北斗电离层模型改正精度分析

电离层误差是影响单频用户机定位精度的主要误差源。卫星导航系统播发电离层模型改正参数供用户使用,模型改正精度会对定位结果产生直接影响。北斗卫星导航系统根据连续监测站实测数据,计算并发播地理坐标系下8参数Klobuchar电离层模型参数,且每2 h更新一次。为了科学评估北斗电离层模型改正效果,文中基于北斗最新观测数据,首先,以CODE提供的GIM模型作为比对基准,详细分析了不同纬度地区、不同时间段内的电离层模型改正精度;其次,分别按照以下定位模式进行计算:1)北斗单频不加电离层改正,2)北斗单频+北斗K8模型,3)北斗单频+GPS K8模型,并分析了电离层改正残差对定位结果影响大小。结果表明,北斗电离层模型改正精度在北半球优于南半球,中纬度地区改正效果最好,其改正残差RMS均值在0.6 m左右,往低纬和高纬度地区呈递减趋势;北京地区北斗单频+北斗K8模型定位精度优于GPS K8模型。     

北斗卫星导航系统Klobuchar模型精度评估

目前,我国北斗卫星导航系统已完成星座区域组网,系统每2h提供一组电离层延迟Klobuchar模型参数。利用欧洲定轨中心(CODE)的高精度电离层格网数据作为参考,对北斗卫星导航系统电离层参数性能进行了精度评估分析,并进行了定位分析。数据表明,其修正精度一般在70%以上,北半球的修正误差在1.5m左右,而南半球的修正误差在3.5m左右;在北半球中纬度地区的修正精度比高纬度、低纬度地区高;北斗单频伪距定位采用北斗Klobuchar模型在平面上的精度为3m左右,高程上为7m左右,与采用GPS的Klobuchar模型相比较,定位精度提高了约10%,高程方向尤为明显。     

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。     

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。     

不同电离层映射函数对导航精度的影响分析

介绍广播星历映射函数、投影映射函数、几何映射函数和椭球映射函数4种不同的电离层映射函数,基于Klobuchar电离层模型分析不同电离层映射函数对导航精度的影响。结果表明,不同电离层映射函数对导航精度的影响在厘米级到分米级;在不同太阳活动期,椭球映射函数和几何映射函数对导航精度影响基本相同;在太阳活动活跃期,导航精度由高到低依次为几何映射函数、投影映射函数、广播星历映射函数;在太阳活动平稳期,导航精度由高到低依次为广播星历映射函数、投影映射函数、几何映射函数。建议在导航定位中,电离层映射函数在太阳活动活跃期时采用几何映射函数,在太阳活动低谷期时采用广播星历映射函数。     

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。     

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。     

NeQuick模型算法研究及性能比较

研究了NeQuick2算法改进及其实现方法,从不同角度分析了NeQuick2模型在全球区域和中国区域内的性能优势。一个太阳活动周期内,中国区域NeQuick2模型计算的电子总含量（total electron content,TEC）比NeQuick1模型精度有显著提升,改正精度与太阳活动水平具有较强的相关性,低年比高年的改善效果更为显著。以全球电离层数据（global ionosphere maps,GIM）为参考标准,中国中高纬区域太阳活动低年NeQuick2模型TEC的系统年平均偏差减少了76%,年平均均方根（root mean square,RMS）值减少了约72%。太阳活动高年NeQuick2模型TEC的系统年平均偏差减少了38%,平均RMS减少了13%左右,且中高纬区域改正精度优于低纬区域11%~13%。全球区域太阳活动峰值期间NeQuick2模型TEC比NeQuick1模型日平均偏差改善了25%,日平均RMS改善了30%左右。分别用NeQuick1和NeQuick2模型得出F₂层顶部区域在太阳活动峰值期电子密度随高度剖面分布,顶部电子密度剖面精度改善近40%。最后分别得出了两个模型中国区域中高纬地区E和F₁层区域在100 km、150 km和200 km高度的电子密度分布图,结果显示NeQuick2模型改善了电子密度分布状况,有效避免了NeQuick1在底部区域电子密度梯度不连续以及电离层异常结构的情况。     

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%。     

常用电离层模型对单点定位精度的影响分析

电离层延迟是限制GNSS定位精度的主要误差源之一,采用合理的电离层改正模型能够削弱定位误差。本文对Klobuchar模型、GIM模型以及NTCM-BC模型的原理进行了阐述,并以九峰台站2016-01-07~2016-01-09观测数据为对象,从不同的角度对BDS K8、GPS K8、GIM和NTCM-BC电离层模型对单点定位的精度的改正效果进行了分析。实验结果表明,九峰台站处,GPS K8和BDS K8模型改正后的单点定位误差RMS分别为2.8553m和1.7932m,NTCM-BC模型改正后的单点定位误差RMS为1.7290m,GIM模型改正后的单点定位误差RMS为1.2834m。     

弱电离层组合SPP在极区定位效果分析

研究了Klobuchar电离层改正模型和双频消电离层组合在伪距单点定位中的应用。通过实验验证了Klobuchar模型在极区的不适用性,并从理论上分析了消电离层组合在伪码噪声放大方面的缺点。针对消电离层组合中的不足,将噪声放大视为伪距定位中的主要矛盾。在降低伪距噪声和电离层延迟的不完全消除之间寻求平衡,提出了一种兼顾降噪与电离层改正的双频组合,称之为弱电离层组合。利用南极地区多个IGS跟踪站的多天数据,验证了弱电离层组合伪距单点定位相对于消电离层组合具有更好的定位效果,定位精度普遍可以提高15%~30%。不同测站对应的改善程度不尽相同,接收机内部因素造成的观测质量不佳也会使得定位精度改善不显著。     

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.     

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。     

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。     

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.     

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.