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High precision Global Navigation Satellite Systems (GNSS) positioning and time transfer require correcting signal delays, in particular higher-order ionospheric (I2+) terms. We present a consolidated model to correct second- and third-order terms, geometric bending and differential STEC bending effects in GNSS data. The model has been implemented in an online service correcting observations from submitted RINEX files for I2+ effects. We performed GNSS data processing with and without including I2+ corrections, in order to investigate the impact of I2+ corrections on GNSS products. We selected three time periods representing different ionospheric conditions. We used GPS and GLONASS observations from a global network and two regional networks in Poland and Brazil. We estimated satellite orbits, satellite clock corrections, Earth rotation parameters, troposphere delays, horizontal gradients, and receiver positions using a global GNSS solution, Real-Time Kinematic (RTK) and Precise Point Positioning (PPP) techniques. The satellite-related products captured most of the impact of I2+ corrections, with the magnitude up to 2 cm for clock corrections, 1 cm for the along- and cross-track orbit components, and below 5 mm for the radial component. The impact of I2+ on troposphere products turned out to be insignificant in general. I2+ corrections had limited influence on the performance of ambiguity resolution and the reliability of RTK positioning. Finally, we found that I2+ corrections caused a systematic shift in the coordinate domain that was time- and region-dependent, and reached up to -11 mm for the North component of the Brazilian stations during the most active ionospheric conditions. .

Higher-order ionospheric effects, if not properly accounted for, can propagate into geodetic parameter estimates. For this reason, several investigations have led to the development and refinement of formulas for the correction of second- and third-order ionospheric errors, bending effects and total electron content variations due to excess path length. Standard procedures for computing higher-order terms typically rely on slant total electron content computed either from global ionospheric maps (GIMs) or using GNSS observations corrected using differential code biases (DCBs) provided by an external process. In this study, we investigate the feasibility of estimating slant ionospheric delay parameters accounting for both first- and second-order ionospheric effects directly within a precise point positioning (PPP) solution. It is demonstrated that proper handling of the receiver DCB is critical for the PPP method to provide unbiased estimates of the position. The proposed approach is therefore not entirely free from external inputs since GIMs are required for isolating the receiver DCB, unless the latter is provided to the PPP filter. In terms of positioning performance, the PPP approach is capable of mitigating higher-order ionospheric effects to the same level as existing approaches. Due to the inherent risks associated with constraining slant ionospheric delay parameters in PPP during disturbed ionospheric conditions, the reliability of the method can be greatly enhanced when the receiver DCB is available a priori, such as for permanent GNSS stations.

The space segment of the European Global Navigation Satellite System (GNSS) Galileo consists of In-Orbit Validation (IOV) and Full Operational Capability (FOC) spacecraft. The first pair of FOC satellites was launched into an incorrect, highly eccentric orbital plane with a lower than nominal inclination angle. All Galileo satellites are equipped with satellite laser ranging (SLR) retroreflectors which allow, for example, for the assessment of the orbit quality or for the SLR–GNSS co-location in space. The number of SLR observations to Galileo satellites has been continuously increasing thanks to a series of intensive campaigns devoted to SLR tracking of GNSS satellites initiated by the International Laser Ranging Service. This paper assesses systematic effects and quality of Galileo orbits using SLR data with a main focus on Galileo satellites launched into incorrect orbits. We compare the SLR observations with respect to microwave-based Galileo orbits generated by the Center for Orbit Determination in Europe (CODE) in the framework of the International GNSS Service Multi-GNSS Experiment for the period 2014.0–2016.5. We analyze the SLR signature effect, which is characterized by the dependency of SLR residuals with respect to various incidence angles of laser beams for stations equipped with single-photon and multi-photon detectors. Surprisingly, the CODE orbit quality of satellites in the incorrect orbital planes is not worse than that of nominal FOC and IOV orbits. The RMS of SLR residuals is even lower by 5.0 and 1.5 mm for satellites in the incorrect orbital planes than for FOC and IOV satellites, respectively. The mean SLR offsets equal $$-44.9, -35.0$$ , and $$-22.4$$ mm for IOV, FOC, and satellites in the incorrect orbital plane. Finally, we found that the empirical orbit models, which were originally designed for precise orbit determination of GNSS satellites in circular orbits, provide fully appropriate results also for highly eccentric orbits with variable linear and angular velocities.

The recent development of the Galileo space segment and the accompanying support of the International GNSS Service (IGS) allows for worldwide Galileo-only positioning. In this study, different techniques of dual-frequency absolute positioning using the fully serviceable Galileo constellation are evaluated for the first time and compared to the performance of GPS positioning. The daily static positioning based on the broadcast ephemeris using Galileo pseudoranges is significantly more accurate than the corresponding GPS solutions, obtaining the accuracy of a few decimeters. In the kinematic mode, the accuracy is better than 10 m and 20 m for the horizontal and vertical components, respectively, which is comparable to that of GPS. Precise absolute positioning using pseudorange and carrier phase Galileo observations combined with IGS Real-Time Service (RTS) or Multi-GNSS Experiment products is not yet as good as the corresponding GPS solutions. In the static mode, the root mean squared error (RMSE) between estimated and reference coordinates does not exceed 0.05 m and 0.06 m for the horizontal and vertical components, respectively. In the kinematic mode, the respective accuracies are better than 0.17 m and 0.21 m. Moreover, we show that both GPS and Galileo pseudorange solutions benefit from the RTS when compared to the broadcast solutions with the improvement in the accuracy between 10 and 59%. Remarkable results are achieved for Galileo Precise Point Positioning (PPP) solutions based on the broadcast ephemeris. In the static mode, the RMSE is 0.07 and 0.10 m for the horizontal and vertical components which is three and two times better, respectively, then the corresponding solutions based on GPS.

The tropospheric delay is one of the major error sources in precise point positioning (PPP), affecting the accuracy and precision of estimated coordinates and convergence time, which raises demand for a reliable tropospheric model, suitable to support PPP. In this study, we investigate the impact of three tropospheric models and mapping functions regarding position accuracy and convergence time. We propose a routine to constrain the tropospheric estimates, which we implemented in the in-house developed real-time PPP software. We take advantage of the high spatial resolution (4 × 4 km2) numerical weather prediction Weather Research and Forecasting (WRF) model and near real-time GNSS data combined by the least-squares collocation estimation to reconstruct the tropospheric delays. We also present mapping functions calculated from the WRF model using the ray-tracing technique. The performance tests are conducted on 14 Polish EUREF Permanent Network (EPN) stations during 3 weeks of different tropospheric conditions: calm, standard and severe. We consider six GNSS data processing variants, including two commonly used variants using a priori ZTD and mapping functions from UNB3m and VMF1-FC models, one with a priori ZTD and mapping functions calculated directly from WRF model and three variants using the aforementioned mapping functions but with ZTD model based on GNSS and WRF data used as a priori troposphere and to constrain tropospheric estimates. The application of a high-resolution GNSS/WRF-based ZTD model and mapping functions results in the best agreement with the official EPN coordinates. In both static and kinematic modes, this approach results in an average reduction of 3D bias by 20 and 10 mm, respectively, but an increase of 3D SDs by 1.5 and 4 mm, respectively. The application of high-resolution tropospheric model also shortens the convergence time, for example, for a 10 cm convergence level, from 67 to 58 min for the horizontal components and from 79 to 63 min for the vertical component.

In this paper, the authors summarize a simple and efficient approach developed to mitigate the problem in precise Global Navigation Satellite Systems (GNSS) positioning originated by the most frequent ionospheric wave signatures: the medium-scale traveling ionospheric disturbances (MSTIDs). The direct GNSS Ionospheric Interferometry technique (hereinafter dGII), presented in this paper, is applied for correcting MSTID effects on precise Real Time Kinematic (RTK) and tropospheric determination. It consists of the evolution of the former climatic Differential Delay Mitigation Model for MSTIDs (DMTID), for real-time conditions, using ionospheric data from a single permanent receiver only. The performance is demonstrated with networks of GNSS receivers in Poland, treated as users under real-time conditions, during two representative days in winter and summer seasons (days 353 and 168 of year 2013). In range domain, dGII typically reduces the ionospheric delay error up to 10–90% of the value when the MSTID mitigation model is not applied. The main dGII impact on precise positioning is that we can obtain reliable RTK position faster. In particular, the ambiguity success rate parameter increases, from 74% to 83%, with respect to the original uncorrected observations. The average of time to first fix is shortened from 30 s to 13 s. The improvement in troposphere estimaton, due to any potential impact of the MSTID mitigation model, was most difficult to demonstrate.

An increasing number of satellites of global navigation satellite systems (GNSS) and their constant modernization allow improving positioning accuracy and enable performing the GNSS measurements in challenging environments. Since 2016, the Centre National d’Etudes Spatiales (CNES) has been providing real-time corrections for all GNSS and thus allows for the actual multi-GNSS precise point positioning in real time without any issues associated with the latency of orbit and clock products as in the case of the IGS final products. We provide a comprehensive evaluation of the availability and the quality of multi-GNSS real-time orbit and clock products through the comparison to the final Center for Orbit Determination in Europe (CODE) orbits, fitting long continuous orbital arcs, analyzing the orbit position differences with respect to satellite laser ranging observations, as well as the assessment of clock stability using modified Allan deviation diagrams. The 3D orbit RMS over a 1-month test period, when compared to CODE products, is 5, 10, 18, 18 and 36 cm for GPS, GLONASS, Galileo, BeiDou MEO and BeiDou IGSO, respectively. The error of BeiDou geostationary orbits is above the 1-m level. Finally, we found that the quality of orbits and clocks is a function of the satellite system, orbital plane and the elevation of the Sun above the orbital plane, the satellite altitude, as well as the satellite block and generation.

This paper presents accuracy analyses of two near real-time tropospheric delay estimation models, IGGHZG and IGGHZM, in fast-static precise positioning. The first model is based on the processing of GPS data collected from ground-based reference stations, and the second one uses metrological data fed into the Saastamoinen model. These two methods were developed within the ASG+ project by researchers from Wroclaw University of Environmental and Life Sciences. The accuracy of these models was evaluated by comparison to tropospheric zenith total delays (ZTDs) obtained from the ASG-EUPOS network final solution and the UNB3m model. The applicability of these models to precise positioning was studied by their application to ultra-fast-static positioning, in which the resulting coordinates' accuracy and ambiguity resolution performance were analysed. Baselines from 65 to 72 km, with height differences from 39 to 379 m, were processed. The obtained results show that the GPS-based model can be successfully used in precise positioning, and the meteo-based model still requires improvements, mostly related to the interpolation technique.

The GNSS precise point positioning (PPP) technique requires high quality product (orbits and clocks) application, since their error directly affects the quality of positioning. For real-time purposes it is possible to utilize ultra-rapid precise orbits and clocks which are disseminated through the Internet. In order to eliminate as many unknown parameters as possible, one may introduce external information on zenith troposphere delay (ZTD). It is desirable that the a priori model is accurate and reliable, especially for real-time application. One of the open problems in GNSS positioning is troposphere delay modelling on the basis of ground meteorological observations. Institute of Geodesy and Geoinformatics of Wroclaw University of Environmental and Life Sciences (IGG WUELS) has developed two independent regional troposphere models for the territory of Poland. The first one is estimated in near-real-time regime using GNSS data from a Polish ground-based augmentation system named ASG-EUPOS established by Polish Head Office of Geodesy and Cartography (GUGiK) in 2008. The second one is based on meteorological parameters (temperature, pressure and humidity) gathered from various meteorological networks operating over the area of Poland and surrounding countries. This paper describes the methodology of both model calculation and verification. It also presents results of applying various ZTD models into kinematic PPP in the post-processing mode using Bernese GPS Software. Positioning results were used to assess the quality of the developed models during changing weather conditions. Finally, the impact of model application to simulated real-time PPP on precision, accuracy and convergence time is discussed.