45°(N)纬度带的Klobuchar like电离层延迟季节修正模型与评估

电离层延迟是全球卫星导航系统（GNSS）的主要误差源之一。对于装配GNSS单频接收机的航空器,选择简单有效的Klobuchar广播电离层模型来改正电离层延迟误差,其修正率为50%～60%。针对45°（N）纬度带,提出了更高电离层修正需求。考虑到季节因素对中高纬度地区电离层的显著影响,利用GIMs（Global Ionospheric Maps）分析了昼夜中TEC（Total Electron Content）的峰值和谷值随季节（年积日）的变化,建立了一种适用于45°（N）纬度带的Klobuchar like电离层模型。该模型不增加广播模型系数,新模型的夜间和VTEC高峰时电离层修正率分别达到了82%和80%,表明在穿刺点集中的45°(N)纬度地区使用该模型可以更精确地描述该地区的电离层,帮助航空器实现更高精度的定位。     

Klobuchar电离层模型误差分析及预测

电离层延迟误差是全球导航卫星系统（global navigation satellite system，GNSS）中的重要误差源之一。目前在电离层延迟改正模型中，应用最广泛的是Klobuchar参数模型，但是该模型的改正率仅能达到60%左右，无法满足日益增长的精度需求。将国际GNSS监测评估系统（international GNSS monitoring & assessment system，iGMAS）发布的高精度电离层格网数据作为对照，对Klobuchar电离层模型误差进行计算和分析，结果发现在中纬度区域误差存在明显的周期性特征。为进一步提高Klobuchar电离层模型在中纬度区域的改正精度，建立了基于粒子群优化反向传播（back propagation，BP）神经网络的Klobuchar电离层误差预测模型,并以2019年10月的采样数据为例进行误差预测。结果表明，用该模型对中纬度区域电离层延迟提供误差补偿，可将精度提高到90%左右。     

Galileo卫星导航系统广播Nequick模型及其参数拟合

提出了基于IGRF模型的Galileo广播Nequick模型及其参数拟合算法, 解决了Galileo信号仿真中地理场景映射与地磁坐标下的电离层延时修正参数拟合问题. 应用IGRF模型, 可计算出任意给定位置和时间点的地磁参数以及E层、 F₁层、F₂层的电子密度, 从而计算出Galileo电离层修正参数. 仿真结果表明, 该算法拟合的全球电离层延时与IGS提供的实际观测值基本一致, 仿真精度高于一般的经验电离层模型, 实现了Galileo卫星信号的电离层延时修正参数的精确仿真.      

基于空间统计方法的电离层折射修正技术

针对中国上空电离层所具有的特殊性和GPS观测站在中国西部分布相对稀疏的特点, 尝试探索中国卫星增强系统电离层时延信息修正技术, 为卫星导航定位以及遥感、遥测等空间应用工程的电波修正提供数据. 利用中国地壳形变监测网提供的双频GPS数据, 以空间统计方法为主要工具, 给出了普通Kriging电离层估计算法, 构建了平静期和磁暴期电离层理论变异模型, 详细分析了电离层折射修正的精度. 结果表明, 将空间统计方法应用于卫星增强系统中的电离层时延改正问题, 有利于提高增强系统的电离层折射修正精度, 特别是在观测样点相对较少的情况下, 有利于系统完整性的实现.      

北斗区域Klobuchar改进模型及其修正精度分析

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,由于此模型从亚洲地区应用角度考虑,在某一特定区域的修正精度甚至不足50%。为进一步提高区域电离层延迟修正精度,提出在原模型8个改正参数的基础上增加5个关键参数的Klobuchar改进模型,并采用松弛迭代与直线搜索法中的黄金分割相结合的算法对新增参数进行求解。以天津及其附近区域为例,利用GPStation6接收机采集到的实测数据对改进模型与原模型进行计算。将国际全球导航卫星系统服务组织（International GNSS Service,IGS）发布的全球电离层格网数据作为参考值,对比分析改进模型与原模型的修正精度。结果表明,区域Klobuchar改进模型在天津及其附近区域的电离层延迟平均修正精度比原模型提升了10.46%,平均修正精度达到77.51%。     

南极GPS定位中的电离层延迟分析

基于南极地区国际GNSS服务组织(IGS,International GNSS Service)跟踪站的全球定位系统(GPS,Global Position System)双频实测数据,分析了南极地区电离层延迟的变化情况及其二阶项延迟对南极GPS定位结果的影响.结果表明:南极地区的总电子含量(TEC,Total Electron Content)日间波动频繁,其日间TEC最大值变化较中纬度地区剧烈;在南极地区夏季,电离层二阶项延迟对GPS定位结果的影响可达cm级.同时,由于欧洲定轨中心(CODE,The European Center for Orbit Determination)提供的全球电离层模型(GIM,Global Ionosphere Maps)在南极区域应用的局限性,通过选取南极地区6个IGS跟踪站作为基准站建立了区域电离层TEC模型(RIM,Regional Ionosphere Model).经实测数据计算证明,对于南极地区,RIM的定位精度在一定程度上优于全球电离层模型GIM.     

北斗三号电离层模型性能分析

根据北斗卫星导航系统三步走战略，北斗三号系统空中星座在2020年左右完成部署，信号的覆盖范围从亚太大部分地区扩展至全球.实际上自2018年底北斗三号系统已经可以初步提供全球服务.相应地，北斗系统的单频电离层模型从只适用于亚太大部分地区的BDSKlob模型发展到适用于全球范围的BDGIM模型.为分析北斗三号电离层模型的性能，以IGS GIM最终数据为参考，比较了2019年3月1-31日期间北斗BDGIM模型、BDSKlob模型以及GPSKlob模型在不同时段不同地区的改正效果.结果表明:北斗三号BDGIM模型在中国区域的改正率达75%以上，优于BDSKlob模型59%的改正率；在全球范围的改正率达60%，优于GPSKlob模型49%的改正率.除南半球高纬度地区外，BDGIM模型的电离层误差值均小于GPSKlob模型，其在垂直方向的电离层均方根误差值优于6TECU.      

Klobuchar模型的实用分析与改进

电离层延迟误差是无线电信号传播中不可忽视的误差源.GPS特许用户利用双频接收机的双频观测值直接对电离层延迟进行实时测定,其所得结果精度很高.多数普通用户所使用的单频接收机依靠电离层模型对其进行误差修正,效果不很理想.本文通过WUHN观测站双频接收机10天的实测数据对GPS广播星历采用的Klobuchar模型进行了验证,其结果与前人论述相一致.此外,经由反映太阳活动强度的太阳相对黑子数对Klobuchar模型提出了新的改进方法.实验数据结果表明,该方法对此模型修正效果有大幅提升,对原模型修正效果>50%的修正率由60%左右提升至85%以上,>80%的修正率由10%左右提升至40%以上.在实际应用中单频接收机用户可以参考本文改进方法对Klobuchar模型进行修正.      

一种基于系数择优的低阶球谐电离层延迟改正模型

针对单频接收机的电离层延迟改正问题, 提出了一种基于系数择优的低阶球谐电离层延迟改正模型. 按照电离层延迟改正模型参数择优问题的描述, 明确参数优化的目标和约束条件, 根据参数选择可编码的特点, 提出了利用遗传算法进行参数择优的方法及步骤. 以欧洲定轨中心(CODE)提供的电离层数据作为参考标准, 对参数择优模型、 低阶球谐模型和Klobuchar模型模拟的区域电离层VTEC精度进行了比较分析. 结果表明, 较之相同系数个数的低阶球谐模型, 参数择优模型精度平均改进了1～2TECU, 而且比Klobuchar模型及低阶球谐模型能更好地反映电离层的周日变化及纬度变化特征.      

WAAS系统中电离层折射校正的新方法及计算结果

电离层介质的色散性是影响电磁波信号进行卫星导航定位精度的重要因素之一.配合北斗二代分系绩研制任务,提出了一种新的电离层折射校正算法,并利用2000年7月1日到3日的双频GPS观测数据对6个用户站进行试算,进一步将试算所得均方根误差和电离层网格算法得到的误差进行比较.结果表明,对于中纬区域的用户站,估算的TEC误差约为0.5 m左右;而低纬用户误差相对增大,为1 m左右.文中给出的算法与电离层网格模型所提供的精度相差不多,在未来中国自主的卫星增强系统中采用新方法进行电离层进行修正是可行的及有效的.      

Refinement of global ionospheric coefficients for GNSS applications: Methodology and results

We developed the methodology for the optimal estimation of global ionospheric coefficients of the current Global Navigation Satellite Systems (GNSSs), including the eight- and ten-parameter Klobuchar-like as well as NeQuick models. The ionospheric coefficients of those correction models are calculated from two sets of globally distributed tracking stations of the International GNSS Services (IGS). Performance of the re-estimated Klobuchar-like and NeQuick coefficients are validated during 2002–2014 over the continental and oceanic areas, respectively. Over the continental areas, GPS TECs derived from 40 ground GPS receivers are selected as reference. The eight-, ten-parameter Klobuchar-like and NeQuick models can mitigate the ionospheric delay by 65.8, 67.3 and 75.0%, respectively. Over the global oceans, the independent TECs derived from Jason-1&2 altimeters are used as reference. The re-estimated ionospheric correction models can mitigate 56.1–66.7% of the delay errors. Compared to the original GPS Ionospheric Correction Algorithm (ICA), performance of those eight-, ten-parameter Klobuchar-like and NeQuick models has improved 3.4, 5.9 and 13.4% during the whole test period, respectively. The methodology developed here takes the advantage of high-quality ionospheric TECs derived from the global network of GNSS receivers. The re-estimated ionospheric coefficients can be used as precise ionospheric products to monitor and assess GNSS broadcast ionospheric parameters and to improve the performance of various single-frequency GNSS applications.     

GNSS single frequency ionospheric range delay corrections: NeQuick data ingestion technique

A study of the performance of the NeQuick model and the Klobuchar model for GNSS single frequency range delay correction on a global scale was done using data for moderate solar activity. In this study NeQuick was used in the way intended for Galileo. This study is to assess the performance of the two models at each ionospheric geographic region during moderate solar activity as previously published studies were concentrated only on high solar activity. The results obtained showed that NeQuick outperformed Klobuchar for the whole year at the three geographical regions of the ionosphere. In terms of monthly root mean square of mismodeling, NeQuick outperformed Klobuchar by 15 TECU or more at low-latitudes, 5 TEC or more at mid-latitudes, and 1 TECU or more at high-latitudes.     

Evaluation of COMPASS ionospheric model in GNSS positioning

As important products of GNSS navigation message, ionospheric delay model parameters are broadcasted for single-frequency users to improve their positioning accuracy. GPS provides daily Klobuchar ionospheric model parameters based on geomagnetic reference frame, while the regional satellite navigation system of China’s COMPASS broadcasts an eight-parameter ionospheric model, COMPASS Ionospheric Model(CIM), which was generated by processing data from continuous monitoring stations, with updating the parameters every 2 h. To evaluate its performance, CIM predictions are compared to ionospheric delay measurements, along with GPS positioning accuracy comparisons. Real observed data analysis indicates that CIM provides higher correction precision in middle-latitude regions, but relatively lower correction precision for low-latitude regions where the ionosphere has much higher variability. CIM errors for some users show a common bias for in-coming COMPASS signals from different satellites, and hence ionospheric model errors are somehow translated into the receivers’ clock error estimation. In addition, the CIM from the China regional monitoring network are further evaluated for global ionospheric corrections. Results show that in the Northern Hemisphere areas including Asia, Europe and North America, the three-dimensional positioning accuracy using the CIM for ionospheric delay corrections is improved by 7.8%–35.3% when compared to GPS single-frequency positioning ionospheric delay corrections using the Klobuchar model. However, the positioning accuracy in the Southern Hemisphere is degraded due apparently to the lack of monitoring stations there.     

NeQuick G model based scale factor determination for using SBAS ionosphere corrections at low earth orbit

A space-based augmentation system (SBAS) provides real-time correction data for global navigation satellite system (GNSS) users near ground. In order to use the SBAS ionosphere correction for low Earth orbit (LEO) satellites, the correction should be scaled down for the LEO altitude. This scale factor varies with ionosphere distribution and it is hard to determine the value at LEO in real time. We propose a real-time scale factor determination method by using Galileo GNSS’s NeQuick G model. A LEO satellite GPS data and SBAS data received on ground were used to evaluate the performance of the NeQuick G derived variable scale factor. The NeQuick G derived scale factor shows a significant accuracy improvement over NeQuick G model or pre-determined constant scale factor. It improves a vertical positioning accuracy of the LEO satellite. The error mean reductions of the vertical positioning over NeQuick G and the constant scale factor are 31.5% and 11.7%, respectively.     

Ionospheric climate index as a driving parameter for the NeQuick model

Ionospheric delay is one of the significant error sources for global navigation satellite system (GNSS) positioning. GNSSs broadcast the coefficients of the ionospheric model to correct ionospheric delay for single-frequency users. A modified three-dimensional model (NeQuick G) based on the NeQuick climatological model is adopted for Galileo users. The NeQuick G model uses the effective ionization level (Az) instead of the sunspot number as the driving parameter. In this study, we introduce the ionospheric climate index (ICI) as a new driving parameter for the NeQuick model. In comparison, the ICI-driven NeQuick model has a better performance than the Az-driven NeQuick G model at both low and high latitudes. In addition, only one GNSS station at low latitudes is required to calculate the ICI, which would save maintenance costs and improve the efficiency of updating the broadcast coefficients. This model has potential application value for future upgrades of Galileo’s ionospheric broadcast model.     

基于NTCM-BC模型的全球卫星导航系统单频电离层延迟修正

选择NTCM-BC模型作为单频电离层延迟修正模型,通过非线性最小二乘拟合的方法,利用提前一天预测的电离层图（COPG文件）,计算得到NTCM-BC模型修正系数;利用Klobuchar模型和IGS发布的GIM数据对NTCM-BC模型进行比较和分析.对太阳活动高、中、低年实测数据的分析结果表明:全球平均水平上,NTCM-BC模型的电离层延迟修正性能明显优于Klobuchar模型,NTCM-BC模型的TEC平均误差和均方根误差比Klobuchar模型分别下降了41%和30%;模型的TEC计算误差与太阳活动剧烈程度成正相关,即太阳活动高年模型误差较大,太阳活动低年误差相对较低.相较于磁静日,磁扰日期间Klobuchar模型和NCTM模型的误差均有一定程度的增加.此外,模型的电离层修正误差同时存在明显的纬度、季节和地方时差异.      

An improved approach to model regional ionosphere and accelerate convergence for precise point positioning

Given the severe effects of the ionosphere on global navigation satellite system (GNSS) signals, single-frequency (SF) precise point positioning (PPP) users can only achieve decimeter-level positioning results. Ionosphere-free combinations can eliminate the majority of ionospheric delay, but increase observation noise and slow down dual-frequency (DF) PPP convergence. In this paper, we develop a regional ionosphere modeling and rapid convergence approach to improve SF PPP (SFPPP) accuracy and accelerate DF PPP (DFPPP) convergence speed. Instead of area model, ionospheric delay is modeled for each satellite to be used as a priori correction. With the ionospheric, wide-lane uncalibrated phase delay (UPD) and residuals satellite DCBs product, the wide-lane observations for DF users change to be high-precision pseudorange observations. The validation of a continuously operating reference station (CORS) network was analyzed. The experimental results confirm that the approach considerably improves the accuracy of SFPPP. For DF users, convergence time is substantially reduced.     

The multi-source data fusion global ionospheric modeling software—IonoGim

We introduce a new global ionospheric modeling software—IonoGim, using ground-based GNSS data, the altimetry satellite and LEO (Low Earth Orbit) occultation data to establish the global ionospheric model. The software is programmed by C++ with fast computing speed and highly automatic degree, it is especially suitable for automatic ionosphere modeling. The global ionospheric model and DCBs obtained from IonoGim were compared with the CODE (Center for Orbit Determination in Europe) to verify its accuracy and reliability. The results show that IonoGim and CODE have good agreement with small difference, indicating that IonoGim owns high accuracy and reliability, and can be fully applicable for high-precision ionospheric research. In addition, through comparison between only using ground-based GNSS observations and multi-source data model, it can be demonstrated that the space-based ionospheric data effectively improve the model precision in marine areas where the ground-based GNSS tracking station lacks.     

Using TensorFlow-based Neural Network to estimate GNSS single frequency ionospheric delay (IONONet)

In the last 20?years, and in particular in the last decade, the availability of propagation data for GNSS has increased substantially. In this sense, the ionosphere has been sounded with a large number of receivers that provide an enormous amount of ionospheric data. Moreover, the maturity of the models has also been increased in the same period of time. As an example, IGS has ionospheric maps from GNSS data back to 1998, which would allow for the correlation of these data with other quantities relevant for the user and space weather (such as Solar Flux and Kp). These large datasets would account for almost half a billion points to be analyzed. With the advent and explosion of Big Data algorithms to analyze large databases and find correlations with different kinds of data, and the availability of open source code libraries (for example, the TensorFlow libraries from Google that are used in this paper), the possibility of merging these two worlds has been widely opened. In this paper, a proof of concept for a single frequency correction algorithm based in GNSS GIM vTEC and Fully Connected Neural Networks is provided. Different Neural Network architectures have been tested, including shallow (one hidden layer) and deep (up to five hidden layers) Neural Network models. The error in training data of such models ranges from 50% to 1% depending on the architecture used. Moreover, it is shown that by adjusting a Neural Network with data from 2005 to 2009 but tested with data from 2016 to 2017, Neural Network models could be suitable for the forecast of vTEC for single frequency users. The results indicate that this kind of model can be used in combination with the Galileo Signal-in-Space (SiS) NeQuick G parameters. This combination provides a broadcast model with equivalent performances to NeQuick G and better than GPS ICA for the years 2016 and 2017, showing a 3D position Root Mean Squared (RMS) error of approximately 2?m.