Abstract The European Terrestrial Reference System (ETRS89) is the European Union recommended European geodetic reference system. It is based on the global International Terrestrial Reference System (ITRS), but is fixed to the stable part of the Eurasian tectonic plate. The ETRS89 is realized through the EUREF Permanent Network (EPN), which has been operational since 1996. Today, the EPN includes more than 420 active GNSS (Global Navigation Satellite System) stations spread across almost all of Europe. Since the EPN was set up, a number of improvements have been implemented in the computation standards related to data processing and analysis, the introduction of new satellite navigation systems, such as GLONASS and Galileo, and in antenna and receiver technology. For the maintenance and further development of the reference frame, homogeneous position time series are crucial, but these are affected by the successive modernizations and reference frame updates. Therefore, analogously to the IGS (International GNSS Service), EUREF decided to reprocess all available GNSS data since 1996 in a standardized and homogeneous way. In contrast to our previous work, EUREF stopped using individual antenna calibrations and now uses type mean calibration only. This is motivated both by the need for harmonisation with the IGS and by the fact that many individual antenna calibrations do not contain calibrations for GLONASS and Galileo with their full frequency spectrum. Analysis Centres (ACs), participating in the EPN-Repro3 campaign, computed a sub-network of overlapping EPN stations on a daily basis, providing SINEX solutions that are combined in daily solutions by the EPN Analysis Centre Coordinator. Using these combined solutions, the EPN Reference Frame Coordinator estimates a cumulative multi-year position and velocity solution aligned to the IGS20.

This paper presents a theoretical study on ionospheric reconstruction using GNSS data obtained from Low Earth Orbit (LEO) satellites in a PNT (Position, Navigation, and Timing) configuration, where the LEO satellites not only receive but also transmit GNSS signals, which can be tracked by ground or mobile receivers. The study is intended to pave the way for incorporating slant Total Electron Content (TEC) data from ESA's upcoming LEO-PNT into ionospheric reconstructions. We generate synthetic slant TEC for three observation scenarios: Ground-GNSS, ground-LEO, and LEO-GNSS links. As ground-truth, the IRI-20 model with the Ozhogin plasmasphere extension is used. An inversion to recover the electron density from slant TEC observations is performed using an Extended Kalman Filter (EKF) in the information-filter formulation for all possible combinations of observation scenarios. As the LEO constellation, we will utilize existing LEO satellites that were available in May 2020, including Swarm, COSMIC-2, GRACE-FO, Jason-3, Sentinel-1, Sentinel-2, and Sentinel-3, as well as several Spire satellites. They cover a variety of altitudes between 400 km and 1350 km. For this study, we assume they could transmit dual-frequency GNSS-like signals like a PNT mission, which is not the case for any of the satellites mentioned. We only consider relative slant TEC to be insensitive to calibration biases that may reach a few TEC units. Given a real global ground-station network, LEO and GNSS satellites, we show that 15-min reconstruction solutions, only containing ground stations, cannot compete with solutions including LEO satellites. Furthermore, our results show that the joint use of LEO-POD (Precise Orbit Determination Antenna) and LEO-PNT (RMSE at 500 km: 0 95 10 4 cm 3) provides superior performance compared to configurations where either is substituted by ground-based GNSS (ground-GNSS and PNT: 4 03 10 4 cm 3; Gound-GNSS and POD 1 18 10 4 cm 3). We also show that the reconstruction error roughly doubles when radio occultation measurements are omitted. The dependency of the error on the distribution of the ground stations is also shown. Areas with only a few or no ground stations show the lowest correlation between IRI-20 and the reconstructions, e.g., near Point Nemo, where the correlation drops to 0.5. (c) 2026 The Author(s). Published by Elsevier B.V. on behalf of COSPAR. This is an open access article under the CC BY license (http:// creativecommons.org/licenses/by/4.0/).

Global Navigation Satellite Systems (GNSS) are based on measuring signal propagation time, so that clock information is required for both the transmitting satellite and the receiving ground station. For Precise Point Positioning (PPP), synchronization errors of the receiver clock are usually estimated as epoch-wise biases with white noise as stochastic behavior. A major issue for the receiver clock estimates is the high correlation with the station height and the tropospheric zenith delay that results from the observation geometry. Introducing models to reduce the number of unknown clock parameters is one way to mitigate these correlations. However, adequate modeling requires a high degree of stability for the corresponding clock.In this contribution, we show the results of modeling highly stable GNSS receiver clocks in PPP using piece-wise linear representations. We discuss different options to control the deterministic and stochastic part of the piece-wise linear model (interval length, parameter weighting, etc.). For 56 highly stable hydrogen maser (H-maser) stations of the International GNSS service (IGS), the impact of piece-wise linear clock modeling on correlated parameters, especially the sub-daily height estimates, is presented. The differences in the modeling impact of the individual receiver clocks are explained by categorizing the stations based on statistical and observational quality measures. In addition, the effects of individual processing options (used GNSS constellations, elevation cutoff angle) are shown.

Modeling highly stable GNSS receiver clocks helps to increase the stability of correlated parameters, especially the station height. The use of a piece-wise linear receiver clock model, which is a common method for clock parametrization in Very Long Baseline Interferometry, has not yet been extensively investigated for GNSS. In this work, we examine piece-wise linear receiver clock modeling for GNSS. Based on a one-month series of kinematic Precise Point Positioning analyses for 56 highly stable hydrogen maser stations, the effects of piece-wise linear clock modeling are demonstrated. For the stochastic part of the model, the process for determining the optimal relative constraint weight is explained in detail, whereas the deterministic component consists of piece-wise linear segments with interval lengths of 8, 4 and 2 hours to represent the clocks of highly stable hydrogen maser stations. Compared to the epoch-wise clock estimation, there are no significant differences for the tropospheric zenith delay. However, applying a piece-wise linear model leads to more stable height estimates. The larger the modeling interval, the more stable the sub-daily height estimates get: the median standard deviation decreases by -1.6 mm (-10%) for 2-hour and -3.0 mm (-20%) for 8-hour intervals. Stations with a higher error of unit weight and a smaller number of observations tend to show larger improvements in height stability (up to 45%). When observations are limited by satellite system exclusion or high elevation cutoff angles, piece-wise linear clock models become especially advantageous in terms of height stability.

To achieve the 1 mm accuracy and 0.1 mm/year stability of Terrestrial Reference Frame (TRF) required by Global Geodetic Observing System (GGOS), various surface displacements have to be precisely modeled. Non-tidal atmosphere, ocean, and hydrology loading displacements are major sources causing stochastic and systematic effects in station coordinates estimated by space geodetic techniques such as Global Navigation Satellite Systems (GNSS). Studies show that the correction of non-tidal loading displacements in GNSS station coordinate time series reduces coordinate repeatability and thereby improves stability. Currently, non-tidal loading displacements are corrected on the observation level in Very Long Baseline Interferometry (VLBI) data analysis for standard IVS (International VLBI Service for Geodesy and Astrometry) products, but not in GNSS data analysis. We applied the ESMGFZ non-tidal atmosphere and ocean loading displacements (NTAOL) on the observation, normal equation, and parameter levels for global GNSS network solutions in 2005-2019. We demonstrate that the station coordinate repeatability can be significantly improved when correcting NTAOL displacements, especially in the up component where a reduction of 20-30% can be observed at middle and high latitudes. Whereas for other geodetic parameters, such as satellite orbits, Earth Rotation Parameters (ERP), and geocenter motion, however, the impact of NTAOL displacements is insignificant. The difference between applying NTAOL displacements on the observation to that on the normal equation level is on sub-daily scales and we show that most of these differences are absorbed by receiver clocks. As for the differences of applying NTAOL on the observation and on the parameter levels, small but systematic effects on the horizontal components of station coordinates appear, which are mainly due to network alignment. We also demonstrate that the a priori tropospheric delay modeling affects the non-tidal atmosphere loading signals in station coordinates, i.e., when applying empirical tropospheric delay models, e.g., GPT3, NTAL correction introduces a significantly smaller improvement of station coordinate repeatabilities (below 5% in up component). Hence, we recommend always using discrete tropospheric delay products from Numerical Weather Model (NWM) as a priori values when NTAL corrections are applied.

Global Navigation Satellite Systems (GNSS) are based on measuring the time that elapses between the signal’s transmission at the satellite and its reception on the ground. Therefore, clock information is required on both sides. While the GNSS satellites are equipped with atomic clocks, ground stations usually use the time information from the internal oscillator of their GNSS receiver, which has a much lower time-keeping performance compared to the satellite clocks. Nevertheless, some continuously operated tracking stations obtain their time information from an external atomic clock, as it is the case with many stations of the International GNSS Service (IGS). To compensate for synchronization errors, current GNSS analysis models generally introduce clock biases for satellites and receivers into the observation equations. The often-made assumption of a pure white noise behavior for the estimated clocks may lead to high correlations with other geodetic parameters, such as the radial orbit error for the satellite clock, or the station height coordinate and tropospheric delay parameters for the station clock. A general solution to this problem is to reduce the amount of unknown clock parameters by modeling them in the adjustment process. In order to be modeled adequately, the corresponding clock must have a high degree of stability, which is particularly crucial for the ground stations. In this contribution, we investigate the clock stability of globally distributed IGS tracking stations. Those IGS stations, that are steered by an external Hydrogen-Maser (H-Maser) clock, are considered in a global network analysis over a period of several weeks. The generated clock products are used to compare the frequency stabilities within the station network, as well as with the mean behavior of GPS and Galileo satellite blocks. After some further research on stations with significantly higher deviations, the final result of this contribution will be a set of reliable ground stations, that will serve as a basis for future clock modeling approaches at GFZ.

Abstract:Machine Learning (ML) is emerging as a powerful tool for data analysis. Anomaly detection based on classical approaches is sometimes limited in processing speed on big data, especially for massive datasets. Meanwhile, quantum algorithms have been shown to have the potential for optimization, scenario simulation, and artificial intelligence. Thus, this study combines quantum algorithms and ML to improve the binary classification performance of ML models for better sensitivity of surface deformation detection. We experimented with GNSS-InSAR combination data to identify significant deformation regions in Northern Germany. We classify the movement characteristics based on four main features: vertical movement velocities, root mean square errors, standard deviations, and outliers in the GNSS-InSAR time series. Our primary results reveal that the classification accuracy based on Quantum Machine Learning (QML) is outstanding compared to the pure ML technique. Specifically, on the same sample dataset, the classification performance of the neural network based on pure ML is only around 50 to 70%, while that of the QML technique can reach ~90%. The significant deformation regions are concentrated in the river basins of Elbe, Weser, Ems, and Rhine, where the average surface subsidence speed varies around -4.5 mm/yr. Also, we suggest dividing the surface movement features in Northern Germany into five classes to reduce the effect of the data quality variety and algorithm uncertainty. Our findings will advocate the development of quantum computing applications as well as promote the potential of the QML for deformation analyses. Keywords: Quantum Machine Learning, Binary Classification, GNSS-InSAR Data, Deformation Detection.

Global Navigation Satellite Systems (GNSS) are based on measurements of signal propagation time, so that clock information is required for both the transmitting satellite and the receiving ground station. In undifferenced GNSS network analyses, synchronization errors of the satellite and station clocks are usually estimated by epoch-wise biases. If, as is common in practice, white noise is assumed as stochastic behavior for the clocks, there are high correlations between the clock estimates and other geodetic parameters. While the satellite clock is correlated with the radial orbit component and geocenter parameters, the station clock shows high correlations with the station height coordinate and the tropospheric zenith delay. These effects can be reduced by introducing proper models for describing the clock characteristics. Especially for global network solutions, deterministic clock modeling is suitable to reduce a substantial number of clock estimates. However, adequate modeling requires a high degree of stability for the corresponding clocks.In this contribution, we show preliminary results of modeling highly stable GNSS ground and space clocks using piece-wise linear representations. For the satellites, we select the rubidium clocks of the GPS IIF and IIIA blocks as well as the passive hydrogen maser clocks of the Galileo FOC spacecraft for modeling. In addition, a selection of hydrogen maser stations of the International GNSS Service (IGS) is also modeled. Over a period of several weeks, daily network solutions with and without piece-wise linear clock modeling are processed and then compared. We discuss different strategies and show the effects of various modeling options (length of split interval, parameter weighting) on the correlations of the estimated parameters.

The 79° North Glacier (Nioghalvfjerdsbrae, 79NG) is one of three glaciers with a floating tongue in Greenland. Recent investigations indicate an increased subglacial discharge due to a considerably enlarged area of summer surface melt due to the warming of the atmosphere, resulting in increased water input to the base of glaciers. Consequently, ice velocities measured at the surface respond directly to changes in water pressure, revealing detailed insights about the ice dynamics. Global Navigation Satellite System, like GPS and Galileo, can observe ice velocities with high temporal resolution in horizontal and vertical directions.We will present results from the 2022-2023 GNSS measurement campaign where two tinyBlack GNSS receivers were installed at 79NG. Firstly, data quality regarding common indicators like the number of tracked satellites, signal strength, and multipath will be discussed. Secondly, variations in the ice reflection characteristics will be presented based on the GNSS-reflectometry technique. The final processing was carried out as kinematic precise point processing (sampling rate 30s) using GFZ’s processing software EPOS.P8 and GFZ’s operational GNSS products. Thus, thirdly, the derived time series will be discussed with a focus on short-term variations in the surface velocity. We can link speed-up events in July 2022 to rapid lake drainage using optical satellite imagery and interferometrically derived digital elevation models.

Global Navigation Satellite Systems (GNSS) like GPS or Galileo allow high-accurate positioning and geolocation. GNSS has been used in geosciences for more than three decades for surface deformation monitoring, including tectonics, earthquake cycle, and vertical land motion associated with postglacial rebound. The possibility of observing atmospheric conditions, especially electron content and water vapor distribution, allows multi-purpose applications. Thanks to modernizations in the GNSS constellations, including new signals, advanced and cost-efficient receiver equipment has been developed over the past few years. This allows the establishment of dense observation networks and advanced observation scenarios.GFZ recently integrated GNSS receivers into the Geophysical Instrument Pool (GIPP) to support GNSS-based applications in various domains. This research infrastructure facility is open to all national and international academic applicants; the instruments are provided free of charge following a transparent application and evaluation procedure. This contribution presents the available GNSS equipment, potential applications, and the user pipeline from deployment to results. Results from two supported projects will be presented in more detail. The first focuses on surface deformation across the Irpinia and Pergola-Melandro fault system and the second on monitoring seasonal acceleration at the 79°N Glacier in Greenland. Both examples highlight the value of accurate, in-situ coordinate time series.

The International GNSS Service (IGS) requires advanced multi-GNSS orbit combination strategies to replace current GPS/GLONASS-focused operations with consistent products covering GPS, GLONASS, Galileo, and BDS. We developed an enhanced orbit combination methodology using a modified Förstner Variance Component Estimation (VCE) scheme that optimizes weighting strategies through data clustering approaches, including individual satellite weighting, satellite-type grouping, and machine-learning-generated clusters. Our novel approach incorporates a priori knowledge from Satellite Laser Ranging (SLR) orbit validations and sequential weight information from previous combinations to refine Analysis Center (AC) weights. Sequential weight estimation significantly reduces day boundary orbit misclosures and stabilizes temporal AC weight variability. The combined solutions demonstrate exceptional inter-consistency with RMS values below 3–5 mm for GPS and Galileo, while GLONASS and BDS show higher variability (10–15 mm), highlighting the importance of satellite grouping strategies. Intermediate grouping approaches based on IGS metadata or hierarchical clustering provide optimal balance between constellation-level oversimplification and satellite-specific day-to-day variability. SLR-based knowledge incorporation offers targeted improvements, particularly for challenging high and low β angle conditions, demonstrating the effectiveness of external validation in multi-GNSS orbit combination.

Non‐tidal loading (NTL) introduces surface deformation on the Earth and increases the variability in coordinates measured by space geodetic techniques. Correcting NTL displacements in Global Navigation Satellite Systems (GNSS) analysis has been discussed extensively, commonly at the parameter level. We investigate the three levels of correcting non‐tidal atmospheric and oceanic loading (NTAOL) displacements systematically in long‐term analysis of GNSS global network solution, including the observation, normal equation, and parameter levels. The difference between the observation and normal equation levels lies in addressing high‐frequency (sub‐daily) displacements, and that between the normal equation and parameter levels concerns datum realization. Correcting NTAOL at the observation (or normal equation) level improves the station coordinate repeatability by 3%–4% horizontally and 13% vertically, slightly greater than that at the parameter level by 0.5%. Discrepancies in station coordinates between the observation (or normal equation) and the parameter level are minor but systematic, and the horizontal discrepancies can be largely reduced by Helmert transformation. These transformation parameters correspond to the datum parameters, including polar motion offsets and geocenter coordinates. High‐frequency loading displacements mainly impact site‐wise tropospheric parameters and especially receiver clocks, albeit with small magnitudes at the sub‐mm level. Satellite orbits in the along and cross components are affected by both datum differences (between normal equation and parameter levels) and high‐frequency displacements (between observation and normal equation levels), while radial component and satellite clocks are solely affected by the latter.

Cost-effective multi-frequency GNSS receivers harbour opportunities for geoscientific displacement-monitoring applications, such as economically deploying large networks of accurate GNSS stations. We use the tinyBlack data logger, developed to facilitate such applications, to test the performance of such receivers. We first compare different receivers, independently of any built-in antenna quality, in a zero-baseline test. Two cost-efficient dual-frequency receivers (u-blox F9P and Swift Navigation Piksi Multi) and a tri-frequency Septentrio receiver (AsteRx-m3), housed in tinyBlacks, together with a stand-alone reference geodetic receiver (Septentrio PolaRx5), are simultaneously connected to a geodetic choke-ring antenna using a splitter. We analyse observation quality, including availability, multipath linear combinations, and signal-to-noise ratios. We process observations in a precise point positioning (PPP) scheme, with both daily-coordinate and kinematic solutions, and assess solutions and residuals. Results show the cost-efficient receivers are most affected by multipath effects and produce greater residuals and less accurate vertical coordinates, differing by more than 1 mm on average from the reference and higher-end receivers. A step-displacement test then evaluates the ability of the Piksi receiver to recover a repeated 5-cm displacement in two-hour cycles, in separate north-south and vertical subtests, using a geodetic rover antenna. We perform PPP processing without ambiguity resolution and compute the displacement in each cycle as the difference of average coordinates. Results show that the receiver can recover the average amplitude of repeated 5-cm displacements with sub-cm accuracy, also in the vertical direction, although the spread of individual recovered displacements and individual coordinates is greater than in the horizontal test.

Combined precise satellite orbits and clocks stand as core contributions from the International GNSS Service (IGS), integrating the individual inputs of various Analysis Centers (AC). The availability and quality of multi-GNSS products developed by ACs within the IGS multi-GNSS Pilot Project propel IGS towards replacing combined GPS and GLONASS products with homogeneous combined products encompassing all GPS, GLONASS, Galileo, BeiDou, and QZSS systems. A primary challenge faced by the IGS lies in refining the combination algorithm for multi-GNSS orbits and clocks to provide users with the utmost quality products. This study delves into concepts aimed at enhancing the orbit combination algorithm, with a specific focus on adjusting the weighting scheme and detecting outlier observations. The core of the combination methodology adheres to the concept proposed by GFZ, employing a least-squares framework wherein weights used for combining AC orbits are determined through least-squares variance component estimation (VCE). Four distinct weighting strategies are introduced and compared in this study. These strategies involve utilizing either the constellation, satellite type, satellite type on the same orbital plane, or each satellite individually to form datasets used in determining weights for each AC. Furthermore, a novel approach is developed to correct the weights for individual ACs based on the results of Satellite Laser Ranging orbit validation. This serves as an additional factor in the combination, mitigating the impact of systematic AC-dependent orbit mismodeling issues. All proposed strategies underwent testing using multi-GNSS orbit solutions over a 10-month period in 2023. Firstly, the combination results show an agreement between the different AC’s input orbits around 15, 20, 30, 50, and 100 mm for GPS, GLONASS, Galileo, BeiDou, and QZSS, respectively. Regarding the AC weighting strategy, the constellation-specific weighting approach provides the most robust solution and allows for handling differences between AC-specific issues in the orbit modeling of individual constellations. The satellite-specific weighting approach offers better resilience against the adverse effects caused by the inhomogeneous quality of satellite blocks/types/generations within a constellation, especially for BeiDou. However, the satellite-specific weighting encounters problems related to the appearance of invalid negative variances/weights for individual satellites as the output of VCE, mainly for BDS-3 and QZSS. The negative variance component can be an important indication of defects in our variance component model. Grouping satellites of similar characteristics in a satellite-type-specific weighting approach increases redundancy and reduces the issue but not entirely. Ultimately, we demonstrate potential solutions to address this issue. This involves simplifying the iterated VCE or resorting to the legacy inverse mean square differences between the mean orbit and the AC’s orbits as weights, particularly in cases where the classic VCE proves ineffective.

GFZRNX-QC software is designed to streamline the processing of Receiver Independent Exchange Format (RINEX) observations and the generation of overall information by providing a robust and efficient solution for data cleaning and quality control. With a focus on multiple Global Navigation Satellite System (multi-GNSS) observations, GFZRNX-QC offers a comprehensive approach to ensuring data accuracy and reliability. GFZRNX-QC can allow users to efficiently manage and analyze data from various GNSS receivers, especially for low-cost GNSS receivers. The software incorporates advanced algorithms for data cleaning, helping users to eliminate inconsistencies and enhance the overall quality of GNSS observations. GFZRNX-QC conducts comprehensive quality control assessments on GNSS observations. This ensures that the processed data meets the highest standards of accuracy. The software generates detailed statistical results, offering insights into the performance and reliability of observations across the five major GNSS systems. This information aids researchers and analysts in making informed decisions. GFZRNX-QC produces various outputs that can be e.g. compatible to former processing tools like teqc. This can enhance user convenience and interoperability with other geodetic processing tools. GFZRNX-QC has been extensively tested by utilizing multi-year data from IGS stations to enable comprehensive long-term statistical analysis. By combining efficient data processing, advanced cleaning algorithms, and extensive quality control measures, GFZRNX-QC serves as a valuable tool for researchers, geodesists, and GNSS professionals seeking reliable and accurate observations and overall information from multiple satellite systems.

Global Navigation Satellite Systems (GNSS) rely on one-way signal travel time measurements from satellites to receivers. To ensure accurate ranging, GNSS must estimate and compensate for clock offsets on at least one end of the transmitter-receiver system. Consequently, clock offsets are highly correlated with GNSS-derived parameters such as station coordinates, tropospheric delay estimates, satellite radial orbit parameters, and apparent geocenter coordinates. Improper handling of clock offsets can lead to their absorption into these parameters, degrading geodetic product accuracy. Traditionally, clocks have been handled within individual techniques without being specially addressed. However, some research efforts and experimental trials have explored using VLBI to synchronize clocks for GNSS and refining clock models to reduce correlations with other estimated parameters in GNSS, thereby improving overall precision.With recent advancements, high-precision optical clocks and fiber-optic time transfer technologies provide new possibilities for enhancing clock synchronization in GNSS. Optical fiber offers a stable, interference-free medium for time and frequency transfer, eliminating atmospheric effects such as ionospheric and tropospheric delays that impact GNSS-based synchronization. Moreover, fiber-optic time transfer is inherently two-way, removing the need for external clock offset estimation. Thus, fiber-optic clock synchronization represents the most precise timing technique currently available. Establishing a common clock by connecting multiple GNSS receivers via optical fiber could significantly reduce the number of estimated clock parameters in GNSS solutions, leading to improved geodetic measurement precision and a more accurate geodetic reference frame.Despite its potential, the approach of implementing a common clock with optical fiber for GNSS receivers remains largely untested. Although optical fiber links have been successfully used in clock synchronization, their integration into GNSS receiver clocking is still in an experimental stage. Notable existing efforts include: (1) the Geodetic Observatory Wettzell, where multiple receivers are connected to a single clock via optical fiber, representing a local baseline setup, and (2) the GFZ experiment, where a receiver is linked to the ultra-stable clock of PTB, representing a regional baseline approach.This study characterizes existing fiber-optic connections among GNSS receivers to identify practical challenges and evaluate their impact on GNSS parameter estimation. We process data from receivers sharing a common clock using Bernese GNSS Software. Initially, PPP will be performed to compare GNSS-derived clock parameters across receivers sharing a common clock, verifying the effectiveness of fiber-optic clock synchronization. Following this validation, we will leverage GNSS-derived clock parameters to evaluate inter-receiver clock differences measured via optical fiber. Subsequently, we will implement a strategy in which only one receiver’s clock parameters are estimated, using fiber-measured clock differences as a priori constraints for other receivers in the PPP solution. This approach reduces the number of estimated clock parameters and serves as a preliminary test of the feasibility of a GNSS common clock framework.Future developments will focus on refining our analysis framework to enable simultaneous estimation of GNSS receivers operating under a common clock. This research contributes to the broader goal of integrating ultra-stable clocks into global GNSS networks, ultimately enhancing the stability of geodetic reference frames and improving GNSS-derived geodetic products.

Throughout the earthquake cycling at fault zones, Earth’s crust undergoes deformations. GNSS coordinate time series record linear tectonic motion, seismic displacements, postseismic decays, and periodic signatures such as non-tidal loading. Any additional motions can be classed as transient tectonic signals, i.e., unexpected accelerations with respect to the standard trajectory model. As the number of permanent stations increases and as time series grow, we are increasingly able to recognise transient tectonic signals. Since some of these suspected tectonic transients have subtle magnitudes or sometimes unusual spatiotemporal features, we need to develop methods for determining which transients are artifacts and which are of tectonic origin. Here, we investigate the impact of certain GNSS processing choices and how they affect the appearance of transients in the GNSS displacement time series solutions. In this study, we choose data from Cascadia, a region for which the occurrence of transient signals in the GNSS time series is well known. We processed data based from 189 selected stations in network mode for the time span 2015 to 2019. After producing coordinate time series, we then built a pipeline to isolate processing artifacts and tectonic transients, using the regression model-based algorithm known as GrAtSiD (Greedy Automatic Signal Decomposition). The residuals of GNSS observations show that most sites have a precision of 5 mm to 10 mm. Using the GrAtSiD algorithm, we detected transient signals with velocities exceeding 0.3 mm/day near the ALBH station.

Modeling station and satellite clocks in the GNSS analysis in order to reduce existing correlations requires a high level of stability for the corresponding clocks. In this contribution, we provide a comprehensive and up-to-date status regarding the stability of on-board clocks of GPS, GLONASS, and Galileo satellites, as well as hydrogen maser stations within the International GNSS Service network. We use exemplary events of irregularities to show which factors need to be taken into account when analyzing a longer period of GNSS clocks. Based on epoch-wise clock biases estimated for different sampling rates (5 min / 30 s) in a daily network solution from May 2023 to April 2024, various stability analyses are carried out. About 60 of the 80 hydrogen maser stations distributed worldwide show a high stability with an average daily standard deviation of less than 75 picoseconds. For the satellite clocks the stability depends mainly on the atomic clock type and the age of the satellite block. In a further stability analysis, the 5-min clock estimates are subjected to a linear regression analysis with different interval lengths. The clock estimates of the younger satellite generations (GPS IIF, GPS IIIA, Galileo FOC) and the highly stable hydrogen maser stations can be well characterized by linear representations; assuming 10 mm as a threshold for the mean regression fit RMS, the maximum interval lengths are two and eight hours, respectively.

Among the core products of the International GNSS Service (IGS) are precise satellite orbits and clocks, which are generated by the Analysis Center Coordinator (ACC) as a combination of the solutions provided by different Analysis Centers (AC). A strategic goal of the IGS is to facilitate multi-GNSS solutions, implying that the currently operational system-wise GPS and GLONASS combinations should be replaced by a consistent set of multi-GNSS products, eventually containing at least GPS, GLONASS, Galileo, BeiDou, and QZSS. Over the past years, the Satellite Precise Orbit and Clock Combination (SPOCC) software tool has been developed at GFZ. It provides a fully consistent multi-GNSS orbit and clock combination that covers all available and possible future constellations and is based on a well-defined unified least-squares framework. The resulting combined orbit and clock products are a weighted average of the individual AC solutions with weights determined through least-squares variance component estimation (VCE). A main objective is to support multi-GNSS precise point positioning (PPP) users. We will introduce the combination workflow, which essentially consists of alignments harmonizing the AC products followed by the VCE and the weighted averaging, and is complemented by quality checks such as outlier detection. For the orbit combination, the alignment consists of Helmert transformations applied to the AC orbits, which is iterated with the VCE-based weighted averaging until convergence. The clock alignments consist of a radial correction from the orbit differences between the AC solutions, a removal of the impact of different reference clocks in the AC solutions, as well as an adjustment of all non-GPS satellite clocks for different inter-system bias (ISB) references at the ACs. The combination can be configured for different weighting schemes, including AC specific weights, AC+constellation specific weights, up to satellite type or even satellite specific weights, and the Helmert transformations can be based on different sets of satellite orbits. The SPOCC software has been extensively tested with the operational IGS products, the IGS Multi-GNSS Experiment (MGEX) products, and the IGS repro3 products. Performance evaluations by means of a comparison of the combination with the input products and the official IGS combination, through a satellite laser ranging (SLR) validation, and with PPP results will be used to show that the software achieves reliable results that are suitable for the users’ high precision GNSS applications. SPOCC is implemented in Python and will be provided as open source software.