Ionosphere modelling for Galileo single frequency users: Illustration of the combination of the NeQuick model and GNSS data ingestion

The ionospheric effect remains one of the main factors limiting the accuracy of Global Navigation Satellite Systems (GNSS) including Galileo. For single frequency users, this contribution to the error budget will be mitigated by an algorithm based on the NeQuick global ionospheric model. This quick-run empirical model provides flexible solutions for combining ionospheric information obtained from various sources, from GNSS to ionosondes and topside sounders. Hence it constitutes an interesting simulation tool not only serving Galileo needs for mitigation of the ionospheric effect but also widening the use of new data.     

GNSS电离层模型改正精度评估与分析

电离层时延误差是导航定位信号在空间传播路径上的主要误差源之一,因此全面了解GNSS电离层模型的改正精度具有一定现实意义.根据GPS,BDS和Galileo系统所采用的电离层修正模型,利用2014年电离层校正参数,以高精度全球电离层图为基准,评估分析了三大系统电离层时延的改正精度.结果表明:目前GNSS使用的几种电离层修正模型的改正率在65~75%左右;Galileo系统使用的第二版NeQuick模型与第一版NeQuick模型相比在修正精度上并无显著提高;GPS使用的Klobuchar 8参数模型在北半球25°-45°N的中纬度地区精度很高,但是在全球其他区域精度较低,分布性较差,而NeQuick模型全球改正率分布则较为平均且平滑.      

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.     

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.     

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。     

NeQuick2 validation using multi-satellite and ground data

Global Navigation Satellite System’s (GNSS) positioning calculation is prone to ionospheric errors. Single frequency GNSS users receive ionospheric corrections through broadcast ionospheric models. Therefore, the accuracy of ionospheric models must be validated based on various geographic and geomagnetic conditions. In this work, an attempt is made to validate NeQuick2 electron density (Ne) using multiple sources of space-based and ground-based data at the Arabian Peninsula and for low solar activity conditions. These sources include space-based data from Swarm, DMSP and COSMIC-2 satellite constellations and ground-based data from GNSS receiver and the ionosonde. The period of this study is 1 year from October 2019 to September 2020. Analysis shows that the agreement between NeQuick2 and experimental Ne close to the peak density height depends on seasons and time of the day with the largest errors found in Autumn and during the daytime. NeQuick2 generally overestimates Ne during the daytime. During the early morning and evening hours, Ne estimates seem to be fairly accurate with slight underestimation in Winter and Spring. Estimation of slab thickness by NeQuick2 is found to be close to the values calculated using collocated ionosonde and GNSS receiver.     

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.     

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.     

Assessment of the NeQuick model at mid-latitudes using GNSS TEC and ionosonde data

The modelling of the total electron content (TEC) plays an important role in global navigation satellite systems (GNSS) accuracy, especially for single-frequency receivers, the most common ones constituting the mass market. For the latter and in the framework of Galileo, the NeQuick model has been chosen for correcting the ionospheric error contribution and will be integrated into a global algorithm providing the users with daily updated information.     

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.      

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。     

实时电离层格网数据精度评估

电离层延迟是制约单频接收机定位精度的重要误差源之一.为提高单频接收机的实时电离层改正精度，需要实时电离层数据.以中国科学院空天信息创新研究院提供的实时电离层数据为例，对比分析不同太阳活动期实时电离层数据及预报电离层数据与IGS最终电离层数据之间的差值以及不同太阳活动期、不同纬度测站的电离层数据对电离层延迟进行改正后得到的定位精度.结果表明:在低太阳活动期和高太阳活动期，实时电离层数据无法很好地反映大部分海洋上空的电离层变化特性；对不同太阳活动期，实时电离层数据在高纬度测站的定位精度优于预报数据和广播模型，在中纬度测站的定位精度略低于预报数据而与广播模型定位精度相当，在低纬度测站的定位精度略优于预报数据和广播模型.      

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.     

Compatibility of Terrestrial Reference Frames used in GNSS broadcast messages during an 8 week period of 2019

The operational Terrestrial Reference Frames (TRFs) realized through the evaluation of broadcast ephemerides for GPS, GLONASS, Galileo, BeiDou-2 and BeiDou-3 have been compared to IGS14, the TRF realized by the International GNSS Service (IGS). The TRFs realized by the GPS, GLONASS, Galileo, and BeiDou-2 and BeiDou-3 broadcast ephemerides are the orbital realizations of WGS 84 (G1762′), PZ90.11, GTRF19v01, and BDCS respectively. These TRFs are compared using up to 56 days of data (21 July-14 Sept 2019) at a 5 or 15-min rate. The operational TRFs are compared to IGS14 in a 7-parameter similarity (Helmert) transformation. Numerical results show that the operational GNSS TRFs differ from IGS14 at a level no greater than 4 cm for Galileo, 6 cm for GPS and BeiDou-3, 13 cm for GLONASS, and 48 cm for a limited set of BeiDou-2 Medium Earth Orbit (MEO) vehicles.     

Examining the use of the NeQuick bottomside and topside parameterizations at high latitudes

An examination of the high latitude performance of the bottomside and topside F-layer parameterizations of the NeQuick electron density model is presented using measurements from high latitude ionosonde and Incoherent Scatter Radar (ISR) facilities.For the bottomside, we present a comparison between modeled and measured B2Bot thickness parameter. In this comparison, it is seen that the use of the NeQuick parameterization at high latitudes results in significantly underestimated bottomside thicknesses, regularly exceeding 50%. We show that these errors can be attributed to two main issues in the NeQuick parameterization:(1) through the relationship relating foF2 and M3000F2 to the maximum derivative of F2 electron density, which is used to derive the bottomside thickness, and (2) through a fundamental inability of a constant thickness parameter, semi-Epstein shape function to fit the curvature of the high latitude F-region electron density profile.For the topside, a comparison is undertaken between the NeQuick topside thickness parameterization, using measured and CCIR-modeled ionospheric parameters, and that derived from fitting the NeQuick topside function to Incoherent Scatter Radar-measured topside electron density profiles. Through this comparison, we show that using CCIR-derived foF2 and M3000F2, used in both the NeQuick and IRI, results in significantly underestimated topside thickness during summer periods, overestimated thickness during winter periods, and an overall tendency to underestimate diurnal, seasonal, and solar cycle variability. These issues see no improvement through the use of measured foF2 and M(3000)F2 values. Such measured parameters result in a tendency for the parametrization to produce a declining trend in topside thickness with increasing solar activity, to produce damped seasonal variations, and to produce significantly overestimated topside thickness during winter periods.     

Ionospheric parameters in the European sector during the magnetic storm of August 25–26, 2018

Variations of ionospheric parameters Total Electron Content (TEC) by GNSS, critical frequency (foF2) by vertical sounding and electron density (Ne) by low-altitude satellite were studied at high, mid and low latitudes of the European sector during the magnetic storm of August 25–26, 2018. During the main phase of the storm the ionospheric F2-layer was under the positive disturbance at mid and low latitudes. Then the transition from the positive to negative ΔfoF2 values occurred at all latitudes. The recovery phase was characterized by negative ionospheric disturbance at all latitudes. This is due to the decrease of thermospheric O/N2 ratio during the recovery phase of the storm. The intense Es layers screened the reflections from the F2-layer on August 26th at high and at low latitudes but at different times. Some blackouts occurred due to the high absorption level at high latitudes. In general, foF2 and TEC data were highly correlated. The major Ne changes were at the low latitudes. In general, Ne data confirmed the ionospheric dynamics revealed with foF2 and TEC.     

Ionospheric correction using GPS Klobuchar coefficients with an empirical night-time delay model

We proposed an ionospheric correction approach called NKlob to mitigate the ionospheric delay errors. NKlob is a modification of the original GPS Ionospheric Correction Algorithm (ICA), which uses an empirical night-time model depending on the time, geomagnetic location and periodicities of the ionospheric behavior to replace the night-time constant delay in GPS ICA. Performance of NKlob was evaluated by the independent total electron contents (TECs) derived from Global Ionospheric Maps (GIMs) of the International GNSS Services (IGS) and Jason-2 altimetry satellite during 2013–2017. Compared to GIM TECs, NKlob corrects 51.5% of the ionospheric delay errors, which outperforms GPS ICA by 6.3%. Compared to Jason-2 TECs, NKlob mitigates the ionospheric errors by 58.1%, which is approximately 3.7% better than that of GPS ICA. NKlob shows significant improvement in low-latitude and equatorial regions with respect to GPS ICA, meanwhile exhibiting comparable performance at middle and high latitudes. Since NKlob only requires slight technical changes at the processing level of GPS receivers, we suppose that it can be easily implemented for better ionospheric delay corrections of real-time GPS single-frequency applications.     

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.     

The ionosphere,radio navigation,and global navigation satellite systems

This article is a review of Global Navigation Satellite Systems (GNSS) for space scientists who are interested in how GNSS signals and observables can be used to understand ionospheric dynamics and, conversely, how ionospheric dynamics affect the operational capabilities of GNSS receivers. The most common form of GNSS is the Global Positioning System (GPS); we will first review its operating principles and then present a discussion of errors, of which ionospheric propagation is the most significant. Methods and systems for mitigating errors will be introduced, along with a discussion of modernization plans for GPS and for entirely new systems such as Galileo. In the second half of this article the effects of the ionosphere on GPS signals will be examined in more detail, particularly ionospheric propagation, leading to a discussion of the relation of TEC to ranging errors. Next, the subject of scintillations will also be introduced and connected to the presence and scale sizes of irregularities. Scintillations will be examined as spatial and temporal structures. The method of measuring scintillation pattern drift and ionospheric velocity will be discussed. We conclude by examining ionospheric effects on GPS at midlatitudes.