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.      

Performance assessment of real-time multi-GNSS integrated PPP with uncombined and ionospheric-free combined observables

For precise position services, the real-time precise point positioning (PPP) is a promising technology. The real-time PPP performance is expected to be improved by multi-system combination. The performance of real-time multi-system PPP needs to be periodically investigated, with the increasing number of available satellites and the continuously improved quality of real-time precise products of satellite clocks and orbits. In this study, a comprehensive performance assessment is conducted for the four-system integrated real-time PPP (FSIRT-PPP) with GPS, BDS, Galileo and GLONASS in both static and kinematic modes. The datasets from 118 stations spanning approximately a month are used for analysis, and the real-time stream CLK93 is employed. The superior performance of FSIRT-PPP is validated by comparing with the results of GPS/BDS, GPS/Galileo, GPS/GLONASS, GPS-only, BDS-only, Galileo-only and GLONASS-only cases. The FSIRT-PPP using ionospheric-free (IF) combined observables can achieve a convergence time of 10.9, 4.8 and 11.8 min and a positioning accuracy of 0.4, 0.5 and 0.7 cm in the static mode in the east, north and up directions, respectively, while the derived statistic is 15.4, 7.0 and 16.4 min, and 1.6, 1.2 and 3.4 cm in the kinematic mode in the three directions, respectively. Moreover, we also compare the position solutions of real-time PPP adopting IF combined and uncombined (UC) observables, and prove the mathematical equivalence between the two PPP models in the converged stage, provided that there are no external ionospheric corrections or constraints given to the estimated ionospheric delays in the UC model. The difference between the fully converged positioning accuracy of IF-based and UC-based real-time PPP is marginal, but the UC-based real-time PPP has longer convergence time due to the influence of the significant unmodeled time-varying errors in the real-time precise products as well as the different parameterization between them. For completeness, the real-time kinematic PPP results in harsh environments and the post-processed PPP results are also presented.     

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.     

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.     

Estimation of QZSS differential code biases using QZSS/GPS combined observations from MGEX

As an important error source in Global Navigation Satellite System (GNSS) positioning and ionospheric modeling, the differential code biases (DCB) need to be estimated accurately, e.g., the regional Quasi-Zenith satellite system (QZSS). In this paper, the DCB of QZSS is estimated by adopting the global ionospheric modeling method based on QZSS/GPS combined observations from Multi-GNSS experiment (MGEX). The performance of QZSS satellite and receiver DCB is analyzed with observations from day of year (DOY) 275–364, 2018. Good agreement between our estimated QZSS satellite DCB and the products from DLR and CAS is obtained. The bias and root mean square (RMS) of DCB are mostly within ±0.3 ns. The day-to-day fluctuation of the DCB time series is less than 0.5 ns with about 96% of the cases for all satellites. However, the receiver DCB is a little less stable than satellite DCB, and their standard deviations (STDs) are within 1.9 ns. The result shows that the stability of the receiver DCBs is not significantly related to the types of receiver or antenna.     

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.     

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.     

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.     

单接收机GNSS数据组合硬件延迟的联合求解方法

利用GNSS观测数据解算TEC的最大误差源是硬件延迟,包括卫星硬件延迟和接收机硬件延迟.在单接收机情况下,由于数据稀疏以及接收到的卫星信号时间不对齐等特点,已有的解算硬件延迟方法的求解结果往往不理想.在应用局域模式拟合方法和SCORE方法求解单接收机数据基础上,利用局域模型拟合法在电离层平静期拟合较准确的优点,提出一种联合改进方法,同时改正了SCORE方法解算过程中约束过强的缺点.通过利用GPStation-6接收机的GPS和BDS实际观测数据进行解算分析,验证了所提方法的有效性与准确性.      

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.     

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.     

Rapid local ionosphere modeling based on Precise Point Positioning over Iran: A case study under 2014 solar maximum

Presently, the ionosphere effect is the main source of the error in the Global Positioning System (GPS) observations. This effect can largely be removed by using the two-frequency measurements, while to obtain the reasonable results in the single-frequency applications, an accurate ionosphere model is required. Since the global ionosphere models do not meet our needs everywhere, the local ionosphere models are developed. In this paper, a rapid local ionosphere model over Iran is presented. For this purpose, the GPS observations obtained from 40 GPS stations of the Iranian Permanent GPS Network (IPGN) and 16 other GPS stations around Iran have been used. The observations have been selected under 2014 solar maximum, from the days 058, 107, 188 and 271 of the year 2014 with different geomagnetic activities. Moreover, ionospheric observables based on the precise point positioning (PPP) have been applied to model the ionosphere. To represent our ionosphere model, the B-spline basis functions have been employed and the variance component estimation (VCE) method has been used to regularize the problem.To show the efficiency our PPP-derived local ionosphere model with respect to the International GNSS Service (IGS) global models, these models are applied on the single point positioning using single-frequency observations and their results are compared with the precise coordinates obtained from the double-differenced solution using dual-frequency observations. The results show that the 95th percentile of horizontal and vertical positioning errors of the single-frequency point positioning are about 3.1 and 13.6?m, respectively, when any ionosphere model are not applied. These values significantly improve when the ionosphere models are applied in the solutions. Applying CODE’s Rapid Global ionosphere map (CORG), improvements of 59% and 81% in horizontal and vertical components are observed. These values for the IGS Global ionosphere map (IGSG) are 70% and 82%, respectively. The best results are obtained from our local ionosphere model, where 84% and 87% improvements in horizontal and vertical components are observed. These results confirm the efficiency of our local ionosphere model over Iran with respect to the global models. As a by-product, the Differential Code Biases (DCBs) of the receivers are also estimated. In this line, we found that the intra-day variations of the receiver DCBs could be significant. Therefore, these variations must be taken into account for the precise ionosphere modeling.     

A real-time ionospheric model based on GNSS Precise Point Positioning

This paper proposes a method of real-time monitoring and modeling the ionospheric Total Electron Content (TEC) by Precise Point Positioning (PPP). Firstly, the ionospheric TEC and receiver’s Differential Code Biases (DCB) are estimated with the undifferenced raw observation in real-time, then the ionospheric TEC model is established based on the Single Layer Model (SLM) assumption and the recovered ionospheric TEC. In this study, phase observations with high precision are directly used instead of phase smoothed code observations. In addition, the DCB estimation is separated from the establishment of the ionospheric model which will limit the impacts of the SLM assumption impacts. The ionospheric model is established at every epoch for real time application. The method is validated with three different GNSS networks on a local, regional, and global basis. The results show that the method is feasible and effective, the real-time ionosphere and DCB results are very consistent with the IGS final products, with a bias of 1–2 TECU and 0.4 ns respectively.     

A method of estimating GPS instrumental biases with a convolution algorithm

This paper presents a method of deriving the instrumental differential code biases (DCBs) of GPS satellites and dual frequency receivers. Considering that the total electron content (TEC) varies smoothly over a small area, one ionospheric pierce point (IPP) and four more nearby IPPs were selected to build an equation with a convolution algorithm. In addition, unknown DCB parameters were arranged into a set of equations with GPS observations in a day unit by assuming that DCBs do not vary within a day. Then, the DCBs of satellites and receivers were determined by solving the equation set with the least-squares fitting technique. The performance of this method is examined by applying it to 361?days in 2014 using the observation data from 1311 GPS Earth Observation Network (GEONET) receivers. The result was crosswise-compared with the DCB estimated by the mesh method and the IONEX products from the Center for Orbit Determination in Europe (CODE). The DCB values derived by this method agree with those of the mesh method and the CODE products, with biases of 0.091?ns and 0.321?ns, respectively. The convolution method's accuracy and stability were quite good and showed improvements over the mesh method.     

The realization and convergence analysis of combined PPP based on raw observation

In order to speed up Precise Point Positioning (PPP)’s convergence, a combined PPP method with GPS and GLONASS which is based on using raw observations is proposed, and the positioning results and convergence time have been compared with that of single system. The ionospheric delays and receiver’s Differential Code Bias (DCB) corrections are estimated as unknown parameters in this method. The numerical results show that the combined PPP has not caused significant impacts on the final solutions, but it greatly improved Position Dilution of Precision (PDOP) and convergence speed and enhanced the reliability of the solution. Meanwhile, the convergence speed is greatly influenced by the receiver’s DCB, positioning results in horizontal which are better than 10 cm can be realized within 10 min. In addition, the ionosphere and DCB products can be provided with high precision.     

MGEX北斗差分码偏差两种精确处理方法对比分析

差分码偏差是北斗卫星导航系统（BDS）在高精度定位和电离层建模中需精确处理的系统误差之一.利用MGEX发布的2017年全年和2018年6月的BDS卫星的差分码偏差数据,比较分析了DLR和CAS分别解算的BDS卫星差分码偏差的日解值、月平均值和稳定性的变化特性.分析结果表明,DLR与CAS估算的BDS卫星差分码偏差值差异不大,具有较好的一致性;2017年CAS估算的BDS卫星C2I-C6I差分码偏差稳定性略优于DLR,C2I-C7I差分码偏差稳定性与DLR相当,且均具有较高稳定性;2018年6月DLR C2I-C6I差分码偏差月平均值稳定性优于CAS;C2I-C7I差分码偏差的稳定性明显优于C2I-C6I差分码偏差,卫星差分码偏差月平均值稳定性优于日解值稳定性.      

精密进近阶段的多系统GNSS组合RAIM可用性算法及分析

给出了多系统全球卫星导航系统（GNSS）组合接收机自主完好性监测（ReceiverAutonomousIntegrityMonitoring,RAIM）可用性计算方法,在此基础上利用GPS、GLONASS实测数据与BDS、Galileo全星座仿真数据,分析了BDS、GPS、GLONASS和Galileo不同组合在精密进近阶段的RAIM可用性。通过试验分析发现,BDS的5颗地球同步轨道卫星和3颗倾斜地球同步轨道卫星对亚洲、非洲和欧洲大部分地区的RAIM可用性有很大的贡献。这些地区站星间几何观测结构得到改善,使得RAIM可用性相对于其他地区有很大幅度的提升。在亚太地区APV-I阶段单系统导航情况下,北斗导航系统RAIM可用性达到99.5%,高于其他三个导航系统。在精密进近阶段（APV-I、APV-II和CAT-I）,BDS与其他导航系统（GPS、GLONASS和Galileo）的组合导航可以满足全球大部分区域的RAIM可用性需求,大多可达到100%。     

Performance assessment of RTPPP positioning with SSR corrections and PPP-AR positioning with FCB for multi-GNSS from MADOCA products

The state-space representation (SSR) product of satellite orbit and clock is one of the most essential corrections for real-time precise point positioning (RTPPP). When it comes to PPP ambiguity resolution (PPP-AR), the fractional cycle bias (FCB) matters. The Japan Aerospace Exploration Agency (JAXA) has developed a multi-GNSS (i.e., global navigation satellite system) advanced demonstration tool for orbit and clock analysis (MADOCA), providing free and precise orbit and clock products. Because of the shortage of relevant studies on performance evaluation, this paper focuses on the performance assessment of RTPPP and PPP-AR by real-time and offline MADOCA products. To begin with, the real-time MADOCA products are evaluated by comparing orbit and clock with JAXA final products, which gives an objective impression of the correction. Second, PPP tests in static and simulated kinematic mode are conducted to further verify the quality of real-time MADOCA products. Finally, the offline MADOCA products are assessed by PPP and PPP-AR comparisons. The results are as follows: (1) Orbit comparisons produced an average error of about 0.04–0.13 m for the global positioning system (GPS), 0.14–0.16 m for the global navigation satellite system (GLONASS), and 0.07–0.08 m for the quasi-zenith satellite system (QZSS). The G15 satellite had the most accurate orbit, with a difference of 0.04 m between the JAXA orbit products and MADOCA’s counterpart, while the R07 satellite had the least accurate orbit with a difference of 0.16 m. Clock products had an accuracy of 0.4–1.3 ns for GPS, 1.4–1.6 ns for GLONASS, and 0.7–0.8 ns for QZSS in general. The G15 satellite had the most accurate clock with a difference of only 0.40 ns between the JAXA clock products and MADOCA products, and the R07 satellite had the least accurate clock with a difference of 1.55 ns. The orbit and clock products for GLONASS performed worse than those of GPS and QZSS. (2) After convergence, the positioning accuracy was 3.0–8.1 cm for static PPP and 8.1–13.7 cm for kinematic PPP when using multi-GNSS observations and precise orbit and clock products. The PFRR station performed the good performance both in static and kinematic mode with an accuracy of 2.99 cm and 8.08 cm, respectively, whereas the CPNM station produced the worst static performance with an error of 8.09 cm, and the ANMG station produced the worst kinematic performance with a counterpart of 13.69 cm. (3) The PPP-AR solution was superior to the PPP solution, given that, with respect to PPP, post-processing PPP-AR improved the positioning accuracy and convergence time by 13–32 % (3–89 %) in GPS-only mode by 2–15 % (5–60 %) in GPS/QZSS mode. Thus, we conclude that the current MADOCA products can provide SSR corrections and FCB products with positioning accuracy at the decimeter or even centimeter level, which could meet the demands of the RTPPP and PPP-AR solutions.     

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.