Ionospheric path delay models for spaceborne GPS receivers flying in formation with large baselines

GPS relative navigation filters could benefit notably from an accurate modeling of the ionospheric delays, especially over large baselines (>100 km) where double difference delays can be higher than several carrier wavelengths. This paper analyzes the capability of ionospheric path delay models proposed for spaceborne GPS receivers in predicting both zero-difference and double difference ionospheric delays. We specifically refer to relatively simple ionospheric models, which are suitable for real-time filtering schemes. Specifically, two ionospheric delay models are evaluated, one assuming an isotropic electron density and the other considering the effect on the electron density of the Sun aspect angle. The prediction capability of these models is investigated by comparing predicted ionospheric delays with measured ones on real flight data from the Gravity Recovery and Climate Experiment mission, in which two satellites fly separated of more than 200 km. Results demonstrate that both models exhibit a correlation in the excess of 80% between predicted and measured double-difference ionospheric delays. Despite its higher simplicity, the isotropic model performs better than the model including the Sun effect, being able to predict double differenced delays with accuracy smaller than the carrier wavelength in most cases. The model is thus fit for supporting integer ambiguity fixing in real-time filters for relative navigation over large baselines. Concerning zero-difference ionospheric delays, results demonstrate that delays predicted by the isotropic model are highly correlated (around 90%) with those estimated using GPS measurements. However, the difference between predicted and measured delays has a root mean square error in the excess of 30 cm. Thus, the zero-difference ionospheric delays model is not likely to be an alternative to methods exploiting carrier-phase observables for cancelling out the ionosphere contribution in single-frequency absolute navigation filters.     

Precision analysis of troposphere sensing using GPS single-frequency signals

Various studies have been performed to investigate the accuracy of troposphere zenith wet delays (ZWDs) determined from GPS. Most of these studies use dual-frequency GPS data of large-scale networks with long baselines to determine the absolute ZWDs. For small-scale networks the estimability of the absolute ZWDs deteriorates due to high correlation between the solutions of the ZWDs and satellite-specific parameters as satellite clocks. However, as relative ZWDs (rZWDs) can always be estimated, irrespective of the size of the network, it is of interest to understand how the large-scale network rZWD-performance of dual-frequency GPS using an ionosphere-float model compares to the small-scale network rZWD-performance of single-frequency GPS using an ionosphere-weighted model. In this contribution such an analysis is performed using undifferenced and uncombined network parametrization modelling. In this context we demonstrate the ionosphere weighted constraints, which allows the determination of the rZWDs independent from signals on the second frequency. Based on an analysis of both simulated and real data, it is found that under quiet ionosphere conditions, the accuracy of the single-frequency determined rZWDs in the ionosphere-weighted network is comparable to that of the large-scale dual-frequency network without ionospheric constraints. Making use of the real data from two baselines of 15?days, it was found that the absolute differences of the rZWDs applying the two strategies are within 1?cm in over 90% and 95% of the time for ambiguity-float and -fixed cases, respectively.     

Kalman滤波估算电离层延迟的一种优化方法

频间偏差（Inter Frequency Bias,IFB）通常会给电离层延迟的解算带来误差.目前从电离层延迟中消除频间偏差的方法是基于GPS双频观测数据建立垂直电离层模型,利用卡尔曼滤波实时估算电离层模型系数和频间偏差.然而滤波过程中的测量噪声协方差矩阵没有考虑系统观测量之间的相关性,这会导致滤波模型不准确,进而影响最后求解的电离层延迟的准确性.本文选取了美国19个参考站的GPS双频观测数据,利用卡尔曼滤波实时估算电离层模型系数以及频间偏差.在滤波过程中,通过将先验频间偏差的估计方差引入测量噪声方差,实现对测量噪声协方差矩阵的优化.计算结果表明,优化后得到的卫星频间偏差与欧洲定轨中心（Center for Orbit Determination in Europe,CODE）得到的频间偏差更接近.将优化后的电离层延迟代入伪距解算,得到的位置误差的标准差在东向和天顶向分别下降了12.5%和15.4%,天顶向误差平均值下降了17.6%,定位精度得到提高.      

Higher order ionospheric propagation effects on GPS radio occultation signals

With the increasing number of remote sensing satellites using the GPS radio occultation technique for atmospheric sounding, the estimation of higher order ionospheric effects and their mitigation have become relevant and important. Due to long ionospheric limb paths, GPS signals are strongly affected by ionospheric refraction during radio occultation. Standard dual-frequency GPS measurements may be used to estimate the first order term of the refractive index. However, non-linear terms such as the second and third order ionospheric terms and ray path bending effects are not considered in occultation measurements so far. Analysing selected CHAMP–GPS occultation events different higher order ionospheric terms are estimated and their effects on dual-frequency range estimation and total electron content (TEC) estimation are discussed. We have found that the separation between the GPS L1 and L2 ray paths exceeds the kilometer level during occultation for a vertical TEC level of more than 160 TEC units. Corresponding errors in the GPS dual-frequency range estimation and TEC estimation are found to exceed the meter and 10 TEC units level, respectively.     

基于单频星载GPS数据的低轨卫星精密定轨

为满足搭载单频GPS接收机低轨卫星的精密定轨需求以及深化单频定轨研究,文中解决了单频星载GPS数据的周跳探测问题,并利用“海洋二号”（HY-2A）卫星及“资源三号”（ZY-3）卫星的单频星载GPS实测数据采用两种方法确定了二者的简化动力学轨道,并通过观测值残差分析、与双频精密轨道比较、激光测卫数据检核等方法对所得轨道精度进行评定。结果表明,在不考虑电离层延迟影响的情况下,HY-2A卫星定轨精度为2~3dm,ZY-3卫星为1m左右;而采用半和改正组合消除电离层延迟一阶项影响后,二者定轨精度均显著提高,HY-2A卫星三维精度提高至1dm左右,ZY-3卫星提高至1~2dm。文章的研究成果表明,搭载单频GPS接收机的低轨卫星也可获得厘米级的定轨精度。     

Demonstration of the use of the Doppler Orbitography and Radio positioning Integrated by Satellite (DORIS) measurements to validate GPS ionospheric imaging

There is a lack of independent ionospheric data that can be used to validate GPS imaging results at mid latitudes over severe storm times. Doppler Orbitography and Radio positioning Integrated by Satellite (DORIS), a global network of dual-frequency ground to satellite observations, provides this missing data and here is employed as verification to show the accuracy of the ionospheric GPS images in terms of the total electron content (TEC). In this paper, the large-scale ionospheric structures that appeared during the strong geomagnetic storm of 20 November 2003 are reconstructed with a GPS tomographic algorithm, known as MIDAS, and validated with DORIS TEC measurements. The main trough shown in an extreme equatorward position in the ionospheric imaging over mainland Europe is confirmed by DORIS satellite measurements. Throughout the disturbed day, the variations of relative slant TECs between DORIS data and MIDAS results agree quite well, with the average of the mean differences about 2 TECu. We conclude that as a valuable supplement to GPS data, DORIS ionospheric measurements can be used to analyse TEC variations with a relatively high resolution, ∼10 s in time and tens of kilometres in space. This will be very helpful for identification of some highly dynamic structures in the ionosphere found at mid-latitudes, such as the main trough, TID (Travelling Ionospheric Disturbances) and SED (Storm Enhanced Density), and could be used as a valuable auxiliary data source in ionospheric imaging.     

Total electron content measurements in ionospheric physics

With the advent of modern global networks of dual-frequency Global Positioning System (GPS), total electron content (TEC) measurements along slant paths connecting GPS receivers and satellites at 22,000 km have become the largest data set available to ionospheric scientists. The TEC can be calculated from the time and phase delay in the GPS signal using the GPS Toolkit, but an unknown bias will remain. In addition, UHF/VHF radio beacons on board low-Earth-orbiting satellites can also be used to measure the electron content. However, the TEC measurements are obtained by integrating TEC differences between slant paths, but also contain biases. It is often necessary to use data assimilative algorithms like the Ionospheric Data Assimilation Three-Dimensional (IDA3D), and to treat both GPS- and LEO-beacon TEC measurements as relative data in order to conduct ionospheric studies.     

GPS data processing of networks with mixed single- and dual-frequency receivers for deformation monitoring

In order to obtain crustal deformations of higher spatial resolution, existing GPS networks must be densified. This densification can be carried out using single-frequency receivers at moderate costs. However, ionospheric delay handling is required in the data processing. We adapt the Satellite-specific Epoch-differenced Ionospheric Delay model (SEID) for GPS networks with mixed single- and dual-frequency receivers. The SEID model is modified to utilize the observations from the three nearest dual-frequency reference stations in order to avoid contaminations from more remote stations. As data of only three stations are used, an efficient missing data constructing approach with polynomial fitting is implemented to minimize data losses. Data from large scale reference networks extended with single-frequency receivers can now be processed, based on the adapted SEID model. A new data processing scheme is developed in order to make use of existing GPS data processing software packages without any modifications. This processing scheme is evaluated using a sub-network of the German SAPOS network. The results verify that the new scheme provides an efficient way to densify existing GPS networks with single-frequency receivers.     

Sensing snow height and surface temperature variations in Greenland from GPS reflected signals

The in situ measurements of snow surface temperature (SST) and snow height (SH) are very difficult with high costs, particularly in Greenland Ice Sheet (GrIS). Since the snow depth variations coupling with surface temperature are related to GPS multipath, it is possible to estimate the snow depth and surface air temperature variations by incorporating GPS-Reflectometry (GPS-R). In this paper, the reflected signals from ground GPS receivers are used to sense the SST and SH variations based on the thermophysical behavior and variations of snow layer from April to June 2010 at SMM1 site and from March to December 2010 at MARG site in Greenland. The results show that the mean daily changes in the ionospheric geometrical-free linear combination (GPS-L4) of dual-frequency GPS signals are related to daily SST and SH variations. The nonparametric bootstrapping model in direct (forward) and inverse models are developed and applied to estimate the SST and SH variations. The mean biases of SST and SH estimates are 0.18 °C and 0.23 m at SMM1 site, respectively, and 3.8 °C and 0.13 m at MARG site, respectively.     

Evaluation of COMPASS ionospheric model in GNSS positioning

As important products of GNSS navigation message, ionospheric delay model parameters are broadcasted for single-frequency users to improve their positioning accuracy. GPS provides daily Klobuchar ionospheric model parameters based on geomagnetic reference frame, while the regional satellite navigation system of China’s COMPASS broadcasts an eight-parameter ionospheric model, COMPASS Ionospheric Model(CIM), which was generated by processing data from continuous monitoring stations, with updating the parameters every 2 h. To evaluate its performance, CIM predictions are compared to ionospheric delay measurements, along with GPS positioning accuracy comparisons. Real observed data analysis indicates that CIM provides higher correction precision in middle-latitude regions, but relatively lower correction precision for low-latitude regions where the ionosphere has much higher variability. CIM errors for some users show a common bias for in-coming COMPASS signals from different satellites, and hence ionospheric model errors are somehow translated into the receivers’ clock error estimation. In addition, the CIM from the China regional monitoring network are further evaluated for global ionospheric corrections. Results show that in the Northern Hemisphere areas including Asia, Europe and North America, the three-dimensional positioning accuracy using the CIM for ionospheric delay corrections is improved by 7.8%–35.3% when compared to GPS single-frequency positioning ionospheric delay corrections using the Klobuchar model. However, the positioning accuracy in the Southern Hemisphere is degraded due apparently to the lack of monitoring stations there.     

Calibration errors in determining slant Total Electron Content (TEC) from multi-GNSS data

The global navigation satellite system (GNSS) is presently a powerful tool for sensing the Earth's ionosphere. For this purpose, the ionospheric measurements (IMs), which are by definition slant total electron content biased by satellite and receiver differential code biases (DCBs), need to be first extracted from GNSS data and then used as inputs for further ionospheric representations such as tomography. By using the customary phase-to-code leveling procedure, this research comparatively evaluates the calibration errors on experimental IMs obtained from three GNSS, namely the US Global Positioning System (GPS), the Chinese BeiDou Navigation Satellite System (BDS), and the European Galileo. On the basis of ten days of dual-frequency, triple-GNSS observations collected from eight co-located ground receivers that independently form short-baselines and zero-baselines, the IMs are determined for each receiver for all tracked satellites and then for each satellite differenced for each baseline to evaluate their calibration errors. As first derived from the short-baseline analysis, the effects of calibration errors on IMs range, in total electron content units, from 1.58 to 2.16, 0.70 to 1.87, and 1.13 to 1.56 for GPS, Galileo, and BDS, respectively. Additionally, for short-baseline experiment, it is shown that the code multipath effect accounts for their main budget. Sidereal periodicity is found in single-differenced (SD) IMs for GPS and BDS geostationary satellites, and the correlation of SD IMs over two consecutive days achieves the maximum value when the time tag is around 4?min. Moreover, as byproducts of zero-baseline analysis, daily between-receiver DCBs for GPS are subject to more significant intra-day variations than those for BDS and Galileo.     

基于双频GPS观测的电离层TEC与硬件延迟反演方法

利用全球定位系统（Global Positioning System,GPS）的双频观测数据反演得到电离层的总电子含量（Total Electron Content,TEC）,使得广域甚至全球范围高时空分辨率的电离层观测研究成为可能,但由于GPS卫星和接收机对信号的硬件延迟可导致TEC测量系统偏差,因此,需要探索反演TEC并估测GPS卫星与接收机硬件延迟的有效算法.本文根据电离层电波传播理论,阐述了基于双频GPS观测提取电离层TEC的方法,给出TEC与硬件延迟的基本关系.综合研究了TEC与硬件延迟的反演方法,进行分析与归纳分类,在此基础上提出了有待深入研究的问题.      

GPS scintillation and TEC gradients at equatorial latitudes in April 2006

We use observations of ionospheric scintillation at equatorial latitudes from two GPS receivers specially modified for recording, at a sampling rate of 50 Hz, the phase and the amplitude of the L1 signal and the Total Electron Content (TEC) from L1 and L2. The receivers, called GISTM (GPS Ionospheric Scintillation and TEC Monitor), are located in Vietnam (Hue, 16.4°N, 107.6°E; Hoc Mon, 10.9°N, 106.6°E). These experimental observations are analysed together with the tomographic reconstruction of the ionosphere produced by the Multi-Instrument Data Analysis System (MIDAS) for investigating the moderate geomagnetic storm which occurred on early April 2006, under low solar activity. The synergic adoption of the ionospheric imaging and of the GISTM measurements supports the identification of the scale-sizes of the ionospheric irregularities causing scintillations and helps the interpretation of the physical mechanisms generating or inhibiting the appearance of the equatorial F layer irregularities. In particular, our study attributes to the turning of the IMF (Interplanetary Magnetic Field) between northward and southward direction an important role in the inhibition of the generation of spread F irregularities resulting in a lack of scintillation enhancement in the post-sunset hours.     

Preliminary analysis of the quality and positioning performance of BDS-3 global interoperable signal B1C&B2a

BeiDou-3 Navigation Satellite System (BDS-3) satellites are equipped with the new generation GNSS signals B1C and B2a, which support the interoperability with GPS and Galileo systems. In this study, the pseudo-range multipath error and carrier phase observation noise of the BDS-3 B1C and B2a signals were evaluated based on zero baseline measurements from the day of year (DOY) 113 to 116, 2020. Further, the precision and performance of the single point positioning (SPP) and precise point positioning (PPP) are assessed at 9 stations. This assessment manifests that the standard deviations (STDs) of the pseudo-range multipath error are about 0.09 ~ 0.22 m, while STDs of the carrier phase observation noise are about 0.075 mm. For the single-frequency SPP, its positioning precision is about 2.03 ~ 4.85 m and 3.29 ~ 10.73 m at the 99.99% confidence level in horizontal and vertical directions, respectively, while the dual-frequency SPP precision is about 1.92 ~ 8.02 m and 4.81 ~ 12.77 m in horizontal and vertical directions, respectively. For the daily static PPP, the convergence time is about 20 ~ 30 min, while the daily positioning precision can reach 1.38 ~ 4.42 cm and -1.31 ~ 4.34 cm in horizontal and vertical directions, respectively. In general, the quality and the SPP and PPP performance of the BDS-3 B1C&B2a signals are comparable to the GPS and Galileo.     

Ionospheric scintillations at Guilin detected by GPS ground-based and radio occultation observations

The occurrence of ionospheric scintillations with S4 ? 0.2 was studied using GPS measurements at Guilin, China (25.29°N, 110.33°E; geomagnetic: 15.04°N, 181.98°E), a station located near the northern crest of the equatorial anomaly. The results are presented for data collected from January 2009 to March 2010. The results show that nighttime amplitude scintillations only took place in February and March of the considered years, while daytime amplitude scintillations occurred in August and December of 2009. Nighttime amplitude scintillations, observed in the south of Guilin, always occurred with phase scintillations, TEC (Total Electron Content) depletions, and ROT (Rate Of change of TEC) fluctuations. However, TEC depletions and ROT fluctuations were weak during daytime amplitude scintillations, and daytime amplitude scintillations always took place simultaneously for most of the GPS satellites which appeared over Guilin in different azimuth directions. Ground-based GPS scintillation/TEC observations recorded at Guilin and signal-to-noise-ratio (SNR) measurements obtained from GPS-COSMIC radio occultation indicate that nighttime and daytime scintillations are very likely caused by ionospheric F region irregularities and sporadic E, respectively. Moreover, strong daytime amplitude scintillations may be associated with the plasma density enhancements in ionospheric E region caused by the Perseid and Geminid meteor shower activities.     

基于北斗GEO卫星双频观测值连续监测电离层延迟

利用北斗GEO卫星观测数据直接计算电离层延迟。由于GEO卫星具有固定穿刺点和静地的特性,使得观测站监测电离层变化时可不考虑空间变化,并可进行连续不间断监测。通过分析北斗GEO卫星三种频率码伪距和载波相位观测值不同组合,选取B1&B2双频计算电离层延迟为最优组合,采用相位平滑伪距的方法计算电离层延迟TEC,相较其他电离层模型,该方法的优点是不会引入模型误差,可得到连续的高精度的电离层延迟监测结果。     

The impact of microwave absorber and radome geometries on GNSS measurements of station coordinates and atmospheric water vapour

We have used microwave absorbing material in different geometries around ground-based Global Navigation Satellite System (GNSS) antennas in order to mitigate multipath effects on the estimates of station coordinates and atmospheric water vapour. The influence of a hemispheric radome – of the same type as in the Swedish GPS network SWEPOS – was also investigated. Two GNSS stations at the Onsala Space Observatory were used forming a 12 m baseline. GPS data from October 2008 to November 2009 were analyzed by the GIPSY/OASIS II software using the Precise Point Positioning (PPP) processing strategy for five different elevation cutoff angles from 5° to 25°. We found that the use of the absorbing material decreases the offset in the estimated vertical component of the baseline from ∼27 mm to ∼4 mm when the elevation cutoff angle varies from 5° to 20°. The horizontal components are much less affected. The corresponding offset in the estimates of the atmospheric Integrated Water Vapour (IWV) decreases from ∼1.6 kg/m² to ∼0.3 kg/m². Changes less than 5 mm in the offsets in the vertical component of the baseline are seen for all five elevation cutoff angle solutions when the antenna was covered by a hemispheric radome. Using the radome affects the IWV estimates less than 0.4 kg/m² for all different solutions. IWV comparisons between a Water Vapour Radiometer (WVR) and the GPS data give consistent results.     

Global characteristics of ionospheric electric fields and disturbances during the first hours of magnetic storms

The ionospheric plasma density can be significantly disturbed during magnetic storms. In the conventional scenario of ionospheric storms, the negative storm phases with plasma density decreases are caused by neutral composition changes, and the positive storm phases with plasma density increases are often related to atmospheric gravity waves. However, recent studies show that the global redistribution of the ionospheric plasma is dominated primarily by electric fields during the first hours of magnetic storms. In this paper, we present the measurements of ionospheric disturbances by the DMSP satellites and GPS network during the magnetic storm on 6 April 2000. The DMSP measurements include the F region ion velocity and density at the altitude of ∼840 km, and the GPS receiver network provides total electron content (TEC) measurements. The storm-time ionospheric disturbances show the following characteristics. The plasma density is deeply depleted in a latitudinal range of ∼20° over the equatorial region in the evening sector, and the depletions represent plasma bubbles. The ionospheric plasma density at middle latitudes (20°–40° magnetic latitudes) is significantly increased. The dayside TEC is increased simultaneously over a large latitudinal range. An enhanced TEC band forms in the afternoon sector, goes through the cusp region, and enters the polar cap. All the observed ionospheric disturbances occur within 1–5 h from the storm sudden commencement. The observations suggest that penetration electric fields play a major role in the rapid generation of equatorial plasma bubbles and the simultaneous increases of the dayside TEC within the first 2 h during the storm main phase. The ionospheric disturbances at later times may be caused by the combination of penetration electric fields and neutral wind dynamo process.     

The GFZ real-time GNSS precise positioning service system and its adaption for COMPASS

Motivated by the IGS real-time Pilot Project, GFZ has been developing its own real-time precise positioning service for various applications. An operational system at GFZ is now broadcasting real-time orbits, clocks, global ionospheric model, uncalibrated phase delays and regional atmospheric corrections for standard PPP, PPP with ambiguity fixing, single-frequency PPP and regional augmented PPP. To avoid developing various algorithms for different applications, we proposed a uniform algorithm and implemented it into our real-time software. In the new processing scheme, we employed un-differenced raw observations with atmospheric delays as parameters, which are properly constrained by real-time derived global ionospheric model or regional atmospheric corrections and by the empirical characteristics of the atmospheric delay variation in time and space. The positioning performance in terms of convergence time and ambiguity fixing depends mainly on the quality of the received atmospheric information and the spatial and temporal constraints. The un-differenced raw observation model can not only integrate PPP and NRTK into a seamless positioning service, but also syncretize these two techniques into a unique model and algorithm. Furthermore, it is suitable for both dual-frequency and sing-frequency receivers. Based on the real-time data streams from IGS, EUREF and SAPOS reference networks, we can provide services of global precise point positioning (PPP) with 5–10 cm accuracy, PPP with ambiguity-fixing of 2–5 cm accuracy, PPP using single-frequency receiver with accuracy of better than 50 cm and PPP with regional augmentation for instantaneous ambiguity resolution of 1–3 cm accuracy. We adapted the system for current COMPASS to provide PPP service. COMPASS observations from a regional network of nine stations are used for precise orbit determination and clock estimation in simulated real-time mode, the orbit and clock products are applied for real-time precise point positioning. The simulated real-time PPP service confirms that real-time positioning services of accuracy at dm-level and even cm-level is achievable with COMPASS only.     

A MARS-based method for estimating regional 2-D ionospheric VTEC and receiver differential code bias

The geometry-free linear combination of dual-frequency GNSS reference station ground observations are currently used to build the Vertical Total Electron Content (VTEC) model of the ionosphere. As it is known, besides ionospheric delays, there are differential code bias (DCB) of satellite (SDCB) and receiver (RDCB) in the geometry-free observation equation. The SDCB can be obtained using the International GNSS Service (IGS) analysis centers, but the RDCB for regional and local network receivers are not provided. Therefore, estimating the RDCB and VTEC model accurately and simultaneously is a critical factor investigated by researchers. This study uses Multivariate Adaptive Regression Splines (MARS) to estimate the VTEC approximate model and then substitutes this model in the observation equation to form the normal equation. The least squares method is used to solve the RDCB and VTEC model together. The research findings show that this method has good modeling effectiveness and the estimated RDCB has good reliability. The estimated VTEC model applied to GPS single-frequency precise point positioning has better positioning accuracy in comparison to the IGS global ionosphere map (GIM).