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In GNSS analysis, tropospheric modelling is done in the form of Zenith Hydrostatic Delay (ZHD), which can be empirically computed from surface pressure and temperature, and Zenith Wet Delay (ZWD), which is estimated together with the other unknown parameters. Analysis methods based on undifferenced GNSS code- and carrier-phase observations like Precise Point Positioning (PPP), which can achieve millimeter-accurate positioning results, provide therefore also time-series of ZWD, which can be used for meteorologic applications. However, due to receiver noise and system characteristics like cycle-slips the accuracy as well as the precision of such ZWD estimates is limited. Thus, we propose a novel approach for sites, which have several receivers connected to a single antenna or which are separated horizontally by only a few meters. For such sites, one can simultaneously process multi-frequency GNSS data by fusing observations from several receivers, while estimating a common ZWD parameter.For this purpose, we have implemented a PPP algorithm based on an Extended Kalman Filter (EKF) approach, which has the advantage that ZWD estimates are available in real-time for meteorologic applications. We demonstrate that those combined ZWD estimates are superior to single receiver estimates in term of precision and accuracy. For the latter measure, we make use of a GNSS hardware simulator and show that the RMS between the simulated and estimated ZWD significantly decreases when having two or more receivers at that site. Based on real-data we show that this concept provides less noisy ZWD estimates which agree better with physical properties of the local wet refractivity field.Moreover, we demonstrate that fusing data from several receivers by estimating a common ZWD parameter improves also positioning accuracy and precision, in particular in the up-component. In order to properly combine observations from geodetic-grade and low-cost GNSS receivers, we present our adaptive Kalman filter approach, which adjusts the observation noise covariance matrix automatically during processing. The presentation concludes with an outlook on the usage of this approach for larger networks and answers the question how arrays of low-cost GNSS receivers can compete against geodetic-grade GNSS hardware in term of providing ZWD estimates for meteorology.

Global Navigation Satellite Systems (GNSS) have revolutionized land surveying, by determining position coordinates with centimeter-level accuracy in real-time or up to sub-millimeter accuracy in post-processing solutions. Although low-cost single-frequency receivers do not meet the accuracy requirements of many surveying applications, multi-frequency hardware is expected to overcome the major issues. Therefore, this paper is aimed at investigating the performance of a u-blox ZED-F9P receiver, connected to a u-blox ANN-MB-00-00 antenna, during multiple field experiments. Satisfactory signal acquisition was noticed but it resulted as >7 dB Hz weaker than with a geodetic-grade receiver, especially for low-elevation mask signals. In the static mode, the ambiguity fixing rate reaches 80%, and a horizontal accuracy of few centimeters was achieved during an hour-long session. Similar accuracy was achieved with the Precise Point Positioning (PPP) if a session is extended to at least 2.5 h. Real-Time Kinematic (RTK) and Network RTK measurements achieved a horizontal accuracy better than 5 cm and a sub-decimeter vertical accuracy. If a base station constituted by a low-cost receiver is used, the horizontal accuracy degrades by a factor of two and such a setup may lead to an inaccurate height determination under dynamic surveying conditions, e.g., rotating antenna of the mobile receiver., Horizon 2020

The dynamics of water vapor distribution in the troposphere, measured with Global Navigation Satellite Systems (GNSS), is a subject of weather research and climate studies. With GNSS, remote sensing of the troposphere in Europe is performed continuously and operationally under the E-GVAP (http://egvap.dmi.dk/) program with more than 2000 permanent stations. These data are one of the assimilation system component of mesoscale weather prediction models (10 km scale) for many nations across Europe. However, advancing precise local forecasts for severe weather requires high resolution models and observing system. Further densification of the tracking network, e.g. in urban or mountain areas, will be costly when considering geodetic-grade equipment. However, the rapid development of GNSS-based applications results in a dynamic release of mass-market GNSS receivers. It has been demonstrated that post-processing of GPS-data from a dual-frequency low-cost receiver allows retrieving ZTD with high accuracy. Although low-cost receivers are a promising solution to the problem of densifying GNSS networks for water vapor monitoring, there are still some technological limitations and they require further development and calibration.We have developed a low-cost GNSS station, dedicated to real-time GNSS meteorology, which provides GPS, GLONASS and Galileo dual-frequency observations either in RINEX v3.04 format or via RTCM v3.3 stream, with either Ethernet or GSM data transmission. The first two units are deployed in a close vicinity of permanent station WROC, which belongs to the International GNSS Service (IGS) network. Therefore, we compare results from real-time and near real-time processing of GNSS observations from a low-cost unit with IGS Final products. We also investigate the impact of replacing a standard patch antenna with an inexpensive survey-grade antenna. Finally, we deploy a local network of low-cost receivers in and around the city of Wroclaw, Poland, in order to analyze the dynamics of troposphere delay at a very high spatial resolution.As a measure of accuracy, we use the standard deviation of ZTD differences between estimated ZTD and IGS Final product. For the near real-time mode, that accuracy is 5 mm and 6 mm, for single- (L1) and dual-frequency (L1/L5,E5b) solution, respectively. Lower accuracy of the dual-frequency relative solution we justify by the missing antenna phase center correction model for L5 and E5b frequencies. With the real-time Precise Point Positioning technique, we estimate ZTD with the accuracy of 7.5 – 8.6 mm. After antenna replacement, the accuracy is improved almost by a factor of 2 (to 4.1 mm), which is close to the 3.1 mm accuracy which we obtain in real-time using data from the WROC station.

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.

The near real-time (NRT) high resolution water vapour distribution models can be constructed based on GNSS observations delivered from Ground Base Augmentation Systems (GBAS) and ground meteorological data. Since 2008 in the territory of Poland, a GBAS system called ASG-EUPOS (Active Geodetic Network) has been operating. This paper addresses the problems concerning construction of the NRT model of water vapour distribution in the troposphere near Poland. The first section presents all available GNSS and ground meteorological stations in the area of Poland and neighbouring countries. In this section, data feeding scheme is discussed, together with timeline and time resolution. The high consistency between measured and interpolated temperature value is shown, whereas some discrepancy in the pressure is observed. In the second section, the NRT GNSS data processing strategy of ASG-EUPOS network is discussed. Preliminary results show fine alignment of the obtained Zenith Troposphere Delays (ZTDs) with reference data from European Permanent Network (EPN) processing center. The validation of NRT troposphere products against daily solution shows 15 mm standard deviation of obtained ZTD differences. The last section presents the first results of 2-D water vapour distribution above the GNSS network and application of the tomographic model to 3-D distribution of water vapour in the atmosphere. The GNSS tomography model, working on the simulated data from numerical forecast model, shows high consistency with the reference data (by means of standard deviation 4 mm km−1 or 4 ppm), however, noise analysis shows high solution sensitivity to errors in observations. The discrepancy for real data preliminary solution (measured as a mean standard deviation) between reference NWP data and tomography data was on the level of 9 mm km−1 (or 9 ppm) in terms of wet refractivity.

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.

The International GNSS Service (IGS) real-time service (RTS) provides access to real-time precise products such as orbits, clocks and code biases, which can be used as a substitute for ultra-rapid products in real-time applications. The true performance of these products can be assessed by the Analysis Centers daily statistics derived from the comparison with IGS rapid products. Additionally, indirect verification is performed by their application to various precise point positioning strategies. Monitoring results and basic descriptions of these products are available at the official RTS Web page ( http://rts.igs.org/ ). We present a more detailed description of RTS products. Information from various sources is collected to provide products application methodology and describe their important features. We provide extended verification of the products using 1 week of real-time correction data. Results are presented separately for GNSS constellations, considering satellite block and type of onboard clock. Comparison with ESA/European Space Operations Centre final products proves the high accuracy of RTS orbits and clocks, which is 5 cm for GPS orbits, 8 cm for GPS clocks, 13 cm for GLONASS orbits and 24 cm for GLONASS clocks. The real-time correction performance is also examined regarding availability and latency. In general, the availability of corrections was beyond 95 % for GPS and beyond 90 % for GLONASS. Since the increasing degradation of product quality with latency is critical for real-time applications, the relation between product latency and accuracy is analyzed. It confirms that high-rate stream update intervals are suitable for the data provided and that the obsolete data should not be used. To avoid this, we propose a method of short-term prediction of RTS corrections that extends the application period of obsolete correction data without a significant loss in orbit quality. Using polynomial fitting, it is possible to forecast the orbit corrections reliably up to 8 min for GPS and 4 min for GLONASS.

In GNSS data processing, the station height, receiver clock and tropospheric delay (ZTD) are highly correlated to each other. Although the zenith hydrostatic delay of the troposphere can be provided with sufficient accuracy, zenith wet delay (ZWD) has to be estimated, which is usually done in a random walk process. Since ZWD temporal variation depends on the water vapor content in the atmosphere, it seems to be reasonable that ZWD constraints in GNSS processing should be geographically and/or time dependent. We propose to take benefit from numerical weather prediction models to define optimum random walk process noise. In the first approach, we used archived VMF1-G data to calculate a grid of yearly and monthly means of the difference of ZWD between two consecutive epochs divided by the root square of the time lapsed, which can be considered as a random walk process noise. Alternatively, we used the Global Forecast System model from National Centres for Environmental Prediction to calculate random walk process noise dynamically in real-time. We performed two representative experimental campaigns with 20 globally distributed International GNSS Service (IGS) stations and compared real-time ZTD estimates with the official ZTD product from the IGS. With both our approaches, we obtained an improvement of up to 10% in accuracy of the ZTD estimates compared to any uniformly fixed random walk process noise applied for all stations.

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.