山东区域电离层模型的建立及精度评估

针对电离层延迟改正对单频接收机用户带来误差较大的问题,该文基于球谐函数借助山东区域CORS双频观测数据建立山东区域电离层模型,并对硬件延迟偏差(DCB)和电子含量进行可靠性、稳定性分析,进一步使用单频精密单点定位(PPP)验证山东区域电离层模型的有效性。实验结果表明:测站DCB解算精度稳定在0.4ns内,解算卫星DCB与欧洲定轨中心(CODE)的偏差总体稳定在0.5ns内,区域电离层模型与CODE解算VTEC差值的均方根为1.22TECU,STD为0.93TECU,对山东区域单频PPP而言,山东区域电离层模型比CODE发布全球电离层模型在N、E、U方向精度明显提高。同时,建立的山东区域电离层模型从时间分辨率、空间分辨率上均优于CODE中心发布全球电离层模型。     

基于BDS/GPS观测的北斗硬件延迟解算

研究了联合BDS/GPS观测数据基于球冠谐函数的中国区域电离层建模,并精确估计了北斗卫星和接收机DCB。联合解算得到的GPS卫星DCB相对CODE精度优于0.2 ns,GPS接收机DCB相对CODE精度优于1 ns;联合解算得到的中国区域上空VTEC相对CODE事后产品的精度可达2~3 TECU。     

基于河北省CORS的区域电离层模型精度分析

为提高区域电离层模型和导航定位服务的精度,利用河北省连续运行参考站系统（CORS） 6个基准站的GPS卫星观测数据进行区域电离层建模和接收机差分码偏差（DCB）估计,并引入中国科学院（CAS）发布的电离层产品内插得到的垂直总电子含量（VTEC）进行区域电离层模型精度验证。实验结果表明,估计的单日GPS卫星DCB与产品值精度相当,偏差控制在0.5 ns以内;河北省CORS站GPS系统接收机DCB稳定性较好,5 d的标准偏差均小于0.1 ns;利用河北省CORS建立的区域电离层TEC在地磁平静期与磁暴期均与CAS产品值具有较高的一致性,TEC偏差控制在2 TECU以内。河北省区域电离层模型能有效监测电离层TEC在不同地磁状态下的时空变化,提高区域导航定位服务水平。     

GPS和GLONASS组合的全球实测电离层TEC建模

根据高精度卫星导航和电离层活动监测的需要,利用全球238个GPS基准站的双频实测数据,通过建立球谐函数模型的同时解算电离层电子含量以及GPS与GLONASS卫星DCB及其相应的接收机DCB;将其结果与CODE、IGS分析中心的结果进行比较分析,表明该方法建立的模型是可靠的,其GPS和GLONASS卫星DCB相对于CODE精度优于0.1ns,相对于IGS精度优于0.2ns,其GPS测站DCB和GLONASS测站DCB相对于CODE和IGS精度优于1ns,垂直总电子含量相对CODE和IGS精度优于3TECU,组合结果精度高于组合前。     

基于球谐函数模型的GPS差分码延迟估计

电离层延迟是GNSS观测值中最大的误差源,因此如何利用GNSS观测值确定高精度电离层模型逐渐成为实时导航、定位及大气相关研究的重要内容。在通常采用组合观测值建立模型的方法中,精确估计电离层总电子含量（TEC）的重要误差之一是差分码硬件延迟（DCBs）。为了实时得到P1、P2、C2相互间硬件差分码延迟偏差,本文采用IGS跟踪站的观测数据并利用载波平滑后的差分伪距建立观测方程,对卫星和接收机硬件差分码延迟偏差进行实时解算。经比较模型解算DCB值与IGS最大差异不超过0.8 ns,C1、P1码延迟偏差72%差异值小于0.3 ns,P1、P2的74%差异值小于0.3 ns。     

北斗三号卫星导航信号接收机端伪距偏差建模与验证

接收机端伪距偏差是指非理想的卫星导航信号在接收机前端带宽和相关器间隔不同时产生的伪距测量系统性偏差。研究表明,北斗二号、GPS和Galileo系统均存在与接收机类型相关的伪距偏差,影响基于混合类型接收机站网的精密数据处理。本文基于iGMAS网和MGEX网观测数据,采用MW组合、伪距残差和伪距无几何距离无电离层组合3种方法分析北斗三号接收机端伪距偏差特性。试验结果表明,北斗三号同样存在与接收机类型相关的伪距偏差,且无电离层组合的伪距偏差可以达到6 ns。根据偏差特性,按接收机类型建立了8类伪距偏差改正模型。将上述模型应用于卫星差分码偏差(DCB)估计与单频伪距单点定位,结果表明,模型改正后可以显著提升不同接收机类型估计的卫星DCB一致性,其中基于iGMAS网和MGEX网两个不同接收机站网估计得到的北斗三号C2I-C6I、C1P-C5P和C2I-C7D DCB差值分别平均降低了91.6%、64.7%和71.9%;模型改正后单频伪距单点定位水平方向和高程方向精度分别提升了13.9%和11.0%。     

基于非组合精密单点定位的区域电离层建模

电离层是地球空间的重要组成部分,电离层延迟是全球导航卫星系统(global navigation satellite system,GNSS)数据处理的重要误差源,电离层的影响主要表现为地面站接收到的卫星载波和伪距信号的附加时延效应,最大可达几十米,精确的电离层模型可以有效提高GNSS单频数据处理的精度。利用GNSS观测值研究电离层,一般采用无几何距离组合的码和相位观测值,使用相位平滑伪距方法得到平滑电离层观测值,但是该方法容易受到伪距多路径和观测噪声的影响,导致电离层估计不准确。因此,先基于非组合精密单点定位(precise point positioning,PPP)提取电离层,利用国际GNSS服务的轨道、钟差等产品,有效减少待估参数个数,提高电离层延迟的估计精度;再使用纬度差和太阳时角差的多项式拟合进行区域电离层建模。利用某省连续运行参考站系统数据提取了天顶方向总电子含量信息进行建模,与PPP解算结果进行比较,在测站天顶方向上的模型值和解算值差异较小(除个别卫星外),可达到2 TECU左右。     

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。     

多系统双频精密单点定位不同模型下性能比较分析

通过2018年1月多全球卫星导航系统（GNSS）实验(MGEX)的十个测站数据,采用无电离层模型和非差非组合模型,对单系统、双系统和四系统精密单点定位（PPP）进行定位性能分析,定位性能包括收敛时间和定位精度. 实验结果表明,两种PPP模型定位性能相当,但优于单频PPP,在E、N和U方向收敛时间缩短20 min左右,定位精度提高1.6 cm左右;联合多系统能够增加卫星数,改善卫星间几何构型,提升PPP的定位性能. 对GLONASS伪距频间偏差（IFB）采用估计每颗GLONASS卫星的伪距IFB模型和伪距IFB为频率二次多项式模型提升PPP的定位性能,结果表明估计每颗GLONASS卫星的伪距IFB模型要优于伪距IFB为频率二次多项式模型,估计伪距IFB相比忽略伪距IFB在PPP定位性能上有不同程度的提升.      

利用GPS双频数据进行区域电离层TEC提取

从利用GPS提取区域电离层总电子含量(total electron content,TEC)的基本原理出发,解决了伪距观测值优化以及硬件延迟(DCB)处理问题,并将提取的TEC信息与欧洲定轨中心(CODE)计算的全球电离层(GIM)模型内插值应用在单频精密单点定位中,进行电离层延迟改正实验。结果表明,利用本文提取的TEC值进行单频精密单点定位电(PPP)离层延迟改正时,点位精度能提高到0.2~0.4m左右,明显优于利用GIM内插值的改正精度。     

Calibration errors on experimental slant total electron content (TEC) determined with GPS

The Global Positioning System (GPS) has become a powerful tool for ionospheric studies. In addition, ionospheric corrections are necessary for the augmentation systems required for Global Navigation Satellite Systems (GNSS) use. Dual-frequency carrier-phase and code-delay GPS observations are combined to obtain ionospheric observables related to the slant total electron content (sTEC) along the satellite-receiver line-of-sight (LoS). This observable is affected by inter-frequency biases [IFB; often called differential code biases (DCB)] due to the transmitting and the receiving hardware. These biases must be estimated and eliminated from the data in order to calibrate the experimental sTEC obtained from GPS observations. Based on the analysis of single differences of the ionospheric observations obtained from pairs of co-located dual-frequency GPS receivers, this research addresses two major issues: (1) assessing the errors translated from the code-delay to the carrier-phase ionospheric observable by the so-called levelling process, applied to reduce carrier-phase ambiguities from the data; and (2) assessing the short-term stability of receiver IFB. The conclusions achieved are: (1) the levelled carrier-phase ionospheric observable is affected by a systematic error, produced by code-delay multi-path through the levelling procedure; and (2) receiver IFB may experience significant changes during 1 day. The magnitude of both effects depends on the receiver/antenna configuration. Levelling errors found in this research vary from 1.4 total electron content units (TECU) to 5.3 TECU. In addition, intra-day vaiations of code-delay receiver IFB ranging from 1.4 to 8.8 TECU were detected.     

Galileo single frequency ionospheric correction: performances in terms of position

For GPS single frequency users, the ionospheric contribution to the error budget is estimated by the well-known Klobuchar algorithm. For Galileo, it will be mitigated by a global algorithm based on the NeQuick model. This algorithm relies on the adaptation of the model to slant Total Electron Content (sTEC) measurements. Although the performance specifications of these algorithms are expressed in terms of delay and TEC, the users might be more interested in their impact on positioning. Therefore, we assessed the ability of the algorithms to improve the positioning accuracy using globally distributed permanent stations for the year 2002 marked by a high level of solar activity. We present uncorrected and corrected performances, interpret these and identify potential causes for Galileo correction discrepancies. We show vertical errors dropping by 56–64 % due to the analyzed ionospheric corrections, but horizontal errors decreasing by 27 % at most. By means of a fictitious symmetric satellite distribution, we highlight the role of TEC gradients in residual errors. We describe mechanisms permitted by the Galileo correction, which combine sTEC adaptation and topside mismodeling, and limit the horizontal accuracy. Hence, we support further investigation of potential alternative ionospheric corrections. We also provide an interesting insight into the ionospheric effects possibly experienced during the next solar maximum coinciding with Galileo Initial Operation Capability.     

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.     

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.     

Evaluation of three ionospheric delay computation methods for ground-based GNSS receivers

GNSS observables for ionospheric estimation are commonly based on carrier-to-code leveling (CCL) and precise point positioning (PPP) methods. The CCL method is a geometry-free method which uses carrier phase to level pseudorange observation for decreasing multipath error and observation noise. However, the ionospheric observable based on the CCL has been proven to be affected by leveling errors. The leveling errors are caused by pseudorange multipath and intraday variation of receiver DCB. To obtain more accurate ionospheric observable, the PPP method takes advantage of precise satellite-to-ground range for retrieving slant total electron content and is less affected by the leveling errors. Previous studies have only proven that the ionospheric observables extracted by the two methods are affected by the leveling errors. The influence on ionospheric observable by the pseudorange inter-receiver satellite bias (IRSB) of the receiver has not been taken into consideration. Also, the magnitude of the differences between the ionospheric observables extracted by the two methods has also not been given. In this work, three methods, namely, the CCL, the conventional ionospheric-free PPP method which uses the ionospheric-free Hatch–Melbourne–Wubbena (HMW) function, and the University of Calgary (UOFC) PPP method, are selected to analyze and compare the differences of ionospheric observables and the global ionospheric maps, using a large number of measured data from international GNSS service global stations. Experimental results show that the accuracy of ionospheric observables obtained by the three methods is not only related to the leveling error, but also pseudorange IRSB. The IRSB of the receiver exerts a major effect on the ionospheric observables obtained by the CCL method and a minor effect on the ionospheric observables obtained by the HMW and UOFC methods. The accuracies in the latter case are similar and superior to those obtained by the CCL. The differences of the ionospheric observables obtained by the CCL and UOFC methods, or the CCL and HMW methods, are at decimeter level, whereas the difference of the ionospheric observables obtained by the UOFC and HMW methods is at centimeter level. The UOFC method presented the highest single-frequency pseudorange positioning accuracy using estimated global ionospheric products, followed by the HMW and the CCL methods which presented the lowest positioning accuracy.     

Remarks on correcting ionospheric distortions in L-band radar interferometry

The L-band synthetic aperture radar (SAR) interferometry (InSAR) technique has a lower accuracy due to ionospheric phase distortions. Recently, a multiple-aperture interferometry (MAI)-based ionospheric correction method has been proposed. Using four types of ionosphere-distorted interferograms, the performance of the correction method was evaluated and then analyzed the feasibility of the correction method. The test interferograms contained severe azimuth streaking, low-frequency ionospheric phase distortion and drastic phase change due to the ionosphere. The results showed that (i) the existence and magnitude of ionospheric phase distortions can be recognized from MAI interferograms and (ii) the MAI-based ionospheric correction method efficiently reduced severe azimuth streaking and low-frequency distortion but did not mitigate the drastic phase change perfectly. It is allowed (i) to determine whether a given SAR interferogram has an ionospheric distortion and (ii) to predict whether the ionospheric distortion can be corrected by using the MAI-based ionospheric correction method.     

Ground- and space-based GPS data ingestion into the NeQuick model

This paper presents a technique for ingesting ground- and space-based dual-frequency GPS observations into a semi-empirical global electron density model. The NeQuick-2 model is used as the basis for describing the global electron density distribution. This model is mainly driven by the F2 ionosphere layer parameters (i.e. the electron density, N _m F2, and the height, h _m F2 of the F2 peak), which, in the absence of directly measured values, are computed from the ITU-R database (ITU-R 1997). This database was established using observations collected from 1954 to 1958 by a network of around 150 ionospheric sounders with uneven global coverage. It allows computing monthly median values of N _m F2 and h _m F2 (intra-month variations are averaged), for low and high solar activity. For intermediate solar activity a linear interpolation must be performed. Ground-based GNSS observations from a global network of ~350 receivers are pre-processed in order to retrieve slant total electron content (sTEC) information, and space-based GPS observations (radio occultation data from the FORMOSAT-3/COSMIC constellation) are pre-processed to retrieve electron density (ED) information. Both, sTEC and ED are ingested into the NeQuick-2 model in order to adapt N _m F2 and h _m F2, and reduce simultaneously both, the observed minus computed sTEC and ED differences. The first experimental results presented in this paper suggest that the data ingestion technique is self consistent and able to reduce the observed minus computed sTEC and ED differences to ~25–30% of the values computed from the ITU-R database. Although sTEC and ED are both derived from GPS observations, independent algorithm and models are used to compute their values from ground-based GPS observations and space-based FORMOSAT-3/COSMIC radio occultations. This fact encourages us to pursue this research with the aim to improve the results presented here and assess their accuracy in a reliable way.     

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.     

GNSS three carrier ambiguity resolution using ionosphere-reduced virtual signals

This paper presents a general modeling strategy for ambiguity resolution (AR) and position estimation (PE) using three or more phase-based ranging signals from a global navigation satellite system (GNSS). The proposed strategy will identify three best “virtual” signals to allow for more reliable AR under certain observational conditions characterized by ionospheric and tropospheric delay variability, level of phase noise and orbit accuracy. The selected virtual signals suffer from minimal or relatively low ionospheric effects, and thus are known as ionosphere-reduced virtual signals. As a result, the ionospheric parameters in the geometry-based observational models can be eliminated for long baselines, typically those of length tens to hundreds of kilometres. The proposed modeling comprises three major steps. Step 1 is the geometry-free determination of the extra-widelane (EWL) formed between the two closest L-band carrier measurements, directly from the two corresponding code measurements. Step 2 forms the second EWL signal and resolves the integer ambiguity with a geometry-based estimator alone or together with the first EWL. This is followed by a procedure to correct for the first-order ionospheric delay using the two ambiguity-fixed widelane (WL) signals derived from the integer-fixed EWL signals. Step 3 finds an independent narrow-lane (NL) signal, which is used together with a refined WL to resolve NL ambiguity with geometry-based integer estimation and search algorithms. As a result, the above two AR processes performed with WL/NL and EWL/WL signals respectively, either in sequence or in parallel, can support real time kinematic (RTK) positioning over baselines of tens to hundreds of kilometres, thus enabling centimetre-to-decimentre positioning at the local, regional and even global scales in the future.     

基于原始观测值的单频精密单点定位算法

研究了一种基于GPS原始观测值的单频PPP算法。该算法通过增加电离层延迟先验信息、空间和时间约束的虚拟观测方程,将电离层延迟当作未知参数与其他定位参数一并进行估计来高效修正电离层延迟误差。通过使用全球178个IGS站1d的实测数据对本算法的收敛速度、定位精度和电离层VTEC的精度进行检验与分析。结果表明,该算法的收敛速度和稳定性均得到了改善,其静态单频单天PPP解的精度可达2~3cm、模拟动态单频单天PPP解的精度可达2~3dm,并且单频PPP与双频PPP提取的电离层总电子含量平均偏差小于5个TECU,可作为一种附属定位产品使用。