Climatological study of ionospheric irregularities over the European mid-latitude sector with GPS

High-frequency variability of the ionosphere, or irregularities, constitutes the main threat for real-time precise positioning techniques based on Global Navigation Satellite Systems (GNSS) measurements. Indeed, during periods of enhanced ionospheric variability, GNSS users in the field—who cannot verify the integrity of their measurements—will experience positioning errors that can reach several decimeters, while the nominal accuracy of the technique is cm-level. In the frame of this paper, a climatological analysis of irregularities over the European mid-latitude region is presented. Based on a 10 years GPS dataset over Belgium, the work analyzes the occurrence rate (as a function of the solar cycle, season and local time) as well as the amplitude of ionospheric irregularities observed at a single GPS station. The study covers irregularities either due to space weather events (solar origin) or of terrestrial origin. If space weather irregularities are responsible for the largest effects in terms of ionospheric error, their occurrence rate highly depends on solar activity. Indeed, the occurrence rate of ionospheric irregularities is about 9 % during solar maximum, whereas it drops to about 0 % during medium or low solar activity periods. Medium-scale ionospheric disturbances (MSTIDs) occurring during daytime in autumn/winter are the most recurrent pattern of the time series, with yearly proportions slightly varying with the solar cycle and an amplitude of about 10 % of the TEC background. Another recurrent irregularity type, though less frequent than MSTIDs, is the noise-like variability in TEC observed during summer nighttime, under quiet geomagnetic conditions. These summer nighttime irregularities exhibit amplitudes ranging between 8 and 15 % of the TEC background.     

Mitigation of higher order ionospheric effects on GNSS users in Europe

Current dual-frequency GPS measurements can only eliminate the first-order ionospheric term and may cause a higher-order range bias of several centimeters. This research investigates the second-order ionospheric effect for GNSS users in Europe. In comparison to previous studies, the electron density profiles of the ionosphere/plasmasphere are modeled as the sum of three Chapman layers describing electron densities of the ionospheric F₂, F₁ and E layers and a superposed exponential decay function describing the plasmasphere. The International Geomagnetic Reference Field model is used to calculate the geomagnetic field vectors at numerous points along the incoming ray paths. Based on extended simulation studies, we derive a correction formula to compute the average value of the longitudinal component of the earth’s magnetic field along the line-of-sight as a function of geographic latitude and longitude, and geometrical parameters such as elevation and azimuth angles. Using our correction formula in conjunction with the total electron content (TEC) along the line-of-sight, the second-order ionospheric term can be corrected to the millimeter level for a vertical TEC level of 10¹⁸ electrons/m².     

The ionospheric eclipse factor method (IEFM) and its application to determining the ionospheric delay for GPS

A new method for modeling the ionospheric delay using global positioning system (GPS) data is proposed, called the ionospheric eclipse factor method (IEFM). It is based on establishing a concept referred to as the ionospheric eclipse factor (IEF) λ of the ionospheric pierce point (IPP) and the IEF’s influence factor (IFF) . The IEF can be used to make a relatively precise distinction between ionospheric daytime and nighttime, whereas the IFF is advantageous for describing the IEF’s variations with day, month, season and year, associated with seasonal variations of total electron content (TEC) of the ionosphere. By combining λ and with the local time t of IPP, the IEFM has the ability to precisely distinguish between ionospheric daytime and nighttime, as well as efficiently combine them during different seasons or months over a year at the IPP. The IEFM-based ionospheric delay estimates are validated by combining an absolute positioning mode with several ionospheric delay correction models or algorithms, using GPS data at an international Global Navigation Satellite System (GNSS) service (IGS) station (WTZR). Our results indicate that the IEFM may further improve ionospheric delay modeling using GPS data.     

A two-step ionospheric modeling algorithm considering the impact of GLONASS pseudo-range inter-channel biases

The Global Navigation Satellite System presents a plausible and cost-effective way of computing the total electron content (TEC). But TEC estimated value could be seriously affected by the differential code biases (DCB) of frequency-dependent satellites and receivers. Unlike GPS and other satellite systems, GLONASS adopts a frequency-division multiplexing access mode to distinguish different satellites. This strategy leads to different wavelengths and inter-frequency biases (IFBs) for both pseudo-range and carrier phase observations, whose impacts are rarely considered in ionospheric modeling. We obtained observations from four groups of co-stations to analyze the characteristics of the GLONASS receiver P1P2 pseudo-range IFB with a double-difference method. The results showed that the GLONASS P1P2 pseudo-range IFB remained stable for a period of time and could catch up to several meters, which cannot be absorbed by the receiver DCB during ionospheric modeling. Given the characteristics of the GLONASS P1P2 pseudo-range IFB, we proposed a two-step ionosphere modeling method with the priori IFB information. The experimental analysis showed that the new algorithm can effectively eliminate the adverse effects on ionospheric model and hardware delay parameters estimation in different space environments. During high solar activity period, compared to the traditional GPS + GLONASS modeling algorithm, the absolute average deviation of TEC decreased from 2.17 to 2.07 TECu (TEC unit); simultaneously, the average RMS of GPS satellite DCB decreased from 0.225 to 0.219 ns, and the average deviation of GLONASS satellite DCB decreased from 0.253 to 0.113 ns with a great improvement in over 55%.     

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。     

Total electron content processing from GPS observations to facilitate ionospheric modeling

With the increasing global distribution of high rate dual-frequency global positioning system (GPS) receivers, the production of a real-time atmospheric constituent definition, total electron content (TEC), has become a beneficial contributor to the modeling applications used in the assessment of GPS position accuracy and the composition of the ionosphere, plasmasphere, and troposphere. Historically, TEC measurements have been obtained through post processing techniques to produce the quality of data necessary for modeling applications with rigorous error estimate requirements. These procedures necessitated the collection of large volumes of data to address the various abnormalities in the computation of TEC associated with the use of greater data quality controls and source selection while real-time modeling environments must rely on autonomous controls and filtration techniques to prevent the production of erroneous model results. In this paper we present methods for processing TEC in real time, which utilize several procedures including the application of an ionospheric model to automatically perform quality control on the TEC output and the computational techniques used to address receiver multipath, faulty receiver observations, cycle-slips, segmented processing, and receiver calibrations. The resulting TEC measurements are provided with rigorous error estimates validated using the vertical TEC from the Jason satellite mission.

Ionospheric calibration of single frequency VLBI and GPS observations using dual GPS data

Summary The ionospheric effect is one of the main sources of error in Very Long Baseline Interferometry (VLBI) and Global Positioning System (GPS) high precision geodesy. Although the use of two frequencies allows the estimation of this effect, in some cases dual observations are not possible due to the available equipment or the type of observation. This paper presents the ionospheric calibration of single frequency VLBI and GPS observations based on the ionospheric electron content estimated from dual frequency GPS data. The ionospheric delays obtained with this procedure and the VLBI baseline length results have been compared with those obtained with dual frequency data. For the European geodetic VLBI baselines, both solutions agree at the 3–5 parts in 10^–9 level. The noise introduced by the GPS-based calibration is in the order of 3 cm for the VLBI observables and of 10 cm for the GPS observables.     

一种融合测高仪与地面GPS数据的单站电离层反演方法

电离层层析成像技术非常适用于检测电离层电子密度的大尺度空间分布及其扰动。利用地面单站的GPSTEC值和另一站的数字测高仪观测数据,结合国际参考电离层（IRI）,利用MART算法反演得到测站上空电子密度的垂直分布。利用白天和夜间的实测数据进行了CIT反演,结果表明了该方法的可靠性。     

Eye on the Ionosphere: The Correlation between Solar 10.7 cm Radio Flux and Ionospheric Range Delay

Patricia Doherty joins the regular contributors of this column to discuss the correlation between measurements of solar 10.7 cm radio flux and ionospheric range delay effects on GPS. Mrs. Doherty has extensive experience in the analysis of ionospheric range delays from worldwide systems and in the utilization and development of analytical and theoretical models of the Earth's ionosphere. Ionospheric range delay effects on GPS and other satellite ranging systems are directly proportional to the Total Electron Content (TEC) encountered along slant paths from a satellite to a ground location. TEC is a highly variable and complex parameer that is a function of geographic location, local time, season, geomagnetic activity, and solar activity. When insufficiently accounted for, ionospheric TEC can seriously limit the performance of satellite ranging applications. Since the ionosphere is a dispersive medium, dual-frequency Global Positoning System (GPS) users can make automatic corrections for ionospheric range delay by computing the apparent difference in the time delays between the two signals. Single-frequency GPS users must depend on alternate methods to account for the ionospheric range delay. Various models of the ionosphere have been used to provide estimates of ionospheric range delay. These models range from the GPS system's simple eight-coefficient algorithm designed to correct for approximately 50% rms of the TEC, to state-of-the-art models derived from physical first principles, which can correct for up to 70 to 80% rms of the TEC but at a much greater computational cost. In an effort to improve corrections for the day-to-day variability of the ionosphere, some attempts have been made to predict the TEC by using the daily values of solar 10.7 cm radio flux (F_10,7). The purpose of this article is to show that this type of prediction is not useful due to irregular, and sometimes very poor, correlation between daily values of TEC and F_10.7. Long-term measurements of solar radio flux, however, have been shown to be well correlated with monthly mean TEC, as well as with the critical frequency of the inonospheric F2 region (foF2), which is proportional to the electron density at the peak of the ionospheric F2 region. ? 2000 John Wiley & Sons, Inc.     

Estimation and analysis of GPS satellite DCB based on LEO observations

The Global Positioning System (GPS) satellite differential code bias (DCB) should be precisely calibrated when obtaining ionospheric slant total electron content (TEC). So far, it is ground-based GPS observations that have been used to estimate GPS satellite DCB. With the increased Low Earth Orbit (LEO) missions in the near future, the real-time satellite DCB estimation is a crucial factor in real-time LEO GPS data applications. One alternative way is estimating GPS DCB based on the LEO observations themselves, instead of using ground observations. We propose an approach to estimate the satellite DCB based on Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) and Challenging Minisatellite Payload (CHAMP) GPS observations during the years 2002–2012. The results have been validated through comparisons with those issued by Center for Orbit Determination in Europe (CODE). The evaluations indicate that: The approach can estimate satellite DCB in a reasonable way; the DCB estimated based on CHAMP observations is much better than those on COSMIC observations; the accuracy and precision of DCB show a possible dependency on the ionospheric ionization level. This method is significance for the real-time processing of LEO-based GNSS TEC data from the perspective of real-time applications.     

Spherical cap harmonic model for mapping and predicting regional TEC

An approach to modeling the regional ionospheric total electron content (TEC) based on spherical cap harmonic analysis is presented. This approach not only provides a better regional TEC mapping accuracy, but also the capability for ionospheric model prediction based on spectrum analysis and least squares collocation. Unlike conventional approaches, which predict the immediate TEC with models using current observations, the spherical cap harmonic approach utilizes models using past observations to predict a model which will provide future TEC values. A significant advantage in comparison with conventional approaches is that the spherical cap harmonic approach can be used to predict the long-term TEC with reasonable accuracy. This study processes a set of GPS data with an observation time span of 1 year from two GPS networks in China. The TEC mapping accuracy of the spherical cap harmonic model is compared with the polynomial model and the global ionosphere model from IGS. The results show that the spherical cap harmonic model has a better TEC mapping accuracy with smoother residual distributions in both temporal and spatial domains. The TEC prediction with the spherical cap harmonic model has been investigated for both short- and long-term intervals. For the short-term interval, the prediction accuracies for the latencies of 1-day, 2-days, and 3-days are 2.5 TECU, 3.5 TECU, and 4.5 TECU, respectively. For the long-term interval, the prediction accuracy is 4.5 TECU for a 2-month latency.     

利用GPS三频观测值监测电离层TEC及其变化率

三频观测数据为监测电离层总电子含量提供了更多的观测值选择。在双频观测值估算电离层总电子含量的原理基础上,利用不同纬度地区的三频GPS观测资料计算获得了电离层总电子含量值及其变化率。分析结果表明：由于GPS接收机码间偏差的影响,不同频率间组合获得的电离层总电子含量结果出现较大的系统差异,使用不同频率组合获得的电离层TEC变化率有很好的一致性。     

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.     

The ionospheric impact of the October 2003 storm event on Wide Area Augmentation System

The United States Federal Aviation Administrations (FAA) Wide-Area Augmentation System (WAAS) for civil aircraft navigation is focused primarily on the Conterminous United States (CONUS). Other Satellite-Based Augmentation Systems (SBAS) include the European Geostationary Navigation Overlay Service (EGNOS) and the Japanese Multi-transport Satellite-based Augmentation System (MSAS). Navigation using WAAS requires accurate calibration of ionospheric delays. To provide delay corrections for single frequency global positioning system (GPS) users, the wide-area differential GPS systems depend upon accurate determination of ionospheric total electron content (TEC) along radio links. Dual-frequency transmissions from GPS satellites have been used for many years to measure and map ionospheric TEC on regional and global scales. The October 2003 solar-terrestrial events are significant not only for their dramatic scale, but also for their unique phasing of solar irradiance and geomagnetic events. During 28 October, the solar X-ray and EUV irradiances were exceptionally high while the geomagnetic activity was relatively normal. Conversely, 29–31 October was geomagnetically active while solar irradiances were relatively low. These events had the most severe impact in recent history on the CONUS region and therefore had a significant effect on the WAAS performance. To help better understand the event and its impact on WAAS, we examine in detail the WAAS reference site (WRS) data consisting of triple redundant dual-frequency GPS receivers at 25 different locations within the US. To provide ground-truth, we take advantage of the three co-located GPS receivers at each WAAS reference site. To generate ground-truth and calibrate GPS receiver and transmitter inter-frequency biases, we process the GPS data using the Global Ionospheric Mapping (GIM) software developed at the Jet Propulsion Laboratory. This software allows us to compute calibrated high resolution observations of TEC. We found ionospheric range delays up to 35 m for the day-time CONUS during quiet conditions and up to 100 m during storm time conditions. For a quiet day, we obtained WAAS planar fit slant residuals less than 2 m (0.4 m root mean square (RMS)) and less than 25 m (3.4 m RMS) for the storm day. We also investigated ionospheric gradients, averaged over distances of a few hundred kilometers. The gradients were no larger than 0.5 m over 100 km for a quiet day. For the storm day, we found gradients at the 4 m level over 100 km. Similar level gradients are typically observed in the low-latitude region for quiet or storm conditions.     

Ionospheric TEC predictions over a local area GPS reference network

Single layer ionosphere models are frequently used for ionospheric modeling and estimation using GPS measurements from a network of GPS reference stations. However, the accuracies of single layer models are inherently constrained by the assumption that the ionospheric electrons are concentrated in a thin shell located at an altitude of about 350 km above Earths surface. This assumption is only an approximation to the physical truth because the electrons are distributed in the entire ionosphere region approximately from 50 to 1,000 km. To provide instantaneous ionospheric corrections for the real-time GPS positioning applications, the ionospheric corrections need to be predicted in advance to eliminate the latency caused by the correction computation. This paper will investigate ionospheric total electron content (TEC) predictions using a multiple-layer tomographic method for ionospheric modeling over a local area GPS reference network. The data analysis focuses on the accuracy evaluation of short-term (5 min in this study) TEC predictions. The results have indicated that the obtainable TEC prediction accuracy is at a level of about 2.8 TECU in the zenith direction and 95% of the total electron content can be recovered using the proposed tomography-based ionosphere model.     

南极威德尔海电离层异常的综合观测及分析

威德尔海异常是西南极沿海地区在夏季出现的电离层异常现象。本文用西南极地区的GPS跟踪站数据和测高卫星Jason-2数据,分别提取了陆地和海洋地区大范围的电离层TEC参数。GPS反演结果的优势是获取测站上空高精度的TEC时间序列,测高反演的结果整体与GPS的结果精度相当,虽然测高的时间分辨率较低,但其优势是获取海洋广大区域的TEC值。两种观测手段的研究区域互补,可以充分观测威德尔海异常在西南极的变化特征,从空间上来看,威德尔海异常出现在以别林斯高晋海为中心的广大区域,而威德尔海异常也是覆盖了西南极的别林斯高晋海、威德尔海以及可达80°S的西南极陆地区域。从时间上来看,出现时段在每年的10月底到次年3月初,夜晚电子密度增加,白天电子密度降低,随着太阳活动的增强,其异常程度也变大。     

Analysis of long-range network RTK during a severe ionospheric storm

The network-based GPS technique provides a broad spectrum of corrections to support RTK (real-time kinematic) surveying and geodetic applications. The most important among them are the ionospheric corrections generated in the reference network. The accuracy of these corrections depends upon the ionospheric conditions and may not always be sufficient to support ambiguity resolution (AR), and hence accurate GPS positioning. This paper presents the analyses of the network-derived ionospheric correction accuracy under extremely varying – quiet and stormy – geomagnetic and ionospheric conditions. In addition, the influence of the correction accuracy on the instantaneous (single-epoch) and on-the-fly (OTF) AR in long-range RTK GPS positioning is investigated, and the results, based on post-processed GPS data, are provided. The network used here to generate the ionospheric corrections consists of three permanent stations selected from the Ohio Continuously Operating Reference Stations (CORS) network. The average separation between the reference stations was ∼200 km and the test baseline was 121 km long. The results show that, during the severe ionospheric storm, the correction accuracy deteriorates to the point when the instantaneous AR is no longer possible, and the OTF AR requires much more time to fix the integers. The analyses presented here also outline the importance of the correct selection of the stochastic constraints in the rover solution applied to the network-derived ionospheric corrections.     

An improved and extended GPS-derived 3D velocity field of the glacial isostatic adjustment (GIA) in Fennoscandia

We present a new GPS-derived 3D velocity field for the Fennoscandia glacial isostatic adjustment (GIA) area. This new solution is based upon ∼3,000 days of continuous GPS observations obtained from the permanent networks in Fennoscandia. The period encompasses a prolongated phase of stable observation conditions after the northern autumn of 1996. Several significant improvements have led to smaller uncertainties and lower systematic errors in the new solutions compared to our previous results. The GPS satellite elevation cut-off angle was lowered to 10°, we fixed ambiguities to integers where possible, and only a few hardware changes occurred over the entire network. The GAMIT/GLOBK software package was used for the GPS analysis and reference frame realization. Our new results confirmed earlier findings of maximum discrepancies between GIA models and observations in northern Finland. The reason may be related to overestimated ice-sheet thickness and glaciation period in the north. In general, the new solutions are more coherent in the velocity field, as some of the perturbations are now avoided. We compared GPS-derived GIA rates with sea-level rates from tide-gauge observations, repeated precise leveling, and with GIA model computations, which showed consistency.     

卫星VLBI测轨资料处理中的电离层延迟改正

结合我国探月项目卫星VLBI测轨资料分析中的实际需求讨论了两个问题：一是在S、X波段时延测量精度均为1ns情况下，电离层延迟改正所能够达到的精度；二是在飞行器VLBI测轨过程中，不能确保S、X波段双频观测情况下获取电离层时延改正的可能途径，包括借助于相关电离层模型、利用常规VLB1历史观测资料积累、借助于局域GPS观测网和IGS网单站GPS测量以及借助于专门设计的单站GPS测量等。最后对电离层VLB1和GPS技术实测结果进行了比较和问题分析。     

Global ionosphere map constructed by using total electron content from ground-based GNSS receiver and FORMOSAT-3/COSMIC GPS occultation experiment

Effects of rapidly changing ionospheric weather are critical in high accuracy positioning, navigation, and communication applications. A system used to construct the global total electron content (TEC) distribution for monitoring the ionospheric weather in near-real time is needed in the modern society. Here we build the TEC map named Taiwan Ionosphere Group for Education and Research (TIGER) Global Ionospheric Map (GIM) from observations of ground-based GNSS receivers and space-based FORMOSAT-3/COSMIC (F3/C) GPS radio occultation observations using the spherical harmonic expansion and Kalman filter update formula. The TIGER GIM (TGIM) will be published in near-real time of 4-h delay with a spatial resolution of 2.5° in latitude and 5° in longitude and a high temporal resolution of every 5 min. The F3/C TEC results in an improvement on the GIM of about 15.5%, especially over the ocean areas. The TGIM highly correlates with the GIMs published by other international organizations. Therefore, the routinely published TGIM in near-real time is not only for communication, positioning, and navigation applications but also for monitoring and scientific study of ionospheric weathers, such as magnetic storms and seismo-ionospheric anomalies.