Accuracy assessment of the GPS-based slant total electron content

The main scope of this research is to assess the ultimate accuracy that can be achieved for the slant total electron content (sTEC) estimated from dual-frequency global positioning system (GPS) observations which depends, primarily, on the calibration of the inter-frequency biases (IFB). Two different calibration approaches are analyzed: the so-called satellite-by-satellite one, which involves levelling the carrier-phase to the code-delay GPS observations and then the IFB estimation; and the so-called arc-by-arc one, which avoids the use of code-delay observations but requires the estimation of arc-dependent biases. Two strategies are used for the analysis: the first one compares calibrated sTEC from two co-located GPS receivers that serve to assess the levelling errors; and the second one, assesses the model error using synthetic data free of calibration error, produced with a specially developed technique. The results show that the arc-by-arc calibration technique performs better than the satellite-by-satellite one for mid-latitudes, while the opposite happens for low-latitudes.     

利用非组合精密单点定位技术确定斜向电离层总电子含量和站星差分码偏差

联合双频GPS数据,利用相位平滑伪距算法,可得到包含斜向电离层总电子含量（slant total electron content,sTEC）、测站和卫星差分码偏差（differential code bias,DCB）的电离层观测值（称之为＂平滑伪距电离层观测值＂）,常应用于与电离层有关的研究。然而,平滑伪距电离层观测值易受平滑弧段长度和与测站有关的误差影响。提出一种新算法：利用非组合精密单点定位技术（precise point positioning,PPP）计算电离层观测值（称之为＂PPP电离层观测值＂）,进而估计sTEC和站星DCB。基于短基线试验,先用一台接收机按上述两种方法估计sTEC,用于改正另一接收机观测值的电离层延迟以实施单频PPP,结果表明,利用PPP电离层观测值得到的sTEC精度较高,定位结果的可靠性较强。随后,选取全球分布的8个IGS（internationalGNSS service）连续跟踪站2009年1月内某四天的观测数据,利用上述两种电离层观测值计算所有卫星的DCB,并将计算结果与CODE发布的月平均值进行比较,其中,平滑伪距电离层观测值的卫星DCB估值与CODE（Centre for Orbit Deter mination in Europe）发布值的差别较大,部分卫星甚至可达0.2～0.3 ns,而PPP电离层观测值而言,绝大多数卫星对应的差异均在0.1 ns以内。     

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.     

确定卫星与接收机信号延迟偏差的新方法及其应用

单频ＧＰＳ接收机用户通常需要进行电离层延迟改正,电离层延迟改正量通常来源于电离层延迟改正模型或双频ＧＰＳ基准站信息,后者即是利用双频ＧＰＳ观测值估计电子含量总数,求解电离层延迟改正量。利用双频ＧＰＳ观测值估计电子含量总数,一个关键总是是去掉卫星与接收信号延迟偏差。     

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%.     

Revisit the calibration errors on experimental slant total electron content (TEC) determined with GPS

The calibration errors on experimental slant total electron content (TEC) determined with global positioning system (GPS) observations is revisited. Instead of the analysis of the calibration errors on the carrier phase leveled to code ionospheric observable, we focus on the accuracy analysis of the undifferenced ambiguity-fixed carrier phase ionospheric observable determined from a global distribution of permanent receivers. The results achieved are: (1) using data from an entire month within the last solar cycle maximum, the undifferenced ambiguity-fixed carrier phase ionospheric observable is found to be over one order of magnitude more accurate than the carrier phase leveled to code ionospheric observable and the raw code ionospheric observable. The observation error of the undifferenced ambiguity-fixed carrier phase ionospheric observable ranges from 0.05 to 0.11 total electron content unit (TECU) while that of the carrier phase leveled to code and the raw code ionospheric observable is from 0.65 to 1.65 and 3.14 to 7.48 TECU, respectively. (2) The time-varying receiver differential code bias (DCB), which presents clear day boundary discontinuity and intra-day variability pattern, contributes the most part of the observation error. This contribution is assessed by the short-term stability of the between-receiver DCB, which ranges from 0.06 to 0.17 TECU in a single day. (3) The remaining part of the observation errors presents a sidereal time cycle pattern, indicating the effects of the multipath. Further, the magnitude of the remaining part implies that the code multipath effects are much reduced. (4) The intra-day variation of the between-receiver DCB of the collocated stations suggests that estimating DCBs as a daily constant can have a mis-modeling error of at least several tenths of 1 TECU.     

Determining receiver biases in GPS-derived total electron content in the auroral oval and polar cap region using ionosonde measurements

Global Positioning System (GPS) total electron content (TEC) measurements, although highly precise, are often rendered inaccurate due to satellite and receiver differential code biases (DCBs). Calculated satellite DCB values are now available from a variety of sources, but receiver DCBs generally remain an undertaking of receiver operators and processing centers. A procedure for removing these receiver DCBs from GPS-derived ionospheric TEC at high latitudes, using Canadian Advanced Digital Ionosonde (CADI) measurements, is presented. Here, we will test the applicability of common numerical methods for estimating receiver DCBs in high-latitude regions and compare our CADI-calibrated GPS vertical TEC (vTEC) measurements to corresponding International GNSS Service IONEX-interpolated vTEC map data. We demonstrate that the bias values determined using the CADI method are largely independent of the topside model (exponential, Epstein, and α-Chapman) used. We further confirm our results via comparing bias-calibrated GPS vTEC with those derived from incoherent scatter radar (ISR) measurements. These CADI method results are found to be within 1.0 TEC units (TECU) of ISR measurements. The numerical methods tested demonstrate agreement varying from within 1.6 TECU to in excess of 6.0 TECU when compared to ISR measurements.     

Joint estimation of vertical total electron content (VTEC) and satellite differential code biases (SDCBs) using low-cost receivers

Vertical total electron content (VTEC) parameters estimated using global navigation satellite system (GNSS) data are of great interest for ionosphere sensing. Satellite differential code biases (SDCBs) account for one source of error which, if left uncorrected, can deteriorate performance of positioning, timing and other applications. The customary approach to estimate VTEC along with SDCBs from dual-frequency GNSS data, hereinafter referred to as DF approach, consists of two sequential steps. The first step seeks to retrieve ionospheric observables through the carrier-to-code leveling technique. This observable, related to the slant total electron content (STEC) along the satellite–receiver line-of-sight, is biased also by the SDCBs and the receiver differential code biases (RDCBs). By means of thin-layer ionospheric model, in the second step one is able to isolate the VTEC, the SDCBs and the RDCBs from the ionospheric observables. In this work, we present a single-frequency (SF) approach, enabling the joint estimation of VTEC and SDCBs using low-cost receivers; this approach is also based on two steps and it differs from the DF approach only in the first step, where we turn to the precise point positioning technique to retrieve from the single-frequency GNSS data the ionospheric observables, interpreted as the combination of the STEC, the SDCBs and the biased receiver clocks at the pivot epoch. Our numerical analyses clarify how SF approach performs when being applied to GPS L1 data collected by a single receiver under both calm and disturbed ionospheric conditions. The daily time series of zenith VTEC estimates has an accuracy ranging from a few tenths of a TEC unit (TECU) to approximately 2 TECU. For 73–96% of GPS satellites in view, the daily estimates of SDCBs do not deviate, in absolute value, more than 1 ns from their ground truth values published by the Centre for Orbit Determination in Europe.     

多频多模接收机差分码偏差的精密估计与特性分析

全球导航卫星系统（Global Navigation Satellite System,GNSS）探测大气电离层需要精确处理由接收机差分码偏差（differential cade bias,DCB）引起的系统误差。准确掌握接收机DCB的多时间尺度精细变化等特性是联合美国GPS、中国北斗卫星导航系统（BeiDou navigation satellite system,BDS）和欧盟Galileo等多GNSS技术监测电离层所面临的主要科学问题之一。为此,提出了基于零基线精密估计站间单差接收机DCB的方法,并对站间单差接收机DCB的日加权平均值进行了分析。基于4台多模接收机采集于2013年的双频观测值,揭示了站间单差接收机DCB的变化可能受3种因素的影响,即接收机内置软件的版本升级（实验中引起了约3 ns的显著增加）、拆卸个别接收机所导致的观测条件改变（实验中引起了约1.3 ns的显著减少）和估计方法的误差（引起了与导航系统卫星几何结构重复性相一致的周期性变化）等。     

估计接收机差分码偏差的GPS/BDS非组合精密单点定位模型

在传统多系统非差非组合精密单点定位（precise point positioning,PPP）模型中,电离层延迟会吸收部分接收机码硬件延迟,其估计值可能为负数。提出了一种估计接收机差分码偏差（differential code bias,DCB）参数的GPS（Global Positioning System）/BDS（BeiDou Navigation Satellite System）非组合PPP模型,将每个系统第1个频率上的接收机码硬件延迟约束为零,对接收机DCB进行参数估计,达到了分离电离层延迟和接收机码硬件延迟的目的,降低了接收机钟差和电离层延迟的相关程度。利用4个多星座实验（multi-GNSS experiment,MGEX）跟踪站的GPS/BDS数据进行了静态和动态PPP试验,结果表明,与不估计DCB参数的PPP模型相比,采用估计DCB参数PPP模型后,静态模式下定位精度和收敛速度平均提高了29.3%和29.8%,动态模式下定位精度和收敛速度平均提高了15.7%和21.6%。     

On the short-term temporal variations of GNSS receiver differential phase biases

As a first step towards studying the ionosphere with the global navigation satellite system (GNSS), leveling the phase to the code geometry-free observations on an arc-by-arc basis yields the ionospheric observables, interpreted as a combination of slant total electron content along with satellite and receiver differential code biases (DCB). The leveling errors in the ionospheric observables may arise during this procedure, which, according to previous studies by other researchers, are due to the combined effects of the code multipath and the intra-day variability in the receiver DCB. In this paper we further identify the short-term temporal variations of receiver differential phase biases (DPB) as another possible cause of leveling errors. Our investigation starts by the development of a method to epoch-wise estimate between-receiver DPB (BR-DPB) employing (inter-receiver) single-differenced, phase-only GNSS observations collected from a pair of receivers creating a zero or short baseline. The key issue for this method is to get rid of the possible discontinuities in the epoch-wise BR-DPB estimates, occurring when satellite assigned as pivot changes. Our numerical tests, carried out using Global Positioning System (GPS, US GNSS) and BeiDou Navigation Satellite System (BDS, Chinese GNSS) observations sampled every 30 s by a dedicatedly selected set of zero and short baselines, suggest two major findings. First, epoch-wise BR-DPB estimates can exhibit remarkable variability over a rather short period of time (e.g. 6 cm over 3 h), thus significant from a statistical point of view. Second, a dominant factor driving this variability is the changes of ambient temperature, instead of the un-modelled phase multipath.     

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。     

基于球谐函数区域电离层模型建立

利用GPS双频观测数据建立高精度、准实时的区域电离层总电子含量(TEC)模型是电离层研究的一个重要手段。文中探讨IGS观测站数据结合4阶球谐函数建立区域电离层格网模型的方法,并对硬件延迟(DCB)和TEC建模结果的可靠性进行分析,结果表明,DCB解算精度在0.4ns以内,TEC内外精度优于1.4TECU(1TECU=1016电子数/m2)和1.5TECU,满足导航定位中电离层改正的需要。     

GPS接收机硬件延迟时变特性分析

在全球定位系统(Global Positioning System,GPS)中,接收机硬件延迟引起的码偏差和相位偏差是影响精密授时、电离层建模以及非差模糊度解算的重要因素。利用GPS对电离层总电子含量进行估计和建模时,通常假定GPS接收机硬件延迟偏差是稳定不变的量,对其可能存在的波动及影响因素考虑不充分。因此,对GPS接收机硬件延迟偏差的时变特性进行分析,有助于提高电离层电子含量估值的准确性和可靠性。分析了GPS接收机差分码偏差(differential code bias,DCB)和差分相位偏差(differential phase bias,DPB)单历元及单天解的时间变化特性,并对温度变化与接收机DCB、DPB变化之间的相关性进行了实验探究。结果表明,接收机重启前后其DCB值会发生突变,重启之后接收机DCB和DPB大约需要25 min才能趋于稳定。接收机DCB和DPB并不能长期保持稳定,实验数据显示,在2~3 h内,DCB的变化量可以达到0.8 m左右,DPB的变化量可以达到4 mm左右,接收机DCB和DPB的波动与周围环境温度的变化具有较强相关性。     

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。     

Higher order ionospheric effects in precise GNSS positioning

With the increasing number of precise navigation and positioning applications using Global Navigation Satellite Systems (GNSS) such as the Global Positioning System (GPS), higher order ionospheric effects and their correction become more and more important. Whereas the first-order error can be completely eliminated by a linear combination of dual- frequency measurements, the second- and third-order residual effects remain uncorrected in this approach. To quantify the second-order residual effect, a simple formula has been derived for GNSS users in Germany. Our proposed correction algorithm reduces the second-order effects to a residual error of fractions of 1 mm up to 2 mm at a vertical total electron content level of 10¹⁸ electrons/m² (100 TECU), depending on satellite azimuth and elevation angles. The correction formula can be implemented in real-time applications as it does not require the knowledge of the geomagnetic field or the electron density distribution in the ionosphere along the signal path. It is expected that the correction will enable more accurate positioning using the line-of-sight carrier-phase measurements.     

Simulation study of the influence of the ionospheric layer height in the thin layer ionospheric model

This work aims to contribute to the understanding of the influence of the ionospheric layer height (ILH) on the thin layer ionospheric model (TLIM) used to retrieve ionospheric information from the GNSS observations. Particular attention is paid to the errors caused on the estimation of the vertical total electron content (vTEC) and the GNSS satellites and receivers inter-frequency biases (IFB), by the use of an inappropriate ILH. The work relies upon numerical simulations performed with an empirical model of the Earth’s ionosphere: the model is used to create realistic but controlled ionospheric scenarios and the errors are evaluated after recovering those scenarios with the TLIM. The error assessment is performed in the Central and the northern part of the South American continents, a region where large errors are expected due to the combined actions of the Appleton Anomaly of the ionosphere and the South-Atlantic anomaly of the geomagnetic field. According to this study, there does not exist a unique ILH that cancels the vTEC error for the whole region under consideration. The ILH that cancels the regional mean vTEC error varies with the solar activity and season. The latitude-dependent conversion error propagates to the parameters of the model used to represent the latitudinal variation on the vTEC on the ionospheric layer, and to the IFB, when these values are simultaneously estimated from the observed sTEC. Besides, the ILH that cancels the regional mean vTEC error is different from the one that cancels the IFB error and the difference between both ILH varies with the solar activity and season.     

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。     

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.     

不同NeQuick电离层模型参数的应用精度分析

Galileo采用NeQuick作为全球广播电离层模型,其实际应用中以有效电离水平因子Az代替太阳活动指数作为NeQuick的输入参数,并利用二次多项式拟合得到广播星历中播发的3个电离层参数。本文在总结和讨论NeQuick模型参数估计方法及其变化特征的基础上,分别以全球电离层格网、GPS基准站及JASON-2测高卫星提供的电离层TEC为参考,分析不同NeQuick模型参数(包括以太阳活动参数F10.7为输入的NeQuick2、以本文解算参数为输入的NeQuickC和以Galileo广播电离层参数为输入的NeQuickG)在全球大陆及海洋地区的应用精度,并与GPS广播的Klobuchar模型对比。结果表明,NeQuickG在全球范围内的修正精度为54.2%~65.8%,NeQuickC的修正精度为71.1%~74.2%,NeQuick2的修正精度与NeQuickG相当,略优于GPS广播星历中播发的Klobuchar模型。