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.     

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.     

北斗系统电离层模型参数改正精度分析

本文讨论了电离层垂直电子总含量比较法和单频单点定位法两种电离层模型参数改正精度评估方法,介绍了北斗系统发播的电离层模型参数的使用方法,基于欧州定轨中心提供的全球电离层数据评估北斗系统发播的电离层模型参数精度,分析结果表明：北斗系统发播的Klobuchar电离层模型参数在西安地区的改正比例,白天为80％左右,夜间为75％左右。     

Preliminary analysis of grid ionospheric vertical error for GAGAN

The inverse distance weighted model (IDWM) represents a geo-spatial interpolation technique used for estimation of ionospheric vertical delays at the ionospheric grid points (IGPs) and user ionospheric pierce points (IPPs). The GPS Aided Geo Augmented Navigation (GAGAN) system is planned for air-navigation over the Indian service region using a space based augmentation. One of the main needs for GAGAN is to develop a suitable grid-based ionospheric model for estimating the vertical delay and its error bound, i.e., grid ionospheric vertical error (GIVE) at all the IGPs covering the Indian subcontinent. Dual frequency GPS receiver data obtained from 17 total electron content (TEC) stations are considered in the analysis. For a typical IGP (25°N, 75°E), variations in the GIVE for a few days of quiet ionosphere are presented. For a quiet and magnetically moderate day, the mean and standard deviations of the user IPP (UIPP) estimation error and the mean GIVE are presented using the IDWM with Klobuchar, Junkins and bilinear models.     

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...     

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％      

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。     

北斗不同电离层模型精度分析

目前北斗系统播发多种电离层模型参数,用户使用时容易产生以下问题：①同一历元不同卫星播发同一电离层模型,其值不完全相同;②北斗二号、北斗三号分别播发的Klobuchar电离层模型参数值存在差异;③对于能同时接收到3种电离层模型（BDS-2 Klobuchar、BDS-3 Klobuchar及北斗全球电离层延迟修正模型（BDGIM））的基本导航用户如何选取合适的电离层模型。针对以上问题,本文首先提出采用最大投票法策略,对同一历元相同电离层模型但值不同的参数进行合理合并,然后以IGS分析中心的电离层产品为基准,对以上3种北斗电离层模型进行了精度分析和对比,最后基于等效距离误差进行了验证分析。试验结果表明,BDS-2 Klobuchar、BDS-3 Klobuchar虽然模型值差异较大但模型精度十分接近,而BDGIM模型精度最高,相对于前两者在中低纬地区平均提升10%,在两极地区的提升更加明显,平均提升61%。     

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.     

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.     

利用标准单点定位技术评价电离层模型

针对电离层模型的评价问题,提出了标准单点定位的方法,验证了该方法的可行性,并深入分析了GIM模型/Klobuchar模型在空域、时域上对SPP定位精度的影响。实验结果表明:选择GIM模型或Klobuchar模型,中纬地区SPP定位精度最高,低纬地区最差。与Klobuchar模型相比,高、中、低纬地区选择GIM模型的三维定位精度均有较大幅度提升,最大改进达34.20%;在太阳活跃期、低谷期,GIM模型的三维定位精度也明显高于Klobuchar模型,且活跃期GIM模型相对Klobuchar模型的改进率达20.14%,比低谷期高12.25%。从定位精度看,SPP解算选择GIM模型整体优于采用Klobuchar模型。     

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。     

基于Holt指数平滑模型的Klobuchar模型精化

利用IGS（International GNSS Service）中心提供的中、低纬度地区平静期、活跃期观测数据,通过Klobuchar模型与双频观测模型解算电离层总电子含量（total electron content,TEC）值。采用Holt指数平滑模型对每个历元前6 d两种模型差值进行1 d预测,利用预测所得差值对Klobuchar模型第7 d的TEC值进行改进。实验结果表明,无论在电离层活跃期还是平静期,改进模型改正效果比基本模型有显著提升,改进模型能更好地反映电离层变化特性,尤其是夜间电离层变化特性。     

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。     

北斗全球系统广播电离层模型性能初步评估

北斗三号系统于2017年正式启动建设,将采用新的北斗全球电离层延迟修正模型（BeiDou global ionospheric delay correction model,BDGIM）。使用高精度格网电离层数据和双频实测电离层延迟数据作为参考,对北斗试验卫星系统播发的BDGIM模型精度进行了相应分析和评估,并与北斗Klobuchar和GPS Klobuchar模型精度进行了比较。研究结果表明,在中国区域,BDGIM模型和北斗Klobuchar模型精度相当,优于GPS Klobuchar模型;在全球范围内,BDGIM模型精度优于北斗Klobuchar和GPS Klobuchar模型。采用不同电离层模型进行伪距单频单点定位,并对定位结果进行对比分析,结果显示,使用BDGIM模型比北斗Klobuchar模型的定位精度有13%的提高,比GPS Klobuchar模型有7%~10%的提高。     

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。     

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。     

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。     

区域电离层建模的单频伪距定位验证

针对电离层单层模型无法满足单频用户定位精度要求的问题,该文建立了区域电离层斜路径模型和单星多项式函数模型。基于河北省区域CORS站的实验结果表明:该文建立的区域电离层模型的拟合精度比CODE中心的格网电离层模型提高了近80%。并将其应用于北斗、GPS单频伪距单点定位,得出北斗的单点定位高程和平面定位精度分别优于3和2m,GPS的单点定位高程和平面定位精度分别优于1.5和1m;相对于CODE,GPS和北斗在平面及高程方向的定位精度均提高了50%左右。结果证明,采用斜路径电离层模型和多项式函数模型,可以较好地反映区域电离层的精细结构。