Geodetic Reference Frames

A rigorous approach to simultaneously determine both a terrestrial reference frame (TRF) materialized by station coordinates and Earth Orientation Parameters (EOP) is now currently applied on a routine basis in a coordinated project of the Groupe de Recherches de Géodésie Spatiale (GRGS). To date, various techniques allow the determination of all or a part of the Earth Orientation Parameters: Laser Ranging to the Moon (LLR) and to dedicated artificial satellites (SLR), Very Large Baseline Interferometry on extra-galactic sources (VLBI), Global Positioning System (GPS) and more recently DORIS introduced in the IERS activities in 1995. Observations of the different astro-geodetic techniques are separately processed at different analysis centres using unique software package GINS DYNAMO, developed and maintained at GRGS. The datum-free normal equation matrices weekly derived from the analyses of the different techniques are then stacked to derive solutions of station coordinates and Earth Orientation Parameters (EOP). Two approaches are made: the first one consists to accumulate normal equations (NEQs) derived from intra-technique single run solution in a single run combined solution; the second one leads to weekly combinations of NEQs. Results are made available at the IERS site (ftp iers1.bkg.bund.de) in the form of SINEX files. The strength of the method is the use of a set of identical up-to-date models and standards in unique software for all techniques. In addition the solution benefits from mutual constraints brought by the various techniques; in particular UT1 and nutation offsets series derived from VLBI are densified and complemented by respectively LOD and nutation rates estimated by GPS. The analyses we have performed over the first four months of the year 2006 are still preliminary; they show that the accuracy and stability of the EOP solution are very sensitive to a number of critical parameters mostly linked to the terrestrial reference frame realization, the way that minimum constraints are applied and the quality of local ties. We present thereafter the procedures which were applied, recent analyses and the latest results obtained.

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.

The parameter space that can be covered by GPS, VLBI and SLR is very broad, and many overlaps exist between the techniques. Up to now, this is not yet fully exploited in inter-technique comparisons and combinations as in most cases only station positions and Earth orientation parameters (EOP) are considered. In this contribution we include the troposphere parameters additionally, and it is demonstrated that a combined terrestrial reference frame (TRF) improves the agreement of the GPS- and VLBI-derived troposphere zenith delays (ZD). The benefit of a combination is shown for the EOP as well, although non-continuous VLBI observations complicate the situation for Universal Time (UT). Finally, the potential of connecting GPS and SLR by estimating degree one spherical harmonic coefficients of the Earth’s gravity field is analyzed.

Mass redistributions in various components of the Earth system exert time-variable surface loads on the solid Earth. The resulting variations of the Earth’s geometry are reflected by vertical and horizontal displacements of geodetic markers. Usually the effect of loading on crustal deformation is computed by means of a weighting function which is based on site-independent load Love numbers (Green’s function). But as the Earth’s crust is composed of heterogeneous material, the adequateness of a site-independent approach deserves a review. We propose a procedure for the computation of vertical crustal deformations in which the Green’s function is substituted by a site-dependent exponential function. Its parameters are estimated by means of least-squares adjustment using time series of globally distributed GPS sites. On the basis of the crustal model Crust2.0 regions are predefined for which identical parameters are determined. Pressure fields of atmosphere, continentalhydrosphere and oceans are considered as forcing. In order to validate the numerical results, model time series from both the traditional and the site-dependent approach are compared with GPS observations. Explicit improvement is achieved in regions which are covered well with observations and feature strong pressure variability. However in regions like Africa and Antarctica parameter estimation is difficult due to the sparse distribution of GPS sites.

Time series of geodetic Earth system parameters have been derived by means of dynamic satellite orbit adjustment. The procedures applied are the integrated approach where GPS sender satellites, GPS and SLR ground stations, and the Low Earth Orbiter (LEO) CHAMP are processed simultaneously within one model. On the other hand we present a pure SLR solution from LAGEOS-1 and -2 data based on the same standards. The particular advantage of the integrated approach is the high sensitivity of the LEO to the geocenter, and the dense coverage of GPS data sets the basis to a high resolution of the solved-for parameters. The classical SLR-only approach provides a reference for comparison to the integrated approach and to published external results. The set of estimated Earth system parameters includes coordinates of ground stations, low degree harmonic coefficients of the Earth’s gravity field, and Earth Orientation Parameters. The parameter time series are characterized concerning accuracy and reliability. Comparisons between both methods are presented as well as comparisons with external series.

The rigorous variance component estimation (VCE) is a nonlinear procedure for estimating variance components of covariance matrices within a linear Gauss-Markov Model (GMM). The VCE results are strongly dependent on the structure of the covariance matrices for a given GMM. Here VCE is applied to the li-near model of intra-technique combination with SLR input solutions and of the inter technique combination with DORIS, GPS, SLR, and VLBI input solutions, both with an observation range of one week -except VLBI with a session range of 24 hours. The parameters to be estimated are weekly 3D station coordinates and daily earth orientation parameters. The data sets used here are taken from the official input solutions of ILRS and ITRF2005. After having introduced the VCE formulae for this special combination model the characteristics between intra-and inter-technique combination w.r.t. VCE are outlined. For the SLR intra-technique it is shown by examples how VCE results are used not only for the weighting of the input solutions, but also for the formulation of outlier and fail/pass criteria within automatic processing. In the inter-technique combination the VCE processing is more complicated, because two additional problems exist: the handling of different parameter set sizes (e.g GPS sets are much larger than VLBI sets) and of the stochastic behaviour of local tie sets. The question here is whether VCE is also suitable for weighting and outlier analysis in the inter–technique case. First simulation results are presented here which prove the sensitivity of VCE to deterministic and stochastic variations and hence the suitability of VCE for automatic weighting and outlier search.

Various important aspects should be taken into account in the combination of different space geodetic techniques. Consistency of models and standards, quality checks of solutions from individual Analysis Centers (AC), proper scaling of these solutions within the combination process, usage of rigorous combination methods and quality checks of the final combined solution are some of those. In this study, variance component estimation (VCE) is implemented to obtain optimal scaling (weighting) factors for the VLBI (Very Long Baseline Interferometry) intra-technique combination on the basis of normal equations. Afterwards, we apply a Tikhonov-type regularization method to stabilize a combined solution by imposing additional constraints about the solution. The regularization parameters are calculated with two different methods, variance component estimation and generalized cross-validation. The results show that the use of regularization significantly reduces the effect of instability in combined normal equation systems and provides more reasonable results.

Lunar Laser Ranging (LLR) has provided observations for more than 36 years. There is enormous science potential of LLR to further our understanding of the dynamics of the Earth-Moon system (e.g.Earth orientation parameters (EOP) or the secular increase of the Earth-Moon distance: 3.8 cm/year) and to determine relativistic quantities such as the equivalence principle or any time variation of the gravitational constant. Here, we discuss the potential of LLR to contribute to the realisation of various reference systems, i.e. the terrestrial and selenocentric frame, but also thedynamic realisation of the celestial reference system, where most benefit is obtained from the long-term stability of the lunar orbit. Because of the tight link budget, only a handful terrestrial laser ranging stations are capable to routinely carry out the distance measurements (at cm level of precision). Therefore, we propose a next-generation lunar ranging experiment. Lunar landers shall deploy laser ’beacons’pointing at Earth.We estimate that the received pulse strength froma50 mJ Laser is 3 orders of magnitude larger than at classical LLR. Such laser shots could be received by most existing Satellite Laser Ranging (SLR) stations and measurement accuracies at mm level can then be accomplished. The contribution to the realisations of the aforementioned geodetic reference systems could be further improved.If in addition radio transponders were deployed at the same locations, a strong tie to the kinematic VLBI system couldbe established.

This paper gives an overview about the progress of the simulation work, carried out at the Institute of Geodesy and Geophysics (IGG), with the goal to design a new geodetic Very Long Baseline Interferometry (VLBI) system. Influences of the schedule, the network geometry and the main stochastic processes on the geodetic results are investigated. For this purpose temporally very dense schedules are prepared with the software package SKED (Vandenberg 1999), which are then compared in terms of baseline length repeatabilities. For the simulation of VLBI observations a Monte Carlo Simulator was set up which creates artificial observations by randomly simulating zenith wet delay and clock values as well as additive white noise representing the antenna errors. For this purpose the VLBI analysis software OCCAM (Titov et al. 2004) was adapted to run the simulator and analyze the simulated observations. Random walk processes with power spectral densities of 0.7 and 0.1 psec2/sec are used for the simulation of zenith wet delays. The clocks are simulated with Allan Standard Deviations of 1·10-14@50 min and 2·10-15@15 min and three levels of white noise, 4 psec, 8 psec and, 16 psec are added to the artificial observations. The variations of the power spectrum densities of the clocks and zenith wet delays and the application of different white noise levels show clearly that the wet delay is the critical factor for the improvement of the geodetic VLBI system.

Today it is common practice to derive terrestrial reference frames (TRF) by the combined analysis of the following space-geodetic techniques: VLBI, GPS, SLR, DORIS. Various validations and cross-check calculations show a high consistency in the range of a few millimetres for recent solutions of the International Terrestrial Reference Frame (ITRF). However, several factors limit the quality of intra-technique and inter-technique combinations such as the use of different parameterizations, different correction models for the same physical effects, individual constraints for stabilization or regularization, or low-quality local ties. In addition, not all applied analysis procedures are rigorous from a mathematical point of view. This is mainly due to the fact that intra-technique solutions which are based on identical observation data are considered as independent. As the normal equations or the variance-covariance matrices of the intra-technique combined solutions are used for the weighting of the inter-technique combinations (and thus for the final product ‘reference frame’) a dedicated study is urgently required.The scope of this paper is twofold. On the one hand there are the above-mentioned factors which are relevant for the proper assessment of the quality of intra-technique and inter-technique combi-nations. They are discussed and modelled from a general point of view. This includes effects of different software packages and operators. On the other hand the impact of identical observation data on the quality measures of intra-technique combinations is modelled and quantified. For this purpose some typical observations of space-geodetic techniques (i.e. VLBI) are analysed. Finally, recommendations are given for improved intra-technique and inter-technique combinations.

As the International Terrestrial Reference Frame (ITRF) is constructed by combination of space geodesy technique solutions together with terrestrial local ties in co-location sites, it then inherits strengths and weaknesses of the combined data. This paper uses the ITRF2005 results in order to illustrate the critical aspects of the combination that impact the ITRF datum definition: the origin, the scale and the No Net Rotation condition. The main ITRF2005 results, using as input data time series of station positions, indicate a drift of 1.8 mm/yr in the origin Z-translation component with respect to ITRF2000, while SLR solutions are used to define the origins of both frames. A scale bias of about 1 ppb between VLBI and SLR solutions is also detected. Possible causes of this inconsistency include the poor SLR and VLBI networks and their co-locations, systematic errors and possible inconsistent model corrections used in the data analysis of both techniques. As conclusion of this paper, some recommendations for improvements of future ITRF solutions are addressed.

The International Terrestrial Reference Frame (ITRF) is intended to be the standard reference for all geodetic and Earth science applications, ranging from national geodetic datums to Earth rotation, satellite navigation and geophysical interpretation of crustal deformation and tectonic plate motion. The ITRF is under the responsibility of the International Earth Rotation and Reference Systems Service (IERS). It is constructed upon combination of station positions and velocities of geodetic markers and instrument reference points, as determined by space geodesy techniques such as VLBI, SLR, GPS and DORIS. Since the creation of the IERS in 1988, more than 10 versions of the ITRF were determined, the up to date version is being the ITRF2005. Unlike the previous ITRF versions, the ITRF2005 is based on input data under the form of time series (weekly for satellite techniques, and daily for VLBI) of station positions and daily Earth Orientation Parameters (EOPs). This short paper briefly summarizes the contribution to the ITRF of the international technique services, the ITRF history and ITRF2005 main results. It also provides the reader a selected list of a certain number of publications related to the ITRF and ITRF2005 in particular.

In GPS week 1400, the International GNSS Service (IGS) switched from a relative antenna phase center model (APCM) for receiver antennas only to an absolute model including receiver and satellite antenna corrections. At the same time the International Terrestrial Reference Frame 2005 (ITRF2005) was adopted. These changes had a significant influence on the terrestrial reference frame (TRF). In order to study the influence of different APCMs on GPS-derived TRFs, four TRF solutions have been computed from 11 years of homogeneously reprocessed GPS data. The processing strategy for the four solutions is completely identical except for the APCM applied. The following models have been used: (1) the relative model IGS01 used by the IGS till GPS week 1400, (2) the new absolute IGS model IGS05 including radome calibrations, (3) IGS05 ignoring the radome calibrations for the receiver antennas, and (4) IGS05 including azimuth-dependent satellite antenna phase center variations (PCVs). Station coordinates and velocities have been estimated simultaneously with daily pole coordinates. Consistent time series of station coordinates have been generated using the corresponding reference frames for datum definition. This paper compares the station coordinates and velocities as well as the station coordinate time series arising from the four different reference frames.

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.As part of the reference frame computation with the ITRF2005 data sets at DGFI, we have computed multi-year solutions of each technique with the combination software DOGS-CS. We compared individual weekly data sets to the multi-year solution by aligning them with a 7 parameter similarity transformation and analyzed the resulting time series of station positions and transformation parameters. This is done with respect to discontinuities (caused e.g. by instrumental changes or earthquakes) or periodic signals such as annual variations. This information is then used to compute a second improved iteration of technique multi-year solutions, where these effects are taken into account.

A present-day plate kinematic and crustal deformation model is needed as a reference system for station velocities in the ITRF. The common rotation of all points of the Earth surface has to become zero in order to be consistent with Earth rotation parameters (condition of no net rotation, NNR). To realize this condition, we divide the surface into rigid plates and inter-plate deformation zones. Both, plate motions and deformations are modelled from the observed station velocities. The plate motions are represented by one rotation vector per plate, the inter-plate deformations are computed using a least squares collocation approach. In the APKIM2005, rotation vectors of 17 major plates and deformations in five plate boundary zones (Alps-Aegean, Persia-Tibet-Burma, Alaska-Yukon, Gorda-California, Andes) are estimated. The global integration is done in a 1°x1° grid covering the entire Earth surface. The ITRF2005 velocities result in a rotation of about 0.06 mas/year compared with the non-rotating terrestrial reference frame.

The Metsähovi research station of the Finnish Geodetic Institute hosts instruments of all basic space geodetic techniques, including geodetic VLBI, SLR, GNSS and DORIS. The local control network is an essential part of the station. Tie measurements between the network benchmark bolts and pillars and instrument reference points are needed to control the stability of the installations, and to tie them with each others and to the global reference frame.We use precision tacheometry to determine relative positions, and GPS for measurements for orientation of the local control network. Precise levelling data is available, too. One millimetre 3-D accuracy is expected. We describe measurement methods and give results obtained so far. Further measurements are required to obtain the final ties for the VLBI reference point and the new SLR instrumentation, which currently is under construction. Results are compared with the control measurements in 1997.

Local ties are key elements for the computation of combined space geodetic products: the different ITRF realizations determined by merging single technique geodetic reference frames rely on the availability of accurate eccentricities (or intra-site vectors) linking the instrumental reference points (RPs) at co-located observatories. If the RPs cannot be physically materialized and/or directly measured, an indirect approach can be used for their estimation: it is entirely based on a geometrical conditioning applied to observed points’ positions of the space geodetic instruments. Intra-site vectors are typically measured by combining terrestrial observations of angles, distances and height differences along with ancillary GPS measurements for assuring a correct alignment of the eccentricity into a global frame (terrestrial local ties). An alternative indirect approach can be used entirely relying on GPS measurements: it may efficiently be applied to VLBI-GPS eccentricities as well as at all co-location sites where ITRF tracking points can be surveyed with GPS technique (GPS-based local ties). In principle such an approach offers advantages with respect to that terrestrial, since it is (i) faster, (ii) semi-automatic and (iii) it provides an immediate eccentricity vector alignment into a global frame. This paper presents the results of the computation of the VLBI-GPS eccentricity at Medicina based on the GPS procedure, with the aim of assessing its quality and repeatability. To this respect, two GPS measurement sessions were performed in 2002 and 2006: the positive results obtained with the first campaign led us to repeat the survey in 2006 in order to better investigate the potential of GPS-based ties. 2002 and 2006 GPS-based ties were compared with terrestrial local ties surveyed at Medicina’s observatory in 2001, 2002, 2003. Each of the intra-site vectors was estimated by applying different configurations of the geometrical conditioning with the aim of investigating the effects on the RPs estimations in the terrestrial and in the GPS case. The results demonstrate the efficiency and the precision of the GPS approach for eccentricity vector computation which can be used as an alternative to terrestrial based ties.

In 1998 Land Information New Zealand introduced New Zealand Geodetic Datum 2000 (NZGD2000) as its new national datum. It is defined as a semi-dynamic datum and incorporates a national deformation model to ensure that the accuracy of the datum is maintained. The deformation model allows observations made at an epoch other than the datum reference epoch of 2000.0 to be modeled so that coordinates at the reference epoch can be generated. From a geodetic perspective its implementation is relatively straight forward. In New Zealand the geodetic system and datum also underpin the cadastre and spatial positioning. Cadastral surveys are made in terms of NZGD2000 and about 70% of parcels have NZGD2000 survey accurate coordinates. Many users of the geodetic system are non-technical users, for whom managing the dynamics of the datum presents a potential annoyance and complexity. LINZ manages the dynamics of the geodetic system which enables other spatial datasets connected to it to be updated. The implementation of a Continuously Operating Reference Station (CORS) network in New Zealand also presents a set of issues that need to be considered when CORS stations are incorporated as part of a semi-dynamic datum. This paper presents some of the implications and limitations for users of geodetic and related datasets when implementing a semi-dynamic datum and discusses solutions based on New Zealand experiences.

The declaration of the Russian President Vladimir Putin on completing the GLONASS 24 satellite constellation until end of 2009 revitalized the activities in the geodetic world to make use of that satellite navigation system. There are today various combined GPS/GLONASS receivers operating at permanent reference stations, corresponding observation files are stored in public data archives, and also analysis software exists. But the introduction of GLONASS observations into regional GPS permanent networks, e.g., one of the sub-networks of the EUREF GPS Permanent Network, could not satisfactory demonstrate any benefit from this approach. Therefore potential analysis options for GLONASS observations has been evaluated in a test analysis of only a few selected sites. The test scenario considers especially the fact of the un-complete GLONASS satellite constellation and the mixture of GPS and combined GPS/GLONASS receivers in the network. This study confirms that only sporadic improvements of regional network station coordinates could be expected when adding GLONASS observations today, but this may change in future.

EUREF, the IAG (International Association of Geodesy) Reference Frame Sub-commission for Europe, deals with the definition, realization and maintenance of the European Reference Frame. EUREF works in close cooperation with the pertinent IAG components and EuroGeographics, the consortium of the NMCA (National Mapping and Cadastre Agencies) in Europe.This paper presents an overview of EUREF and describes its missions, activities and the recent developments, aiming at upgrading European-wide geodetic reference systems to support both scientific and continental geo-referencing activities.

The EUREF Permanent Network (EPN) is a network of continuously operating GPS or GPS/GLONASS stations installed throughout the European continent. The EPN Central Bureau (CB), responsible for the daily management of the EPN, uses several monitoring procedures to verify the meta-data, latencies and quality of the observation data files in order to assess if the data meets the requirements of the analysis. In addition, several types of coordinate time series allow analysing the long-term stability of the site coordinates. All monitoring procedures result in regularly updated plots made available at the EPN CB website; they are created to be easily understood by all EPN station managers, even the non-specialists.This paper outlines the on-line resources available from the EPN Central Bureau and summarizes the procedures used to obtain this information.

The EUREF Permanent Network (EPN) has been installed in 1996 with some 30 stations and now includes more than 190 permanent GNSS sites (see Fig. 1). The network is operated according to the standards of the International GNSS Service (IGS) and it is considered as a regional densification of the ITRF (International Terrestrial Reference Frame). The EPN is primarily a geodetic reference network, but its results are also widely used for geophysical studies. In order to better serve the user needs, the EUREF Time Series Analysis special project monitors the weekly combined SINEX solutions, cleans the individual station coordinate series, and maintains and publishes the database of the detected coordinate offsets and outliers. Using this info, cleaned cumulative solutions are then computed with the CATREF software (Altamimi et al 2004). The estimated coordinates and velocities, together with the outlier and offset database are regularly updated and published on the EPN CB website (www.epncb.oma.be ).In this study we focus on the noise and harmonic analysis of the EPN coordinate series. The analysis is done with the CATS software (Williams SD, Proudman Oceanographic Laboratory), which uses a MLE (Maximum Likelihood Estimator) to determine the noise characteristic and seasonal variation of the coordinate time series. The EPN weekly SINEX files from GPS week 860 to 1385 are involved in the computations.We proved the presence of the colored noise in the EPN time series. The harmonic analysis showed moderate seasonal amplitudes. The phase lag distribution for the horizontal components are not random, well determined phase lag values were found. The Up component shows a more diffuse phase lag distribution. The physical reality of the phase lag values are not discussed here.

Cooperation of 14 Central European countries in the framework of the Central Europe Regional Geodynamics Project (CERGOP) resulted in determination of coordinates and velocities for more than 50 sites in Central Europe, Alpine-Adria region and Balkan Peninsula. The set of selected stations with carefully checked monumentation and observational environment comprises the Central Europe Geodynamics Reference Network (CEGRN). This network is recently strengthened by new permanent stations in the region. Epoch campaigns at CEGRN sites were performed annually or bi-annually during period from 1994 to 2005. In 2006 one week of observations at permanent CEGRN stations was arranged as additional campaign. Simultaneous processing of all campaigns allowed defining horizontal coordinates with accuracy at 2 – 4 mm level and horizontal velocities with accuracy 0.5 – 1.0 mm/year. The link to the ITRS is achieved through a set of IGS and EPN permanent stations which were intentionally included in analysis of CEGRN epoch campaigns. The accuracy and reliability of obtained velocities is examined by the comparison with data from independent sources. We present here the obtained final velocities referred to ITRF2000 as well as the plots of intraplate velocities.

Typically, the local permanent GNSS networks for positioning services are adjusted in the IGS realization of ITRS (at the present, IGb00): therefore, the positions estimated by their users are expressed in this reference frame; however, typically in surveys finalized to cartographic purposes within Europe, ETRS89 coordinates may be required. A time series of ETRS89 realizations is published by IERS and EPN: the present is ETRF2000; in Italy the official cartographic realization is materialized by the IGM95 network, originally constituted of about 1250 markers, surveyed in the ‘90 and adjusted in ETRF89. At the present epoch, the planimetric differences between current realizations of ITRS and ETRS89 are of some decimeters; due to the survey accuracy and the elapsed time, IGM95 exhibits both correlated, from the national to the local scale, deformations and sparse errors, up to one dm. The analysis of the relationships between the above reference frames is strategic for GNSS positioning services, in order to provide coordinates in the reference frame required by the users. At a national scale, the published IGb00 and ETRF2000 coordinates of the Italian permanent stations have been used to estimate a similarity transformation; at a local scale, for the Piemonte, and Lombardia regions, where data were available, the estimated IGb00 and the published ETRF89 coordinates of the IGM95 markers have been used to validate the transformation and to investigate in more detail the local deformations. The paper discusses the analysis approach, the developed software and the first results.

SIRGAS is the geocentric reference system for the Americas. Its definition corresponds to the IERS International Terrestrial Reference System (ITRS) and it is realized by a regional densification of the IERS International Terrestrial Reference Frame (ITRF). The SIRGAS activities are coordinated by three working groups: SIRGAS-WGI (Reference System) is committed to establish and maintain a continental-wide geocentric reference frame within the ITRF. This objective was initially accomplished through two continental GPS campaigns in 1995 and 2000, comprising 58 and 184 stations, respectively. Today, it is realized by around 130 continuously operating GNSS sites, which are processed weekly by the IGS Regional Network Associate Analysis Centre for SIRGAS (IGSRNAAC-SIR). SIRGAS-WGII (Geocentric Datum) is primarily in charge of realising the SIRGAS geodetic datum in the individual countries, which is given by the origin, orientation and scale of the SIRGAS system, and the parameters of the GRS80 ellipsoid. SIRGAS-WGII is concentrating on promoting and supporting the adoption of SIRGAS in the Latin American and Caribbean countries by means of national densifications of the continental network. SIRGAS-WGIII (Vertical Datum) is dedicated to the definition and realization of a unified vertical reference system within a global frame. Its central purpose is to refer the geopotential numbers (or physical heights) in all countries to one and the same equipotential surface (W0), which has to be defined globally. This includes also the transformation of the existing height datums into the new system.

Since 1996 the German Geodetic Research Institute (DGFI) acts as the Regional Network Associate Analysis Centre for the Geocentric Reference System of the Americas (SIRGAS) within the International GNSS Service (IGS RNAAC SIR). It is processing the observations of all permanent GPS stations (IGS and regional stations) of South America, Central America, Mexico, the Caribbean and surrounding areas. Each week a coordinate solution is submitted to the IGS data centres.the IGS data centres. This paper reports on the accummulative combination of all weekly normal equations resulting in the multi-year position and velocity solution DGF06P01, and the comparison with the latest ITRF realization. The future plans for the IGS RNAAC SIR within the SIRGAS project are discussed.

The technological advance allowed the improvement of existent Geodetic Reference Systems (GRS) in their definition (system) as well in their realization (frame). Usually, the coordinate transformation among the different GRS is done in an analytical way by formulae based on transformation parameters which are not able to model local deformations present in the classical networks. The objective of this work is to evaluate an Artificial Neural Network (ANN) as a basis of a transformation method. For this study coordinates in the system PSAD56 (Provisional South American Datum 1956) in Ecuador were chosen and the cartesian geodetic coordinates in the system SIRGAS95 (Geocentric Reference System for Americas 1995) were determined. Firstly, a set of point coordinates was transformed by a seven parameter transformation derived from the similarity mapping among known coordinates of homologous points in both systems. Secondly, an Artificial Neural Network with Radial Basis Functions (ANN-RBF) was trained to predict coordinates from one system to the other. The results found that the ANN-RBF gave better results for the transformation. These better results would indicate that an ANN-RBF is superior to model the existent deformations in classical networks like PSAD56 when transferred to a new geocentric system like the SIRGAS95.

Through the first years after the full deployment of the GPS constellation, the number of permanent GPS stations around the world increased significantly. This process rendered the initial structure of IERS and IGS insufficient and by 1996 led to the creation of the Regional Network Associate Analysis Centers (RNAAC).Ten years later, a large number of new permanent GPS stations have been established by a rather heterogeneous group of organizations that see in collaboration with IGS-IERS a means to access to the advantages of the global geodetic infrastructure. On the one hand, this has improved the distribution of ITRF on previously poorly covered areas. On the other hand, significant efforts were necessary to improve regional organization and to make collaboration more efficient.The SIRGAS permanent GPS network, which is known as the IGS network densification for the American continent, consists today of more than 200 GPS stations covering almost all the continent and islands. The South America network is processed by the IGS RNAAC SIR at Deutsches Geodätisches Forschungsinstitut (DGFI). It produces weekly free solutions. This center works in cooperation with the SIRGAS project. Last year, at the SIRGAS Workshop held in Aguascalientes, México, the SIRGAS WGI decided to establish three pilot processing centers within the region. One of them, the Centro de Procesamiento La Plata (CPLat) in Argentina, processes the data from all the permanent stations of Argentina and Chile. It also produces weekly solutions.In this work we describe the processing strategy applied for CPLat, including comparisons of our results with the regional solutions produced by the IGS RNAAC SIR. We also discuss a set of recommendations for users who are interested in using the observations from this network and refer the results to the realization of SIRGAS in Argentina, the frame POSGAR 98.

The Geocentric Reference System for the Americas (SIRGAS) in its realization of ITRF94, epoch 1995.4 in South America was introduced in January 2005 as the official reference frame in Colombia. It replaces the classical horizontal datum (BOGOTA Datum) defined in 1941. This official adoption implies that all coordinates in the country shall refer to SIRGAS. Since this decision affects the whole geodetic and surveying activities of the country, the National Geographical Institute ‘Agustin Codazzi’ (IGAC) has implemented a strategy to facilitate this adoption and to generalise the reliable use of SIRGAS. We present here the densification of the SIRGAS network in our country (MAGNA network), the continuously operating network (MAGNA-ECO network), and the introduced measures to make feasible the modernisation of the geometrical reference system in Colombia. These are in particular the specifications for the use of the new reference frame and the transformations from the old to the new system.

Many GPS sites show significant seasonal position variations (especially in the vertical), resulting from a combination of geophysical loading and systematic errors. It is common to realize a regional reference frame or align a time series with a model by transforming each epoch solution into ITRF (or a local or regional frame) using a regional set of sites, where these reference frame sites are assumed to move linearly with time. Seasonal variations in the frame sites can bias this frame realization and the seasonal variations are then aliased into the site coordinates.I estimate seasonal variations at a set of sites across northern North America and the Arctic using an iterative non-parameteric approach. Seasonal variations at most sites exceed 4-5 mm in the vertical. A test with synthetic time series shows that ignoring these variations when realizing a daily or weekly reference frame can cause apparent seasonal variations in other sites as large as 4 mm amplitude. We should work toward a linear + seasonal model as part of our reference frame definition.

The modern geodetic reference systems (e.g. ITRS) are realized by reference frames, i.e. a set of stations with position coordinates at a reference epoch and station velocities (e.g. ITRF2000). IGS (International GNSS Service) global network and EPN (EUREF Permanent Network) regional network stations are parametrized in this way. The main IGS/EPN products (gained daily and weekly) are estimated station coordinates and velocities, as well as orbits’ and ionospheric and tropospheric parameters. The connection of local GPS networks with IGS/EPN stations enables to use the above products. In this publication the method of EPN/IGS reference stations selection for the purpose of local GPS networks is presented. Two approaches are applied: station velocity analysis and cluster analysis. It has also been suggested to process permanent and epoch observations in local GPS networks, which are based on IGS global networks and EPN regional networks’ solutions jointly.

For the concrete “Introduction of ETRS89 into Baden-Württemberg” the transformation which transforms the existing two-dimensional Gauss-Krueger coordinates in German geodetic reference system (DHDN) into UTM coordinates in the ETRS89 datum with the models of the 7-parameter Helmert transformation and the 6-parameter affine transformation using the 131 collocated points (131 BWREF points in Baden-Württemberg) are tested and discussed. Because of the special characteristic of the main triangulation network in Baden-Württemberg (state-wide variable net scales, inhomogeneous point accuracies and network distortions in the decimetre level) an alternative transformation procedure based on the polynomial model is performed. Further more the Total Least-Squares method is also applied in estimating the parameters of the 6-parameter affine-transformation based on the 131 collocated points. The result is analysed and compared with these results of the conventional LS method. A systematic analysis of the transformation results is concluded.

In order to determine the transformation parameters between two reference frames empirically, a sufficient number of point coordinates (or possibly higher dimensional features such as, e.g., straight lines or conics) need to be observed in both systems. A proper adjustment of the observed data must take the different variances and covariances into account.The resulting adjustment model is of type Errors-in-Variables rather than of type Gauss-Markov because both sets of coordinates are associated with errors. In the homoscedastic case, the least-squares principle thus leads to the Total Least-Squares Solution (TLSS) rather than the standard Least-Squares Solution (LESS).Here, we generalize the TLSS by allowing the individual variances to be different and the covariances to be non-zero, while still maintaining a certain reasonable variance-covariance structure. This leads to the Weighted TLSS. We show experimentally that the Weighted TLSS yields slightly better estimates (in terms of precision) than LESS or TLSS, but significantly more accurate dispersion measures.

In the error budget of high-rate GPS coordinate time series the geometry satellite – antenna plays a significant role, by means of which the repeat time interval of the identical configuration of GPS satellites must be determined. Instead of the sidereal time interval a more detailed investigation yields a smaller value, namely the so-called “modified sidereal time interval”. The exact value depends on an average of the orbit repeat period of satellites under consideration.The recurrence period can be determined also empirically by the cross covariance function of time series of consecutive days. For the example noted above the diminution w.r.t. the sidereal time interval amounts to 10-14 seconds, and within this range being equal for position and height.The difference reduces the root mean square error in the time series to up to half of the original value. With respect to the sidereal time interval the modified one reduces the rms again by a few percent. In the spectral domain the improvement can be seen within the range of 50 to 500 sec.The spectrum of displacements due to waves caused by the Sumatra earthquake of Dec 26, 2004 could be determined, using 1 Hz GPS data covering Central Europe. With respect to the ground truth given by the STS-2 seismometer the agreement in sharp lines is very satisfying, particularly for the horizontal components.

Regional Reference Frames are being proposed, established and adopted under the assumption time independent coordinates are better suited for geo-referencing locations than time dependent coordinates when practical purposes are concerned. The RRF (Regional Reference Frame) tries to respond to the request of maintaining wide areas like Europe, North America, South America or Africa, under fixed coordinates along the time, while establishing, at the same time, a modern Geo-Centric System, a TRS (Terrestrial Reference System).This two objectives are contradictory: if the frame’s coordinates are kept fixed along the time it will no longer realize a TRS; and if the frame is supposed to realize a TRS its coordinates should vary with time.In order to try to solve this contradiction some RRF, like ETRS89/ETRF89 (European Terrestrial Reference System/European Terrestrial Reference Frame) are not allowed to evolve with time: the actual Frame coordinates are transformed back into the original past epoch. But this “solution” raises more problems than the ones it is supposed to solve, namely the need to know the non-linear displacements suffered by the frame stations between the past epoch and the present time.According the author’s view point this annoying problem can be avoided if instead of trying to keep the coordinates for some Regions fixed, we use a Global Reference Frame, like ITRF2005 (International Terrestrial Reference Frame 2005) including in the Metadata file of the product, information about the epoch of the coordinates and about the velocities for the area.Cartography nowadays is Digital Cartography and GIS products are also, obviously, Digital. It won’t therefore pose a problem to transform the Reference System of this kind of Geographical Information products into whatever Reference System is, for the moment, needed.

It is customary to perform analysis of the Earth’s rotation in two steps: first, to present results of estimation of the Earth orientation parameters in the form of time series based on a simplified model of variations of the Earth’s rotation for a short period of time, and then to process this time series of adjustmentsby applying smoothing, re-sampling and other numerical algorithms. This approach suffers from self-inconsistency: the total set of Earth orientation parameters depends on a subjective choice of the apriori Earth orientation model, crosscorrelations between points of the time series are lost, and results of an operational analysis per se have a limited use for end users. Here, an alternative approach of direct estimation of the coefficients of expansion of Euler angle perturbations into basis functions is developed. These coefficients describe the Earth’s rotation over the entire period of observations and are evaluated simultaneously with stationpositions, source coordinates and other parameters in a single LSQ solution. In the framework of this approach considerably larger errors in apriori EOP model are tolerated. This approachgives a significant conceptual simplification of representation and estimation of the Earth’s rotation.

ITRF2005 is the first realization of the International Terrestrial Reference Frame (ITRF) using a time series combination of multi-technique solutions to yield fully consistent station positions and Earth orientation parameters (EOPs), with full variance-covariance information. However, it is not as easy to combine universal time (UT1) and length of day (LOD) as for polar motion within the ITRF combination itself. Only the UT1 and LOD results from 24-hr very long baseline interferometry (VLBI) sessions have been included because the denser set of short-duration, single-baseline VLBI sessions can distort station position estimates and daily satellite-based LOD estimates suffer from large, time-varying biases.This paper outlines a multi-step procedure to utilize all the available UT1 and LOD results to produce a nearly optimal, complete time series combination consistent with ITRF2005: 1) The ITRF2005 solution for VLBI station positions and velocities, as well as daily polar motion and UT1/LOD at VLBI epochs, is adopted with associated variance-covariances. 2) The short-duration, single-baseline VLBI sessions must be reduced to SINEX form with UT1 freely adjusted and with station positions and polar motion constrained to the ITRF2005 values. Alternatively and probably better, the initial VLBI analyses can use non-ITRF constraints, which must later be modified by back-substitution, provided that all the necessary a priori information is included in the session SINEX files. 3) The set of ITRF2005 UT1/LOD estimates and sigmas merged with those from the short-duration VLBI sessions should form a consistent time series, but only at VLBI epochs. 4) Biased LOD estimates from satellite techniques can be used to densify and regularize the epochs of VLBI UT1 estimates in a Kalman filter. In addition to coupled models for the stochastic variations of LOD (random walk) and UT1 (integrated random walk) due to geophysical processes, an empirical stochastic model is needed for each satellite technique to account for the behavior of its LOD biases.The resulting Kalman filter output of UT1 and LOD estimates and sigmas will be optimal in the general estimation sense, assuming reasonable stochastic models and parameters are derived for the satellite LOD biases, and will be quasi-optimal as they relate to the ITRF2005 frame. But more specifically and importantly, unbiased estimates and realistic sigmas are ensured by the direct modeling of the LOD biases, unlike in simpler methods that “calibrate” the biases in a pre-combination step.

Atmosphere pressure and air temperature are input quantities for corrections applied to the observables of space geodetic techniques, such as Very Long Baseline Interferometry (VLBI) and Global Navigation Satellite Systems (GNSS). A priori troposphere zenith delay and atmosphere loading models are directly connected with the atmosphere pressure and thermal deformations of the antennas depend on temperature variations. In this study effects on the VLBI terrestrial and celestial reference frames (TRF, CRF) are investigated using atmosphere pressure and temperature from various sources: the numerical weather model (NWM) of the European Centre for Medium-Range Weather Forecasts (ECMWF), the empirical global pressure and temperature model (GPT), the Berg atmosphere model and meteorological observations acquired in-situ or in the vicinity of the site. While Vienna Mapping Functions 1 and atmosphere loading corrections are applied and kept constant during the analysis, zenith delay and thermal deformation models are considered separately. Comparing the Helmert parameters estimated between the different TRF solutions, the rotations and translations do not significantly differ when applying pressure data of various sources, but the scale varies up to 0.32 ppb. The time series of vertical station positions can show significant variations in the range of ± 5 mm. Antenna thermal deformations driven by temperature cause annual scale variations of up to 0.6 ppb. Source position differences stay at the 0.1 mas level. We recommend the application of homogeneous in-situ meteorological observations, for the determination of the TRF and in particular, zenith delay and vertical station position time series.

We have made an attempt to link Universal time 1 (UT1) variation with the pressure gradient in the upper atmosphere. These two regimes are linked via the geostrophic relation. We also introduce an index for the pressure gradient and check its feasibility for describing length-of-day (LOD) variation. Since we can easily obtain a rough picture of the atmospheric pressure field from daily weather charts, this method enables us to interpret the UT1 events in terms of the pressure field of the atmosphere. The obtained index shows a strong correlation with the AAM functions; this index can be used to estimate the UT1 variation. This method may be used to monitor the atmospheric conditions from geodetic observations.

The precession and nutation model IAU 2000 is based on the ‘‘ecliptic in the inertial sense’’, whereas former precession models referred to the ‘‘ecliptic in the rotational sense’’. The kinematical relationships between these two ecliptics are analysed. The ‘‘conventional ecliptic’’ is found by an adjustment of the position vector of the Earth-Moon barycentre so that it is always lying in this plane which has only a secular rotation. It also contains the time derivative of the adjusted position vector relative to the conventional ecliptic, but not the one relative to an inertial system. The ‘‘true ecliptic’’, which is spanned by the adjusted position vector and its time derivative relative to an inertial system, rotates not only secularly, but also periodically with a half-year period. Splitting off the periodic parts leads to the ‘‘mean ecliptic’’, which rotates purely secularly, but contains only approximately the adjusted position vector and velocity vector of the Earth-Moon barycentre. The conventional ecliptic is the ‘‘ecliptic in the rotational sense’’, and the mean ecliptic is the ‘‘ecliptic in the inertial sense’’. The relative orientation between the conventional and mean ecliptics is derived in accordance with formulae given by Standish (1981).

The Earth Orientation Center of the IERS, located at Paris Observatory, SYRTE, has the task to provide to the scientific community the international reference time series for the Earth Orientation Parameters (EOP), referred as ”IERS C04” (Combined 04), resulting from a combination of operational EOP series, each of them associated with a given geodetic technique. The procedure developed to derive the C04 solution was recently upgraded for several reasons: first we have implemented the new IAU2000 conventions; secondly it has been necessary to re-align the solution to improve its consistency with respect to the ITRF. Due to the separate determination of both celestial and terrestrial reference frames and EOP, there has been a slow degradation of the overall consistency and discrepancies at the level of 300 micro-arc-seconds were existing between the current IERS C04 and the ITRF realization. We have taken this opportunity to upgrade the numerical combination procedure; improvements concern in particular routines, tables dimensions, generalized double precisions. Using the combined polar motion solution associated with the newly release International Terrestrial Reference Frame 2005 (ITRF 2005), we produce a better solution including estimates of the errors of combined values. Individual EOP series have been reprocessed since 1984. Pole coordinates are now fully consistent with ITRF. The nutation offsets and UT1 are made consistent with the International Celestial Reference Frame (ICRF). The new C04 solution, referred as 05 C04, updated two times per week became the offcial C04 solution since October 2007.

The present paper proposes to define a global vertical reference system based in two components: a geometricalone, given by a level ellipsoid as a reference surface and ellipsoidal heights as coordinates, and a physical one, defined by a fixed W ₀ value as zero height level and geopotential numbers as coordinates. The global W ₀ value is estimated by solving the fixed gravimetric geodetic boundary value problem (GBVP) on marine areas, whereas the local reference levels W₀j existing on continents are determined by solving the free gravimetric GBVP. The relationship between W ₀ and the different W₀jis determined in three approaches: at the reference points (mainly tide gauges) of the classical height datums, on the marine areas closed to the tide gauges, and at fiducial stations of the terrestrial reference frame ITRF. The realization of the new vertical reference system is appointed as a global set of very good (reproducible) benchmarks referred to the ITRS/ITRF and with known geopotential numbers and anomalous potential values. The transformation into physical heights (orthometric or normal heights) and the introduction of the corresponding reference surface (geoid or quasigeoid) are then carried out as the last step in the vertical data analysis.

GPS Gravity-potential Leveling (GGL), a method of determining heights above sea level, is proposed in this paper. The method determines gravity potential and, in turn, heights above sea level of a point using GPS positioning, integrated with a geopotential model. Initial results show that the accuracy is attainable with 0.5m for the heights above MSL and with a few cm for the height differences above MSL over a distance up to several tens of kilometers. The error of geopotential modeling is the major error source of the heights above MSL, whereas the error of geodetic height difference obtained by GPS is the limiting factor on the accuracy of the normal height differences above MSL over a short distance.

DGFI participates in the IGS TIGA Project by i) operating continuously observing GPS stations at six tide gauges in the Atlantic Ocean and ii) processing a network of about sixty GNSS sites as a TIGA Analysis Centre. The weekly processing of this network results in a seven years time series of station coordinates starting in January 2000, and a multi year solution (DGF07P01-TIGA) of epoch station coordinates with linear velocities. The vertical velocities derived from GPS at coastal sites are analyzed together with sea level trends derived from tide gauge records to distinguish sea level variations from vertical crustal movements. This procedure is complemented by including the sea surface trend obtained from satellite altimetry in the marine areas surrounding the tide gauge sites. The absolute sea level trends derived from satellite altimetry data and from the combination of GPS positioning and tide gauge records are in a good agreement. These results should be applied to refer the local mean sea levels (which realize the reference level of classical height datums) to a global reference surface W0.

Few benchmarks of the Brazilian Fundamental Vertical Network (BFVN) have measured gravity values. While its leveling lines have been established since 1945 with approximately the same technical specifications, different institutions performed gravity surveys with different standards. To improve the BFVN aiming its connection with a “world height system”, studies were started in 1995 focusing on the area of the Brazilian Vertical Datum. Since 2004 the lack of gravity data and other particular aspects of BFVN were included in those investigations, as well as the integration of satellite altimetry data as a way to evaluate the BFVN at some selected tide gauges. The first step of the work was the definition of procedures for integrating gravity values into the BFVN. This led to selecting a test area where recent leveling lines are entirely covered by fairly homogeneous gravity surveys from the same institution, allowing for investigations on methods for gravity interpolation, and the resulting error propagation from leveling and gravity data into geopotential numbers. Parallel efforts were performed to collect and analyse gravity data from other institutions, resulting in the detection of some systematic discrepancies.

The new Finnish height system N2000 is based on the third levelling of Finland (1978–2006). The datum is the Normaal Amsterdams Peil (NAP), the same as for the European Vertical Reference Frame 2000 (EVRF2000). All levelling is corrected for vertical motion to the epoch 2000.0. The zero system for the permanent tide is used. Geopotential numbers are converted to normal heights.Much of the work defining the N2000 was done in Nordic cooperation within the Working Group for Height Determination of the Nordic Geodetic Commission (NKG). In 2002 the General Assembly of the NKG accepted a resolution, which emphasize that it is desirable that the Nordic countries “adopt [height] systems with minimal differences from each other and from the European Vertical Datum”. Now, the N2000 and the new Swedish height system RH 2000 derive their datums from the NAP using the Baltic Levelling Ring (Mäkinen et al., 2006). They also use the same land uplift model NKG2005LU (a.k.a. RH 2000 LU) to correct for the postglacial rebound (PGR). At the Swedish-Finnish boundary the differences between RH 2000 and N2000 are millimetres only.The National Datum Point for N2000 is located at Metsähovi. Geopotential number for this bench mark was derived from the NAP with the Finnish adjustment of the Baltic Levelling Ring (BLR/FI). The solution of Baltic Levelling Ring made by the working group for Height Determination of the NKG is called in this paper BLR2000. The N2000 heights are determined by adjusting the Finnish levelling, together with the adjoining loops of the BLR/FI in Sweden and Norway.

For many modern regional geoid and quasigeoid models accuracies of one or a few centimeters are given. Validation of these models, however, is often difficult due to the lack of independent data. In a test area of the Bavarian Alps, Germany, with dense data coverage, we carry out validation experiments using GPS, levelling and astrogeodetic observations as well as state-of-the-art regional quasigeoid models. The data cover very rough terrain and mountain peaks. We find a good mutual agreement with a typical scatter of height residuals of 1 – 2 cm. In some areas, however, systematic residual mean values of several centimeters are obtained which are possibly due to residual quasigeoid errors or due to a weak tie to the GPS reference frame.

In this paper we propose the use of the modip (instead of the geomagnetic) latitude for both: i) to compute Global Ionospheric Maps (GIMs) of vertical Total Electron Content (vTEC) based on GNSS observations; and ii) to validate those maps by means of comparisons to other vTEC sources of information, as TOPEX/Poseidon. We show several examples that indicate that mis-model problems of GIMs are both: i) better identified if the differences between the vTEC coming from different sources of information (GPS and TOPEX in this case) are analyzed in terms of the modip latitude; and ii) reduced by modeling the vTEC variability in terms of the modip latitude.

State-of-the-art modelling of the neutral atmosphere delays in GNSS (Global Navigation Satellite Systems), VLBI (Very Long Baseline Interferometry), and DORIS (Doppler Orbitography by Radiopositioning Integrated on Satellite) analyses requires information about the a priori hydrostatic zenith delays (or the pressure values, respectively) and the hydrostatic and wet mapping functions at the sites. We compare empirical models for the pressure (Global Pressure and Temperature, GPT) and for troposphere mapping functions (Global Mapping Functions, GMF) with discrete time series derived from numerical weather models for the hydrostatic zenith delays and mapping functions (Vienna Mapping Functions 1, VMF1) in terms of accuracy, precision and availability for the radio space geodetic techniques. Unlike prior models which have large deficiencies at around Antarctica, the empirical GPT does not cause significant station height biases, but the degradation of station height standard deviations when using the empirical models GPT and GMF instead of the discrete time series from the numerical weather models is by about 3 mm at the equator and 6 mm at ± 60° latitude.