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As one of the major contributors to the realisation of the International Terrestrial Reference System (ITRS), the Global Navigation Satellite Systems (GNSS) are prone to suffer from irregularities and discontinuities in time series. While often associated with hardware/software changes and the influence of the local environment, these discrepancies constitute a major threat for ITRS realisations. Co-located GNSS at fundamental sites, with two or more available instruments, provide the opportunity to mitigate their influence while improving the accuracy of estimated positions by examining data breaks, local biases, deformations, time-dependent variations and the comparison of GNSS baselines with existing local tie measurements. With the use of co-located GNSS data from a subset sites of the International GNSS Service network, this paper discusses a global multi-year analysis with the aim of delivering homogeneous time series of coordinates to analyse system-specific error sources in the local baselines. Results based on the comparison of different GNSS-based solutions with the local survey ties show discrepancies of up to 10 mm despite GNSS coordinate repeatabilities at the sub-mm level. The discrepancies are especially large for the solutions using the ionosphere-free linear combination and estimating tropospheric zenith delays, thus corresponding to the processing strategy used for global solutions. Snow on the antennas causes further problems and seasonal variations of the station coordinates. These demonstrate the need for a permanent high-quality monitoring of the effects present in the short GNSS baselines at fundamental sites.

A new algorithm for global navigation satellite system attitude determination onboard a spacecraft was developed. A distinct feature of the algorithm is the extrapolation of the measurements to a common epoch within a Kalman filter. The necessity for the extrapolation arises from the usage of non-synchronized low-cost receivers. The extrapolation terms typically range from $$- 6$$ to + $$6$$ m for u-blox receivers. Thus, no solution can be obtained without a proper extrapolation. A validation was carried out with synthetic data as well as with signal simulator data. The algorithm delivers an attitude estimation with an accuracy below 1° for three orthogonal baselines of 10 cm length. In conclusion, the algorithm is proven to work, offering a very efficient method of attitude determination onboard a spacecraft.

GNSS observations provided by the global tracking network of the International GNSS Service (IGS, Dow et al. in J Geod 83(3):191–198, 2009) play an important role in the realization of a unique terrestrial reference frame that is accurate enough to allow a detailed monitoring of the Earth’s system. Combining these ground-based data with GPS observations tracked by high-quality dual-frequency receivers on-board low earth orbiters (LEOs) is a promising way to further improve the realization of the terrestrial reference frame and the estimation of geocenter coordinates, GPS satellite orbits and Earth rotation parameters. To assess the scope of the improvement on the geocenter coordinates, we processed a network of 53 globally distributed and stable IGS stations together with four LEOs (GRACE-A, GRACE-B, OSTM/Jason-2 and GOCE) over a time interval of 3 years (2010–2012). To ensure fully consistent solutions, the zero-difference phase observations of the ground stations and LEOs were processed in a common least-squares adjustment, estimating all the relevant parameters such as GPS and LEO orbits, station coordinates, Earth rotation parameters and geocenter motion. We present the significant impact of the individual LEO and a combination of all four LEOs on the geocenter coordinates. The formal errors are reduced by around 20% due to the inclusion of one LEO into the ground-only solution, while in a solution with four LEOs LEO-specific characteristics are significantly reduced. We compare the derived geocenter coordinates w.r.t. LAGEOS results and external solutions based on GPS and SLR data. We found good agreement in the amplitudes of all components; however, the phases in x- and z-direction do not agree well.

Tracking L-band signals of GNSS satellites by radio telescopes became a new observation type in recent years and will be used to improve reference system realizations and links between Earth- and space-fixed frames. First successful test observations were done, with the drawback of being single-frequency only. In order to correct the ionospheric delay by using GNSS phase observations from co-located receivers, the L4R approach was developed. Based on residuals derived by a least-squares processing of the GNSS geometry-free linear combination corresponding corrections could be derived. As a first validation step L4R corrections were applied to GNSS $$L_1$$ data analysis. Station coordinate repeatibilities at the 1-cm level were obtained for baselines of a few thousand kilometers. Comparing the derived delay corrections to VLBI ionospheric delays for quasars located in same directions, differences with a standard deviation of 2.2 TECU could be achieved.

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.

Surface mass variations of low spherical harmonic degree are derived from residual displacements of continuously tracking global positioning system (GPS) sites. Reprocessed GPS observations of 14 years are adjusted to obtain surface load coefficients up to degree n max = 6 together with station positions and velocities from a rigorous parameter combination. Amplitude and phase estimates of the degree-1 annual variations are partly in good agreement with previously published results, but also show interannual differences of up to 2 mm and about 30 days, respectively. The results of this paper reveal significant impacts from different GPS observation modeling approaches on estimated degree-1 coefficients. We obtain displacements of the center of figure (CF) relative to the center of mass (CM), Δr CF–CM, that differ by about 10 mm in maximum when compared to those of the commonly used coordinate residual approach. Neglected higher-order ionospheric terms are found to induce artificial seasonal and long-term variations especially for the z-component of Δr CF–CM. Daily degree-1 estimates are examined in the frequency domain to assess alias contributions from model deficiencies with regard to satellite orbits. Finally, we directly compare our estimated low-degree surface load coefficients with recent results that involve data from the Gravity Recovery and Climate Experiment (GRACE) satellite mission.

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.

Results of the estimation of azimuth-dependent phase center variations (PCVs) of GPS satellite antennas using global GPS data are presented. Significant variations of up to ±3–4 mm that are demonstrated show excellent repeatability over eight years. The application of the azimuthal PCVs besides the nadir-dependent ones will lead to a further reduction in systematic antenna effects. In addition, the paper focuses on the benefit of a possible transition from relative to absolute PCVs. Apart from systematic changes in the global station coordinates, one can expect the GPS results to be less dependent on the elevation cut-off angle. This, together with the significant reduction of tropospheric zenith delay biases between GPS and VLBI, stands for an important step toward more consistency between different space geodetic techniques.

A method for the estimation of the phase center variations of GPS satellite antennas using global GPS data is presented. First estimations have shown an encouraging repeatability from day to day and between satellites of the same block. Thus, two different satellite antenna patterns for Block II/IIA and for Block IIR with a range of about 4 cm and an accuracy of less than 1 mm could be found. The present approach allows the creation of a consistent set of receiver and satellite antenna patterns and phase center offsets. Thereby, it is possible to switch from relative to absolute phase center variations without a scale problem in global networks. This changeover has an influence on troposphere parameters, reduces systematic effects due to uncorrect antenna modeling and should diminish the elevation dependence of GPS results.

Preprocessing is an essential aspect for zero- and double-difference GPS software packages. In the first case we have to produce “clean” code and phase observations on the single receiver and single satellite level, in the second case solely double-difference observations have to be checked. The checks usually are performed on the “minimum constellation” level, i.e., the single receiver level for zero-, the single baseline level for double-difference packages. When analyzing the code observations stemming from a permanent array, this step may be performed in a much more efficient and robust way because the known geometry and, if available, the known atmospheric delays may be removed from the original observations. In an array of n receivers observing m satellites this leaves us with n · m observations and n+m − 1 unknowns (the clock parameters relative to a reference clock). The degree of freedom of f=n · m − ( n +m − 1 ) (for, e.g., n= 10 and m= 10, we have f= 81) allows for a very robust detection of outliers and enables generating a satellite clock file based on code measurements (with very much reduced multipath and noise characteristics). A similar step may be performed with the differences of phase observations between subsequent epochs. Using an analogous procedure as in the case of code observations we may generate phase files with all cycle slips flagged or, in the case of “small-area” arrays, even with cycle slips repaired. Both steps, phase and code cleaning, are performed in the same program unit. We discuss this new development and present first results and applications using data from the AGNES (Automated GPS Network Switzerland) and the IGS (International GPS Service) Networks.

The solutions of the CODE Analysis Center submitted to the IGS, the International Global Position System (GPS) Service for Geodynamics, are based on three days of observation of about 80–100 stations of the IGS network. The Earth rotation parameters (ERPs) are assumed to vary linearly over the three days with respect to an a priori model. Continuity at the day boundaries as well as the continuity of the first derivatives are enforced by constraints. Since early April 1995 CODE has calculated a new ERP series with an increased time resolution of 2 hours. Again continuity is enforced at the 2-hours-interval boundaries. The analysis method is described, particularly how to deal with retrograde diurnal terms in the ERP series which may not be estimated with satellite geodetic methods. The results obtained from the first year of data covered by the time series (time interval from 4 April 1995 to 30 June 1996) are also discussed. The series is relatively homogeneous in the sense of the used orbit model and the a priori model for the ERPs. The largest source of excitation at daily and sub-daily periods is likely to be the effect of the ocean tides. There is good agreement between the present results and Topex/Poseidon ocean tide models, as well as with models based on Very Long Baseline Interferometry (VLBI) and Satellite Laser Ranging (SLR) data. Non-oceanic periodic variations are also observed in the series. Their origin is most probably a consequence of the GPS solution strategy; other possible sources are the atmospheric tides.

The Extended Center for Orbit Determination in Europe (CODE) Orbit Model, an empirical orbit model proposed by Beutler and colleagues in 1994, has been tested extensively since January 1996. Apart from six osculating Keplerian elements, this orbit model consists of nine (instead of the conventional two) parameters to take into account the deterministic part of the force field acting on the satellites. Based on the test results an improved orbit parameterization is proposed. The new orbit parameterization consists of the conventional two parameters plus three additional parameters, a constant and two periodic terms (a cosine and a sine term), in the X-direction to model the effects of the solar radiation pressure. Results based on one full year of routine orbit estimation, using the original and the new orbit parameterization, are presented to demonstrate the superiority of the new approach. An improvement of the orbit estimates with at least a factor of two is observed!

The largest error in currently used GPS orbit models is due to the effect of solar radiation pressure. Over the last few years many improvements were made in modeling the orbits of GPS satellites within the International GPS Service (IGS). Howeer, most improvements were achieved by increasing the number of estimated orbit and/or solar radiation pressure parameters. This increase in the number of estimated satellite parameters weakens the solutions of all estimated parameters (not only orbit parameters). Because of correlations the additional orbit parameters may introduce biases in other estimated quantities, for example the length of day. We present a recently developed solar radiation pressure model for the GPS satellites. This model is based on experiences and results gained at the Center for Orbit Determination in Europe (CODE) in the context of its IGS activities since June 1992. The performance of the new model is almost an order of magnitude better than that of the existing ROCK models. It also allows a reduction of the number of orbit parameters that have to be estimated. © 1999 John Wiley & Sons, Inc.

The final products of theCODE Analysis Center (Center for Orbit Determination in Europe) of theInternational GPS Service for Geodynamics (IGS) stem fromoverlapping 3-day-arcs. Until 31 December, 1994 these long arcs were computedfrom scratch, i.e. by processing three days of observations of about 40 stations (by mid 1995 about 60 stations were used) of the IGS Global Network in our parameter estimation program GPSEST. Becauseone-day-arcs have to be produced first (for the purpose of error detection etc.) the actual procedure was rather time-consuming. In the present article we develop the mathematical tools necessary to form long arcs based on the normal equation systems of consecutive short arcs (one-day-solutions in the case of CODE). The procedure in its simplest version is as follows: From the point of view of the result the new procedure iscompletely equivalent to an actual re-evaluation of all observations pertaining to the long arc. It is much more efficient and flexible, however because it allows us to construct 2-day-arcs, 3-day-arcs, etc. based on the previously stored daily normal equation systems without requiring much additional CPU time. The theory is developed in the first four sections. Technical aspects are dealt with in appendices A and B. The actual implementation into the Bernese GPS Software system and test results are given in section 5.

Resolving the initial phase ambiguities of GPS carrier phase observations was always considered an important aspect of GPS processing techniques. Resolution of the so-called wide-lane ambiguities using a special linear combination of theL1 andL2 carrier and code observations has become standard. New aspects have to be considered today: (1) Soon AS, the so-called Anti-Spoofing, will be turned on for all Block II spacecrafts. This means that precise code observations will be no longer available, which in turn means that the mentioned approach to resolve the wide-lane ambiguities will fail. (2) Most encouraging is the establishment of the new International GPS Geodynamics Service (IGS), from where high quality orbits, earth rotation parameters, and eventually also ionospheric models will be available. We are reviewing the ambiguity resolution problem under these new aspects: We look for methods to resolve the initial phase ambiguities without using code observations but using high quality orbits and ionospheric models from IGS, and we study the resolution of the ”narrow-lane ambiguities” (after wide-lane ambiguity resolution) using IGS orbits.

The 1986 GPS survey of Iceland aimed to: (1) establish geodetic control in the South Iceland Seismic Zone (SISZ), to study destructive earthquakes there, (2) measure a country-wide network to form the basis of a new first order national network. 51 points were surveyed, with 20–30 km spacings within the SISZ and 100 km spacings elsewhere. The data were processed using the Bernese GPS software Version 3. Analysis was difficult due to poor satellite geometry and short-period ionospheric variations. However, an ambiguity-fixed, ionosphere-free solution gave accuracies of 1–2 cm in the horizontal and 2–3 cm in the vertical for the SISZ network and an ambiguity-free, ionosphere-free solution yielded accuracies of about 5 cm for the country-wide network. An ionosphere-free solution for the total survey with ambiguities fixed for the SISZ network only gave marginal additional improvements over the two separate solutions. GPS surveying has continued annually in Iceland with measurements in South Iceland in 1989 and 1992 (Hackman 1991; Sigmundsson 1992) and in North Iceland in 1987, 1990 and 1992 (Jahn et al. 1992; Foulger et al. 1992).

Since 18 June 2007 navigation data messages transmitted by the GPS constellation are recorded by five receivers within GeoForschungsZentrum’s global groundstation network. We describe the recording, processing, validation, analysis and archiving of the navigation data. During the 197 days between 18 June 2007 and 31 December 2007 a total of 125,723,666 subframes were collected. By taking into consideration that the same data set frequently is observed by two or more receivers concurrently, 65,153,955 unique subframes could be extracted from the observations. With an estimated 88,099,200 subframes transmitted by the constellation during this time period a data yield of about 74% was achieved. Simulation studies suggest that with two additional GPS receivers, which are scheduled for addition to the network in 2008, about 95% of the transmitted subframes will be retrieved. The message data archive is open to the scientific community for non-commercial purposes and may be accessed through GFZ’s Information System and Data Center (http://isdc.gfz-potsdam.de).

Carrier phase measurements are potentially the most precise observations available from theGPS satellite system, the formal precision being of the order of one centimeter per observation. If the so called double differences are used as the basic observable, the analysis is relatively simple, since satellite- and receiver-clocks may be represented by basic models. We investigate the feasibility of double difference phase observations for orbit determination using the material of the 1985 High Precision Baseline Test, where the coordinates of the so called fiducial points (Haystack, Ft. Davis Richmond and Mojave) are held fixed.TI-4100 andAFGL-receiver observations were used in the same orbit determination process. Although no surface weather data had been available to us, the orbit quality seems to be of the order of0.1 ppm. When we use these orbits to estimate the coordinates of the five “non-fiducial points” Owens Valley, Hat Creek Mammoth Lake, Austin and Dahlgren we get a repeatability of the order of5 cm for latitude and longitude and10 cm for height, if the observations of the first four days of the campaign are compared to those of the second four days. If we use our orbits estimated withTI andAFGL observations to process the Mojave—Owens Valley baseline (length245 km) measured by the twoSERIES-X receivers, we obtain day to day repeatabilities of1.6 cm (0.06 ppm) in length,2 cm (0.08 ppm) in latitude,4 cm (0.16 ppm) in longitude and7 cm (0.29 ppm) in height. Since there are indications that regional networks will be realized in the near future, the results presented here should encourage the realization of regional high precision orbit determination services.