A new two-step algorithm for ionospheric tomography solution

Ionospheric tomography inverse algorithms are usually an ill-conditioned problem because the geometric distribution of continuously operating reference GPS stations is not ideal for this task. In order to cope with such ill-conditioning, a new tomographic algorithm, termed two-step algorithm (TSA), is presented. The electron density is estimated in two steps: Phillips smoothing method (PSM) is first used to resolve the ill-conditioned problem in the ionospheric tomography system, and then, the PSM solution is input as an initial value to the multiplicative algebraic reconstruction technique (MART) and iteratively improved. Numerical simulations using the International Reference Ionosphere 2007 model demonstrate that the TSA is applicable to GPS-based ionospheric tomography reconstruction and is superior to PSM and MART when these techniques are used alone. The new algorithm is applied to reconstruct the ionospheric electron density distribution over China using GPS observations, and a comparison with ionosonde observations is made.     

Tomographic reconstruction of ionospheric electron density based on constrained algebraic reconstruction technique

A constrained algebraic reconstruction technique (CART) is proposed for the tomographic reconstruction of the ionospheric electron density distribution. The method uses a popular two-dimensional multi-point finite difference approximation of the second order Laplace operator to provide the constraint matrix. The tomographic results of a numerical simulation show that the reconstruction accuracy of electron density distribution is significantly improved. A careful validation of the reliability and superiority of CART is made. Finally, we applied the new method to the analysis of actual Global Navigation Satellite Systems (GNSS) observations and compared the results with ionosonde observation of Wuhan station.     

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.     

基于混合罚函数法的多尺度电离层层析确权方法

在利用GNSS进行像素基电离层层析时,多尺度层析方法利用权重因子将反演区域不同像素层析模型结合在一起,最终得到电离层电子密度反演结果,可以有效地解决电离层层析过程中不适应问题和最终的电离层电子密度失真现象。在多尺度电离层层析中,不同像素尺度层析模型之间权重是影响最终的电离层电子密度精度的重要因素。为了获得高精度电离层层析模型,考虑到权重因子存在着等式和不等式限制条件,采用解决最优化问题的罚函数法确定不同像素尺度电离层层析模型之间的权重。通过采用实测GNSS观测数据进行电离层多尺度电离层层析,对比了多尺度层析模型的各个子模型建模精度并进行分析,同时将罚函数法获得的模型精度与其他确权方法进行了对比,该方法可以有效地应用于多尺电离层度层析,且最终的层析模型精度优于其他确权方法,更优于单尺度电离层层析模型精度。     

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。     

A modified three-dimensional ionospheric tomography algorithm with side rays

The three-dimensional ionospheric tomography (3DCIT) algorithm based on Global Navigation Satellite System (GNSS) observations have been developed into an effective tool for ionospheric monitoring in recent years. However, because the rays that come into or come out from the side of the inversion region cannot be used, the distribution of the rays in the edge and bottom part of the inversion region is scarce and the electron density cannot be effectively improved in the inversion process. We present a three-dimensional tomography algorithm with side rays (3DCIT-SR) applying the side rays to the inversion. The partial slant total electron content (STEC) of side rays in the inversion region is obtained based on the NeQuick2 model and GNSS-STEC. The simulation experiment results show that the algorithm can effectively improve the distribution of GNSS rays in the inversion region. Meanwhile, the iteration accuracy has also been significantly improved. After the same number of iterations, the iterative results of 3DCIT-SR are closer to the truth than 3DCIT, in particular, the inversion of the edge regions is improved noticeably. The GNSS data of the International GNSS Service (IGS) stations in Europe are used to perform real data experiments, and the inversion results show that the electron density profiles of 3DCIT-SR are closer to the ionosonde measurements. The accuracy improvement of 3DCIT-SR is up to 56.3% while the improvement is more obvious during the magnetic storm compared to the case of a calm ionospheric state .     

Evaluating the effect of the global ionospheric map on aiding retrieval of radio occultation electron density profiles

Radio occultation (RO) has been proven to be a powerful technique for ionospheric electron density profile (EDP) retrieval. The Abel inversion currently used in RO EDP retrieval has degraded performance in regions with large horizontal gradients because of an assumption of spherical symmetry as indicated by many studies. Some alternative methods have been proposed in the past; the global ionospheric map (GIM)-aided Abel inversion is most frequently studied. Since the number of RO observations will likely increase rapidly in the near future, it is worthwhile to continue to improve retrieval method. In this study, both the simulations and the real data test have been done to evaluate the GIM-aided Abel inversion method. It is found that the GIM-aided Abel inversion can significantly improve upon the standard Abel inversion in either the F or the E region if an accurate GIM is available. However, the current IGS GIM does not appear accurate enough to improve retrieval results significantly, because of the spherical symmetry assumption and sparse global navigation satellite system (GNSS) stations used in its creation. Generating accurate GIM based on dense GNSS network to aid the Abel inversion might be an alternative method.     

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.     

电离层CT数据采集和图像重建

介绍低纬电离层CT实验所使用的数据自动采集系统并提出一种电离层CT算法。在数据采集过程中引入了GPS标准时间；重建算法的特点是利用差分多普勒频率数据避免了相位积分常数的计算，提高了对较弱的电离层扰动和不规则结构的检测能力。数值模拟反演结果表明了该算法对电离层CT重建的有效性，并给出有关实测数据的重建结果。     

利用区域地基GPS的电离层层析成像研究

电离层是近地空间的重要组成部分,如何对电离层的异常扰动进行合理监测与预报一直是空间物理领域的研究课题。本文将计算机层析成像技术引入到电离层扰动监测中,利用大量的区域地基GPS观测数据,借助代数层析迭代算法反演得到三维电离层电子密度;并将层析结果与国际电离层参考模型IRI2007进行对比分析,结果表明:地基GPS层析所得的电离层电子密度与IRI2007基本一致,但层析结果精度略高于IRI2007模型。     

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.     

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。     

日本九州岛地震震前电离层TEC异常

采用IGS发布的GIM数据,提出了一种结合滑动时窗法和临近格网点电离层TEC相关性分析法的联合分析方法,研究了震前电离层异常变化与地震的关系。通过分析震区附近5个格网点TEC的异常变化情况,发现震前电离层TEC发生明显异常变化,且格网点之间的TEC序列相关性受地震显著影响;通过分析二维电离层图的TEC异常空间分布,发现震前三天震中附近分别出现6h、12h和6h的异常。最后利用电离层层析的方法,对电离层异常时刻进行了电子密度的反演,进一步分析了电子密度在电离层异常时刻的分布情况。     

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。     

一种改进的电离层层析投影矩阵生成算法

<正>确建立投影矩阵是电离层层析的必要条件。由于反演区域较大且观测数据繁多,同时考虑到离散后格网的复杂性,传统的投影矩阵的计算算法中存在大量的重复计算,严重影响计算效率。文中对传统算法流程进行调整,在不改变计算结果的情况下,消除冗余计算,大大提高了计算效率。     

Analysis of inversion errors of ionospheric radio occultation

The retrieved electron density profile of ionospheric radio occultation (RO) simulation data can be compared with the background model value during the simulation and the inversion error can be obtained exactly. This paper studies the inversion error of ionospheric RO through simulation. The sources of the inversion errors are analyzed. The impacts of measurement errors, such as the errors in phase measurements and satellite orbits, are very small and can be neglected. The approximation of straight-line propagation introduces errors at the height of the F1 layer under solar maximum condition. The spherical symmetry approximation of the electron density distribution is found to be the main source of the inversion error. The statistical results reveal some characteristics of the inversion errors. (1) The relative error increases with enhanced solar activity. (2) It is larger in winter than in equinox season, and it is smallest in summer. (3) For all seasons, it is smaller at middle latitude than at other latitudes. (4) For all seasons and geomagnetic latitudes, it is smaller at daytime than at other times. The NmF2 of the ROs from COSMIC are compared with the measurements of ionosondes, and the relative differences show the same dependencies on season, geomagnetic latitude and local time, as the relative errors of the simulated ionospheric ROs.

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。     

Performance of the improved Abel transform to estimate electron density profiles from GPS occultation data

The Abel inversion is a straightforward tool to retrieve high-resolution vertical profiles of electron density from GPS radio occultations gathered by low earth orbiters (LEO). Nevertheless, the classical approach of this technique is limited by the assumption that the electron density in the vicinity of the occultation depends only on height (i.e., spherical symmetry), which is not realistic particularly in low-latitude regions or during ionospheric storms. Moreover, with the advent of recent satellite missions with orbits placed around 400 km (such as CHAMP satellite), an additional issue has to be dealt with: the treatment of the electron content above the satellite orbits. This paper extends the performance study of a method, proposed by the authors in previous works, which tackles both problems using an assumption of electron-density separability between the vertical total electron content and a shape function. This allows introducing horizontal information into the classic Abel inversion. Moreover, using both positive and negative elevation data makes it feasible to take into account the electron content above the LEO as well. Different data sets involving different periods of the solar cycle, periods of the day and satellites are studied in this work, confirming the benefits of this improved Abel transform approach.     

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.     

函数极值法求解三频GNSS最优载波相位组合观测量

GNSS三频载波相位组合观测量可以提高模糊度解算成功率和周跳探测与修复的可靠性。本文将载波相位组合观测量的噪声放大系数表示为与组合观测量波长和电离层延迟影响系数相关参数的函数,提出基于函数极值法求解特定波长和电离层延迟影响系数下的噪声最优线性组合系数。理论推导和计算结果表明,波长较长且以周为单位噪声放大系数较小的三频载波相位组合观测量,其以周为单位的电离层延迟放大系数随组合系数之和的增大而增大,约为线性组合系数之和的2.3倍;而电离层延迟影响较小且以周为单位噪声放大系数较小的三频载波相位组合观测量,其波长随线性组合系数之和的增大而减小。