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.     

北斗三号全球导航卫星系统全球广播电离层延迟修正模型(BDGIM)应用性能评估

2020年6月23日,我国北斗三号全球导航卫星系统正式完成星座全球组网。北斗三号全球导航卫星系统采用新一代全球广播电离层延迟修正模型(BDGIM),为用户提供电离层延迟改正服务。本文利用高精度全球电离层格网(GIM)以及实测BDS/GPS数据提供的电离层TEC作为参考,从延迟改正精度及北斗单频伪距单点定位应用、模型系数性能等方面,对北斗三号系统组网前后(2020年5月1日至2020年7月20日)BDGIM模型的改正精度等应用性能进行了分析与研究,并将其与美国GPS播发的Klobuchar模型和北斗二号卫星导航系统播发的BDS Klobuchar模型进行对比。研究表明,BDGIM模型在对北斗三号系统组网完成前后电离层延迟修正精度没有发生显著变化。上述时段内,以国际GNSS服务(IGS)发布的最终GIM产品为参考,BDGIM模型在中国区域、亚太地区和全球范围内的电离层修正百分比分别达到84.45%、74.74%和64.57%;以选取的全球83个GNSS检测站BDS、GPS双频数据实测电离层TEC为参考,BDGIM在中国区域、亚太地区和全球范围内的电离层修正百分比分别为73.12%、70.18%及68.06%;当BDGIM模型应用于北斗单频伪距单点定位时,在中国区域、亚太地区和全球范围内分别实现了2.22、2.66和2.96 m的三维定位精度。     

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.     

适用于不同尺度区域的Klobuchar-like电离层模型

导航定位中运用最广泛的电离层修正模型是Klobuchar模型,但经典的Klobuchar模型不能满足日益增长的导航定位精度的需求,因此不同的精化模型被提出。本文利用GIMs分析了夜间电离层随地方时的变化和电离层电子总含量随纬度的变化情况,在对各种适用范围较广的模型精化方案进行归纳总结的基础上,提出了一种适用于不同尺度区域的Klobuchar-like模型,并利用不同太阳活动时期不同季节的GIMs建立了适用于单站、大区域和全球的Klobuchar-like模型、14参数Klobuchar模型和8参数Klobuchar模型。Klobuchar-like模型单站、区域、全球的修正率分别达到了92.96%、91.55%、72.67%,均高于14参数、8参数Klobuchar模型和GPS Klobuchar模型,表明了该模型的有效性与实用性。     

Klobuchar电离层模型精化进展

电离层延迟是卫星导航定位的重要误差源之一。采用合适的电离层延迟模型可以有效地减弱电离层延迟误差对定位结果的影响。目前在导航定位中运用最广泛的是Klobuchar模型,但Klobuchar模型的修正率只有50%~60%。为了满足日益增长的导航定位精度的需求,不同的精化模型被提出。本文介绍了Klobuchar模型在GPS和BDS系统中的应用,比较了在两个系统应用时的差异。回顾概括了文献在Klobuchar模型的参数精化和模型精化两个方面的研究,并对各种精化模型进行了对比总结。模型精化的结果优于参数精化,未来对于Klobuchar模型的精化更趋向于模型精化。     

基于北斗GEO的电离层延迟修正方法比较与分析

电离层延迟是影响导航定位精度的最主要因素。北斗卫星导航系统采用Klobuchar模型修正单频接收机用户的电离层延迟误差,对于双频接收机,可以利用不同频率信号的伪距观测数据解算得到电离层延迟值。为比较两种方法在天津地区的电离层延迟修正效果,利用NovAtel GPStation6接收机(GNSS电离层闪烁和TEC监测接收机)采集到的卫星实测数据进行计算。以国际全球导航卫星系统服务组织(IGS)发布的全球电离层格网数据为参考,对两种方法的修正效果进行比较分析。结果表明,在天津地区,利用双频观测值解算电离层延迟比Klobuchar模型计算结果更加精确,且平均每天的修正值达到IGS发布数据的82.11％,比Klobuchar模型计算值高948％      

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.     

Klobuchar电离层延迟改正模型精化方法的研究

在GPS导航定位中,单频接收机利用导航电文发播的Klobuchar电离层改正模型对电离层误差进行改正,但改正效果不太理想,为了提高其改正精度,并利用它进行电离层实时预报,我们通过电离层电子含量实测数据,对其进行精化,以满足要求。本文在原有Klobuchar电离层改正模型精化的基础之上,提出了一种新的精化方法,并对两种方法进行了比较研究,结果表明这两种精化方法对电离层的改正均有很好地提高,且本文提出的方法更优良。     

Application of the TaiWan Ionospheric Model to single-frequency ionospheric delay corrections for GPS positioning

The performance of a three-dimensional ionospheric electron density model derived from FormoSat3/COSMIC GPS Radio Occultation measurements, called the TaiWan Ionosphere Model (TWIM), in removing the ionospheric delays in single-frequency pseudorange observations is presented. Positioning results using TWIM have been compared with positioning results using other ionospheric models, such as the Klobuchar (KLOB) and the global ionospheric model (GIM). C/A code pseudoranges have been observed at three International GPS Service reference stations that are representative of mid-latitude (BOR1 and IRKJ) and low-latitude (TWTF) regions of the ionosphere. The observations took place during 27 geomagnetically quiet days from April 2010 to October 2011. We perform separate solutions using the TWIM, KLOB, GIM ionospheric models and carry out a solution applying no ionospheric correction at all. We compute the daily mean horizontal errors (DMEAN) and the daily RMS (DRMS) for these solutions with respect to the published reference station coordinates. It has demonstrated that TEC maps generate using the TWIM exhibit a detailed structure of the ionosphere, particularly at low-latitude region, whereas the Klobuchar and the GIM only provide the basic diurnal and geographic features of the ionosphere. Also, it is shown that even for lower satellite elevations, the TWIM provides better positioning than the Klobuchar and GIM models. Specifically, using TWIM, the difference of the uncorrected solution (no ionospheric correction), and the other solutions, relative to the uncorrected solution, is 45 % for the mean horizontal error (DMEAN) and 42 % for the horizontal root-mean-square error (DRMS). Using Klobuchar and GIM, the percent for DMEAN only reaches to about 12 % and 3 %, while the values for the DRMS are only 12 and 4 %, respectively. In the vertical direction, all models have a percentage of about 99 and 70 % for the mean vertical error (VMEAN) and vertical root-mean-square error (VRMS), respectively. These percentages show the greater impact of TWIM on the ionospheric correction compared to the other models. In at least 40 % of the observed days and across all stations, TWIM has the smallest DMEAN, VMEAN, DRMS, and VRMS daily values. These values reach 100 % at station TWTF. This shows the overall performance of TWIM is better than the Klobuchar and GIM.     

不同NeQuick电离层模型参数的应用精度分析

Galileo采用NeQuick作为全球广播电离层模型,其实际应用中以有效电离水平因子Az代替太阳活动指数作为NeQuick的输入参数,并利用二次多项式拟合得到广播星历中播发的3个电离层参数。本文在总结和讨论NeQuick模型参数估计方法及其变化特征的基础上,分别以全球电离层格网、GPS基准站及JASON-2测高卫星提供的电离层TEC为参考,分析不同NeQuick模型参数(包括以太阳活动参数F10.7为输入的NeQuick2、以本文解算参数为输入的NeQuickC和以Galileo广播电离层参数为输入的NeQuickG)在全球大陆及海洋地区的应用精度,并与GPS广播的Klobuchar模型对比。结果表明,NeQuickG在全球范围内的修正精度为54.2%~65.8%,NeQuickC的修正精度为71.1%~74.2%,NeQuick2的修正精度与NeQuickG相当,略优于GPS广播星历中播发的Klobuchar模型。     

几种电离层模型对单频单点定位的影响分析

针对实时GNSS单频定位中电离层延迟改正问题,本文采用可用于实时GNSS单频定位的几种电离层模型对电离层延迟进行改正并分析其对GNSS单频单点定位性能的影响。其中,对单频SPP的电离层延迟采用模型直接进行改正,采用Klobuchar模型、CODE的预报产品c1pg、原国家测绘地理信息局的实时球谐电离层产品cosong和CODE事后产品codg计算的电离层精度依次提高;采用不同电离层模型作为电离层估计的先验约束进行单频PPP定位。结果表明:采用精度较好的电离层产品作为先验约束可加快单频PPP收敛。     

不同Klobuchar模型参数的性能比较

对于GPS单频用户而言,电离层延迟是最重要的误差来源之一。GPS系统使用Klobuchar模型对电离层延迟进行改正,其改正数从370组常数中选取。目前全球分布的GPS测站可以获得高精度的全球电离层监测结果,GPS为什么不发播采用实测数据计算得到的Klobuchar模型参数呢？本文针对这一问题进行分析。首先对欧洲定轨中心CODE提供的全球电离层图GIM预报COPG电离层进行精度评估,然后根据COPG电离层进行Klobuchar模型参数拟合并利用IGS提供的事后高精度电离层图进行精度分析,最后将不同的电离层模型参数应用于单点定位以评估其对单频用户的影响。分析结果表明：受8参数的Klobuchar模型本身结构限制,采用全球实测数据计算的电离层模型参数与导航电文中发播的电离层模型精度相当,为55%左右。而仅采用地磁纬度45oS以北的数据拟合得到的模型参数,其电离层改正精度有明显提升,可达65%左右,但其对单频用户定位精度改善不明显。本文研究结果为我国全球电离层建模提供参考。     

单站区域电离层TEC建模及精度分析

为了分析单站区域电离层总电子含量(total electron content,TEC)模型的适用范围和精度,基于2～15阶次球谐函数,分别建立了欧洲区域16个单站区域电离层TEC模型,生成了区域格网TEC,并与欧洲定轨中心(Center for Orbit Determination in Europe,CODE)、...     

Klobuchar模型和NeQuick模型在中国地区的精度评估

将CODE以及GPS广播星历提供的8个系数分别作为Klobuchar模型的输入参数,利用Klobuchar模型及NeQuick模型计算得到中国地壳运动观测网15个GPS基准站上2000～2008年的电离层VTEC序列,以欧洲定轨中心CODE提供的事后电离层产品作为参考标准,得到了两个模型在中国地区的精度评估结果。     

Climatological study of ionospheric irregularities over the European mid-latitude sector with GPS

High-frequency variability of the ionosphere, or irregularities, constitutes the main threat for real-time precise positioning techniques based on Global Navigation Satellite Systems (GNSS) measurements. Indeed, during periods of enhanced ionospheric variability, GNSS users in the field—who cannot verify the integrity of their measurements—will experience positioning errors that can reach several decimeters, while the nominal accuracy of the technique is cm-level. In the frame of this paper, a climatological analysis of irregularities over the European mid-latitude region is presented. Based on a 10 years GPS dataset over Belgium, the work analyzes the occurrence rate (as a function of the solar cycle, season and local time) as well as the amplitude of ionospheric irregularities observed at a single GPS station. The study covers irregularities either due to space weather events (solar origin) or of terrestrial origin. If space weather irregularities are responsible for the largest effects in terms of ionospheric error, their occurrence rate highly depends on solar activity. Indeed, the occurrence rate of ionospheric irregularities is about 9 % during solar maximum, whereas it drops to about 0 % during medium or low solar activity periods. Medium-scale ionospheric disturbances (MSTIDs) occurring during daytime in autumn/winter are the most recurrent pattern of the time series, with yearly proportions slightly varying with the solar cycle and an amplitude of about 10 % of the TEC background. Another recurrent irregularity type, though less frequent than MSTIDs, is the noise-like variability in TEC observed during summer nighttime, under quiet geomagnetic conditions. These summer nighttime irregularities exhibit amplitudes ranging between 8 and 15 % of the TEC background.     

NTCM广播电离层模型性能评估

对于全球卫星导航系统单频用户而言，广播电离层模型是改正电离层误差的主要方法之一。对NTCM-BC模型、MNTCM-BC模型、NTCM-Klobuchar模型和传统Klobuchar模型的性能进行了对比分析。结果表明，在一个太阳活动周期内，NTCM-BC和MNTCM-BC模型计算的垂直总电子含量精度相当，且精度最高，NTCM-Klobuchar模型次之，Klobuchar模型最低。在低纬度测站，NTCM系列模型较Klobuchar模型最高能减少20 TECU左右的误差。与Klobuchar模型相比，采用NTCM-BC和MNTCM-BC模型进行伪距单点定位，高程精度提高约38%，特别是太阳活动高峰期间，低纬度测站最高能提高3 m左右。     

Performance evaluation of different ionospheric models in single-frequency code-based differential GPS positioning

Differential ionospheric slant delays are obtained from a quiet-time, three-dimensional ionospheric electron density model, called the TaiWan Ionosphere Model (TWIM), to be used in code-based differential GPS positioning. The code observations are acquired from nine continuously operating GPS stations around Taiwan whose baseline ranged from 19 to 340 km. Daily 24-hour epoch-per-epoch positioning obtained for 70 most geomagnetic quiet days (2008–2010) for each of the 72 baselines. The performance of TWIM has been compared with the standard operational Klobuchar model (KLB) used by typical single-frequency receivers and the IGS global ionospheric model (GIM). Generally, TWIM performed well in reducing the differential ionospheric delay especially for long baselines and different levels of low solar activity. It has a much better performance compared to the operational KLB model. TWIM also performed similarly with GIM, though GIM has the best performance overall. GIM has the best ionospheric gradient estimates among the three models whose differential ionospheric delay-to-horizontal error ratio is more than 0.25. This is followed closely by TWIM with about 0.20. KLB only has a ratio of <0.10. The similarity of the performance of TWIM and GIM demonstrates the feasibility of TWIM in correcting for differential ionospheric delays in the C/A code pseudorange that is caused by electron density gradients in the ionosphere. It can provide decimeter-to-centimeter level accuracy in differential GPS positioning for single-frequency receivers during geomagnetic quiet conditions across all seasons and different levels of low solar activities.     

An all-pass filter for compensation of ionospheric dispersion effects on wideband GNSS signals

Compared with the traditional GPS L1 C/A BPSK-R(1) signal, wideband global navigation satellite system (GNSS) signals suffer more severe distortion due to ionospheric dispersion. Ionospheric dispersion inevitably introduces additional errors in pseudorange and carrier phase observations that cannot be readily eliminated by traditional methods. Researchers have reported power losses, waveform ripples, correlation peak asymmetries, and carrier phase shifts caused by ionospheric dispersion. We analyze the code tracking bias induced by ionospheric dispersion and propose an efficient all-pass filter to compensate the corresponding nonlinear group delay over the signal bandwidth. The filter is constructed in a cascaded biquad form based on the estimated total electron content (TEC). The effects of TEC accuracy, filter order, and fraction parameter on the filter fitting error are explored. Taking the AltBOC(15,10) signal as an example, we compare the time domain signal waveforms, correlation peaks, code tracking biases, and carrier phase biases with and without this all-pass filter and demonstrate that the proposed delay-equalization all-pass filter is a potential solution to ionospheric dispersion compensation and mitigation of observation biases for wideband GNSS signals.     

Anomalies in broadcast ionospheric coefficients recorded by GPS receivers over the past two solar cycles (1992–2013)

The anomaly phenomenon of broadcast ionospheric model coefficients of the Global Positioning System (GPS) is revealed after analyzing the navigation file data collected from all the IGS (International GNSS Service) stations worldwide over a 22-year period (1992–2013). GPS broadcast ionospheric coefficients widely used by many single-frequency users to correct the ionosphere errors for numerous GPS applications are usually believed to have only one set/version per day. However, it is found that GPS receivers from the IGS network can report as many as eight sets/versions of ionospheric coefficients in a day. In order to investigate the possible factors for such an anomalous phenomenon, the relationship between the number of coefficient sets and solar cycle, the receiver geographic locations, and receiver types/models are analyzed in detail. The results indicate that most of the coefficients show an annual variation. During the active solar cycle period from mid-1999 to mid-2001, all of the coefficients extracted from IGS navigation files behaved anomalously. Our analysis shows that the anomaly is also associated with GPS receiver types/models. Some types/models of GPS receivers report one set/version of ionospheric coefficients daily, while others report multiple sets. Our analysis also suggests that the ionospheric coefficient anomaly is not necessarily related to ionospheric scintillations. No correlation between the anomaly and geographic location of GPS receivers has been found in the analysis. Using the ionospheric coefficient data collected from 1998 to 2013, the impact of ionospheric coefficient anomaly on vertical total electron content (VTEC) calculation using the Klobuchar model has been evaluated with respect to the Global Ionospheric Maps generated by the Center for Orbit Determination in Europe. With different sets of coefficients recorded on the same day, the resulting VTEC values are dramatically different. For instance on June 1, 2000, the largest VTEC at one of our test stations can be as large as 153.3 TECu (total electron content unit) using one set of coefficients, which is 16.36 times larger than the smallest VTEC of 9.37 TECu computed from using another set of coefficients.     

基于不同电离层模型的精密单点定位精度分析

随着PPP的发展与应用,对PPP误差源的研究更加精细、更加科学。电离层折射是高精度PPP的主要误差之一,国内外通用方法是用大气传播理论建立电离层修正模型。本文主要探讨了电离层对精密单点定位影响的基本理论,总结了目前常用方法;研究了Klobuchar模型的改正公式及计算方法;系统地研究了双频观测值建立消电离层延迟模型的理论和方法。使用相同时段的观测数据,将广播星历、Klobuchar模型和双频观测值改正消电离层模型的结果进行比较,发现用GPS双频观测值建立的消电离层模型的精度明显优于广播星历及Klobuchar模型。