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.     

Ionospheric correction using NTCM driven by GPS Klobuchar coefficients for GNSS applications

Global Navigation Satellite Systems (GNSS) require mitigation of ionospheric propagation errors because the ionospheric range errors might be larger than tens of meters at the zenith direction. Taking advantage of the frequency-dispersive property of ionospheric refractivity, the ionospheric range errors can be mitigated in dual-frequency applications to a great extent by a linear combination of carrier phases or pseudoranges. However, single-frequency GNSS operations require additional ionospheric information to apply signal delay or range error corrections. To aid single-frequency operations, the global positioning system (GPS) broadcasts 8 coefficients as part of the navigation message to drive the ionospheric correction algorithm (ICA) also known as Klobuchar model. We presented here an ionospheric correction algorithm called Neustrelitz TEC model (NTCM) which can be used as complementary to the GPS ICA. Our investigation shows that the NTCM can be driven by Klobuchar model parameters to achieve a significantly better performance than obtained by the mother ICA algorithm. Our research, using post-processed reference total electron content (TEC) data from more than one solar cycle, shows that on average the RMS modeled TEC errors are up to 40% less for the proposed NTCM model compared to the Klobuchar model during high solar activity period, and about 10% less during low solar activity period. Such an approach does not require major technology changes for GPS users rather requires only introducing the NTCM approach a complement to the existing ICA algorithm while maintaining the simplicity of ionospheric range error mitigation with an improved model performance.     

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％      

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。     

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。     

Ionospheric tomography using GNSS: multiplicative algebraic reconstruction technique applied to the area of Brazil

Experimental analysis was performed using multiplicative algebraic reconstruction technique (MART) to map the ionosphere over Brazil. Code and phase observations from the global navigation satellite system (GNSS) together with the international reference ionosphere (IRI) enabled the estimation of ionospheric profiles and total electron content (TEC) over the entire region. Twenty-four days of data collected from existing ground-based GNSS receivers during the recent solar maximum period were used to analyze the performance of the MART algorithm. The results were compared with four ionosondes. It was demonstrated that MART estimated the electron density peak with the same degree of accuracy as the IRI model in regions with appropriate geometrical coverage by GNSS receivers for tomographic reconstruction. In addition, the slant TEC, as estimated with MART, presented lower root-mean-square error than the TEC calculated by ionospheric maps available from the International GNSS Service (IGS). Furthermore, the daily variations of the ionosphere were better represented with the algebraic techniques, compared to the IRI model and IGS maps, enabling a correlation of the elevation of the ionosphere at higher altitudes with the equatorial ionization anomaly intensification. The tomographic representations also enabled the detection of high vertical gradients at the same instants in which ionospheric irregularities were evident.     

Ionospheric error contribution to GNSS single-frequency navigation at the 2014 solar maximum

For single-frequency users of the global satellite navigation system (GNSS), one of the main error contributors is the ionospheric delay, which impacts the received signals. As is well-known, GPS and Galileo transmit global models to correct the ionospheric delay, while the international GNSS service (IGS) computes precise post-process global ionospheric maps (GIM) that are considered reference ionospheres. Moreover, accurate ionospheric maps have been recently introduced, which allow for the fast convergence of the real-time precise point position (PPP) globally. Therefore, testing of the ionospheric models is a key issue for code-based single-frequency users, which constitute the main user segment. Therefore, the testing proposed in this paper is straightforward and uses the PPP modeling applied to single- and dual-frequency code observations worldwide for 2014. The usage of PPP modeling allows us to quantify—for dual-frequency users—the degradation of the navigation solutions caused by noise and multipath with respect to the different ionospheric modeling solutions, and allows us, in turn, to obtain an independent assessment of the ionospheric models. Compared to the dual-frequency solutions, the GPS and Galileo ionospheric models present worse global performance, with horizontal root mean square (RMS) differences of 1.04 and 0.49 m and vertical RMS differences of 0.83 and 0.40 m, respectively. While very precise global ionospheric models can improve the dual-frequency solution globally, resulting in a horizontal RMS difference of 0.60 m and a vertical RMS difference of 0.74 m, they exhibit a strong dependence on the geographical location and ionospheric activity.     

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。     

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。     

一种基于泰勒级数展开的电离层延迟改正模型

针对电离层延迟误差对定位精度的影响,本文将泰勒级数展开应用于电离层延迟的求解过程中,提出了一种基于泰勒级数展开的电离层改正模型（TSE模型）。将该模型与传统的Klobuchar模型和NeQuick模型在VTEC的求解精度和定位精度上进行了对比分析,用IGS网站提供的测量数据,通过仿真试验验证,得出了TSE模型在提高定位精度上具有较好的可行性与时间适应性的结论。     

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.     

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)、...     

The activities of the Ionosphere Working Group of the International GPS Service (IGS)

This article is based on a position paper presented at the IGS Network, Data and Analysis Center Workshop 2002 in Ottawa, Canada, 8–11 April 2002, and introduces the IGS Ionosphere Working Group (Iono_WG). Detailed information about the IGS in general can be found on the IGS Central Bureau Web page: http://igscb.jpl.nasa.gov. The Iono_WG commenced working in June 1998. The working group's main activity currently is the routine production of ionosphere Total Electron Content (TEC) maps with a 2-h time resolution and daily sets of GPS satellite and receiver hardware differential code bias (DCB) values. The TEC maps and DCB sets are derived from GPS dual-frequency tracking data recorded with the global IGS tracking network. In the medium- and long-term, the working group intends to refine algorithms for the mapping of ionospheric parameters from GPS measurements and to realize near–real–time availability of IGS ionosphere products. The paper will give an overview of the Iono_WG activities that include a summary of activities since its establishment, achievements and future plans. Electronic Publication     

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。     

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。     

RINEX_HO: second- and third-order ionospheric corrections for RINEX observation files

When GNSS receivers capable of collecting dual-frequency data are available, it is possible to eliminate the first-order ionospheric effect in the data processing through the ionosphere-free linear combination. However, the second- and third-order ionospheric effects still remain. The first-, second- and third-order ionospheric effects are directly proportional to the total electron content (TEC), although the second- and third-order effects are influenced, respectively, by the geomagnetic field and the maximum electron density. In recent years, the international scientific community has given more attention to these kinds of effects and some works have shown that for high precision GNSS positioning these effects have to be taken into consideration. We present a software tool called RINEX_HO that was developed to correct GPS observables for second- and third-order ionosphere effects. RINEX_HO requires as input a RINEX observation file, then computes the second- and third-order ionospheric effects, and applies the corrections to the original GPS observables, creating a corrected RINEX file. The mathematical models implemented to compute these effects are presented, as well as the transformations involving the earth’s magnetic field. The use of TEC from global ionospheric maps and TEC calculated from raw pseudorange measurements or pseudoranges smoothed by phase is also investigated.     

Potentialities of multifrequency ionospheric correction in Global Navigation Satellite Systems

The first-order ionospheric error is reduced in the dual-frequency Global Navigation Satellite Systems (GNSS). In this paper, the possibility of eliminating ionospheric higher-order errors in the multifrequency GNSS is explored. Since the second-order error associated with the geomagnetic field effect on the refractive index can be eliminated in dual-frequency measurements, we explore the possibility of eliminating third-order errors in triple-frequency GNSS in view of phase scintillations. A connection between the possibility of improving the multifrequency GNSS accuracy and diffraction effects in radio signal propagation through the randomly inhomogeneous ionosphere is shown. The numerical simulation has revealed that the systematic, residual ionospheric error is considerably reduced when we pass on from dual-frequency to triple-frequency measurements. The change in the residual error variance during such a transition depends however on the relationship between the inner scale of the turbulent spectrum of ionospheric irregularities and the Fresnel radius. Given the inner scale larger than the Fresnel radius, not only the systematic error, but also the standard deviation reduces when we pass on from dual-frequency to triple-frequency measurements. Otherwise, when the Fresnel radius exceeds the inner scale, the variance increases with increasing number of frequencies in use.     

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.     

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.