GLONASS-based precise point positioning and performance analysis

Current precise point positioning (PPP) techniques are mainly based on GPS which has been extensively investigated. With the increase of available GLONASS satellites during its revitalization, GLONASS observations were increasingly integrated into GPS-based PPP. Now that GLONASS has reached its full constellation, there will be a wide interest in PPP systems based on only GLONASS since it provides a PPP implementation independent of GPS. An investigation of GLONASS-based PPP will also help the development of GPS and GLONASS combined PPP techniques for improved precision and reliability. This paper presents an observation model for GLONASS-based PPP in which the GLONASS hardware delay biases are addressed. In view of frequently changed frequency channel number (FCN) for GLONASS satellites, an algorithm has been developed to compute the FCN for GLONASS satellites using code and phase observations, which avoids the need to provide the GLONASS frequency channel information during data processing. The observation residuals from GLONASS-based PPP are analyzed and compared to those from GPS-based PPP. The performance of GLONASS-based PPP is assessed using data from 15 globally distributed stations.     

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.     

GNSS geodetic techniques for time and frequency transfer applications

We performed an initial analysis of the pseudorange data of the GIOVE-B satellite, one of the two experimental Galileo satellites currently in operation, for time transfer.¹ For this specific aim, software was developed to process the GIOVE-B raw pseudoranges and broadcast navigation messages collected by the Galileo Experimental Sensor Stations (GESS) tracking network, yielding station clock phase errors with respect to the Experimental Galileo System Time (EGST). The software also allows processing the Global Positioning System (GPS) P1 and P2 pseudorange data with broadcast navigation message collected at the same stations to obtain the station clock phase errors with respect to the GPS system time (GPST). Differencing these solutions between stations provides two independent means of GNSS time transfer. We compared these time transfer results with Precise Point Positioning (PPP) method applied to GPS data in combined carrier-phase and pseudorange mode as well as in pseudorange-only mode to show their relative merits. The PPP solutions in combined carrier-phase and pseudorange mode showed the least instability of the methods tested herein at all scales, at few parts in 10¹⁵ at 1 day for the stations processed, following a tau^−½ interval dependency. Conversely, the PPP solutions in pseudorange-only mode are an order of magnitude worst (few parts in 10¹⁴ at 1 day for the stations processed) following a tau⁻¹ power-law, but slightly better than the single-satellite raw GPS time transfer solutions obtained using the developed software, since the PPP least-squares solution effectively averages the pseudorange noise. The pseudorange noise levels estimated from PPP pseudorange residuals and from clock solution comparisons are largely consistent, providing a validation of our software operation. The raw GIOVE-B time transfer, as implemented in this work, proves to be slightly better than single-satellite raw GPS satellite time transfer, at least in the medium term. However, one of the processed stations shows a combined GPS P1 and P2 pseudorange noise level at 2 m, a factor 2 worst than usually seen for geodetic receivers, so the GPS time transfer results may not be at their best for the cases processed. Over the short term, the GPS single-satellite time transfer instability outperforms the GIOVE-B by an order of magnitude at 1 s interval, which would be due to the different characteristics of the tracking loop filters for GPS P1 and P2 on one hand and the GIOVE-B signals on the other. Even at this preliminary stage and using an experimental satellite system, results show that the GIOVE-B (and hence Galileo) signals offer interesting perspectives for high precision time transfer between metrological laboratories.     

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.     

Real-time zenith tropospheric delays in support of numerical weather prediction applications

The Geodetic Observatory Pecný (GOP) routinely estimates near real-time zenith total delays (ZTD) from GPS permanent stations for assimilation in numerical weather prediction (NWP) models more than 12 years. Besides European regional, global and GPS and GLONASS solutions, we have recently developed real-time estimates aimed at supporting NWP nowcasting or severe weather event monitoring. While all previous solutions are based on data batch processing in a network mode, the real-time solution exploits real-time global orbits and clocks from the International GNSS Service (IGS) and Precise Point Positioning (PPP) processing strategy. New application G-Nut/Tefnut has been developed and real-time ZTDs have been continuously processed in the nine-month demonstration campaign (February–October, 2013) for selected 36 European and global stations. Resulting ZTDs can be characterized by mean standard deviations of 6–10 mm, but still remaining large biases up to 20 mm due to missing precise models in the software. These results fulfilled threshold requirements for the operational NWP nowcasting (i.e. 30 mm in ZTD). Since remaining ZTD biases can be effectively eliminated using the bias-reduction procedure prior to the assimilation, results are approaching the target requirements in terms of relative accuracy (i.e. 6 mm in ZTD). Real-time strategy and software are under the development and we foresee further improvements in reducing biases and in optimizing the accuracy within required timeliness. The real-time products from the International GNSS Service were found accurate and stable for supporting PPP-based tropospheric estimates for the NWP nowcasting.     

The impact on tsunami detection from space using GNSS-reflectometry when combining GPS with GLONASS and Galileo

The devastating Sumatra tsunami in 2004 demonstrated the need for a tsunami early warning system in the Indian Ocean. Such a system has been installed within the German-Indonesian Tsunami Early Warning System (GITEWS) project. Tsunamis are a global phenomenon and for global observations satellites are predestined. Within the GITEWS project a feasibility study on a future tsunami detection system from space has therefore been carried out. The Global Navigation Satellite System Reflectometry (GNSS-R) is an innovative way of using GNSS signals for remote sensing. It uses ocean reflected GNSS signals for sea surface altimetry. With a dedicated Low Earth Orbit (LEO) constellation of satellites equipped with GNSS-R receivers, densely spaced sea surface height measurements could be established to detect tsunamis. Some general considerations on the geometry between LEO and GNSS are made in this simulation study. It exemplary analyzes the detection performance of a GNSS-R constellation at 900 km altitude and 60° inclination angle when applied to the Sumatra tsunami as it occurred in 2004. GPS is assumed as signal source and the combination with GLONASS and Galileo signals is investigated. It can be demonstrated, that the combination of GPS and Galileo is advantageous for constellations with few satellites while the combination with GLONASS is preferable for constellations with many satellites. If all three GNSS are combined, the best detection performance can be expected for all scenarios considered. In this case an 18 satellite constellation will detect the Sumatra tsunami within 17 min with certainty, while it takes 53 min if only GPS is considered.     

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.     

GPS全视法时间传递回顾与展望

目前,时间传递技术正处于GPS伪码技术到GNSS多种技术组合的过渡时期,介绍了高精度时间传递技术在近年来的发展情况:首先回顾了GPS伪码共视(CV)与全视法(AV)时间传递,并证明全视法比共视法更具优越性。CCTF 2006通过,从MJD 53979,即2006九月(Circular T225)开始,使用AV法进行TAI比对。CV法需要满足共视条件,这限制了载波相位(CP)方法的应用,载波相位观测量比码观测量的观测精度可以高出两个数量级。由于CP观测数据优良,CCTF 2006推荐也可以引用CP观测数据进行时间传递。PPP方法是一种充分研究的时间传递方法,它充分地利用了载波相位信息,可以认为是伪码AV法的自然延伸。最后,给出我们的最新研究成果,即将GPS PPP和TW时间链路结合的方法,该方法结合两种时间传递链路的优点并消除了它们的缺点。     

GNSS water vapour tomography – Expected improvements by combining GPS,GLONASS and Galileo observations

The German Research Centre for Geosciences (GFZ) operates a GNSS water vapour tomography system using about 350 German GNSS stations. The GNSS data processing at the GFZ works in near real-time and provides zenith total delays, integrated water vapour and slant delay data operationally. This large data set of more than 50,000 slant delays per hour is used to reconstruct spatially resolved humidity fields by means of tomographic techniques. It can be expected that additional observations from the future Galileo system provide more information with improved quality. A simulation study covering 12 h at 14 July 2009 was therefore started to estimate the impact of GPS, Galileo and GLONASS data on the GNSS tomography. It is shown that the spatial coverage of the atmosphere with slant paths is highly improved by combining observations from two or three satellite systems. Equally important for a reliable tomographic reconstruction is the distribution of slant path intersections as they are required to locate the integrated delay information. The number of intersection points can be increased by a factor of 4 or 8 if two or three systems are combined and their distribution will cover larger regions of the atmosphere. The combined data sets can be used to increase the spatiotemporal resolution of the reconstructed humidity fields up to 30 km horizontally, 300 m vertically and 15 min. The reconstruction quality could not be improved considerably using the currently available techniques.     

GNSS实时动态授时精度分析

基于GNSS载波相位观测值的实时动态授时，可有效规避PPP授时对实时精密轨道和钟差产品的依赖问题，对短距离动、静态高精度时间用户具有重要意义。为了更好地验证GNSS实时动态授时性能，基于中国科学院国家授时中心时间频率资源和三个GNSS跟踪站长达2个月的观测数据，以GPS系统为例开展了授时试验。与事后PPP时间传递相比，实时动态授时结果差异STD优于0.15ns；与光纤双向时间传递结果相比，实时动态授时结果差异STD优于0.5ns。试验表明，GNSS实时动态授时精度能够达到亚纳秒量级，可为下一步推广应用提供重要参考。     

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.     

Real-time clock comparison and monitoring with multi-GNSS precise point positioning: GPS,GLONASS and Galileo

The precise point positioning (PPP) technique is widely used in time and frequency applications. Because of the real-time service (RTS) project of the International GNSS Service, we can use the PPP technique for real-time clock comparison and monitoring. As a participant in the RTS, the Centre National d’Etudes Spatiales (CNES) implements the PPPWIZARD (Precise Point Positioning with Integer and Zero-difference Ambiguity Resolution Demonstrator) project to validate carrier phase ambiguity resolution. Unlike the Integer-PPP (IPPP) of the CNES, fixing ambiguities in the post-processing mode, the PPPWIZARD operates in the real-time mode, which is also called real-time IPPP (RT-IPPP). This paper focuses on applying the RT-IPPP for real-time clock comparison and monitoring. We review the principle of real-time clock comparison and monitoring, and introduce the methodology of the RT-IPPP technique. The observations of GPS, GLONASS and Galileo were processed for the experiments. Five processing modes were provided in the experiment to analyze the benefits of ambiguity resolution and multi-GNSS. In the clock comparison experiment, the average reduction ratios of standard deviations with respect to the G PPP mode range from 9.7% to 35.0%. In the clock monitoring experiment, G PPP mode can detect clock jumps whose magnitudes are larger than 0.9 ns. The RT-IPPP technique with GRE PPP AR (G) mode allows for the detection of any clock jumps larger than 0.6 ns. For frequency monitoring, G PPP mode allows detection of frequency changes larger than 1.1 × 10⁻¹⁴. When the RT-IPPP technique is applied, monitoring with GRE PPP AR (G) mode can detect frequency changes larger than 6.1 × 10⁻¹⁵.     

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.     

DORIS and GPS monitoring of the Gavdos calibration site in Crete

Due to its specific geographical location as well as its geodetic equipment (DORIS, GNSS, microwave transponder and tide gauges), the Gavdos station in Crete, Greece is one of the very few sites around the world used for satellite altimetry calibration. To investigate the quality of the Gavdos geodetic coordinates and velocities, we analyzed and compared here DORIS and GPS-derived results obtained during several years of observations. The DORIS solution is the latest ignwd11 solution at IGN, expressed in ITRF2008, while the GPS solution was obtained using the GAMIT software package. Current results show that 1–2 mm/yr agreement can be obtained for 3-D velocity, showing a good agreement with current geophysical models. In particular, the agreement obtained for the vertical velocity is around 0.3–0.4 mm/yr, depending on the terrestrial reference frame. As a by-product of these geodetic GPS and DORIS results, Zenith Tropospheric Delays (ZTDs) estimations were also compared in 2010 between these two techniques, and compared to ECMWF values, showing a 6.6 mm agreement in dispersion without any significant difference between GPS and DORIS (with a 97.6% correlation), but with a 13–14 mm agreement in dispersion when comparing to ECMWF model (with only about 90% correlation for both techniques). These tropospheric delay estimations could also provide an external calibration of the tropospheric correction used for the geophysical data of satellite altimetry missions.     

Ambiguity resolution in precise point positioning with hourly data for global single receiver

Integer ambiguity resolution (IAR) can improve precise point positioning (PPP) performance significantly. IAR for PPP became a highlight topic in global positioning system (GPS) community in recent years. More and more researchers focus on this issue. Progress has been made in the latest years. In this paper, we aim at investigating and demonstrating the performance of a global zero-differenced (ZD) PPP IAR service for GPS users by providing routine ZD uncalibrated fractional offsets (UFOs) for wide-lane and narrow-lane. Data sets from all IGS stations collected on DOY 1, 100, 200 and 300 of 2010 are used to validate and demonstrate this global service. Static experiment results show that an accuracy better than 1 cm in horizontal and 1–2 cm in vertical could be achieved in ambiguity-fixed PPP solution with only hourly data. Compared with PPP float solution, an average improvement reaches 58.2% in east, 28.3% in north and 23.8% in vertical for all tested stations. Results of kinematic experiments show that the RMS of kinematic PPP solutions can be improved from 21.6, 16.6 and 37.7 mm to 12.2, 13.3 and 34.3 mm for the fixed solutions in the east, north and vertical components, respectively. Both static and kinematic experiments show that wide-lane and narrow-lane UFO products of all satellites can be generated and provided in a routine way accompanying satellite orbit and clock products for the PPP user anywhere around the world, to obtain accurate and reliable ambiguity-fixed PPP solutions.     

Geocenter coordinates estimated from GNSS data as viewed by perturbation theory

Time series of geocenter coordinates were determined with data of two global navigation satellite systems (GNSSs), namely the U.S. GPS (Global Positioning System) and the Russian GLONASS (Global’naya Nawigatsionnaya Sputnikowaya Sistema). The data was recorded in the years 2008–2011 by a global network of 92 permanently observing GPS/GLONASS receivers. Two types of daily solutions were generated independently for each GNSS, one including the estimation of geocenter coordinates and one without these parameters.     

Compatibility of Terrestrial Reference Frames used in GNSS broadcast messages during an 8 week period of 2019

The operational Terrestrial Reference Frames (TRFs) realized through the evaluation of broadcast ephemerides for GPS, GLONASS, Galileo, BeiDou-2 and BeiDou-3 have been compared to IGS14, the TRF realized by the International GNSS Service (IGS). The TRFs realized by the GPS, GLONASS, Galileo, and BeiDou-2 and BeiDou-3 broadcast ephemerides are the orbital realizations of WGS 84 (G1762′), PZ90.11, GTRF19v01, and BDCS respectively. These TRFs are compared using up to 56 days of data (21 July-14 Sept 2019) at a 5 or 15-min rate. The operational TRFs are compared to IGS14 in a 7-parameter similarity (Helmert) transformation. Numerical results show that the operational GNSS TRFs differ from IGS14 at a level no greater than 4 cm for Galileo, 6 cm for GPS and BeiDou-3, 13 cm for GLONASS, and 48 cm for a limited set of BeiDou-2 Medium Earth Orbit (MEO) vehicles.     

Generating precise and homogeneous orbits for Jason-1 and Jason-2

Driven by the GMES (Global Monitoring for Environment and Security) and GGOS (Global Geodetic Observing System) initiatives the user community has a strong demand for high-quality altimetry products. In order to derive such high-quality altimetry products, precise orbits for the altimetry satellites are a necessity. With the launch of the TOPEX/Poseidon mission in 1992 a still on-going time series of high-accuracy altimetry measurements of ocean topography started, continued by the altimetry missions Jason-1 in 2001 and Jason-2/OSTM in 2008. This paper contributes to the on-going orbit reprocessing carried out by several groups and presents the efforts of the Navigation Support Office at ESA/ESOC using its NAPEOS software for the generation of precise and homogeneous orbits referring to the same reference frame for the altimetry satellites Jason-1 and Jason-2. Data of all three tracking instruments on-board the satellites (beside the altimeter), i.e. GPS, DORIS, and SLR measurements, were used in a combined data analysis. About 7 years of Jason-1 data and more than 1 year of Jason-2 data were processed. Our processing strategy is close to the GDR-C standards. However, we estimated slightly different scaling factors for the solar radiation pressure model of 0.96 and 0.98 for Jason-1 and Jason-2, respectively. We used 30 s sampled GPS data and introduced 30 s satellite clocks stemming from ESOC’s reprocessing of the combined GPS/GLONASS IGS solution. We present the orbit determination results, focusing on the benefits of adding GPS data to the solution. The fully combined solution was found to give the best orbit results. We reach a post-fit RMS of the GPS phase observation residuals of 6 mm for Jason-1 and 7 mm for Jason-2. The DORIS post-fit residuals clearly benefit from using GPS data in addition, as the DORIS data editing improves. The DORIS observation RMS for the fully combined solution is with 3.5 mm and 3.4 mm, respectively, 0.3 mm better than for the DORIS-SLR solution. Our orbit solution agrees well with external solutions from other analysis centers, as CNES, LCA, and JPL. The orbit differences between our fully combined orbits and the CNES GDR-C orbits are of about 0.8 cm for Jason-1 and at 0.9 cm for Jason-2 in the radial direction. In the cross-track component we observe a clear improvement when adding GPS data to the POD process. The 3D-RMS of the orbit differences reveals a good orbit consistency at 2.7 cm and 2.9 cm for Jason-1 and Jason-2. Our resulting orbit series for both Jason satellites refer to the ITRF2005 reference frame and are provided in sp3 file format on our ftp server.     

Towards PPP-RTK: Ambiguity resolution in real-time precise point positioning

Integer ambiguity resolution at a single station can be achieved by introducing predetermined uncalibrated phase delays (UPDs) into the float ambiguity estimates of precise point positioning (PPP). This integer resolution technique has the potential of leading to a PPP-RTK (real-time kinematic) model where PPP provides rapid convergence to a reliable centimeter-level positioning accuracy based on an RTK reference network. Nonetheless, implementing this model is technically subject to how rapidly we can fix wide-lane ambiguities, stabilize narrow-lane UPD estimates, and achieve the first ambiguity-fixed solution. To investigate these issues, we used 7 days of 1-Hz sampling GPS data at 91 stations across Europe. We find that at least 10 min of observations are required for most receiver types to reliably fix about 90% of wide-lane ambiguities corresponding to high elevations, and over 20 min to fix about 90% of those corresponding to low elevations. Moreover, several tens of minutes are usually required for a regional network before a narrow-lane UPD estimate stabilizes to an accuracy of far better than 0.1 cycles. Finally, for hourly data, ambiguity resolution can significantly improve the accuracy of epoch-wise position estimates from 13.7, 7.1 and 11.4 cm to 0.8, 0.9 and 2.5 cm for the East, North and Up components, respectively, but a few tens of minutes is required to achieve the first ambiguity-fixed solution. Therefore, from the timeliness aspect, our PPP-RTK model currently cannot satisfy the critical requirement of instantaneous precise positioning where ambiguity-fixed solutions have to be achieved within at most a few seconds. However, this model can still be potentially applied to some near-real-time remote sensing applications, such as the GPS meteorology.     

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.