Multi-GNSS contributions to differential code biases determination and regional ionospheric modeling in China

Due to the limited number and uneven distribution globally of Beidou Satellite System (BDS) stations, the contributions of BDS to global ionosphere modeling is still not significant. In order to give a more realistic evaluation of the ability for BDS in ionosphere monitoring and multi-GNSS contributions to the performance of Differential Code Biases (DCBs) determination and ionosphere modeling, we select 22 stations from Crustal Movement Observation Network of China (CMONOC) to assess the result of regional ionospheric model and DCBs estimates over China where the visible satellites and monitoring stations for BDS are comparable to those of GPS/GLONASS. Note that all the 22 stations can track the dual- and triple-frequency GPS, GLONASS, and BDS observations. In this study, seven solutions, i.e., GPS-only (G), GLONASS-only (R), BDS-only (C), GPS + BDS (GC), GPS + GLONASS (GR), GLONASS + BDS (RC), GPS + GLONASS + BDS (GRC), are used to test the regional ionosphere modeling over the experimental area. Moreover, the performances of them using single-frequency precise point positioning (SF-PPP) method are presented. The experimental results indicate that BDS has the same ionospheric monitoring capability as GPS and GLONASS. Meanwhile, multi-GNSS observations can significantly improve the accuracy of the regional ionospheric models compared with that of GPS-only or GLONASS-only or BDS-only, especially over the edge of the tested region which the accuracy of the model is improved by reducing the RMS of the maximum differences from 5–15 to 2–3 TECu. For satellite DCBs estimates of different systems, the accuracy of them can be improved significantly after combining different system observations, which is improved by reducing the STD of GPS satellite DCB from 0.243 to 0.213, 0.172, and 0.165 ns after adding R, C, and RC observations respectively, with an increment of about 12.3%, 29.4%, and 32.2%. The STD of GLONASS satellite DCB improved from 0.353 to 0.304, 0.271, and 0.243 ns after adding G, C, and GC observations, respectively. The STD of BDS satellite DCB reduced from 0.265 to 0.237, 0.237 and 0.229 ns with the addition of G, R and GR systems respectively, and increased by 10.6%, 10.4%, and 13.6%. From the experimental positioning result, it can be seen that the regional ionospheric models with multi-GNSS observations are better than that with a single satellite system model.     

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).     

Differential code bias estimation based on uncombined PPP with LEO onboard GPS observations

Differential Code Bias (DCB) is an essential correction that must be provided to the Global Navigation Satellite System (GNSS) users for precise position determination. With the continuous deployment of Low Earth Orbit (LEO) satellites, DCB estimation using observations from GNSS receivers onboard the LEO satellites is drawing increasing interests in order to meet the growing demands on high-quality DCB products from LEO-based applications, such as LEO-based GNSS signal augmentation and space weather research. Previous studies on LEO-based DCB estimation are usually using the geometry-free combination of GNSS observations, and it may suffer from significant leveling errors due to non-zero mean of multipath errors and short-term variations of receiver code and phase biases. In this study, we utilize the uncombined Precise Point Positioning (PPP) model for LEO DCB estimation. The models for uncombined PPP-based LEO DCB estimation are presented and GPS observations acquired from receivers onboard three identical Swarm satellites from February 1 to 28, 2019 are used for the validation. The results show that the average Root Mean Square errors (RMS) of the GPS satellite DCBs estimated with onboard data from each of the three Swarm satellites using the uncombined PPP model are less than 0.18 ns when compared to the GPS satellite DCBs obtained from IGS final daily Global Ionospheric Map (GIM) products. Meanwhile, the corresponding average RMS of GPS satellite DCBs estimated with the conventional geometry-free model are 0.290, 0.210, 0.281 ns, respectively, which are significantly larger than those obtained with the uncombined PPP model. It is also noted that the estimated GPS satellite DCBs by Swarm A and C satellites are highly correlated, likely attributed to their similar orbit type and space environment. On the other hand, the Swarm receiver DCBs estimated with uncombined PPP model, with Standard Deviation (STD) of 0.065, 0.037 and 0.071 ns, are more stable than those obtained from the official Swarm Level 2 products with corresponding STD values of 0.115, 0.101, and 0.109 ns, respectively. The above indicates that high-quality DCB products can be estimated based on uncombined PPP with LEO onboard observations.     

An improved approach to model regional ionosphere and accelerate convergence for precise point positioning

Given the severe effects of the ionosphere on global navigation satellite system (GNSS) signals, single-frequency (SF) precise point positioning (PPP) users can only achieve decimeter-level positioning results. Ionosphere-free combinations can eliminate the majority of ionospheric delay, but increase observation noise and slow down dual-frequency (DF) PPP convergence. In this paper, we develop a regional ionosphere modeling and rapid convergence approach to improve SF PPP (SFPPP) accuracy and accelerate DF PPP (DFPPP) convergence speed. Instead of area model, ionospheric delay is modeled for each satellite to be used as a priori correction. With the ionospheric, wide-lane uncalibrated phase delay (UPD) and residuals satellite DCBs product, the wide-lane observations for DF users change to be high-precision pseudorange observations. The validation of a continuously operating reference station (CORS) network was analyzed. The experimental results confirm that the approach considerably improves the accuracy of SFPPP. For DF users, convergence time is substantially reduced.     

Comparative analysis of four different single-frequency PPP models on positioning performance and atmosphere delay retrieval

Single-frequency precise point positioning (SF-PPP) has attracted increasing attention due to its high precision and cost effectiveness. With various strategies to handle the dominant error, i.e., ionosphere delay, the ionosphere-float (IF), ionosphere-free-half (IFH), ionosphere-corrected (IC), and ionosphere-weighted (IW) SF-PPP models are certain to possess different characteristics and performance levels. This study is dedicated to assessing and comparing the four models from model characteristics, positioning performance, and atmosphere delay retrieval. The model comparison shows that IC and IW models are full-rank while IF and IFH models have a rank deficiency of size one that will result in biased estimations, which means the better solvability of IC and IW models. The experiments are carried out based on the 7-day Global Positioning System (GPS) observations collected at 57 global Multi-GNSS Experiment (MGEX) stations and Global Ionosphere Map (GIM) products. The results indicate that the IW model can accelerate SF-PPP convergence and achieve higher positioning accuracy compared to the other three SF-PPP models, especially in kinematic mode. With convergence criteria of 0.25 m in horizontal and 0.5 m in vertical, the east/north/up convergence times of IW model are 0.5/15.0/25.0 min and 0.5/16.0/36.5 min for static and kinematic modes, respectively. The IW model is able to achieve an instantaneous positioning accuracy of 0.28/0.35/0.75 m. In addition, a real kinematic test also demonstrates the best positioning solutions of IW model. Regarding troposphere delay retrieval, the IF, IFH, and IW models obtain a comparable daily accuracy of 3.0 cm on average, while the IC model achieves the worst accuracy of 8.0 cm. For precise ionosphere delay estimation, IW model only needs an average initialization time of 34.3 min, but a longer initialization time of 51.6 min is required for IF model. The daily precision of ionosphere delay estimation for IW model can reach up to 10.8 cm. At the present accuracy of GIM products, it is suggested that the IW model should be adopted for SF-PPP first due to its superior performance in positioning and atmosphere delay retrieval.     

Contribution analysis of QZSS to single-frequency PPP of GPS/BDS/GLONASS/Galileo

The Quasi-Zenith Satellite System (QZSS) established by the Japan Aerospace Exploration Agency mainly serves the Asia-Pacific region and its surrounding areas. Currently, four in-orbit satellites provide services. Most users of GNSS in the mass market use single-frequency (SF) receivers owing to the low cost. Therefore, it is meaningful to analyze and evaluate the contribution of the QZSS to SF precise point positioning (PPP) of GPS/BDS/GLONASS/Galileo systems with the emergence of GNSS and QZSS. This study compares the performances of three SF PPP models, namely the GRoup and PHase Ionospheric Correction (GRAPHIC) model, GRAPHIC with code observation model, and an ionosphere-constrained model, and evaluated the contribution of the QZSS to the SF PPP of GPS/BDS/GLONASS/Galileo systems. Moreover, the influence of code bias on the SF PPP of the BDS system is also analyzed. A two-week dataset (DOY 013–026, 2019) from 10 stations of the MGEX network is selected for validation, and the results show that: (1) For cut-off elevation angles of 15, 20, and 25°, the convergence times for the static SF PPP of GLONASS + QZSS are reduced by 4.3, 30.8, and 12.7%, respectively, and the positioning accuracy is similar compared with that of the GLONASS system. Compared with the BDS single system, the convergence times for the static SF PPP of BDS + QZSS under 15 and 25° are reduced by 37.6 and 39.2%, the horizontal positioning accuracies are improved by 18.6 and 14.1%, and the vertical components are improved by 13.9 and 21.4%, respectively. At cut-off elevation angles of 15, 20, and 25°, the positioning accuracy and precision of GPS/BDS/GLONASS/Galileo + QZSS is similar to that of GPS/BDS/GLONASS/Galileo. And the convergence times are reduced by 7.4 and 4.3% at cut-off elevation angles of 20 and 25°, respectively. In imitating dynamic PPP, the QZSS significantly improves the positioning accuracy of BDS and GLONASS. However, QZSS has little effect on the GPS-only, Galileo-only and GPS/BDS/GLONASS/Galileo. (2) The code bias of BDS IGSO and MEO cannot be ignored in SF PPP. In static SF PPP, taking the frequency band of B1I whose multipath combination is the largest among the frequency bands as an example, the vertical component has a systematic bias of approximately 0.4–1.0 m. After correcting the code bias, the positioning error in the vertical component is lower than 0.2 m, and the positioning accuracy in the horizontal component are improved accordingly. (3) The SF PPP model with ionosphere constraints has a better convergence speed, while the positioning accuracy of the three models is nearly equal. Therefore the GRAPHIC model can be used to get good positioning accuracy in the absence of external ionosphere products, but its convergence speed is slower.     

电离层周日变化对解算GPS硬件延迟稳定性的影响

针对电离层周日变化特征分析了其可能对SCORE方法估算的硬件延迟稳定性的影响. 利用BJFS以及XIAM台站的GPS观测数据, 解算了位于太阳活动高年(2001年)和太阳活动低年(2009年)的卫星硬件延迟并分析了估算的硬件延迟的稳定性. 研究发现, 电离层周日变化对估算的硬件延迟稳定性具有一定影响, 但是利用不同台站所得到的卫星硬件延迟稳定性在昼夜不同时间上的解算结果存在一定差异. 电离层周日变化对利用 BJFS台站数据解算的硬件延迟稳定性日夜差异较为明显, 在太阳活动高年利用XIAM 台站数据解算的硬件延迟日夜稳定性差异不很明显, 由于XIAM台站处于电离层赤道异常峰附近, 夜间电离层变化很大, 因此对比中纬度地区, 电离层周日变化对赤道异常峰附近地区硬件延迟稳定性解算结果的影响相对较小, 但在太阳活动低年, 其影响仍较为显著.      

Estimation and analysis of GPS receiver differential code biases using KGN in Korean Peninsula

The total electron content (TEC) estimation by the Global Positioning System (GPS) can be seriously affected by the differential code biases (DCB), referred to as inter-frequency biases (IFB), of the satellite and receiver so that an accuracy of GPS–TEC value is dependent on the error of DCBs estimation. In this paper, we proposed the singular value decomposition (SVD) method to estimate the DCB of GPS satellites and receivers using the Korean GPS network (KGN) in South Korea. The receiver DCBs of about 49 GPS reference stations in KGN were determined for the accurate estimation of the regional ionospheric TEC. They obtained from the daily solution have large biases ranging from +5 to +27 ns for geomagnetic quiet days. The receiver DCB of SUWN reference station was compared with the estimates of IGS and JPL global ionosphere map (GIM). The results have shown comparatively good agreement at the level within 0.2 ns. After correction of receiver DCBs and knowing the satellite DCBs, the comparison between the behavior of the estimated TEC and that of GIMs was performed for consecutive three days. We showed that there is a good agreement between KASI model and GIMs.     

南极GPS定位中的电离层延迟分析

基于南极地区国际GNSS服务组织(IGS,International GNSS Service)跟踪站的全球定位系统(GPS,Global Position System)双频实测数据,分析了南极地区电离层延迟的变化情况及其二阶项延迟对南极GPS定位结果的影响.结果表明:南极地区的总电子含量(TEC,Total Electron Content)日间波动频繁,其日间TEC最大值变化较中纬度地区剧烈;在南极地区夏季,电离层二阶项延迟对GPS定位结果的影响可达cm级.同时,由于欧洲定轨中心(CODE,The European Center for Orbit Determination)提供的全球电离层模型(GIM,Global Ionosphere Maps)在南极区域应用的局限性,通过选取南极地区6个IGS跟踪站作为基准站建立了区域电离层TEC模型(RIM,Regional Ionosphere Model).经实测数据计算证明,对于南极地区,RIM的定位精度在一定程度上优于全球电离层模型GIM.     

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.     

基于三频数据的北斗卫星导航系统DCB参数精度评估方法

差分码偏差（Differential Code Biases,DCB）参数作为导航电文中重要的一项,是影响用户PNT服务的主要误差源之一。北斗卫星导航系统（后文简称“北斗系统”）发射三个频点的导航信号,在导航电文中需要发播卫星的2个TGD（Timing Group Delay）参数。文章首先介绍了北斗系统卫星DCB参数最小二乘解算与形式误差评估;其次根据北斗系统三频特点,提出了不同频点组合计算垂直方向电离层电子总含量（VTEC）互差的DCB精度定量评估方法,并与IGS(International GNSS Service)提供的GPS卫星DCB精度进行比较;最后,详细分析了DCB参数精度对用户等效距离误差（UERE）计算和定位计算的影响,分别采用卫星出场标定DCB参数和经过解算DCB参数进行评估。实测数据分析结果表明,北斗系统卫星DCB参数解算形式误差与IGS解算GPS卫星DCB参数形式误差相当,但受卫星类型和解算测站的几何分布限制,北斗系统卫星DCB参数解算不确定度相比IGS略差,估计精度优于0.5ns,不同频率组合计算VTEC互差绝对值均值优于0.6TECU。相比采用卫星出场标定值,采用系统解算DCB参数后,双频用户三维位置误差改善13.80%～47.42%。     

Near real-time PPP-based monitoring of the ionosphere using dual-frequency GPS/BDS/Galileo data

Ionosphere delay is very important to GNSS observations, since it is one of the main error sources which have to be mitigated even eliminated in order to determine reliable and precise positions. The ionosphere is a dispersive medium to radio signal, so the value of the group delay or phase advance of GNSS radio signal depends on the signal frequency. Ground-based GNSS stations have been used for ionosphere monitoring and modeling for a long time. In this paper we will introduce a novel approach suitable for single-receiver operation based on the precise point positioning (PPP) technique. One of the main characteristic is that only carrier-phase observations are used to avoid particular effects of pseudorange observations. The technique consists of introducing ionosphere ambiguity parameters obtained from PPP filter into the geometry-free combination of observations to estimate ionospheric delays. Observational data from stations that are capable of tracking the GPS/BDS/GALILEO from the International GNSS Service (IGS) Multi-GNSS Experiments (MGEX) network are processed. For the purpose of performance validation, ionospheric delays series derived from the novel approach are compared with the global ionospheric map (GIM) from Ionospheric Associate Analysis Centers (IAACs). The results are encouraging and offer potential solutions to the near real-time ionosphere monitoring.     

Estimation of differential code biases with Jason-2/3 onboard GPS observations

With the continuous deployment of Low Earth Orbit (LEO) satellites, the estimation of differential code biases (DCBs) based on GNSS observations from LEO has gained increasing attention. Previous studies on LEO-based DCB estimation are usually using the spherical symmetry ionosphere assumption (SSIA), in which a uniform electron density is assumed in a thick shell. In this study, we propose an approach (named the SHLEO method) to simultaneously estimate the satellite and LEO onboard receiver DCBs by modeling the distribution of the global plasmaspheric total electron content (PTEC) above the satellite orbit with a spherical harmonic (SH) function. Compared to the commonly used SSIA method, the SHLEO model improves the GPS satellite DCB estimation accuracy by 13.46% and the stability by 22.34%, respectively. Compared to the GPS satellite DCBs estimated based on the Jason-3-only observations, the accuracy and monthly stability of the satellite DCBs can be improved by 14.42% and 26.8% when both Jason-2 and Jason-3 onboard observations are jointly processed. Compared with the Jason-2 solutions, the GPS satellite DCB estimates based on the fusion of Jason-2 and Jason-3 observations have an improved consistency of better than 18.26% and 9.71% with the products provided by the Center for Orbit Determination in Europe (CODE) and Chinese Academy of Sciences (CAS). Taking the DCB products provided by the German Aerospace Center (DLR) as references, there is no improvement in accuracy of the GPS satellite DCB estimates based on the fusion of Jason-2 and Jason-3 observations than the Jason-2 solutions alone. A periodic variation is found in the time series of both the Jason-3 and Jason-2 onboard receiver DCB estimates. Preliminary analysis of the PTEC distribution based on the estimated SH coefficients are also presented.     

Eliminating negative VTEC in global ionosphere maps using inequality-constrained least squares

Currently, ground-based Global Navigation Satellite System (GNSS) stations of the International GNSS Service (IGS) are distributed unevenly around the world. Most of them are located on the mainland, while only a small part of them are scattered on some islands in the oceans. As a consequence, many unreasonable zero values (in fact negative values) appear in Vertical Total Electron Content (VTEC) of European Space Agency (ESA) and Center for Orbit Determination in Europe (CODE) IONEX products, especially in 2008 and 2009 when the solar activities were rather quiet. To improve this situation, we directly implement non-negative physical constraints of ionosphere for global ionosphere maps (GIM) with spherical harmonic functions. Mathematically, we propose an inequality-constrained least squares method by imposing non-negative inequality constraints in the areas where negative VTEC values may occur to reconstruct GIM models. We then apply the new method to process the IGS data in 2008. The results have shown that the new algorithm efficiently eliminates the unwanted behavior of negative VTEC values, which could otherwise often be seen in the current CODE and ESA GIM products in both middle and high latitude areas of the Southern Hemisphere (45°S∼90°S) and the Northern Hemisphere (50°N∼90°N). About 64% of GPS receivers’ DCBs have been significantly improved. Finally, we compare the GIM results between with and without the inequality constraints, which has clearly shown that the GIM result with inequality constraints is significantly better than that without the inequality constraints. The inequality-constrained GIM result is also highly consistent with the final IGS products in terms of root mean squared (RMS) and mean VTEC.     

Modeling the ionospheric gradient by using VSS base functions and GPS data over Iran

The spatial and temporal variations of ionosphere play an important role in positioning and navigation by the space geodetic techniques. Therefore, the ionospheric gradient should be calculated, analyzed, and applied in both space and time. Spatial gradients of the ionosphere have remarkable delay on the propagation of electromagnetic waves. This study intends to propose a new method for simultaneous modeling of the spatial gradients of ionosphere and VTECs in the local scale for Iran. Vector Spherical Slepian (VSS) base functions are used for the development of this method.Five VSS models with the maximal degrees of L = 30, 35, 40, 45 and 50 are taken into account. For implementing the VSS method, 24 permanent GPS stations from the Iranian Permanent GPS Network (IPGN) have been used. The unknown coefficients are estimated with the observations of these stations with least squares technique. Four other stations are used for evaluating the accuracy of the models. Repeatability of baselines is the measure that is used for this purpose. Based on the results obtained, L = 40 is the optimum degree for the VSS model with this input data over Iran.The baselines’ repeatability showed that ionospheric gradients have more influence on the north–south component. Moreover, the spatial gradient is negligible in the east–west and up-down component when a short baseline is processed. In other words, this kind of ionospheric modeling has significant application for baseline, which is longer than 1000 km. In the study, proposed method has improved the long baselines' solution by more than 12%, 18% and 10% in east–west, north–south and up-down components, respectively.     

Klobuchar模型的实用分析与改进

电离层延迟误差是无线电信号传播中不可忽视的误差源.GPS特许用户利用双频接收机的双频观测值直接对电离层延迟进行实时测定,其所得结果精度很高.多数普通用户所使用的单频接收机依靠电离层模型对其进行误差修正,效果不很理想.本文通过WUHN观测站双频接收机10天的实测数据对GPS广播星历采用的Klobuchar模型进行了验证,其结果与前人论述相一致.此外,经由反映太阳活动强度的太阳相对黑子数对Klobuchar模型提出了新的改进方法.实验数据结果表明,该方法对此模型修正效果有大幅提升,对原模型修正效果>50%的修正率由60%左右提升至85%以上,>80%的修正率由10%左右提升至40%以上.在实际应用中单频接收机用户可以参考本文改进方法对Klobuchar模型进行修正.      

Precise coseismic displacements from the GPS variometric approach using different precise products: Application to the 2008 MW 7.9 Wenchuan earthquake

The Global Positioning System (GPS) variometric approach has emerged as an attractive alternative to traditional well-developed positioning techniques including relative positioning and precise point positioning. Previous studies have demonstrated the capability of the variometric approach to retrieve coseismic displacements at centimeter-level precision, in a real-time manner using only readily available broadcast ephemeris. This study presents the first results comparing the performance of the variometric approach by using a variety of precise satellite orbit and clock products. Totally six kinds of products are included in our evaluation, namely the broadcast, IGS (International GNSS Service) ultra-rapid (predicted), ultra-rapid (observed), rapid, final (30-s clock) and CODE (Center for Orbit Determination in Europe) final (5-s clock) products. Static and dynamic experiments are conducted using 1-Hz GPS data covering a relatively large area in China during the 2008 Wenchuan M_W 7.9 earthquake. After removing the linear trend, the displacements using broadcast, ultra-rapid (predicted), ultra-rapid (observed) and rapid products reach nearly equivalent precisions at centimeter level. By using final and CODE final products, the precision of displacements can be significantly improved from 1.9–2.0 cm to 0.4–0.7 cm horizontally, and from 6.0–6.2 cm to 1.0–1.7 cm vertically for the dynamic experiments. The displacements using the CODE final products achieve the best precision, improved by more than 40% compared to those using the IGS final products. With the availability of IGS high-rate real-time precise products, this approach is promising to capture coseismic displacements more precisely in real time, which is crucial for earthquake and tsunami early warning.     

A 2-d ionospheric model for low latitude area – Hong Kong

The ionosphere is an important part of the atmosphere and it is the largest error source of GNSS positioning for single-frequency users. So establishing a precise ionosphere model is one of the critical steps for satellite navigation and also for ionospheric research.     

Refinement of global ionospheric coefficients for GNSS applications: Methodology and results

We developed the methodology for the optimal estimation of global ionospheric coefficients of the current Global Navigation Satellite Systems (GNSSs), including the eight- and ten-parameter Klobuchar-like as well as NeQuick models. The ionospheric coefficients of those correction models are calculated from two sets of globally distributed tracking stations of the International GNSS Services (IGS). Performance of the re-estimated Klobuchar-like and NeQuick coefficients are validated during 2002–2014 over the continental and oceanic areas, respectively. Over the continental areas, GPS TECs derived from 40 ground GPS receivers are selected as reference. The eight-, ten-parameter Klobuchar-like and NeQuick models can mitigate the ionospheric delay by 65.8, 67.3 and 75.0%, respectively. Over the global oceans, the independent TECs derived from Jason-1&2 altimeters are used as reference. The re-estimated ionospheric correction models can mitigate 56.1–66.7% of the delay errors. Compared to the original GPS Ionospheric Correction Algorithm (ICA), performance of those eight-, ten-parameter Klobuchar-like and NeQuick models has improved 3.4, 5.9 and 13.4% during the whole test period, respectively. The methodology developed here takes the advantage of high-quality ionospheric TECs derived from the global network of GNSS receivers. The re-estimated ionospheric coefficients can be used as precise ionospheric products to monitor and assess GNSS broadcast ionospheric parameters and to improve the performance of various single-frequency GNSS applications.     

Use of varying shell heights derived from ionosonde data in calculating vertical total electron content (TEC) using GPS – New method

The dispersive nature of the ionosphere makes it possible to measure its total electron content (TEC). Thus Global Positioning System, which uses dual-frequency radio signals, is an ideal system to measure TEC. When data from an ionosonde situated in polar region was observed, the height of an approximated thin shell of electrons (shell height) used in GPS studies was seen not to be fixed but rather changing with time. Here we introduce a new method in which we included the varying shell heights derived from the ionosonde to map the slant total electron content from GPS to obtain a more precise vertical total electron content of the ionosphere contrary to some previous methods which used fixed shell heights. In this paper we also compared the ionosonde derived TEC with the GPS derived vertical TEC (vTEC) values. These GPS vTEC values were obtained from GPS slant TEC (sTEC) measurements using both fixed shell height and varying shell heights (from ionosonde measurements). For the polar regions, the varying shell height approach produced better results than the fixed shell height and compared to exponential function, Chapman function seems to be a better function to model the topside ionosphere.