slightly improved by 0.06 TECU in 2009 and 0.13 TECU in 2014, respectively, while reliability enhances. Furthermore, the average three-dimensional positioning accuracy of 160 globally distributed stations for single-frequency point positioning using the Klobuchar model, the NTCM-BC and the MNTCM-BC is 1.83, 1.21 and 1.20 m during quiet day and 3.15, 2.31 and 2.21 m during perturbed day, respectively. Relative to the Klobuchar model and the NTCM-BC, the average accuracy improvements in the MNTCM-BC are about 30 and 3%, respectively.     

Revisit the calibration errors on experimental slant total electron content (TEC) determined with GPS

The calibration errors on experimental slant total electron content (TEC) determined with global positioning system (GPS) observations is revisited. Instead of the analysis of the calibration errors on the carrier phase leveled to code ionospheric observable, we focus on the accuracy analysis of the undifferenced ambiguity-fixed carrier phase ionospheric observable determined from a global distribution of permanent receivers. The results achieved are: (1) using data from an entire month within the last solar cycle maximum, the undifferenced ambiguity-fixed carrier phase ionospheric observable is found to be over one order of magnitude more accurate than the carrier phase leveled to code ionospheric observable and the raw code ionospheric observable. The observation error of the undifferenced ambiguity-fixed carrier phase ionospheric observable ranges from 0.05 to 0.11 total electron content unit (TECU) while that of the carrier phase leveled to code and the raw code ionospheric observable is from 0.65 to 1.65 and 3.14 to 7.48 TECU, respectively. (2) The time-varying receiver differential code bias (DCB), which presents clear day boundary discontinuity and intra-day variability pattern, contributes the most part of the observation error. This contribution is assessed by the short-term stability of the between-receiver DCB, which ranges from 0.06 to 0.17 TECU in a single day. (3) The remaining part of the observation errors presents a sidereal time cycle pattern, indicating the effects of the multipath. Further, the magnitude of the remaining part implies that the code multipath effects are much reduced. (4) The intra-day variation of the between-receiver DCB of the collocated stations suggests that estimating DCBs as a daily constant can have a mis-modeling error of at least several tenths of 1 TECU.     

利用数据同化技术实现区域电离层TEC重构

电离层参量的提取是开展电离层研究的基础,而数据同化技术则是获取电离层参量的一种重要手段。以NeQuick模型的输出作为背景场,Kalman滤波作为同化算法,利用数据同化技术实现区域电离层TEC重构,结果表明,数据同化方法重构的倾斜总电子含量（TEC）和垂直TEC与实测值较为一致。相比NeQuick模型及全球电离层地图（GIM）数据,数据同化方法重构得到的TEC的平均误差和标准差均有明显的降低,实测数据验证了数据同化技术在区域TEC重构中的精度和可靠性。     

A new global TEC model for estimating transionospheric radio wave propagation errors

Space-based navigation and radar systems operating at single frequencies of <10 GHz require ionospheric corrections of the signal delay or range error. Because this ionospheric propagation error is proportional to the total electron content of the ionosphere along the ray path, a user friendly TEC model covering global scale and all levels of solar activity should be helpful in various applications. Since such a model is not available yet, we present an empirical model approach that allows determining global TEC very easily. Although the number of model coefficients and parameters is rather small, the model describes main ionospheric features with good quality. Presented is the empirical approach describing dependencies on local time, geographic/geomagnetic location and solar irradiance and activity. The non-linear approach needs only 12 coefficients and a few empirically fixed parameters for describing the broad spectrum of TEC variation at all levels of solar activity. The model approach is applied on high-quality global TEC data derived by the Center for Orbit Determination in Europe (CODE) at the University of Berne over more than half a solar cycle (1998–2007). The model fits to these input data with a negative bias of 0.3 TECU and a RMS deviation of 7.5 TECU. As other empirical models too, the proposed Global Neustrelitz TEC Model NTCM-GLis climatological, i.e. the model describes the average behaviour under quiet geomagnetic conditions. During severe space weather events the actual TEC data may deviate from the model values considerably by more than 100%. A preliminary comparison with independent data sets as TOPEX/Poseidon altimeter data reveals similar results for NeQuick and NTCM-GL with RMS deviations in the order of 5 and 11 TECU (1 TECU = 10¹⁶ electrons/m²) for low and high-solar activity conditions, respectively. The more extended data base of ionosphere information that accumulates in the coming years will help in further improving the set of coefficients of the model.     

Integrating GPS and GLONASS to accelerate convergence and initialization times of precise point positioning

The main challenge of dual-frequency precise point positioning (PPP) is that it requires about 30 min to obtain centimeter-level accuracy or to succeed in the first ambiguity-fixing. Currently, PPP is generally conducted with GPS only using the ionosphere-free combination. We adopt a single-differenced (SD) between-satellite PPP model to combine the GPS and GLONASS raw dual-frequency carrier phase measurements, in which the GPS satellite with the highest elevation is selected as the reference satellite to form the SD between-satellite measurements. We use a 7-day data set from 178 IGS stations to investigate the contribution of GLONASS observations to both ambiguity-float and ambiguity-fixed SD PPP solutions, in both kinematic and static modes. In ambiguity-fixed PPP, we only attempt to fix GPS integer ambiguities, leaving GLONASS ambiguities as float values. Numerous experimental results show that PPP with GLONASS and GPS requires much less convergence time than that of PPP with GPS alone. For ambiguity-float PPP, the average convergence time can be reduced by 45.9 % from 22.9 to 12.4 min in static mode and by 57.9 % from 40.6 to 17.7 min in kinematic mode, respectively. For ambiguity-fixed PPP, the average time to the first-fixed solution can be reduced by 27.4 % from 21.6 to 15.7 min in static mode and by 42.0 % from 34.4 to 20.0 min in kinematic mode, respectively. Experimental results also show that the less the GPS satellites are used in float PPP, the more significant is the reduction in convergence time when adding GLONASS observations. In addition, on average, more than 4 GLONASS satellites can be observed for most 2-h observation sessions. Nearly, the same improvement in convergence time reduction is achieved for those observations.     

基于球谐函数区域电离层模型建立

利用GPS双频观测数据建立高精度、准实时的区域电离层总电子含量(TEC)模型是电离层研究的一个重要手段。文中探讨IGS观测站数据结合4阶球谐函数建立区域电离层格网模型的方法,并对硬件延迟(DCB)和TEC建模结果的可靠性进行分析,结果表明,DCB解算精度在0.4ns以内,TEC内外精度优于1.4TECU(1TECU=1016电子数/m2)和1.5TECU,满足导航定位中电离层改正的需要。     

Application of SWACI products as ionospheric correction for single-point positioning: a comparative study

In Global Navigation Satellite Systems (GNSS) using L-band frequencies, the ionosphere causes signal delays that correspond with link related range errors of up to 100 m. In a first order approximation the range error is proportional to the total electron content (TEC) of the ionosphere. Whereas this first order range error can be corrected in dual-frequency measurements by a linear combination of carrier phase- or code-ranges of both frequencies, single-frequency users need additional information to mitigate the ionospheric error. This information can be provided by TEC maps deduced from corresponding GNSS measurements or by ionospheric models. In this paper we discuss and compare different ionospheric correction methods for single-frequency users. The focus is on the comparison of the positioning quality using dual-frequency measurements, the Klobuchar model, the NeQuick model, the IGS TEC maps, the Neustrelitz TEC Model (NTCM-GL) and the reconstructed NTCM-GL TEC maps both provided via the ionosphere data service SWACI (http://swaciweb.dlr.de) in near real-time. For that purpose, data from different locations covering several days in 2011 and 2012 are investigated, including periods of quiet and disturbed ionospheric conditions. In applying the NTCM-GL based corrections instead of the Klobuchar model, positioning accuracy improvements up to several meters have been found for the European region in dependence on the ionospheric conditions. Further in mid- and low-latitudes the NTCM-GL model provides results comparable to NeQuick during the considered time periods. Moreover, in regions with a dense GNSS ground station network the reconstructed NTCM-GL TEC maps are partly at the same level as the final IGS TEC maps.     

OpenMP并行计算在全球电离层反演中的应用

对全球电离层反演数据处理中的计算密集型任务进行分析,针对数据预处理、组建法方程矩阵、参数预消除和法方程矩阵求逆等主要模块设计了基于OpenMP（Open Multi-Processing）的并行计算方案。该实验方案在单台服务器下实施,通过算例验证了本文并行计算方案的有效性和可靠性。实验结果表明:采用并行计算后,全球电离层快速解执行时间只需要10~13 min,计算速度加快了约6倍;最终解执行时间只需要39~47 min,计算速度加快了约5倍。本文全球电离层模型精度约为2.8~3.8 TECU,最终解模型精度相比快速解精度提高了约0.2 TECU,与IGS各个分析中心电离层产品精度基本相当。     

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。     

卫星测高资料的电离层延迟改正交叉检验与误差分析

对单频和双频卫星测高电离层改正进行了分析和比较。以Topex卫星双频电离层改正噪声影响为例,采用沿轨高斯低通滤波后,其交叉点不符值RMS可减小5.7～7.3mm。将平滑后的双频Topex电离层改正与DORIS模型、新发展的IRI2007同化模型和根据全球连续GPS跟踪站实测数据建立的GIM模型进行了交叉比较,结果表明,根据实测数据建立的DORIS和GIM模型精度高于IRI2007模型;与上述3个模型的差值统计结果还显示了平滑后的Topex双频电离层改正存在的10～15mm的系统偏差。     

An enhanced strategy for GNSS data processing of massive networks

Although the computational burden of global navigation satellite systems (GNSS) data processing is nowadays already a big challenge, especially for huge networks, integrated processing of denser networks with data of multi-GNSS and multi-frequency is desired in the expectation of more accurate and reliable products. Based on the concept of carrier range, in this study, the precise point positioning with integer ambiguity resolution is engaged to obtain the integer ambiguities for converting carrier phases to carrier ranges. With such carrier ranges and pseudo-ranges, rigorous integrated processing is realized computational efficiently for the orbit and clock estimation using massive networks. The strategy is validated in terms of computational efficiency and product quality using data of the IGS network with about 460 stations. The experimental validation shows that the computation time of the new strategy increases gradually with the number of stations. It takes about 14 min for precise orbit and clock determination with 460 stations, while the current strategy needs about 82 min. The overlapping orbit RMS is reduced from 27.6 mm with 100 stations to 24.8 mm using the proposed strategy, and the RMS could be further reduced to 23.2 mm by including all 460 stations. Therefore, the new strategy could be applied to massive networks of multi-GNSS and multi-frequency receivers and possibly to achieve GNSS data products of higher quality.     

Spherical cap harmonic model for mapping and predicting regional TEC

An approach to modeling the regional ionospheric total electron content (TEC) based on spherical cap harmonic analysis is presented. This approach not only provides a better regional TEC mapping accuracy, but also the capability for ionospheric model prediction based on spectrum analysis and least squares collocation. Unlike conventional approaches, which predict the immediate TEC with models using current observations, the spherical cap harmonic approach utilizes models using past observations to predict a model which will provide future TEC values. A significant advantage in comparison with conventional approaches is that the spherical cap harmonic approach can be used to predict the long-term TEC with reasonable accuracy. This study processes a set of GPS data with an observation time span of 1 year from two GPS networks in China. The TEC mapping accuracy of the spherical cap harmonic model is compared with the polynomial model and the global ionosphere model from IGS. The results show that the spherical cap harmonic model has a better TEC mapping accuracy with smoother residual distributions in both temporal and spatial domains. The TEC prediction with the spherical cap harmonic model has been investigated for both short- and long-term intervals. For the short-term interval, the prediction accuracies for the latencies of 1-day, 2-days, and 3-days are 2.5 TECU, 3.5 TECU, and 4.5 TECU, respectively. For the long-term interval, the prediction accuracy is 4.5 TECU for a 2-month latency.     

利用中国区域电离层数据拟合 Klobuchar参数

对于单频G PS用户而言,电离层延迟是最重要的误差来源之一。G PS系统使用Klobuchar模型对电离层延迟进行改正,其改正数从根据经验模型和历史数据得到的370组常数选取。在缺少全球观测数据的情况下,仅利用中国区域观测数据拟合电离层模型参数,存在区域外精度下降,参数超限等问题。针对这些问题,提出了利用经验模型外推进行参数拟合的方法。相比广播Klobuchar参数,在太阳活动高峰年RMS误差减小接近7 TECU ,正常年减小1.5 T EC U ,平静年精度也略有提升。2001年至2012年的拟合参数不存在参数超限现象,且量化后或者使用预报的电离层数据进行拟合,精度下降很小,可以用于预报全球电离层模型参数。     

BDS网络RTK中距离参考站整周模糊度单历元解算方法

提出了一种BDS网络RTK中距离(50~100 km)参考站间的双频载波相位整周模糊度单历元解算方法。该方法首先利用B1、B2载波相位整周模糊度间的线性关系选取B1、B2载波相位整周模糊度备选值。利用双频载波相位整周模糊度备选值计算双差电离层延迟误差,根据参考站各卫星电离层延迟误差间的空间关系,使用双差电离层延迟误差构建双差电离层延迟误差的线性计算模型。通过双差电离层延迟误差线性计算模型的建立搜索和确定B1、B2载波相位的整周模糊度。经CORS网实测数据试验算例的验证,该方法只需一个历元的观测数据即可确定参考站间双差B1、B2载波相位整周模糊度,且不受周跳影响。     

A new automated cycle slip detection and repair method for a single dual-frequency GPS receiver

This paper develops a new automated cycle slip detection and repair method that is based on only one single dual-frequency GPS receiver. This method jointly uses the ionospheric total electron contents (TEC) rate (TECR) and Melbourne–Wübbena wide lane (MWWL) linear combination to uniquely determine the cycle slip on both L1 and L2 frequencies. The cycle slips are inferred from the information of ionospheric physical TECR and MWWL ambiguity at the current epoch and that at the previous epoch. The principle of this method is that when there are cycle slips, the MWWL ambiguity will change and the ionospheric TECR will usually be significantly amplified, the part of artificial TECR (caused by cycle slips) being significantly larger than the normal physical TECR. The TECR is calculated based on the dual-frequency carrier phase measurements, and it is highly accurate. We calculate the ionospheric change information (including TECR and TEC acceleration) using the previous epochs (30 epochs in this study) and use the previous data to predict the TECR for the epoch needing cycle slip detection. If the discrepancy is larger than our defined threshold 0.15 TECU/s, cycle slips are regarded to exist at that epoch. The key rational of method is that during a short period (1.0 s in this study) the TECR of physical ionospheric phenomenon will not exceed the threshold. This new algorithm is tested with eight different datasets (including one spaceborne GPS dataset), and the results show that the method can detect and correctly repair almost any cycle slips even under very high level of ionospheric activities (with an average Kp index 7.6 on 31 March 2001). The only exception of a few detected but incorrectly repaired cycle slip is due to a sudden increased pseudorange error on a single satellite (PRN7) under very active ionosphere on 31 March 2001. This method requires dual-frequency carrier phase and pseudorange data from only one single GPS receiver. The other requirement is that the GPS data rate ideally is 1 Hz or higher in order to detect small cycle slips. It is suitable for many applications where one single receiver is used, e.g. real-time kinematic rover station and precise point positioning. An important feature of this method is that it performs cycle slip detection and repair on a satellite-by-satellite basis; thus, the cycle slip detection and repair for each satellite are completely independent and not affected by the data of other satellites.     

Real-Time Precise Point Positioning (RTPPP) with raw observations and its application in real-time regional ionospheric VTEC modeling

Precise Point Positioning (PPP) is an absolute positioning technology mainly used in post data processing. With the continuously increasing demand for real-time high-precision applications in positioning, timing, retrieval of atmospheric parameters, etc., Real-Time PPP (RTPPP) and its applications have drawn more and more research attention in recent years. This study focuses on the models, algorithms and ionospheric applications of RTPPP on the basis of raw observations, in which high-precision slant ionospheric delays are estimated among others in real time. For this purpose, a robust processing strategy for multi-station RTPPP with raw observations has been proposed and realized, in which real-time data streams and State-Space-Representative (SSR) satellite orbit and clock corrections are used. With the RTPPP-derived slant ionospheric delays from a regional network, a real-time regional ionospheric Vertical Total Electron Content (VTEC) modeling method is proposed based on Adjusted Spherical Harmonic Functions and a Moving-Window Filter. SSR satellite orbit and clock corrections from different IGS analysis centers are evaluated. Ten globally distributed real-time stations are used to evaluate the positioning performances of the proposed RTPPP algorithms in both static and kinematic modes. RMS values of positioning errors in static/kinematic mode are 5.2/15.5, 4.7/17.4 and 12.8/46.6 mm, for north, east and up components, respectively. Real-time slant ionospheric delays from RTPPP are compared with those from the traditional Carrier-to-Code Leveling (CCL) method, in terms of function model, formal precision and between-receiver differences of short baseline. Results show that slant ionospheric delays from RTPPP are more precise and have a much better convergence performance than those from the CCL method in real-time processing. 30 real-time stations from the Asia-Pacific Reference Frame network are used to model the ionospheric VTECs over Australia in real time, with slant ionospheric delays from both RTPPP and CCL methods for comparison. RMS of the VTEC differences between RTPPP/CCL method and CODE final products is 0.91/1.09 TECU, and RMS of the VTEC differences between RTPPP and CCL methods is 0.67 TECU. Slant Total Electron Contents retrieved from different VTEC models are also validated with epoch-differenced Geometry-Free combinations of dual-frequency phase observations, and mean RMS values are 2.14, 2.33 and 2.07 TECU for RTPPP method, CCL method and CODE final products, respectively. This shows the superiority of RTPPP-derived slant ionospheric delays in real-time ionospheric VTEC modeling.     

Galileo single frequency ionospheric correction: performances in terms of position

For GPS single frequency users, the ionospheric contribution to the error budget is estimated by the well-known Klobuchar algorithm. For Galileo, it will be mitigated by a global algorithm based on the NeQuick model. This algorithm relies on the adaptation of the model to slant Total Electron Content (sTEC) measurements. Although the performance specifications of these algorithms are expressed in terms of delay and TEC, the users might be more interested in their impact on positioning. Therefore, we assessed the ability of the algorithms to improve the positioning accuracy using globally distributed permanent stations for the year 2002 marked by a high level of solar activity. We present uncorrected and corrected performances, interpret these and identify potential causes for Galileo correction discrepancies. We show vertical errors dropping by 56–64 % due to the analyzed ionospheric corrections, but horizontal errors decreasing by 27 % at most. By means of a fictitious symmetric satellite distribution, we highlight the role of TEC gradients in residual errors. We describe mechanisms permitted by the Galileo correction, which combine sTEC adaptation and topside mismodeling, and limit the horizontal accuracy. Hence, we support further investigation of potential alternative ionospheric corrections. We also provide an interesting insight into the ionospheric effects possibly experienced during the next solar maximum coinciding with Galileo Initial Operation Capability.