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.     

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.     

Instantaneous Precise GPS Positioning under Geomagnetic Storm Conditions

Due to the maximum of the solar cycle, ionospheric activity increased considerably last year. At frequent times warning were sent out announcing geomagnetic storms disturbing the ionospheric electron content. In this article the influence of such geomagnetic storms on fast and precise GPS positioning (for surveying applications at midlatitude regions) is studied. And here with “fast” it is aimed at the shortest observation time possible: carrier ambiguity resolution and position estimation using only one single epoch of data. To apply this instantaneous data processing technique successfully to GPS baselines of medium length (up to 50 km), additional ionospheric information is inevitable, not only under geomagnetic storm but also under more quiet conditions. However, in this article it will be shown that under geomagnetic storm conditions, even for rather short baselines (<10 km), for which the ionospheric delays under more quiet conditions could be neglected, one has to account for significant relative ionospheric delays. Therefore an important facet of this contribution is the investigation of how to process baselines of varying length in a more uniform way, making use of a permanent GPS network (if available in the surveying area) and a stochastic modeling technique of the ionospheric delays. ? 2001 John Wiley & Sons, Inc.     

利用神经网络预报短期电离层TEC变化

利用神经网络,基于IGS提供的(40°N,115°E)网格点TEC数据,本文构造了该点处提前一天的TEC预报模型。神经网络模型的预测目标是待预测日一天内的12个TEC数值。输入参数包括预测日前一日的太阳黑子数、地磁Kp指数、预测日前27天的太阳黑子数三角函数拟合参数,以及预测日前2天16个Kp指数的多项式拟合参数。实验结果表明训练后的神经网络模型可以反映出不同季节的TEC周日变化以及地磁暴情况下的TEC特征。     

Impact of the Halloween 2003 ionospheric storm on kinematic GPS positioning in Europe

Using dual-frequency data from 36 GPS stations from the EUREF Permanent Network (EPN), the influence of the October 30, 2003 Halloween geomagnetic storm on kinematic GPS positioning is investigated. The Halloween storm induced ionospheric disturbances above the northern part of Europe and Scandinavia. It is shown that kinematic position repeatabilities for this period are mainly affected for stations in northern Europe with outliers reaching 12 cm in the horizontal, and 26 cm in the vertical. These magnitudes are shown to be possibly due to the second-order ionospheric delays on GPS signals, not accounted for in the kinematic GPS positioning analysis performed. In parallel, we generate hourly TEC (Total Electron Content) maps on a 1° × 1° grid using the dense EPN network. These TEC maps do not use any interpolation but provide a high resolution in the time and space and therefore allow to better evidence small structures in the ionosphere than the classical 2-hourly 2.5° × 5° grid Global Ionospheric TEC Maps (GIM). Using the hourly 1° × 1° TEC maps, we reconstruct and refine exactly the zones of intense ionosphere activity during the storm, and we show the correlation between the ionospheric activity and assess the quality of GPS-based kinematic positioning performed in the European region.     

Monitoring storm-enhanced density using IGS reference station data

Storm-enhanced density (SED) is a geomagnetic storm phenomenon, characterized by a plume of enhanced total electron content (TEC) that initially moves poleward and sunward extending out from a larger region of enhanced TEC in the mid-latitudes. SED is associated with extreme mid-latitude space weather effects. Sharp gradients in the TEC are found along the borders of SED plumes and at the boundaries of the larger TEC region (the base of the plume). These large TEC gradients can cause significant errors in DGPS and WADGPS positioning and can result in serious consequences for applications such as railway control, highway traffic management, emergency response, commercial aviation and marine navigation, all of which require high precision, real-time positioning. Data from the global IGS network of GPS receivers have enabled the spatial and temporal visualization of these SED plumes, allowing ionospheric researchers to study this phenomenon and investigate the potential for developing prediction techniques and real-time warning systems. GPS TEC maps provided by analysis of the data from the IGS network have now been widely disseminated throughout the atmospheric research community and have become one of the standard means of studying the effects of geomagnetic storms on the ionosphere. These maps have enabled researchers to identify that the SED phenomenon occurs globally, is associated with large TEC gradients (at times greater than 100 TEC units per degree latitude), and is a magnetically conjugate phenomenon. This paper reports on the recent advances in our understanding of the SED phenomenon enabled by GPS observations.     

Preliminary analysis of grid ionospheric vertical error for GAGAN

The inverse distance weighted model (IDWM) represents a geo-spatial interpolation technique used for estimation of ionospheric vertical delays at the ionospheric grid points (IGPs) and user ionospheric pierce points (IPPs). The GPS Aided Geo Augmented Navigation (GAGAN) system is planned for air-navigation over the Indian service region using a space based augmentation. One of the main needs for GAGAN is to develop a suitable grid-based ionospheric model for estimating the vertical delay and its error bound, i.e., grid ionospheric vertical error (GIVE) at all the IGPs covering the Indian subcontinent. Dual frequency GPS receiver data obtained from 17 total electron content (TEC) stations are considered in the analysis. For a typical IGP (25°N, 75°E), variations in the GIVE for a few days of quiet ionosphere are presented. For a quiet and magnetically moderate day, the mean and standard deviations of the user IPP (UIPP) estimation error and the mean GIVE are presented using the IDWM with Klobuchar, Junkins and bilinear models.     

Analysis of ionospheric electron parameters versus geomagnetic index Dst from RO data of FORMOSAT-3/COSMIC

The FORMOSAT-3/COSMIC mission has provided ample ionospheric electron density profiles retrieved from the global positioning system radio occultation technique. Currently, there can be more than 2,000 electron density profiles acquired per day covering the global ionosphere from altitude 90 to 800 km. Utilizing the advantage of such a complete coverage, we statistically analyze how the ionospheric electron parameters NmF2, hmF2, and TEC respond to the geomagnetic index Dst for different magnetic latitudes and magnetic local time (MLT) and on quiet and storm times. A data set of 24 months is used for this study, in which most of the results focus on the low-latitude dayside regions. The results indicate that, in general, NmF2, hmF2, and TEC decrease as Dst increases at all seasons. Only during the sudden commencement phase (SSC) of storm events, NmF2 and TEC appear to increase as Dst increases.     

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.     

GPS slant total electron content accuracy using the single layer model under different geomagnetic regions and ionospheric conditions

The use of observations from the Global Positioning System (GPS) has significantly impacted the study of the ionosphere. As it is widely known, dual-frequency GPS observations can provide very precise estimation of the slant Total Electron Content (sTEC—the linear integral of the electron density along a ray-path) and that the precision level is bounded by the carrier-phase noise and multi-path effects on both frequencies. Despite its precision, GPS sTEC estimations can be systematically affected by errors in the estimation of the satellites and receivers by Inter-Frequency Biases (IFB) that are simultaneously determined with the sTEC. Thus, the ultimate accuracy of the GPS sTEC estimation is determined by the errors with which the IFBs are estimated. This contribution attempts to assess the accuracy of IFBs estimation techniques based on the single layer model for different ionospheric regions (low, mid and high magnetic latitude); different seasons (summer and winter solstices and spring and autumn equinoxes); different solar activity levels (high and low); and different geomagnetic conditions (quiet and very disturbed). The followed strategy relies upon the generation of a synthetic data set free of IFB, multi-path, measurement noise and of any other error source. Therefore, when a data set with such properties is used as the input of the IFB estimation algorithms, any deviation from zero on the estimated IFBs should be taken as indications of the errors introduced by the estimation technique. The truthfulness of this assessment work is warranted by the fact that the synthetic data sets resemble, as realistically as possible, the different conditions that may happen in the real ionosphere. The results of this work show that during the high solar activity period the accuracy for the estimated sTEC is approximately of ±10 TECu for the low geomagnetic region and of ±2.2 TECu for the mid-latitude. During low solar activity the accuracy can be assumed to be in the order of ±2 TECu. For the geomagnetic high-disturbed period, the results show that the accuracy is degraded for those stations located over the region where the storm has the strongest impact, but for those stations over regions where the storm has a moderate effect, the accuracy is comparable to that obtained in the quiet period.     

Effects of ionospheric disturbances on GPS observation in low latitude area

In this paper, ionospheric disturbance data from a local GPS network in Hong Kong (low latitude region) are studied in the solar maximum period (2001–2003). The spatial and temporal distributions of the disturbances in Hong Kong are investigated. It is found that strong ionospheric disturbances occur frequently during the solar maximum period, particularly around March and September, and concentrate at the region around geographic latitude 22°N (geomagnetic latitude 12°N). The effects of the disturbances on GPS geodetic receivers, such as loss of lock and measurement noise level, are also analyzed for the 3-year period. It shows that the measurement noise level and the number of losses of lock in GPS data increase dramatically during ionospheric disturbance periods. The behaviors of different types of GPS receivers during the disturbances are also compared.     

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.     

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%.     

WAAS系统下单频GPS用户电离层延迟改正新方法

对于现有WAAS等差分GPS系统而言,在电离层活动激烈及系统不能正常发送或用户无法正常接收电离层延迟改正信息时,如何确保其所服务区域内单频GPS用户的电离层延迟的实时改正效果,是需要进一步解决的问题。本文提出一种能够同时克服这些不足的单频GPS电离层延迟实时改正方案,并用算例初步验证了其有效性。     

2018年8月磁暴期间北斗GEO卫星电离层TEC时空变化分析

基于北斗GEO卫星独有的静地特性,本文利用其观测数据提取电离层TEC进行磁暴期间电离层TEC时空变化研究。同时利用全球电离层格网图GIM值进行试验对比,结果表明：北斗GEO卫星提取的TEC与GIM模型值变化趋势一致,并且前者可更有效地监测电离层的细微扰动变化。在此次磁暴发生期间,亚太地区电离层TEC变化及扰动响应特征在纬度方向差异明显。其中南北半球较高纬度区域,电离层TEC在磁暴主相阶段主要表现为正响应扰动,而赤道及北半球较低纬度区域,电离层TEC在磁暴主相及恢复相阶段均产生了强度更大、持续时间更长的正响应扰动。结合现有研究,认为造成此次电离层异常扰动的激励因素主要为东向快速穿透电场的增强及热层中性成分的变化。试验结果也证明了GEO卫星可以精准有效地监测在磁暴发生时电离层TEC的变化规律及不同空间位置处TEC产生的扰动响应特征。     

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.     

GPS tomography in the polar cap: comparison with ionosondes and in situ spacecraft data

Tomographic 4D reconstructions of ionospheric anomalies appearing in the high-latitude polar cap region are compared with plasma density measurements by digital ionosonde located near the north magnetic pole at Eureka station and with in situ plasma measurements on-board DMSP spacecraft. The moderate magnetic storm of 14–17 October 2002 is taken as an example of a geomagnetic disturbance which generates large-scale ionospheric plasma anomalies at mid-latitudes and in the polar cap region. Comparison of the GPS tomographic reconstructions over Eureka station with the ionosonde measurements of the F layer peak densities indicates that the GPS tomography correctly predicts the time of arrival and passage of the ionospheric tongue of ionization over the magnetic pole area, although the tomographic technique appears to under-estimate the value of F peak plasma density. Comparison with the in situ plasma measurements by the DMSP SSIES instruments shows that the GPS tomography correctly reproduces the large-scale spatial structure of ionospheric anomalies over a wide range of latitudes from mid-latitudes to the high-latitude polar cap region, though the tomographic reconstructions tend to over-estimate the density of the topside ionosphere at 840 km DMSP orbit. This study is essential for understanding the quality and limitations of the tomographic reconstruction techniques, particularly in high-latitude regions where GPS TEC measurements and other ionospheric data sources are limited.     

Ionospheric tomography using GNSS: multiplicative algebraic reconstruction technique applied to the area of Brazil

Experimental analysis was performed using multiplicative algebraic reconstruction technique (MART) to map the ionosphere over Brazil. Code and phase observations from the global navigation satellite system (GNSS) together with the international reference ionosphere (IRI) enabled the estimation of ionospheric profiles and total electron content (TEC) over the entire region. Twenty-four days of data collected from existing ground-based GNSS receivers during the recent solar maximum period were used to analyze the performance of the MART algorithm. The results were compared with four ionosondes. It was demonstrated that MART estimated the electron density peak with the same degree of accuracy as the IRI model in regions with appropriate geometrical coverage by GNSS receivers for tomographic reconstruction. In addition, the slant TEC, as estimated with MART, presented lower root-mean-square error than the TEC calculated by ionospheric maps available from the International GNSS Service (IGS). Furthermore, the daily variations of the ionosphere were better represented with the algebraic techniques, compared to the IRI model and IGS maps, enabling a correlation of the elevation of the ionosphere at higher altitudes with the equatorial ionization anomaly intensification. The tomographic representations also enabled the detection of high vertical gradients at the same instants in which ionospheric irregularities were evident.     

磁暴期全球电离层电子含量变化分析研究

电离层电子含量(TEC)受太阳活动影响较大,磁暴发生时,TEC变化在全球范围内变化不一,研究该时期的TEC扰动变化情况对电离层的研究至关重要．本文以2015年3月特大磁暴为研究对象,利用包括北斗系统在内的全球卫星导航系统（GNSS）TEC数据和中国区域的电离层测高仪f _oF2数据,对此次电离层磁暴的扰动特性进行研究并讨论其可能的物理机制．      

Anomalies in broadcast ionospheric coefficients recorded by GPS receivers over the past two solar cycles (1992–2013)

The anomaly phenomenon of broadcast ionospheric model coefficients of the Global Positioning System (GPS) is revealed after analyzing the navigation file data collected from all the IGS (International GNSS Service) stations worldwide over a 22-year period (1992–2013). GPS broadcast ionospheric coefficients widely used by many single-frequency users to correct the ionosphere errors for numerous GPS applications are usually believed to have only one set/version per day. However, it is found that GPS receivers from the IGS network can report as many as eight sets/versions of ionospheric coefficients in a day. In order to investigate the possible factors for such an anomalous phenomenon, the relationship between the number of coefficient sets and solar cycle, the receiver geographic locations, and receiver types/models are analyzed in detail. The results indicate that most of the coefficients show an annual variation. During the active solar cycle period from mid-1999 to mid-2001, all of the coefficients extracted from IGS navigation files behaved anomalously. Our analysis shows that the anomaly is also associated with GPS receiver types/models. Some types/models of GPS receivers report one set/version of ionospheric coefficients daily, while others report multiple sets. Our analysis also suggests that the ionospheric coefficient anomaly is not necessarily related to ionospheric scintillations. No correlation between the anomaly and geographic location of GPS receivers has been found in the analysis. Using the ionospheric coefficient data collected from 1998 to 2013, the impact of ionospheric coefficient anomaly on vertical total electron content (VTEC) calculation using the Klobuchar model has been evaluated with respect to the Global Ionospheric Maps generated by the Center for Orbit Determination in Europe. With different sets of coefficients recorded on the same day, the resulting VTEC values are dramatically different. For instance on June 1, 2000, the largest VTEC at one of our test stations can be as large as 153.3 TECu (total electron content unit) using one set of coefficients, which is 16.36 times larger than the smallest VTEC of 9.37 TECu computed from using another set of coefficients.