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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.

In 2016, three new realizations of the International Terrestrial Reference System (ITRS), namely DTRF2014, ITRF2014, and JTRF2014, have been released. In this paper, we evaluate these ITRS realizations for precise orbit determination of ten high and low Earth orbiting geodetic satellites using satellite laser ranging (SLR) observations. We show the reduction of observation residuals and estimated range biases, when using these new ITRS realizations, as compared to the previous ITRS realization for SLR stations -- SLRF2008. Thus, the mean SLR root-mean-square (RMS) fits reduce (improve), on average over all satellites tested, by 3.0, 3.6, 8.1, and 7.7 % at 1993.0 - 2015.0, when using ITRF2014, DTRF2014, DTRF2014 with non-tidal loading, and JTRF2014 realizations, respectively. The improvement of the RMS fits is even larger at 2015.0 - 2017.0: 14.0 and 15.5 % using ITRF2014 and DTRF2014, respectively. For the altimetry satellite Jason-2, we found improvements in the RMS and mean of the sea surface height crossover differences with the new ITRS realizations, as compared to SLRF2008. We show that JTRF2014, after an editing done for SLR stations Conception and Zimmerwald, and DTRF2014 with non-tidal loading corrections result in the smallest RMS and absolute mean fits of SLR observations indicating the best performance among the ITRS realizations tested, while using SLRF2008 and ITRF2014 causes a 0.2-0.3 mm/y trend in the mean of SLR fits at 2001.0-2017.0.

Beside the estimation of station coordinates and the Earth’s gravity field, laser ranging observations to near-Earth satellites can be used to determine the rotation of the Earth. One parameter of this rotation is ΔLOD (excess Length Of Day) which describes the excess revolution time of the Earth w.r.t. 86,400 s. Due to correlations among the different parameter groups, it is difficult to obtain reliable estimates for all parameters. In the official ΔLOD products of the International Earth Rotation and Reference Systems Service (IERS), the ΔLOD information determined from laser ranging observations is excluded from the processing. In this paper, we study the existing correlations between ΔLOD, the orbital node Ω, the even zonal gravity field coefficients, cross-track empirical accelerations and relativistic accelerations caused by the Lense–Thirring and deSitter effect in detail using first order Gaussian perturbation equations. We found discrepancies due to different a priories by using different gravity field models of up to 1.0ms for polar orbits at an altitude of 500 km and up to 40.0ms, if the gravity field coefficients are estimated using only observations to LAGEOS 1. If observations to LAGEOS 2 are included, reliable ΔLOD estimates can be achieved. Nevertheless, an impact of the a priori gravity field even on the multi-satellite ΔLOD estimates can be clearly identified. Furthermore, we investigate the effect of empirical cross-track accelerations and the effect of relativistic accelerations of near-Earth satellites on ΔLOD. A total effect of 0.0088 ms is caused by not modeled Lense–Thirring and deSitter terms. The partial derivatives of these accelerations w.r.t. the position and velocity of the satellite cause very small variations (0.1μs) on ΔLOD.

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 combination of tropospheric parameters derived from different space-geodetic techniques has not been of large interest in geodesy so far. However, due to the high correlation between station coordinates and tropospheric parameters, the latter should not be neglected in combinations. This paper deals with the comparison and combination of tropospheric parameters derived from global positioning system (GPS) and very long baseline interferometry (VLBI) observations stemming from a 15-day campaign of continuous VLBI observations in 2002 (CONT02). The observation data of both techniques were processed homogeneously to avoid systematic differences between the solutions. We compared the tropospheric estimates of GPS and VLBI at eight co-location sites and found a very good agreement in the temporal behavior of the tropospheric zenith path delays (ZPD), reflected by correlation factors up to 0.98. Following this, a combination of the tropospheric parameters was performed. We demonstrate that the combination of tropospheric parameters leads to a stabilization of combined station networks. This becomes visible in the improvement of the repeatabilities of the station height components. Furthermore, the potential use of independent data from water vapor radiometers (WVRs) to validate space-technique-derived tropospheric parameters was investigated. Correlation coefficients of 0.95 or better were estimated between the tropospheric parameters of WVR and GPS or VLBI. Additionally, the utility of the tropospheric parameters for validation of local tie vectors was investigated. Both tropospheric zenith delays and tropospheric gradients were found to be very suitable to validate the height component and the horizontal components of the local tie, respectively.

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.

This paper presents the final geodetic results of the GEODYSSEA project. The GPS data from a 42 station network observed during two field campaigns (1994/1996) were analyzed by four groups using different software packages and analysis strategies. The precision of both campaign coordinate solutions was found to be 4–7 mm for the horizontal, and 1 cm for the vertical component. The campaign solutions were merged into one unique solution, which was accurately mapped into the ITRF-96 reference frame. The global accuracy of this solution with respect to ITRF-96 is ±1 cm, while the resolution of the relative horizontal velocities is estimated to be at the level of 2–3 mm/yr. This solution was used as the basis for all scientific interpretations, which are published in separate papers. The velocity estimates of a part of the network provided the first direct measurement of a relative motion of the Sundaland block with respect to Eurasian plate.