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In this paper, we consistently estimate geodetic parameters such as weekly 3-D station coordinates, Earth orientation parameters (EOP) including daily x/y-pole coordinates and the excess length of day $$\Delta \hbox {LOD}$$ , and selected weekly Earth’s gravitational field (Stokes) coefficients up to degree and order 6 from Satellite Laser Ranging measurements to up to 11 geodetic satellites. The SLR constellation consists of LAGEOS-1/2, Etalon-1/2, Stella, Starlette, Ajisai, Larets, LARES, BLITS and WESTPAC, and its observations cover a time span of 38 years ranging from February 16, 1979, to April 30, 2017. If multiple satellites with various altitudes and orbit inclinations are combined, correlations between estimated parameters are significantly reduced. This allows us (i) to investigate the ability of satellite constellations to reduce existing correlations and (ii) to estimate reliable parameters with higher precision compared to the standard 4-satellite constellation (LAGEOS-1/2, Etalon-1/2) which is currently used by the International Laser Ranging Service for the determination of the Terrestrial Reference Frame (TRF) and EOP products. In particular, the Stokes coefficients, EOP and TRF datum parameters (three translations, three rotations, one scale factor), which are highly correlated with satellite-specific orbit parameters, are improved. From our investigations, we found for an 11-satellite solution compared to the above-mentioned 4-satellite solution a decrease in the scatter of the TRF datum parameters of up to 37%, the transformation residuals are decreased by up to 22%, the scatter of the EOP is decreased by up to 22%, and their mean values are decreased by up to 84% w.r.t. the reference solutions. The largest improvement is obtained for the Stokes coefficients which significantly benefit from a combination of multiple satellites (inclinations and orbit altitudes). In total, single coefficients are improved by up to 93% and the overall improvement is up to 74%. Moreover, it could be clearly identified that Ajisai significantly disturbs the TRF solution due to an erroneous center-of-mass correction. We further quantify the impact of specific satellites on the determination of different geodetic parameters and finally evaluate the potential of the existing SLR-tracked spherical satellite constellation to support the goals of GGOS.

Solutions for the most recent realization of the International Terrestrial Reference System (ITRS) were computed by the three ITRS Combination Centers (CCs) of the International Earth Rotation and Reference Systems Service (IERS), namely the IGN in Paris (France), the JPL in Pasadena (USA), and the DGFI-TUM in Munich (Germany). Thereby, the solutions of IGN and DGFI-TUM comprise conventional parameters of the ITRS (station coordinates and velocities) at a reference epoch as defined in the IERS Conventions 2010. Although the two solutions are based on identical input data, there exist systematic differences between them.

The Celestial Reference System (CRS) is currently realized only by Very Long Baseline Interferometry (VLBI) because it is the space geodetic technique that enables observations in that frame. In contrast, the Terrestrial Reference System (TRS) is realized by means of the combination of four space geodetic techniques: Global Navigation Satellite System (GNSS), VLBI, Satellite Laser Ranging (SLR), and Doppler Orbitography and Radiopositioning Integrated by Satellite. The Earth orientation parameters (EOP) are the link between the two types of systems, CRS and TRS. The EOP series of the International Earth Rotation and Reference Systems Service were combined of specifically selected series from various analysis centers. Other EOP series were generated by a simultaneous estimation together with the TRF while the CRF was fixed. Those computation approaches entail inherent inconsistencies between TRF, EOP, and CRF, also because the input data sets are different. A combined normal equation (NEQ) system, which consists of all the parameters, i.e., TRF, EOP, and CRF, would overcome such an inconsistency. In this paper, we simultaneously estimate TRF, EOP, and CRF from an inter-technique combined NEQ using the latest GNSS, VLBI, and SLR data (2005–2015). The results show that the selection of local ties is most critical to the TRF. The combination of pole coordinates is beneficial for the CRF, whereas the combination of $$\varDelta \hbox {UT1}$$ results in clear rotations of the estimated CRF. However, the standard deviations of the EOP and the CRF improve by the inter-technique combination which indicates the benefits of a common estimation of all parameters. It became evident that the common determination of TRF, EOP, and CRF systematically influences future ICRF computations at the level of several $$\upmu $$ as. Moreover, the CRF is influenced by up to $$50~\upmu $$ as if the station coordinates and EOP are dominated by the satellite techniques.

In the conventions of the International Earth Rotation and Reference Systems Service (e.g. IERS Conventions 2010), it is recommended that the instantaneous station position, which is fixed to the Earth’s crust, is described by a regularized station position and conventional correction models. Current realizations of the International Terrestrial Reference Frame use a station position at a reference epoch and a constant velocity to describe the motion of the regularized station position in time. An advantage of this parameterization is the possibility to provide station coordinates of high accuracy over a long time span. Various publications have shown that residual non-linear station motions can reach a magnitude of a few centimeters due to not considered loading effects. Consistently estimated parameters like the Earth Orientation Parameters (EOP) may be affected if these non-linear station motions are neglected. In this paper, we investigate a new approach, which is based on a frequent (e.g. weekly) estimation of station positions and EOP from a combination of epoch normal equations of the space geodetic techniques Global Positioning System (GPS), Satellite Laser Ranging (SLR) and Very Long Baseline Interferometry (VLBI). The resulting time series of epoch reference frames are studied in detail and are compared with the conventional secular approach. It is shown that both approaches have specific advantages and disadvantages, which are discussed in the paper. A major advantage of the frequently estimated epoch reference frames is that the non-linear station motions are implicitly taken into account, which is a major limiting factor for the accuracy of the secular frames. Various test computations and comparisons between the epoch and secular approach are performed. The authors found that the consistently estimated EOP are systematically affected by the two different combination approaches. The differences between the epoch and secular frames reach magnitudes of $$23.6~\upmu \hbox {as}$$ (0.73 mm) and $$39.8~\upmu \hbox {as}$$ (1.23 mm) for the x-pole and y-pole, respectively, in case of the combined solutions. For the SLR-only solutions, significant differences with amplitudes of $$77.3~\upmu \hbox {as}$$ (2.39 mm) can be found.

In preparation of activities planned for the realization of the Global Geodetic Observing System (GGOS), a group of German scientists has carried out a study under the acronym GGOS-D which closely resembles the ideas behind the GGOS initiative. The objective of the GGOS-D project was the investigation of the methodological and information-technological realization of a global geodetic-geophysical observing system and especially the integration and combination of the space geodetic observations. In the course of this project, highly consistent time series of GPS, VLBI, and SLR results were generated based on common state-of-the-art standards for modeling and parameterization. These series were then combined to consistently and accurately compute a Terrestrial Reference Frame (TRF). This TRF was subsequently used as the basis to produce time series of station coordinates, Earth orientation, and troposphere parameters. In this publication, we present results of processing algorithms and strategies for the integration of the space-geodetic observations which had been developed in the project GGOS-D serving as a prototype or a small and limited version of the data handling and processing part of a global geodetic observing system. From a comparison of the GGOS-D terrestrial reference frame results and the ITRF2005, the accuracy of the datum parameters is about 5–7 mm for the positions and 1.0–1.5 mm/year for the rates. The residuals of the station positions are about 3 mm and between 0.5 and 1.0 mm/year for the station velocities. Applying the GGOS-D TRF, the offset of the polar motion time series from GPS and VLBI is reduced to 50 μas (equivalent to 1.5 mm at the Earth’s surface). With respect to troposphere parameter time series, the offset of the estimates of total zenith delays from co-located VLBI and GPS observations for most stations in this study is smaller than 1.5 mm. The combined polar motion components show a significantly better WRMS agreement with the IERS 05C04 series (96.0/96.0 μas) than VLBI (109.0/100.7 μas) or GPS (98.0/99.5 μas) alone. The time series of the estimated parameters have not yet been combined and exploited to the extent that would be possible. However, the results presented here demonstrate that the experiences made by the GGOS-D project are very valuable for similar developments on an international level as part of the GGOS development.

In its function as an ITRS Combination Centre, DGFI is in charge with the computation of an ITRF2008 solution. The computation methodology of DGFI is based on the combination of datum-free normal equations (weekly or session data sets, respectively) of station positions and Earth orientation parameters (EOP) from the geodetic space techniques DORIS, GPS, SLR and VLBI. In this paper we focus on the DORIS part within the ITRF2008 computations. We present results obtained from the analysis of the DORIS time series for station positions, network translation and scale parameters, as well as for the terrestrial pole coordinates. The submissions to ITRF2008 benefit from improved analysis strategies of the seven contributing IDS analysis centres and from a combination of the weekly solutions of station positions and polar motion. The results show an improvement by a factor of two compared to past DORIS data submitted to ITRF2005, which has been evaluated by investigating the repeatabilities of position time series. The DORIS position time series were analysed w.r.t. discontinuities and other non-linear effects such as seasonal variations. About 40 discontinuities have been identified which have been compared with the results of an earlier study. Within the inter-technique combination we focus on the DORIS contribution to the integration of the different space geodetic observations and on a comparison of the geodetic local ties with the space geodetic solutions. Results are given for the 41 co-location sites between DORIS and GPS.

The International DORIS Service (IDS) submitted input data for the most recent realization of the International Terrestrial Reference System (ITRS), the International Terrestrial Reference Frame 2014 (ITRF2014). As one of the ITRS Combination Centers, DGFI-TUM is in charge to analyze and assess the quality of the submitted data and to compute a combined global TRF solution (called DTRF2014) using observations of the four geodetic space techniques GNSS, VLBI, SLR and DORIS. The combination methodology used at DGFI-TUM is based on the combination of datum-free normal equations. Together with station coordinates and velocities, terrestrial pole coordinates are estimated in one common adjustment. The paper presents the analysis results of the most recent DORIS submission IDS-d09 and evaluates its quality w.r.t. the DTRF2008 (IDS-only) solution. In the most recent version of the analysis, we introduce in total 55 station discontinuities and reduce 15 stations due to a too short time span or too few observations. Time series of weekly IDS solutions are computed and validated w.r.t. DTRF2008. The transformation parameter time series and the station residuals are discussed in detail. Especially the scale parameter time series shows a significant improvement compared to the DTRF2008 input data. The scatter of the x- and y-translation is significantly reduced to 5.7 mm and 7.1 mm compared to 6.6 mm and 8.1 mm for the DTRF2008 (IDS-only) solution. The z-translation time series still shows a high correlation with solar activity. 10% of all station residuals are significantly affected by spectral peaks at draconitic period harmonics of the altimetry satellites Jason and TOPEX/Poseidon and up to 48% of all station residual time series contain significantly determined frequencies with a 14 day period. The multi-year IDS solution is validated w.r.t. DTRF2008 and the consistently estimated terrestrial pole coordinates are analyzed and compared to IERS 08 C04. The x-pole spectra comprises prominent peaks at various draconitic frequencies.

Recent solutions of the terrestrial reference frame such as ITRF2000 are combined from multi-year data sets that contain station positions at a reference epoch and constant velocities. Analysis of time series of station positions of the geodetic space techniques SLR, GPS, VLBI and DORIS show, however, that these techniques allow to detect variations in station position series with up to a few millimetre accuracy. Therefore, the underlying reference frame needs to assure the same accuracy. In this paper we analyse systematic effects in station position and transformation parameter time series that need to be taken into account for future TRF realisations. These are mainly annual signals that show up as common variations of the global networks as well as local effects on individual stations. These annual signals differ significantly from technique to technique for some co-location sites. Apart from periodic signals the time series show discontinuities (e.g. due to earthquakes or instrumentation changes) and periods of non-linear motion (e.g. post-seismic relaxation). We compute TRF technique solutions of five years of epoch normal equations, which allows to adapt the parameterisation in order to account for the effects mentioned above. The accuracy of the technique-specific solutions is evaluated by comparing the results at co-location sites. For this purpose, we transform the VLBI, SLR and DORIS solutions to the GPS solution by using the measured local ties between GPS and the other techniques.

As early as the 15th century Swedes noticed that rocks in their harbors were slowly rising out of the sea [Ekman, 1991]. These local observations were not sufficient to distinguish whether the rocks were rising or the sea level falling. Later, it was realized that Fennoscandia was still rebounding from the last Ice Age. This historical observation is still relevant today. How can you know whether a point on the Earth's surface is slowly moving up, down, or horizontally? One must relate local measurements to a stable and accurate reference frame, one whose scale is much larger than the problem at hand. We remain concerned with sea-level variations, but present-day studies recognize that change must be measured from a global point of view and with respect to a globally well-defined reference frame. Thus, the regional and national geodetic datums developed over the past 200 years are inappropriate for studying global-level problems.

A new realization of the International Terrestrial System was computed at the ITRS Combination Centre at DGFI as a contribution to ITRF2008. The solution is labelled DTRF2008. In the same way as in the DGFI computation for ITRF2005 it is based on either normal equation systems or estimated parameters derived from VLBI, SLR, GPS and DORIS observations by weekly or session-wise processing. The parameter space of the ITRS realization comprises station positions and velocities and daily resolved Earth Orientation Parameters (EOP), whereby for the first time also nutation parameters are included. The advantage of starting from time series of input data is that the temporal behaviour of geophysical parameters can be investigated to decide whether the parameters can contribute to the datum realization of the ITRF. In the same way, a standardized analysis of station position time series can be performed to detect and remove discontinuities. The advantage of including EOP in the ITRS realization is twofold: (1) the combination of the coordinates of the terrestrial pole—estimated from all contributing techniques—links the technique networks in two components of the orientation, leading to an improvement of consistency of the Terrestrial Reference Frame (TRF) and (2) in their capacity as parameters common to all techniques, the terrestrial pole coordinates enhance the selection of local ties as they provide a measure for the consistency of the combined frame. The computation strategy of DGFI is based on the combination of normal equation systems while at the ITRS Combination Centre at IGN solutions are combined. The two independent ITRS realizations provide the possibility to assess the accuracy of ITRF by comparison of the two frames. The accuracy evaluation was done separately for the datum parameters (origin, orientation and scale) and the network geometry. The accuracy of the datum parameters, assessed from the comparison of DTRF2008 and ITRF2008, is between 2–5 mm and 0.1–0.8 mm/year depending on the technique. The network geometry (station positions and velocities) agrees within 3.2 mm and 1.0 mm/year. A comparison of DTRF2008 and ITRF2005 provides similar results for the datum parameters, but there are larger differences for the network geometry. The internal accuracy of DTRF2008—that means the level of conservation of datum information and network geometry within the combination—was derived from comparisons with the technique-only multi-year solutions. From this an internal accuracy of 0.32 mm for the VLBI up to 3.3 mm for the DORIS part of the network is found. The internal accuracy of velocities ranges from 0.05 mm/year for VLBI to 0.83 mm/year for DORIS. The internal consistency of DTRF2008 for orientation can be derived from the analysis of the terrestrial pole coordinates. It is estimated at 1.5–2.5 mm for the GPS, VLBI and SLR parts of the network. The consistency of these three and the DORIS network part is within 6.5 mm.

The GGOS-D terrestrial reference frame has been computed in a common adjustment of station positions and velocities together with the Earth orientation parameters and the quasar coordinates (celestial reference frame). The data were processed as datum-free normal equations from homogeneously generated VLBI, SLR and GPS observation time series using identical standards for the modelling and parameterization. A major focus was on the analysis of the station position time series, investigations regarding seasonal variations in station motions and on the combination methodology for the terrestrial reference frame computation.

The GGOS-D global terrestrial reference frame has been computed from a combination of homogeneously processed VLBI, SLR and GPS observation time series. A major focus was on the analysis of station position time series, investigations regarding the handling of non-linear station motions, and the development of refined combination methods. The terrestrial reference frame (station positions and velocities) has been estimated simultaneously with the Earth orientation parameters and the celestial reference frame (quasar coordinates).

In its function as an ITRS Combination Centre DGFI has computed a solution of the International Terrestrial Reference Frame 2005 (ITRF2005). It is based on the combination of epoch normal equations (weekly or session data sets, respectively) of station positions and Earth Orientation Parameters (EOPs) from the geodetic space techniques VLBI, SLR, GPS and DORIS. The procedure includes the datum free accumulation of technique-specific normal equations, the inter-technique combination using local tie measurements at co-location sites, and the computation of the ITRF2005 solution.

ITRF2005 is the first terrestrial reference frame computed from weekly/ session-wise data sets of the geodetic space techniques GPS, VLBI, SLR and DORIS. This allows to detect time variable effects in station positions, such as discontinuities or seasonal variations. In the combination of the terrestrial reference frame these time variable effects need to be taken into account.

In its function as an ITRS Combination Center, DGFI has developed refined methods for the terrestrial reference frame computation. The advanced approach is based on the combination of epoch normal equations (weekly/daily data sets) containing Station positions and Earth orientation parameters (EOP) obtained from different geodetic space techniques such as VLBI, SLR, GPS and DORIS. This refined approach allows to account for nonlinear effects (e.g., periodic signals and discontinuities) in Station positions and to ensure consistency between TRF and EOP. The ITRF2004 submissions were used as input for a refined realization of the terrestrial reference frame. This paper presents the combination methodology and the current Status of the ITRF2004 computations at DGFI.

This paper investigates the time evolution of the terrestrial reference frame (TRF). We analysed time series of site positions and datum parameters obtained from VLBI, SLR, GPS and DORIS solutions with respect to non-linear motions (e.g. jumps, seasonal signals) and systematic differences. The time series of the translation and scale parameters were used to identify solution- and technique-related problems, and to investigate the contribution of the different techniques to realise the TRF origin and scale. The position time series reveal non-linear motions and jumps for many sites, which have to be considered for future TRF realisations.

In cooperation with various partners in Europe, North America and in the host countries, GFZ Potsdam has established and repeatedly observed three major GPS networks: in South America the SAGA network, in Central Asia the CATS- and in South-East Asia the GEODYSSEA-network.

In the framework of the GEODYnamics of South and South-East Asia (GEODYSSEA) project a network of 42 stations was observed by GPS during two field campaigns in 1994 and 1996. BKG and GFZ realized a third observation of the complete network in 1998. The data was analyzed independently by two analysis centers and a precision of the coordinate solutions was found to be 4–7 mm for the horizontal, and 10 mm for the vertical component. Subsequently, these campaign solutions were merged into one unique solution, which was accurately mapped into the International Terrestrial Reference Frame of 1997 (ITRF97). The global accuracy of this solution with respect to ITRF97 is of the order of 10 mm, while the resolution of the relative horizontal velocities is estimated to be at the level of 2–3 mm/yr. Comparison of the new solution with the previously published GEODYSSEA solution indicates, that improved results for the motion of Sundaland, South China and the overall deformation in the area could be found. Improvements are due to the increased time span and due to a better connection to and the advances in the ITRF reference frame. The new set of coordinates and velocities is used as the basis for scientific interpretations, which have been and will be published in separate papers.