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.     

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。     

单频到五频多系统GNSS精密单点定位参数估计与应用

全球导航卫星系统(GNSS)已发展至多频多系统时代,特别以我国北斗卫星导航系统(BDS)为代表的四大全球导航卫星系统可全天时、全天候播发十几个频率的伪距、相位和多普勒等观测信息。多频多系统GNSS为用户提供更多的观测数据和组合选择,为精密定位、导航和授时(PNT)应用带来了新的机遇,如高精度位置服务、大地测量、空间天气和灾害监测等。但多频多系统GNSS观测为精密单点定位(PPP)组合模型和系统偏差及大气延迟估计等带来诸多问题和挑战。本文给出了单频到五频多系统GNSS精密单点定位(PPP)模型,估计和评估了单频到五频多系统GNSS PPP定位精度、接收机钟差、对流层延迟、卫星和接收机硬件延迟,以及频间偏差。给出了GNSS PPP最新应用进展,包括GNSS气象学、电离层模拟、时间频率传递、建筑物安全和地震监测及其应用。结果表明,多频多系统极大地提高了GNSS PPP参数估计的精度和可靠性,具有重要的应用价值。最后给出了多频多系统GNSS PPP应用前景与展望。     

伽利略卫星导航系统信号质量及定位性能分析

伽利略系统(Galileo)是全球四大卫星导航系统之一,目前已初步具备全球定位能力。研究Galileo的信号质量和双／三频定位性能不仅对Galileo系统应用具有重要价值,对多全球卫星导航系统（GNSS）融合定位也有重要促进作用。在使用基准站网(MGEX)地面跟踪站的基础上,分析了伽利略信号的载噪比、多路径、以及双／三频精密单点定位(PPP)的定位精度。结果表明,Galileo与GPS相比,载噪比E5> E5a≈E5b≈L5>E1≈L1>L2,多路径误差E5      

Mitigating the impact of ionospheric cycle slips in GNSS observations

Processing of data from global navigation satellite systems (GNSS), such as GPS, GLONASS and Galileo, can be considerably impeded by disturbances in the ionosphere. Cycle-slip detection and correction thus becomes a crucial component of robust software. Still, dealing with ionospheric cycle slips is not trivial due to scintillation effects in both the phase and the amplitude of the signals. In this contribution, a geometry-based approach with rigorous handling of the ionosphere is presented. A detailed analysis of the cycle-slip correction process is also tackled by examining its dependence on phase and code noise, non-dispersive effects and, of course, the ionosphere. The importance of stochastic modeling in validating the integer cycle-slip candidates is emphasized and illustrated through simulations. By examining the relationship between ionospheric bias and ionospheric constraint, it is shown that there is a limit in the magnitude of ionospheric delay variation that can be handled by the cycle-slip correction process. Those concepts are applied to GNSS data collected by stations in northern Canada, and show that enhanced cycle-slip detection can lead to decimeter-level improvements in the accuracy of kinematic PPP solutions with a 30-s sampling interval. Cycle-slip correction associated with ionospheric delay variations exceeding 50 cm is also demonstrated, although there are risks with such a procedure and these are pointed out.     

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。     

GNSS基本服务性能评估

针对现有全球卫星导航系统性能评估无规范的评估标准问题,该文提出了以统一模型和算法为评估体系的方法,较详细的评估了全球卫星导航系统公开服务信号的基本性能,主要评估了空间信号误差、广播电离层模型改正效率及伪距单点定位精度等。结果表明:空间信号误差方面,伽利略最优、GPS和北斗三号相当;广播电离层模型方面,北斗全球广播电离层模型改正效果最优,GPSK8与NeQuick模型在低中纬度改正效果相当,北斗区域电离层模型在其服务区内具有较高改正效果;定位方面,北斗、GPS和伽利略静态伪距单点定位的三维位置均方根误差优于5m,格洛纳斯优于10 m;动态伪距单点定位方面,北斗在中国境内定位精度最高;基于统一评估体系下,可以直观对比得到目前各卫星导航系统的性能差异,同时也为后续的建设提供相应的参考。     

Comparison of 4D tomographic mapping versus thin-shell approximation for ionospheric delay corrections for single-frequency GPS receivers over North America

The majority of navigation satellite receivers operate on a single frequency. They compensate for the ionospheric delay using either an ionospheric model which typically only corrects for 50% of the delay or a thin-shell map of the ionosphere. A 4D tomographic imaging technique is used to map the free electron density over the full-height of the ionosphere above North America during autumn 2003. The navigation solutions computed using correction based upon the thin-shell and the full-height maps are compared in this paper. The maps are used to calculate the excess propagation delay on the L1 frequency experienced by GPS receivers at selected locations across North America. The excess delay is applied to correct the single-frequency pseudorange observations at each location, and the improvements to the resulting positioning are calculated. It is shown that the thin-shell and full-height maps perform almost as well as a dual-frequency carrier-smoothed benchmark and for most receivers better than the unfiltered dual-frequency benchmark. The full-height corrections perform well and are considerably better than thin-shell corrections under extreme storm conditions.     

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。     

Absolute Positioning with Single-Frequency GPS Receivers

The use of precise post-processed satellite orbits and satellite clock corrections in absolute positioning, using one GPS receiver only, has proven to be an accurate alternative to the more commonly used differential techniques for many applications in georeferencing. The absolute approach is capable of centimeter accuracy when using state-of-the-art, dual-frequency GPS receivers. When using observations from single-frequency receivers, however, the accuracy, especially in height, decreases. The obvious reason for this degradation in accuracy is the effect of unmodeled ionospheric delay. This paper discusses the availability of some empirical ionospheric models that are publicly available and quantifies their usefulness for absolute positioning using single-frequency GPS receivers. The Global Ionospheric Model supplied by International GPS Service (IGS) is the most accurate one and is recommended for absolute positioning using single-frequency GPS receivers. Using high-quality single-frequency observations, a horizontal epoch-to-epoch accuracy of better than 1 m and a vertical accuracy of approximately 1 m is demonstrated. ? 2002 Wiley Periodicals, Inc.     

BeiDou、Galileo、GLONASS、GPS多系统融合精密单点

随着中国BeiDou系统与欧盟Galileo系统的出现以及俄罗斯GLONASS系统的恢复完善,过去单一的GPS导航卫星系统时代已经逐步过渡为多系统并存且相互兼容的全球性卫星导航系统(multi-constellation global navigation satellite systems,multi-GNSS)时代,多系统GNSS融合精密定位将成为未来GNSS精密定位技术的发展趋势。本文采用GPS、GLONASS、BeiDou、Galileo 4大卫星导航定位系统融合的精密单点定位(precise point positioning,PPP)实测数据,初步研究并分析了4系统融合PPP的定位性能。试验结果表明:在单系统观测几何构型不理想的区域,多系统融合能显著提高PPP的定位精度和收敛速度。4大系统融合的PPP收敛速度相对于单GNSS可提高30%~50%,定位精度可提高10%~30%,特别是对高程方向的贡献更为明显。此外,在卫星截止高度角大于30°的观测环境下,单系统由于可见卫星数不足导致无法连续定位,而多系统融合仍然可以获得PPP定位结果,尤其是水平方向具有较高的定位精度。这对于山区、城市以及遮挡严重的区域具有非常重要的应用价值。     

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.     

四大GNSS广播星历精度评估与对比分析

分析了 目前广播星历精度评估中存在的问题,详细论述了广播星历精度评估过程中对精密星历进行天线相位中心改正的取值方法,提出了利用单颗星单日钟差均值作二次差对广播星历钟差的系统性偏差进行改正的方法.选取2019-09-01-2019-11-01 共计62天的多模 GNSS 实验(multi-GNSS experiment,...     

同时估计电离层延迟的单频精密单点定位方法

提出一种基于单频码和相位观测量的单频精密单点定位方法,将每个观测量的电离层延迟量与接收机钟差、对流层天顶延迟、接收机位置、相位模糊度一起作为未知参数。采用约化参数的平方根信息滤波与平滑算法进行参数解算。该方法适用于实时定位和事后处理,且不需要外部的电离层模型。采用全球分布的32个IGS监测站16 d实测数据进行静态解算试验,结果表明E、N、U方向的RMS分别为0.023 m、0.018 m、0.059 m;基于一组机载GPS数据进行动态解算试验,得到E、N、U方向的RMS(与载波相位动态相对定位结果比较)分别为0.168 m、0.151 m、0.172 m。     

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)、...     

亚太地区BDS-3/GNSS组合系统单频单点定位性能分析

针对北斗三号卫星导航系统(BDS-3)向全球提供定位、导航和授时(PNT)服务后的定位性能评估问题,基于MGEX (Multi-GNSS Experiment) WHU2站7天实测数据,从可视卫星数、几何精度衰减因子(GDOP)、定位精度、定位成功率和伪距残差方面分析了BDS-3及BDS/GNSS组合伪距单点定位(SPP)性能. 结果表明:在亚太地区,BDS-3具有比美国的GPS、俄罗斯的GLONASS、欧洲的Galileo更优的SPP性能,其水平、垂直和三维精度分别为1.19 m、2.34 m、2.38 m,三维精度比北斗二号卫星导航系统(BDS-2)、GPS、GLONASS和Galileo 的SPP精度分别提升了54.8%、27.2%、86.4%和1.2%. 此外,BDS/GPS/Galileo组合能获得最优的SPP精度,其水平、垂直和三维精度分别为0.96 m、1.66 m、1.77 m,相较于BDS-2/BDS-3 SPP分别提升了18.6%、19.4%和17.3%.      

BDS/Galileo四频精密单点定位模型性能分析与比较

北斗卫星导航系统和Galileo卫星系统都可以提供4个频率信号上的服务。本文通过与双频无电离层模型（DF）比较,评估分析了4种BDS/Galileo四频PPP模型性能,即四频无电离层双组合模型（QF1）、四频无电离层组合模型（QF2）、四频非差非组合模型（QF3）和附加电离层约束四频非差非组合模型（QF4）,同时通过等价性原则理论上证明了QF1、QF2、QF3模型的等价性。此外,用1个月参考站的静态数据和1组动态数据分析了四频静态,仿动态和动态PPP性能。试验结果表明,BDS-3 B1C和B2a新频点伪距噪声要略大于B1I和B3I信号,Galileo卫星4个频率上的伪距噪声相差并不明显。对于静态和仿动态PPP模型,QF1、QF2和QF3模型定位性能基本上一致。通过附加外部电离层约束,四频PPP模型性能受到影响,BDS（BDS-2+BDS-3）静态QF4模型相比于QF1、QF2和QF3模型平均收敛时间分别减少了4.4%、4.4%和5.4%,Galileo静态Q4模型平均收敛时间相比于Q3模型增加了16.8 min。对于动态PPP,四频PPP模型相比于双频PPP性能得到提升显著,相比于QF1模型,BDS和Galileo单系统QF4模型三维定位精度分别提高了11.4%和31.4%。BDS/Galileo双系统PPP性能要优于单系统PPP。     

GNSS广播星历轨道和钟差精度分析

为了对多个全球导航卫星系统（global navigation satellite system, GNSS）当前的广播星历精度进行一个全面的分析,对比了2014—2018年共5 a的GNSS广播星历与精密星历,并对全球定位系统（global positioning system, GPS）、格洛纳斯卫星导航系统（global navigation satellite system, GLONASS）、伽利略卫星导航系统（Galileo satellite navigation system, Galileo）、北斗卫星导航系统（BeiDou navigation satellite system, BDS）、准天顶卫星系统（quasi-zenith satellite system, QZSS）等5个系统的广播星历长期精度变化进行了分析。结果表明:5 a中GPS的广播星历轨道及钟差精度最稳定;GLONASS的广播星历轨道精度稳定性较好,但其钟差精度存在较大的离散度;Galileo得益于具备全面运行能力（full operational capability, FOC）卫星的大量发射及运行,其广播星历轨道、钟差精度大幅度变好,切向轨道、法向轨道与钟差精度已赶超GPS;BDS的广播星历轨道精度离散度较大,钟差精度出现不稳定现象;QZSS的广播星历轨道与钟差精度的稳定性与离散度相对最差。以2018年1 a的广播星历与精密星历为例分析了各个系统当前的广播星历精度,结果表明,当前GPS、GLONASS、Galileo、BDS、QZSS的考虑轨道误差与钟差误差贡献的空间信号测距误差（signal-in-space ranging error,SISRE）分别为0.806 m、2.704 m、0.320 m、1.457 m、1.645 m,表明Galileo广播星历整体精度最高,GPS次之,其次分别是BDS、QZSS和GLONASS。只考虑轨道误差贡献的SISRE分别为0.167 m、0.541 m、0.229 m、0.804 m、0.675 m,表明GPS广播星历轨道精度最高,其次分别是Galileo、GLONASS、QZSS和BDS。GPS卫星广播星历中新型号卫星的钟差精度总体要优于旧型号卫星。     

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