The stochastic model, together with the functional model, form the mathematical model of observation that enables the estimation of the unknown parameters. In Global Navigation Satellite Systems (GNSS), the stochastic model is an especially important element as it affects not only the accuracy of the positioning model solution, but also the reliability of the carrier-phase ambiguity resolution (AR). In this paper, we study in detail the stochastic modeling problem for Multi-GNSS positioning models, for which the standard approach used so far was to adopt stochastic parameters from the Global Positioning System (GPS). The aim of this work is to develop an individual, empirical stochastic model for each signal and each satellite block for GPS, GLONASS, Galileo and BeiDou systems. The realistic stochastic model is created in the form of a fully populated variance-covariance (VC) matrix that takes into account, in addition to the Carrier-to-Noise density Ratio (C/N${}_0$)-dependent variance function, also the cross- and time-correlations between the observations. The weekly measurements from a zero-length and very short baseline are utilized to derive stochastic parameters. The impact on the AR and solution accuracy is analyzed for different positioning scenarios using the modified Kalman Filter. Comparing the positioning results obtained for the created model with respect to the results for the standard elevation-dependent model allows to conclude that the individual empirical stochastic model increases the accuracy of positioning solution and the efficiency of AR. The optimal solution is achieved for four-system Multi-GNSS solution using fully populated empirical model individual for satellite blocks, which provides a 2% increase in the effectiveness of the AR (up to 100%), an increase in the number of solutions with errors below 5 mm by 37% and a reduction in the maximum error by 6 mm compared to the Multi-GNSS solution using the elevation-dependent model with neglected measurements correlations.

: We provide a survey on the joint European research project “GeoMetre”, which explores novel technologies and their inclusion to existing surveying strategies to improve the traceability of geodetic reference frames to the SI definition of the metre. This work includes the development of novel distance meters with a range of up to 5 km, the realisation of optical multilateration systems for large structure monitoring at an operation distance of 50 m and beyond, and a novel strategy for GNSS-based distance determination. Different methods for refractivity compensation, based on classical sensors, on dispersion, on spectroscopic thermometry, and on the speed of sound to reduce the meteorological uncertainties in precise distance measurements, are developed further and characterised. These systems are validated at and applied to the novel European standard baseline EURO5000 at the Pieniny Kippen Belt, Poland, which was completely refurbished and intensely studied in this project. We use our novel instruments for a reduced uncertainty of the scale in the surveillance networks solutions for local tie measurements at space-geodetic co-location stations. We also investigate novel approaches like close-range photogrammetry to reference point determination of space-geodetic telescopes. Finally, we also investigate the inclusion of the local gravity field to consider the deviations of the vertical in the data analysis and to reduce the uncertainty of coordinate transformations in this complex problem.

At the Pieniny Klippen Belt in Poland, the novel primary reference baseline EURO5000 is required as part of the European Research project GeoMetre to both validate refractivity-compensated EDM prototypes and investigate the metrological traceability of GNSS-based distances. Since the aimed uncertainty is 1 mm at 5 km (k = 2), the design, construction, and validation must be carefully prepared to fulfil the high standards of the GeoMetre field campaigns which are planned to be carried out in May 2022. This contribution describes the main features of the EURO5000 and presents the results of the preliminary validation which includes a first comparison between the results obtained by using precise currently available EDMs as well as GNSS techniques following the standard GNSS geodetic processing algorithms, on the one hand, and the improved GNSS-Based Distance Meter (GBDM+) approach developed at UPV, on the other hand. The preliminary validation presented in this contribution also permits (1) to detect potential problems in the use of the baseline such as potential geodynamic problems, atmospheric refraction or multipath limitations, (2) to produce a set of reliable results, and (3) to pave the way for the final field comparisons between the novel EDMs and the GBDM+ approach. The result of this metrological experiment may significantly contribute to overcome the limitations of current high-precision deformation monitoring applications that require their scale to be consistent with the SI-metre within 0.1 ppm in several km.

As the peak of Solar Cycle 25 approaches, space weather events such as Equatorial Plasma Bubble (EPBs) and geomagnetic storms are expected to become more frequent. While EPBs are a primary source of scintillation, geomagnetic storms can either enhance or suppress this activity depending on storm timing, intensity, and induced electric field effects, thereby causing significant ionospheric disturbances that degrade Global Navigation Satellite System (GNSS) signal reception performance. This study presents a novel, systematic evaluation of GPS + Galileo Precise Point Positioning (PPP) performance under intense ionospheric scintillation during the rising phase of Solar Cycle 25 using datasets from globally distributed stations. More than twenty months of data have been systematically analysed, with a focus on stations located in equatorial regions, which are the most affected by strong scintillation. PPP processing was performed using final products from the European Space Agency (ESA) with Multi-GNSS Experiment (MGEX) products employed as backups when ESA data were unavailable. It is shown that under severe scintillation the accuracy of the final PPP solution is severely reduced, with errors more than doubled with respect to calm days. In this respect, frequent cycle slips and anomalies in the input observations are detected. A comparative analysis of GPS-only and GPS + Galileo PPP solutions confirms that integrating Galileo not only mitigates the impact of scintillation but also improves the reliability and accuracy of positioning in challenging space weather conditions.

The Galileo High-Accuracy Service (HAS) was declared operational (initial service) in January 2023 after an intense testing phase aimed at assessing its service performance through the transmission of live HAS corrections. The HAS performance at high latitudes is evaluated by analyzing data collected at the Polish Polar Station located in Hornsund, in the Norwegian Svalbard archipelago. At such a location, the reception conditions can be affected by poor satellite geometries and ionospheric scintillation may degrade the signal quality. In this respect, data affected by scintillation events were identified and used for the performance analysis. The assessment is carried out by comparing the HAS corrections with the International GNSS Service (IGS) precise products. Moreover, the retrieved HAS corrections are used to assess the Precise Point Positioning (PPP) performance.