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Phase center offsets (PCOs) of global navigation satellites systems (GNSS) transmit antennas along the boresight axis introduce line-of-sight-dependent range changes in the modeling of GNSS observations that are strongly correlated with the estimated station heights. As a consequence, changes in the adopted PCOs impact the scale of GNSS-based realizations of the terrestrial reference frame (TRF). Vice versa, changes in the adopted TRF scale require corrections to the GNSS transmit antenna PCOs for consistent observation modeling. Early studies have determined an approximate value of $$\alpha =-0.050$$ α = - 0.050 for the ratio of station height changes and satellite PCO changes in GPS orbit determination and phase center adjustment. However, this is mainly an empirical value and limited information is available on the actual PCO-scale relation and how it is influenced by other factors. In view of the recurring need to adjust the IGS antenna models to new ITRF scales, a semi-analytical model is developed to determine values of $$\alpha $$ α for the four current GNSSs from first principles without a need for actual network data processing. Given the close coupling of satellite boresight angle and station zenith angle, satellite PCO changes are essentially compensated by a combination of station height, zenith troposphere delay, and receiver clock offset. As such, the value of $$\alpha $$ α depends not only on the orbital altitude of the considered GNSS but also on the elevation-dependent distribution of GNSS observations and their weighting, as well as the elevation mask angle and the tropospheric mapping function. Based on the model, representative values of $$\alpha _\text {GPS}=-0.051$$ α GPS = - 0.051 , $$\alpha _\text {GLO}=-0.055$$ α GLO = - 0.055 , $$\alpha _\text {GAL}=-0.041$$ α GAL = - 0.041 , and $$\alpha _\text {BDS-3}=-0.046$$ α BDS-3 = - 0.046 are derived for GPS, GLONASS, Galileo, and BeiDou-3 at a $$10^\circ $$ 10 ∘ elevation cutoff angle. These values may vary by $$\varDelta \alpha \approx 0.003$$ Δ α ≈ 0.003 depending on the specific model assumptions and data processing parameters in a precise orbit determination or precise point positioning. Likewise changes of about $$\pm 0.003$$ ± 0.003 can be observed when varying the cutoff angle between $$5^\circ $$ 5 ∘ and $$15^\circ $$ 15 ∘ .

The Center for Orbit Determination in Europe (CODE) is contributing to the most recent reprocessing effort of the International GNSS Service (IGS) with a triple-system solution including GPS (since 1994), GLONASS (since 2002) and Galileo (since 2013). Several model improvements with respect to the operational processing scheme have been implemented and applied for the reprocessing effort: The first group of improvements is related to the update of IERS-related models (mean pole and high-frequency pole models). The second group is related to the inclusion of Galileo with calibrated receiver and satellite antennas. The consistency of the scale for the ground station coordinates was verified based on the estimation of GNSS-specific coordinate biases. It turned out that currently widely used GPS-based receiver antenna calibrations do compensate (just by chance) a discrepancy in the scale when using the pre-launch satellite antenna calibrations for Galileo. Furthermore and third, a long-arc solution over three days is introduced where in particular empirical velocity changes are rescheduled with respect to the operational processing chain at CODE. Instead of simply estimating them every 12 h they are now setup at orbit midnight. This rescheduling reduces the size of orbit misclosures by 10% for GPS and 15% for Galileo; no improvement for GLONASS was observed because there the orbit misclosures are dominated by other effects. Another feature applied for the first time in this reprocessing series is to downweight the observations of a number of GPS satellites with a reduced stability in the attitude control around the year 2000. This change in the analysis strategy reduces the noise level of GNSS-derived products, e.g., of the Earth rotation series. Even if the article is focusing on the reprocessing series as provided by the CODE analysis center many of the conclusions may also be applied to other GNSS series in future.

The Astronomical Institute of the University of Bern (AIUB) has been performing GPS-based Precise Orbit Determination (POD) for a large variety of Low Earth Orbit (LEO) satellites since two decades. Traditionally, LEO orbits have been generated by a reduced-dynamic POD strategy using the Bernese GNSS Software, replacing an explicit modeling of non-gravitational forces by dedicated empirical orbit parametrizations. This LEO POD strategy can be advanced by two main developments: on the one hand, use is made of the GNSS Observation-Specific Bias (OSB) and clock products provided by the Center for Orbit Determination in Europe (CODE), allowing for the resolution of single-receiver GNSS carrier-phase ambiguities. On the other hand, the main focus of this article, a refined satellite non-gravitational force modeling strategy is constructed to reduce the amount of empirical parameters used to compensate for force modeling deficiencies. LEO POD is first performed for Sentinel-3, a satellite formation currently consists of two identical satellites −3A and −3B, which experience a similar in-flight environment and allow for direct POD performance comparisons. A third satellite Swarm-C, which flies at a lower altitude and has a more sophisticated surface geometry, is selected to validate the robustness of the new POD strategy. As a result, both the internal consistency checks and external orbit validations suggest superior orbit quality obtained for the three satellites for a time span of 1.5 years (7 June, 2018 to 31 December, 2019). The ambiguity resolution adds strong constraints to the orbits and the satellite non-gravitational force modeling leads to more tightly constrained (towards zero) pseudo-stochastic empirical parameters. The final orbit solutions agree with external orbit solutions and independent satellite laser ranging measurements at levels of sub-cm, indicating approximately 20 % improvement w.r.t. the nominal reduced-dynamic orbit solutions. This suggests potential benefits to the space geodesy community that always pursues best-possible satellite orbits.

Polar motion (PM) series from various observation methods and sources are analyzed using one and the same simple analysis tool. The maximum time resolution of the Earth Rotation Parameter (ERP) series considered here is one day, which leaves out ERP series with sub-daily time resolution. A longer spacing between subsequent epochs is permissible, a variable spacing between epochs like in the VLBI (Very Long Baseline Interferometry) series as well. The shortest length of the PM time series analyzed, based on GNSS (Global Navigation Satellite Systems), is 26+ years, the longest one, the IERS C01 series, 173+ years. Following the tradition, PM is decomposed into a mean motion, i.e., the motion of the center of the PM curve on the surface of the Earth, a prograde Chandler motion with a nominal period of 432.25 days, and a prograde annual motion with a nominal period of 365.25 days. In our analysis, Secular PM is not assumed as linear, but as piecewise linear and continuous. The defining parameters of the periodic parts of polar motion are not assumed as constant either, but as piecewise linear and continuous functions of time as well. All parameters of the PM model based on one particular ERP series are determined in one and the same linear least squares estimation. Parameters of the same type may be purely deterministic or filtered (smoothed) by constraining the second time differences of the parameters (the second time derivative of the parameter functions) of the same kind. The key results achieved by applying our method to a wide variety of ERP series are visualized and discussed. They include: (a) the description of a sharp bend of mean PM around 1996, (b) strong evidence for a multi-component model for Chandler motion with periods separated by few days, similar to that proposed by Chandler (1901), (c) a reconstruction of mean PM from 1846 to present taking into account the composite nature of the series, and (d) a prediction of Chandler motion for the next decades. A sharp bend of mean PM was found around 1995/96, along the meridian at about 70 ° West to the meridian at about 12–15° West. All PM curves analyzed show a mean motion in this new direction after 1995/95. Smaller excursions w.r.t.d this mean exist, with periods 10 years. A periodic variation with a period of about 180 years was observed in the Chandler signal of PM with an amplitude of more than 200 mas. The variation may be explained approximately by a composite nature of Chandler motion, similar to the model already proposed by Chandler (1901). This simple model was generalized using a Fourier series separated in period by few days. This alternative model of Chandler motion is used to predict the Chandler part of PM, with an amplitude close to zero currently, to reach values of the order of 100 mas around 2028–2030.

The release of the next International Terrestrial Reference Frame (ITRF) 2020 is based on the four geodetic techniques, namely Satellite Laser Ranging (SLR), Very Long Baseline Interferometry (VLBI), Global Navigation Satellite Systems (GNSS), and Doppler Orbitography and Radio-positioning Integrated by Satellite instrument (DORIS). The upcoming release will presumably define the scale based on the first two techniques.The GNSS scale is mainly driven by the z-component of the satellite antenna phase center offsets. With the disclosure of the Galileo metadata by the European GNSS Agency (GSA) the satellite antenna pattern became available to the public and enabled the GNSS scale determination.We aim to analyze the consistency between the preliminary ITRF 2020 solution and the GNSS based scale. In addition, we will extend our study with all available TRF solutions and compare their consistency with the GNSS derived scale and discuss the resulting comparisons.

The use of zero-difference processing schemes becomes more and more popular within the GNSS (Global Navigation Satellite Systems) community. This change from double- to zero-difference approaches increases the demand of PPP-AR (Ambiguity Resolution for Precise Point Positioning) enabling products. Those products can be created in two ways, either estimate the geometrical part (orbits) based on a double-difference global network solution with a separate zero-difference solution for the clocks and phase biases, or in a combined zero-difference solution. The latter one allows a more flexible approach; however, the challenge lies in the handling of the increased number of parameters and ambiguity resolution.The estimation of combined orbit and clock zero-difference enabling products needs a thought-out design of the processing strategy, where the elimination and back-substitution steps are vital to deal with the large number of parameters. Nonetheless, the amount of ambiguity parameters dramatically grows with an increasing size of the network, posing some computational limitations, since they should not be eliminated for a successful ambiguity resolution. Such a restriction originates from fixing float orbits: their accuracy does not allow to estimate reliable ambiguity parameters. To cope with that, we propose a new algorithm capable to decouple them from the orbits, allowing to fix between-satellite ambiguities in a later station-wise parallelisation.On the poster, we describe selected details on the ambiguity resolution strategy that we have developed. The obtained results are characterized and compared to other solutions using classical ambiguity resolution schemes.

The generation and use of GNSS analysis products that allow—particularly for the needs of single-receiver applications—precise point positioning with ambiguity resolution (PPP-AR) are becoming more and more popular. A general uncertainty concerns the question on how the necessary phase bias information should be provided to the PPP-AR user. Until now, each AR-enabling clock/bias representation method had its own practice to provide the necessary bias information. We have generalized the observable-specific signal bias (OSB) representation, as introduced in Villiger (J Geod 93:1487–1500, 2019) originally exclusively for pseudorange measurements, to carrier phase measurements. The existing common clock (CC) approach has been extended in a way that OSBs allowing for flexible signal and frequency handling between multiple GNSS become possible. Advantages of the proposed OSB-based PPP-AR approach are: GNSS biases can be provided in a consistent way for phase and code measurements and it is capable of multi-GNSS and suitable for standardization. This new, extended PPP-AR approach has been implemented by the Center for Orbit Determination in Europe (CODE). CODE clock products that adhere to the integer-cycle property have been submitted to the International GNSS Service (IGS) since mid of 2018 for three analysis lines: Rapid, Final, and MGEX (Multi-GNSS Extension). Ambiguity fixing is performed not only for GPS but also for Galileo. The integer-cycle property of between-satellite clock differences is of fundamental importance when comparing satellite clock estimates among various analysis lines, or at day boundaries. Both kinds of comparisons could be exploited at a very high level of consistency. Any retrieved comparison essentially indicated a standard deviation for between-satellite clocks from CODE of the order of 5 ps (1.5 mm in range). Finally, the integer-cycle property that may be recovered between the CODE Final clock and the accompanying bias product of consecutive daily sessions (using clock estimates additionally provided for the second midnight epoch) allows us to deduce GPS satellite clock and phase bias information that is consistent and continuous with respect to carrier phase observation data over two, three, or, in principle, yet more days. Phase-based clock densification from initially estimated integer-cycle-conform clock corrections at intervals of 300 s to 30 s (5 s in case of our Final clock product) is a matter of particular interest. Based on direct product comparisons and GRACE K-band ranging (KBR) data analysis, the quality of accordingly densified clock corrections could be confirmed to be on a level similar to that of “anchor” (300 s) clock corrections.

The Non-Gravitational Perturbations (NGP), out of which the Solar Radiation Pressure (SRP) is the largest, have a significant impact on GNSS satellite orbits. In addition to the SRP, other relevant perturbations should also be taken into account, as this may result in substantial modelling errors if underestimated. Particularly, the force model should also consider Earth’s albedo in terms of the emitted and reflected radiation, as well as a physical satellite model (box-wing) with its optical and thermal properties.GNSS satellite orbit modelling may suffer from deficiencies for various reasons (simplification of the complexity of the used model or uncertainty of the input information). The impact of such model errors on global GNSS data analyses is assessed in an error propagation study based on simulated observations. The influence of artificially introduced orbit errors on estimated parameters, e.g. Earth rotation parameters, orbit parameters (initial conditions and dynamical orbit parameters), station coordinates, station-wise troposphere parameters, as well as receiver and satellite clock corrections is investigated. In this study a dedicated simulation environment is used to analyse the relation between results and certain individual shortcomings in the NGP models. In addition, apart from a commonly used epoch-wise clock estimation, the analytical models for satellite clock corrections are introduced in order to exploit the high stability of the passive H-masers on-board the Galileo satellites. The simulation environment also allows to assess how the impact of float- versus fixed-ambiguities.Finally, simulation-based analyses offer an excellent framework for more detailed validations and further refinements of the physical satellite models, which will consequently stabilize the global solution.

A classical reduced-dynamic GPS-based Precise Orbit Determination (POD) strategy for Low Earth Orbit (LEO) satellites is often based on a limited explicit modelling of satellite dynamics and modelling deficiencies are compensated by numerous empirical parameters. With better gravitational models and the advances in satellite surface force modeling, uncertainties in the satellite dynamics are significantly reduced. Furthermore, single-receiver ambiguity resolution allows for more robust POD as well. Therefore, a dynamic POD strategy using significantly fewer estimated empirical parameters can be implemented to generate dynamic orbits, which allow for force modeling sensitivity analyses and evaluating potential errors in the adopted GPS antenna reference points or phase center offsets, etc. This presentation outlines the recent dynamic POD methodology developments at the Astronomical Institute of the University of Bern (AIUB) and investigates the POD performances for a few dedicated space geodesy satellite missions (Swarm, GRACE-FO, Sentinel-1, Sentinel-2, Sentinel-3 and Jason-3) that are operated at altitudes ranging from 430 to 1350 km. The focuses will be on satellite gravitational and non-gravitational force modeling, satellite dynamics parametrization, and orbit validations for different types of satellites. Results reveal that the dynamic POD strategy is flexible and robust to generate high-quality orbits for those satellites, showing reliable agreements with the independent ambiguity-fixed kinematic orbits and the external Satellite Laser Ranging (SLR) measurements.

Radiation pressure from the sun and the Earth are not negligible forces for orbit determination. Most analysis centers use empirical approaches (i.e., the classical Empirical CODE Orbit Model ECOM or the adapted version ECOM2), analytical approaches (simplified box wing models or detailed macro models), or a combination of both to account for the solar radiation pressure (SRP) and Earth radiation (albedo).The European GNSS Agency and the Cabinet Office, Government of Japan, disclosed meta data for Galileo resp. QZSS satellites. For the other GNSS constellations either no or incomplete models are available. This is in particular problematic for SRP modeling. In case of albedo the issue is less critical as the corresponding force acting on GNSS satellites is much smaller compared to the SRP. Our approach to overcome this issue is to re-scale the existing box-wing models based on long term analysis (one year) and introduce the re-scaled macro models for the final orbit determination. The main goal is to achieve better orbit quality with fewer empirical parameters compared to our traditional solution based on pure empirical SRP models. The key factors to determine the quality of the re-scaled macro models are, among others, the evaluation of the resulting orbits and the behavior of the long term time series of the corresponding geodynamic parameters.

The International GNSS service (IGS) has been providing precise reference products for the Global Navigation Satellite Systems (GNSS) GPS and (starting later) GLONASS since more than 25 years. These orbit, clock correction, coordinate reference frame, troposphere, ionosphere, and bias products are freely distributed and widely used by scientific, administrative, and commercial users from all over the world. The IGS facilities needed for data collection, product generation, product combination, as well as data and product dissemination, are well established. The Center for Orbit Determination in Europe (CODE) is one of the Analysis Centers (AC) contributing to the IGS from the beginning. It generates IGS products using the Bernese GNSS Software. In the last decade new GNSS (European Galileo and Chinese BeiDou) and regional complementary systems to GPS (Japanese QZSS and Indian IRNSS/NAVIC) were deployed. The existing GNSS are constantly modernized, offering - among others - more stable satellite clocks and new signals. The exploitation of the new data and their integration into the existing IGS infrastructure was the goal of the Multi-GNSS EXtension (MGEX) when it was initiated in 2012. CODE has been participating in the MGEX with its own orbit and clock solution from the beginning. Since 2014 CODE’s MGEX (COM) contribution considers five GNSS, namely GPS, GLONASS, Galileo, BeiDou2 (BDS2), and QZSS. We provide an overview of the latest developments of the COM solution with respect to processing strategy, orbit modelling, attitude modelling, antenna calibrations, handling of code and phase biases, and ambiguity resolution. The impact of these changes on the COM products will be discussed. Recent assessment showed that especially the Galileo analysis within the MGEX has reached a state of maturity, which is almost comparable to GPS and GLONASS. Based on this finding the IGS decided to consider Galileo in its third reprocessing campaign, which will contribute to the next ITRF. Recognizing the demands expressed by the GNSS community, CODE decided in 2019 to go a step further and consider Galileo also in its IGS RAPID and ULTRA-RAPID reference products. We summarize our experiences from the first months of triple-system (ULTRA)-RAPID analysis including GPS, GLONASS, and Galileo. Finally we provide an outlook of CODE’s IGS analysis with the focus on the new GNSS.

With the modernization of GPS and the establishment of additional global navigation satellite system (GNSS) constellations, such as Galileo, Beidou, and QZSS, more and more GNSS satellites are available transmitting on various frequencies with multiple signal modulations. In order to cope with the increasing number of observation types, the commonly used differential approach becomes more and more difficult regarding book-keeping. The actually processed original observation types have to be known in advance to define a linearly independent set of differential signal biases (DSB) while processing GNSS data. An alternative treatment of code biases is the usage of observable-specific signal biases (OSB) where the setup and correction of biases become trivial. Potential dependencies of the bias parameters can be considered after the setup of normal equations (NEQs), e.g., immediately before it is inverted. The code bias results are retrieved on a daily basis and their NEQs stored. This allows to combine bias results from various sources (or analysis lines) and different time periods. By combining all daily bias NEQs, we have generated a coherent multi-year bias solution from 2000 to 2017 with one common datum. If absolute receiver calibrations are available, the multi-year solution could be aligned to those receivers and thus could lead to an absolute estimation of the code biases. Finally, the estimated satellite OSBs are used for the receiver compatibility grouping testing which receivers are compatible with which bias sets. This may be achieved by solving for so-called OSB multipliers.

Earlier studies performed at the Center for Orbit Determination in Europe (CODE) analysis center have revealed conspicuous signatures for certain GLONASS satellites when comparing their orbits with Satellite Laser Ranging (SLR) measurements. In this study we show that this phenomenon can be significantly reduced when using horizontal satellite antenna offsets that differ from the nominal values used by the International GNSS Service (IGS) for specific intervals and satellites. Analysis of multi-year time series shows instantaneous changes in the satellite antenna offset parameters of several centimeters in the X- and Y-component whereas the Z-component is not affected. In some cases the offsets do not agree with the nominal values during the entire lifetime of the satellite. The magnitude of the deviation may vary between 5 and 15 cm. Using these re-estimated satellite antenna offsets in the orbit determination the residuals with respect to the Satellite Laser Ranging (SLR) measurements are significantly reduced whereas the orbit misclosures for one-day arcs are too noisy to detect a positive or negative impact. It is difficult to reconstruct from the available information what actually caused the observed changes. However, changes in the carrier-to-noise density reported in the observation files in Receiver INdependent EXchange format (RINEX) by several IGS stations suggest an issue with the satellite antennas.

The Federal Office of Topography swisstopo is responsible for the maintenance of the coordinate reference frames in Switzerland. Beside the static reference frames, used for national surveying, the development of a kinematic model, mainly used for scientific investigations, is under development since many years. For the determination of vertical movements the analysis of more than 100 years of levelling observations showed a significant alpine uplift of maximally 1.5 mm/year relative to an arbitrarily chosen bench mark in Aarburg (at the south of the Jura mountains). For the determination of horizontal movements the various GPS-campaigns, measured since 1988, are the basis. With the Automated GNSS Network of Switzerland (AGNES), which operates permanently since 1998, valuable information can be extracted for 30 sites. The paper shows that the time series of AGNES nowadays allow statements concerning possible vertical movements. The potential of additional information sources, such as local tie surveys, are discussed. Comparisons of the results of the two independent measuring techniques GNSS and levelling are the main topic of the paper.

The reference frame of a global terrestrial network is defined by the origin, the orientation and the scale. The origin of the ITRF2014 is defined by the ILRS long-term solution, the orientation by no-net rotation conditions w.r.t. the previous reference frame (ITRF2008), and the scale by the mean values from global VLBI and SLR solution series (Altamimi et al. in J Geophys Res Solid Earth 121:6109–6131, 2016). With the release of the Galileo satellite antenna phase center offsets (PCO) w.r.t. the satellites center of mass (GSA in Galileo IOV and FOC satellite metadata, 2019) and the availability of new ground antenna calibrations for GNSS receivers, based on anechoic chamber measurements or on robot calibrations, GNSS global network solutions qualify to contribute to the scale determination of terrestrial networks, as well. Our analysis is based on global multi-GNSS solutions of the years 2017 and 2018 and may be seen as “proof of concept” for the contribution of GNSS data to the scale determination of the terrestrial reference frame. In a first step, the currently used Galileo PCO estimations (Steigenberger et al. in J Geod 90:773–785, 2016) are compared to the released PCO values, which show discrepancies on the decimeter-level. Eventually, the published Galileo PCOs are used in an experimental solution as known values. GNSS-specific PCOs are estimated, as well, for GPS and GLONASS, together with the “standard” parameters set up in global GNSS solutions. From the estimated network coordinates, a time series of daily scale parameters of the terrestrial network is extracted, which shows an offset of the order of 1 ppb (parts per billion, corresponding to a height difference of 6.4 mm on the Earth’s surface) w.r.t. to the ITRF2014 network and an annual variation with an amplitude of about 0.3 ppb.

We present an update on the multi-GNSS orbit and clock solution (COM), the CODE analysis center provides to the International GNSS service (IGS) in the frame of the multi-GNSS extension (MGEX). In recent years substantial progress was achieved in the fields of orbit modelling (Earth albedo, transmit antenna thrust, thermal radiation, eclipse attitude law), receiver and transmitter antenna calibration, ground tracking network, data dissemination, completeness of satellite constellations, availability of spacecraft-related meta information, observation biases, and ambiguity resolution. This led to improvements in orbit and clock parameter estimation, which are substantial for the European GNSS Galileo and are to a large part attributed to the availability of disclosed spacecraft meta data. Orbit and clock validation of the COM results using different validation methods (SLR residuals, orbit misclosures, linear fit of clock corrections) indicate that the quality of the updated Galileo products is meanwhile on the same level as for corresponding GPS and GLONASS products. Based on these achievements CODE decided to include Galileo in its IGS Rapid and Ultra-Rapid products and to contribute to the third reprocessing effort of the IGS with a three-system solution including GPS, GLONASS, and Galileo.