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Abstract

Every few years the International Terrestrial Reference System (ITRS) Center of the International Earth Rotation and Reference Systems Service (IERS) decides to generate a new version of the International Terrestrial Reference Frame (ITRF). For the upcoming ITRF2014 the official contribution of the International VLBI Service for Geodesy and Astrometry (IVS) comprises 5796 combined sessions in SINEX file format from 1979.6 to 2015.0 containing 158 stations, overall. Nine AC contributions were included in the combination process, using five different software packages. Station coordinate time series of the combined solution show an overall repeatability of 3.3 mm for the north, 4.3 mm for the east and 7.5 mm for the height component over all stations. The minimum repeatabilities are 1.5 mm for north, 2.1 mm for east and 2.9 mm for height. One of the important differences between the IVS contribution to the ITRF2014 and the routine IVS combination is the omission of the correction for non-tidal atmospheric pressure loading (NTAL). Comparisons between the amplitudes of the annual signals derived by the VLBI observations and the annual signals from an NTAL model show that for some stations, NTAL has a high impact on station height variation. For other stations, the effect of NTAL is low. Occasionally other loading effects have a higher influence (e.g. continental water storage loading). External comparisons of the scale parameter between the VTRF2014 (a TRF based on combined VLBI solutions), DTRF2008 (DGFI-TUM realization of ITRS) and ITRF2008 revealed a significant difference in the scale. A scale difference of 0.11 ppb (i.e. 0.7 mm on the Earth’s surface) has been detected between the VTRF2014 and the DTRF2008, and a scale difference of 0.44 ppb (i.e. 2.8 mm on the Earth’s surface) between the VTRF2014 and ITRF2008. Internal comparisons between the EOP of the combined solution and the individual solutions from the AC contributions show a WRMS in X- and Y-Pole between 40 and 100 µas and for dUT1 between 5 and 15 µs. External comparisons with respect to the IERS-08-C04 series show a WRMS of 132 and 143 µas for X- and Y-Pole, respectively, and 13 µs for dUT.

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... The DGFI model is based on the combination of the NEQs free from additional constraints. The VLBI Solution Independent Exchange (SINEX) files contain normal equation systems free from datum constraints and resulting from a combination of the Analysis Centers' (ACs) contributions at the NEQ level [21]. Therefore, DGFI-TUM directly stacks VLBI time series of NEQs to generate a multi-year normal equation system [14,22]. ...
... In algebraic terms, minimum constraints can complete the NEQ rank deficiency of long-term solutions and not more [8]. Moreover, when we check the VLBI minimum constraint solution (input solutions to ITRF2014 [21] and the long-term solutions produced in this work), the origin and orientation are indeed expressed in an a priori reference frame. Therefore, the minimum constraints do not affect the scale information of VLBI observations.Based on the above analysis, we believe that internal constraints may affect the datum of long-term solutions obtained from the intra-technical combination. ...
... Similarly, the orientation constraints implemented by these two constraints are also equivalent, only considering columns 5, 6, and 7 of the matrix A. We checked the VLBI minimum constraint solution (input solutions to ITRF2014 [21] and the long-term solutions produced in this work), with the results showing that the origin and orientation datum defined by the minimum constraint conform to the kinematic constraints. ...
Article
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Given that the observations from current space geodetic techniques do not carry all the necessary datum information to realize a Terrestrial Reference System (TRS), and each of the four space geodetic techniques has limits, for instance: Very Long Baseline Interferometry (VLBI) ignores the center of mass and satellite techniques lack the TRS orientation, additional constraints have to be added to the observations. This paper reviews several commonly used constraints, including inner constraints, internal constraints, kinematic constraints, and minimum constraints. Moreover, according to their observation equations and normal equations, the similarities and differences between them are summarized. Finally, we discuss in detail the influence of internal constraints on the scale of VLBI long-term solutions. The results show that there is a strong correlation between the scale parameter and the translation parameter introduced by the combination model at the Institut National de l’Information Géographique et Forestière (IGN), and internal constraints force these two groups of parameters to meet certain conditions, which will lead to the coupling of scale and translation parameters and disturbing the scale information in VLBI observations. The minimum or kinematic constraints are therefore the optimum choices for TRF.
... The combination process itself has been described in several publications, e.g., [5] and [2]. The underlying hypotheses of the combination approach is that improved statistics for a combined solution compared to the individual solutions are expected. ...
... This static approach has been replaced by a dynamic approach using the Least Median of Square method (LMS) described in detail in [2]. Based on normal equations with identical epochs and identical a priori values, the individual solution for each AC is generated. ...
Conference Paper
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Starting with the ITRF2005, the IVS contribution to the ITRF is an intra-technique combined solution using multiple individual contributions from different institutions. For the IVS contribution to the ITRF2014 nine international institutions were used for a combined solution. The data files contain 24-h VLBI sessions from the late 1970s until the end of 2014. 5796 combined sessions in SINEX file format containing datum free normal equations with station coordinates and Earth Orientation Parameters (EOP) have been contributed to the ITRF2014. The overall repeatability for station coordinate time series of the combined solution are 3.3 mm for the north, 4.3 mm for the east and 7.5 mm for the height component over all stations. The minimum repeatabilities are 1.5 mm for north, 2.1 mm for east and 2.9 mm for height. A scale difference of 0.11 ppb (i.e. 0.7 mm on the Earth’s surface) has been detected between the VTRF2014 and the DTRF2008 (DGFI-TUM realization of ITRS), and a scale difference of 0.44 ppb (i.e. 2.8 mm on the Earth’s surface) between the VTRF2014 and ITRF2008. Internal comparisons between the EOP of the combined solution and the individual solutions from the AC contributions show a WRMS in X- and Y-Pole between 40 and 100 µas and for dUT1 between 5 and 15 µs. External comparisons with respect to the IERS-08-C04 series show a WRMS of 132 and 143 µas for X- and Y-Pole, respectively, and 13 µs for dUT.
... The median values are 8.2 mm for the up, 2.7 mm for the east and 3.4 mm for the north component. These results are in line with the IVS contribution to ITRF2014 (Bachmann et al. 2016). ...
... We have not found significant improvement on VLBI repeatabilities in CONT17 legacy-1 network with regard to the values reported by Bachmann et al. (2016) in the IVS input to ITRF2014. Median values of coordinates repeatability for all the solutions analysed for the legacy-1 network are very similar for VLBI and GNSS in north and east components but the up component is worse in VLBI solutions (8.2 mm) than GNSS (5.5 mm). ...
Article
CONT17 is an observation campaign of continuous Very Long Baseline Interferometry (VLBI) sessions for a period of 15 days, carried out by the International VLBI Service for Geodesy and Astrometry (IVS). This campaign represents an interesting opportunity for the inter-comparison of space geodetic techniques given that they share the same observability conditions in co-located sites. In this work, VLBI estimates of Earth orientation parameters (EOP), station coordinates and troposphere—zenith total delays (ZTD) and gradients—are compared to those estimated by means of Global Navigation Satellite Systems (GNSS) observations. We considered solutions from different software packages and processing techniques for this analysis, including all the available IVS and IGS (International GNSS Service) solutions and two VLBI series obtained by the authors. This extensive analysis provides a representative view of the inter-technique differences under the same observation conditions. We considered in the analysis the two VLBI legacy S/X networks that took part in the CONT17 campaign. We found that the EOP WRMS with respect to IGS final products is similar to previous CONT campaigns, even using global VLBI solutions that assimilate the data from both CONT17 legacy-1 and legacy-2 networks. Repeatabilities of estimated VLBI antenna coordinates of the legacy-1 network have a similar behaviour than GNSS-based repeatabilities in east and north components and slightly worse in up component whereas the repeatabilities of the legacy-2 network are smaller than legacy-1 network and similar to the IGS combined solution. Finally, troposphere inter-technique differences in terms of ZTD and gradients also show a similar agreement to different sources of GNSS-based troposphere estimates.
... ITRF2008 is 0.44 ppb and w.r.t. DTRF2008 is 0.11 ppb [14], enforces this assumption. ...
... The terrestrial datum was realized with no-net-rotation/no-nettranslation (NNR/NNT) conditions on the stations contained in the VTRF2014 catalog [14], the celestial with a NNR condition on the ICRF2 defining sources. In case of ITRF2008, the stations not contained (f.ex. ...
Article
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Currently three up-to-date Terrestrial Reference Frames (TRF) are available, the ITRF2014 from IGN, the DTRF2014 from DGFI-TUM, and JTRF2014 from JPL. All use the identical input data of space-geodetic station positions and Earth orientation parameters, but the concept of combining these data is fundamentally different. The IGN approach is based on the combination of technique solutions, while the DGFI is combining the normal equation systems. Both yield in reference epoch coordinates and velocities for a global set of stations. JPL uses a Kalman filter approach, realizing a TRF through weekly time series of geocentric coordinates. As the determination of the CRF is not independent of the TRF and vice versa, the choice of the TRF might impact on the CRF. Within this work we assess this effect. We find that the estimated Earth orientation parameter (EOP) from DTRF2014 agree best with those from ITRF2014, the EOP resulting from JTRF2014 show besides clear yearly signals also some artifacts linked to certain stations. The estimated source position time series however, agree with each other better than ±1μas. When fixing EOP and station positions we can see the maximal effect of the TRF on the CRF. Here large systematics in position as well as proper motion arise. In case of ITRF2008 they can be linked to the missing data after 2008. By allowing the EOP and stations to participate in the adjustment, the agreement increases, however, systematics remain.
... The processing of the single-session VLBI data within this study is mostly identical to what was performed for GFZ's submission to ITRF2014, but the time span was extended until mid-2016. The quality of the GFZ solution was evaluated by the IVS Combination Center and subsequently included in the IVS contribution to ITRF2014 (Bachmann et al. 2016). A comparison of VLBI TRF solutions based on the single-session analysis conducted with VieVS@GFZ is presented in Nilsson et al. (2017). ...
... While consistently positive before 2014, they are negative after 2014, as visible in Fig. 10. The ITRF2014's scale bias of 2-4 mm w.r.t. the VLBI solutions is expected since the scale is derived from both VLBI and SLR and the magnitude is in agreement with other estimates (Bachmann et al. 2016;Altamimi et al. 2016). ...
Article
Full-text available
The Global Geodetic Observing System requirement for the long-term stability of the International Terrestrial Reference Frame is 0.1 mm/year, motivated by rigorous sea level studies. Furthermore, high-quality station velocities are of great importance for the prediction of future station coordinates, which are fundamental for several geodetic applications. In this study, we investigate the performance of predictions from very long baseline interferometry (VLBI) terrestrial reference frames (TRFs) based on Kalman filtering. The predictions are computed by extrapolating the deterministic part of the coordinate model. As observational data, we used over 4000 VLBI sessions between 1980 and the middle of 2016. In order to study the predictions, we computed VLBI TRF solutions only from the data until the end of 2013. The period of 2014 until 2016.5 was used to validate the predictions of the TRF solutions against the measured VLBI station coordinates. To assess the quality, we computed average WRMS values from the coordinate differences as well as from estimated Helmert transformation parameters, in particular, the scale. We found that the results significantly depend on the level of process noise used in the filter. While larger values of process noise allow the TRF station coordinates to more closely follow the input data (decrease in WRMS of about 45%), the TRF predictions exhibit larger deviations from the VLBI station coordinates after 2014 (WRMS increase of about 15%). On the other hand, lower levels of process noise improve the predictions, making them more similar to those of solutions without process noise. Furthermore, our investigations show that additionally estimating annual signals in the coordinates does not significantly impact the results. Finally, we computed TRF solutions mimicking a potential real-time TRF and found significant improvements over the other investigated solutions, all of which rely on extrapolating the coordinate model for their predictions, with WRMS reductions of almost 50%.
... For VLBI, some new and improved models for the IVS analysis have been applied, including a constant drift of 5.8 µas/year on Galactic aberration. Additionally, mid-sessionepoch solutions are calculated to present the best performance of VLBI, but they are transformed to 12 h to ensure the consistency with the epochs of other techniques which are submitted for establishing the ITRF [22,23]. ...
Article
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International terrestrial reference frame (ITRF) input data, generated by Global Navigation Satellite Systems (GNSS), Satellite Laser Ranging (SLR), Very Long Baseline Interferometry (VLBI), and Doppler Orbitography and Radiopositioning integrated by satellite (DORIS) combination centers (CCs), are considered to be relatively high-quality and accurate solutions. Every few years, these input data are submitted to the three ITRS combination centers, namely Institut Géographique National (IGN), Deutsches Geodätisches Forschungsinstitut at the Technische Universität München (DGFI-TUM), and Jet Propulsion Laboratory (JPL), to establish a multi-technique combined terrestrial reference frame (TRF). Generally, these solutions have undergone three rounds of outlier removal: the first at the technique analysis centers during solution generations and the second during the technique-specific combination by the CCs; ITRS CCs then perform a third round of outlier removal and preprocessing during the multi-technique combination of TRFs. However, since the primary objective of CCs is to release the final TRF product, they do not emphasize the publication of analytical preprocessing results, such as the outlier rejection rate. In this paper, our specific focus is on assessing the precision improvement of ITRF input data from 2014 to 2020, which includes evaluating the accuracy of coordinates, the datum accuracy, and the precision of the polar motions, for all four techniques. To achieve the above-mentioned objectives, we independently propose a TRF stacking approach to establish single technical reference frameworks, using software developed by us that is different from the ITRF generation. As a result, roughly 0.5% or less of the SLR observations are identified as outliers, while the ratio of DORIS, GNSS, and VLBI observations are below 1%, around 2%, and ranging from 1% to 1.2%, respectively. It is shown that the consistency between the SLR scale and ITRF has improved, increasing from around −5 mm in ITRF2014 datasets to approximately −1 mm in ITRF2020 datasets. The scale velocity derived from fitting the VLBI scale parameter series with all epochs in ITRF2020 datasets differs by approximately 0.21 mm/year from the velocity obtained by fitting the data up to 2013.75 because of the scale drift of VLBI around 2013. The decreasing standard deviations of the polar motion parameter (XPO, YPO) offsets between Stacking TRFs and 14C04 (20C04) indicate an improvement in the precision of polar motion observations for all four techniques. From the perspective of the weighted root mean square (WRMS) in station coordinates, since the inception of the technique, the station coordinate WRMS of DORIS decreased from 30 mm to 5 mm for X and Y components, and 25 mm to 5 mm for the Z component; SLR WRMS decreased from 20 mm to better than 10 mm (X, Y and Z); GNSS WRMS decreased from 4 mm to 1.5 mm (X and Y) and 5 mm to 2 mm (Z); while VLBI showed no significant change.
... Additionally, mid-session-epoch solutions are calculated to present the best performance of VLBI, but they are transformed to 12-hour to ensure the consistency with the epochs of other techniques which are submitted for establishing the ITRF. [20,21]. ...
Preprint
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ITRF input data which are integrated by GNSS, SLR, VLBI, DORIS combination centers are considered to be relatively high-quality and accurate solutions. However, when utilizing these inputs, one still needs to identify outliers, rescale inaccurate covariance matrix and evaluate the precision of the observed datum information. To achieve the above-mentioned objectives, we propose a terrestrial reference frame (TRF) stacking approach to establish the single technical reference frameworks for the ITRF2014 and ITRF2020 datasets of all four technologies. As a result, roughly 0.5% or less of the SLR observations are identified as outliers, while the ratio of DORIS, GNSS, and VLBI observations are below 1%, around 2%, and ranging from 1% to 1.2%, respectively. The post-rescaling covariance scale factors are 25.07, 27.25, 18.84, 6.98 for GNSS, SLR, VLBI, and DORIS in ITRF2014 datasets, and 8.95, 14.9, 16.8, 7.78 in ITRF2020 datasets, respectively. It is shown that the consistency between the SLR scale and ITRF has improved, increasing from around -5mm in ITRF2014 datasets to approximately -1mm in ITRF2020 datasets. The scale velocity derived from fitting the VLBI scale parameter series with all epochs in ITRF2020 datasets differs by approximately 0.21mm/year from the velocity obtained by fitting the data up to 2013.75 because of the scale drift of VLBI at around 2013. The decreasing standard deviations of the Polar motion parameter (XPO, YPO) offsets between Stacking TRFs and 14C04 (20C04) indicating an improvement in the precision of polar motion observations for all of the four techniques. From the perspective of the Weighted Root Mean Square in station coordinates, the measurement precision of GNSS, SLR, and DORIS techniques has improved, while VLBI shows no significant change.
... This group consists of scientists from Deutsches Geodätisches Forschungsinstitut (DGFI-TUM) at the Technical University of Munich, Federal Agency for Cartography and Geodesy (BKG), Chair of Satellite Geodesy at the Technical University of Munich, Research Group Advanced Geodesy at the Technical University of Vienna, and the Earth System Modelling group at the Helmholtz Centre Potsdam GFZ German Research Centre for Geosciences (ESMGFZ). The work is in particular based on previous experience gained at DGFI-TUM as an IERS ITRS Combination Center (Seitz et al., 2012), and at BKG which is operating the IVS Combination Center jointly together with DGFI-TUM (Bachmann et al., 2016). ...
Article
Full-text available
Different Earth orientation parameter (EOP) time series are publicly available that typically arise from the combination of individual space geodetic technique solutions. The applied processing strategies and choices lead to systematically differing signal and noise characteristics particularly at the shortest periods between 2 and 8 days. We investigate the consequences of typical choices by introducing new experimental EOP solutions obtained from combinations at either normal equation level processed by Deutsches Geodätisches Forschungsinstitut at the Technical University of Munich (DGFI‐TUM) and Federal Agency for Cartography and Geodesy (BKG), or observation level processed by European Space Agency (ESA). All those experiments contribute to an effort initiated by ESA to develop an independent capacity for routine EOP processing and prediction in Europe. Results are benchmarked against geophysical model‐based effective angular momentum functions processed by Helmholtz Centre Potsdam GFZ German Research Centre for Geosciences (ESMGFZ). We find, that a multitechnique combination at normal equation level that explicitly aligns a priori station coordinates to the ITRF2014 frequently outperforms the current International Earth Rotation and Reference Systems Service (IERS) standard solution 14C04. A multi‐Global Navigation Satellite System (GNSS)‐only solution already provides very competitive accuracies for the equatorial components. Quite similar results are also obtained from a short combination at observation level experiment using multi‐GNSS solutions and SLR from Sentinel‐3A and Sentinel‐3B to realize space links. For ΔUT1, however, very long baseline interferometry (VLBI) information is known to be critically important so that experiments combining only GNSS and possibly SLR at observation level perform worse than combinations of all techniques at normal equation level. The low noise floor and smooth spectra obtained from the multi‐GNSS solution nevertheless illustrates the potential of this most rigorous combination approach so that further efforts to include in particular VLBI are strongly recommended.
... Table 1 shows more details of these unequally spaced time series whose measurements (24-hour long observing sessions) are associated with standard deviations (error bars). The baseline data were analyzed during the combination process, and so the same epoch and equal constraints were used for each session (Bachmann et al. 2015(Bachmann et al. 2016. ...
Article
Full-text available
Extensive least-squares wavelet and cross-wavelet analyses are performed on the Very Long Baseline Interferometry (VLBI) baseline length and temperature time series for a network of four VLBI antennas located in different continents. These analyses do not rely on any pre-processing of the measurements including interpolations or gap-filling, and they can provide accurate instantaneous frequency information along with phase differences in the time-frequency domain. Out of four antennas mounted in Fortaleza, Hartebeesthoek, Westford, and Wettzell, the most and the least possibly impacted VLBI time series by the annual temperature variation are Westford-Wettzell and Fortaleza-Hartebeesthoek, respectively. Furthermore, the annual components of the temperature time series in Westford and Wettzell lead the ones in the corresponding VLBI time series by nearly one month, where one of the baseline sides is either in Westford or Wettzell.
... Geodetic very long baseline interferometry (VLBI) is a space geodetic technique that is of major importance (Bachmann et al., 2016) for the International Terrestrial Reference Frame (ITRF) (Altamimi et al., 2016). The ITRF is the most precise and accurate realization of a global geodetic reference frame (GGRF) that is needed by the scientific community as well as society as large. ...
Preprint
We present results from observation, correlation and analysis of interferometric measurements between the three geodetic very long baseline interferometry (VLBI) stations at the Onsala Space Observatory. In total 23 sessions were observed in 2019 and 2020, most of them 24 hours long, all using X band only. These involved the legacy VLBI station ONSALA60 and the Onsala twin telescopes, ONSA13NE and ONSA13SW, two broadband stations for the next generation geodetic VLBI global observing system (VGOS). We used two analysis packages: ν\nuSolve to compare group- and phase-delay parameter estimation, and ASCOT to investigate e.g. the impact of thermal and gravitational deformation of the radio telescopes. Station positions obtained from group-delay analysis with the two software packages agree within 2σ\sigma for all components of both stations. We obtained weighted root mean square postfit residuals on the order of 10-15 ps using group delays ( ASCOT and ν\nuSolve ) and 3-5 ps using phase delays (ν\nuSolve). The best performance was achieved on the (rather short) baseline between the VGOS stations. As the main result of this work we determined the coordinates of the Onsala twin telescopes in VTRF2019D with sub-millimeter precision. This new set of coordinates should be used from now on for scheduling, correlation and as a priori for data analyses e.g. for the upcoming ITRF2020. We also find a systematic offset between the group- and phase- delay solutions from nuSolve, suggesting the phase-delay implementation needs additional testing.
... Der Vorteil von kombinierten Produkten im Vergleich zu den einzelnen Analyseprodukten liegt in verbesserter Stabilität und Genauigkeit, höherer Ausfallsicherheit und einer gleichwertigen Behandlung der einzelnen IVS-Analyseergebnisse. Zusätzlich zu den Routineauswertungen ist das IVS-Kombinationszentrum verantwortlich für den IVS-Beitrag zum ITRF (siehe auchBachmann et al., 2016), der im Abstand von 4-5 Jahren neu berechnet wird. Das BKG hat das IVS-Kombinationszentrum 2008 in Kooperation mit dem Deutschen Geodätischen Forschungsinstitut (DGFI-TUM) übernommen und seither die Produktpalette stetig erweitert. ...
Article
The importance of global satellite navigation systems for everyday life and for numerous surveying tasks is well known to every user. Wherever positioning or navigation tasks are involved, GNSS devices for the use of GPS, GLONASS, Galileo or Beidou are used, which provide coordinates in a reference frame of a global geodetic reference system. What is less known is the elementary activities of the Federal Agency for Cartography and Geodesy (BKG) in global geodesy. The activities are integrated into international cooperation projects, which are primarily coordinated by the International Association of Geodesy (IAG) and its components. - Published in: VDV-Magazin : Geodäsie und Geoinformatik (ISSN 1863-1320) (2020) No. 5, p. 378-388. Online version: https://www.bkg.bund.de/SharedDocs/Downloads/BKG/DE/Downloads-Wettzell/Artikel-2020.html
... Geodetic very long baseline interferometry (VLBI) is a space-geodetic technique with a long tradition of realizing terrestrial (Bachmann et al. 2016) and celestial reference systems (Fey et al. 2009), and uniquely providing the full set of Earth orientation parameters (EOP) that relate those two systems . Observations of radio emission from very distant natural radio sources, objects commonly referred to as quasars, are the basis of geodetic VLBI. ...
Article
Full-text available
Recent efforts of tracking low Earth orbit and medium Earth orbit (MEO) satellites using geodetic very long baseline interferometry (VLBI) raise questions on the potential of this novel observation concept for space geodesy. Therefore, we carry out extensive Monte Carlo simulations in order to investigate the feasibility of geodetic VLBI for precise orbit determination (POD) of MEO satellites and assess the impact of quality and quantity of satellite observations on the derived geodetic parameters. The MEO satellites are represented in our study by LAGEOS-1/-2 and a set of Galileo satellites. The concept is studied on the basis of 3-day solutions in which satellite observations are included into real schedules of the continuous geodetic VLBI campaign 2017 (CONT17) as well as simulated schedules concerning the next-generation VLBI system, known as the VLBI Global Observing System (VGOS). Our results indicate that geodetic VLBI can perform on a comparable level as other space-geodetic techniques concerning POD of MEO satellites. For an assumed satellite observation precision better than 14.1 mm (47 ps), an average 3D orbit precision of 2.0 cm and 6.3 cm is found for schedules including LAGEOS-1/-2 and Galileo satellites, respectively. Moreover, geocenter offsets, which were so far out of scope for the geodetic VLBI analysis, are close to the detection limit for the simulations concerning VGOS observations of Galileo satellites, with the potential to further enhance the results. Concerning the estimated satellite orbits, VGOS leads to an average precision improvement of 80% with respect to legacy VLBI. In absolute terms and for satellite observation precision of 14.1 mm (47 ps), this corresponds to an average value of 17 mm and 7 mm concerning the 3D orbit scatter and precision of geocenter components, respectively. As shown in this study, a poor satellite geometry can degrade the derived Earth rotation parameters and VLBI station positions, compared to the quasar-only reference schedules. Therefore, careful scheduling of both quasar and satellite observations should be performed in order to fully benefit from this novel observation concept.
... The combination is performed session-wise on the normal equation level using the contributions provided by the IVS ACs. The analysis and combination procedure used here is similar to that applied to the operational IVS combination (seeBachmann et al., 2016). The detailed combination process is shown inFigure 1. ...
Book
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This IERS Technical Note includes the description of DTRF2014 and JTRF2014, as well as their inter-comparisons with respect to the official IERS solution, the ITRF2014. It comprises also evaluations of the three solutions by the IERS Technique Centers (IDS, IGS, ILRS and IVS) who constantly provide input solutions to the ITRF. In addition to DGFI, JPL and ITRS Center contributions, the Technical Note includes contributions from IDS, ILRS and IVS.
... The full set of ERPs is estimated from a daily combination of VLBI Intensive and GNSS Final NEQ systems. This approach is already used at BKG in the framework of the IVS Combination Centre ( Bachmann et al., 2016;Bachmann and Thaller, 2017). In a first step, the NEQ systems from both techniques are transformed to common epochs. ...
Article
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The Earth Orientation Parameters (EOPs) are published by the Earth Orientation Centre of the International Earth Rotation and Reference Systems Service (IERS). They are provided as the low-latency Bulletin A and the 30 d latency long-term EOP time series IERS 14 C04. The EOPs are a combined product derived from different geodetic space techniques, namely Global Navigation Satellite Systems (GNSS), Satellite Laser Ranging (SLR) and Lunar Laser Ranging (LLR), Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS) and Very Long Baseline Interferometry (VLBI). Since not all techniques are equally sensitive to every EOP, several parameters rely on specific observation techniques. As an example, dUT1 can only be estimated from VLBI observations. This means VLBI is an essential part of the estimation procedure for consistent EOPs. Within this paper, we are performing a combination of two low-latency space geodetic techniques as they enable the estimation of the full set of Earth Rotation Parameters (ERPs; polar motion, dUT1 and the corresponding rates). In particular, we focus on the development of a robust combination scheme of 1 h VLBI Intensive sessions with so-called GNSS Rapid solutions on the normal equation level of the Gauß-Markov model. The aim of the study is to provide highly accurate low-latency ERPs. So far, a latency of approximately only 1–3 d cold be reached since the main limiting factor is still the latency of the input data. The mathematical background of the applied algorithm is discussed in detail and evaluated by numerical results of empirical investigations. The combination yields a numerical stabilization of the equation system as well as an improvement (reduction) of the corresponding root mean square deviation of the epoch-wise estimated parameters w.r.t. the IERS 14 C04 reference time series.
... Fig. 7 The time series of station coordinates with respect to SLRF2014 for two example SLR stations: Baikonur (Kazakhstan, 1887) and Wettzell (Germany,8834) SLR and VLBI techniques are used for the scale realization in ITRF. In ITRF2014, the scale discrepancy between the two techniques is at the level of 7-8 mm, which constitutes currently a subject of discussions and investigations in both the SLR and VLBI scientific communities (Bachmann et al. 2016;Appleby et al. 2016). In this solution, the mean scale offset and standard deviations equal 6.1 ± 3.1 mm, 5.7 ± 3.2 mm, and 5.2 ± 2.7 mm in LAGEOS-1/2 (Solution 5), LAGEOS + GNSS (Solution 6), and LAGEOS + GNSS with fixed orbits (Solution 7), respectively. ...
Article
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All Galileo, GLONASS, QZSS, and BeiDou satellites are equipped with laser retroreflector arrays dedicated to satellite laser ranging (SLR). Using SLR data to new GNSS systems allows for estimating global geodetic parameters, such as Earth rotation parameters, global scale, and geocenter coordinates. In this study, we evaluate the quality of global geodetic parameters estimated on a basis of SLR tracking of new GNSS satellites and the combined solution based on SLR observations to GNSS and LAGEOS. We show that along with a progressive populating of Galileo orbital planes, the quality of geocenter components based on SLR-GNSS data has been improved to the level of 6 and 15 mm for equatorial and polar geocenter components, respectively. The scale of the reference frame and the geocenter coordinates in the combined LAGEOS + GNSS solutions are dominated by the LAGEOS data. Some noncore SLR stations provide by far more observations to GNSS than to LAGEOS, e.g., Russian and Chinese stations dedicated to supporting GLONASS and BeiDou constellations. The number of solutions for these stations can be increased by up to 40%, whereas the station coordinate repeatability can be improved from about 20-30 mm to the level of 15-20 mm when considering both SLR to LAGEOS and SLR to GNSS.
... In the following, we describe the four sets of data used in the weekly inter-technique combination. The input space geodesy solutions here are provided on a weekly basis by the IAG International Services of satellite techniques: ILRS, IGS and IDS (Valette et al. 2010), and on a daily (VLBI session-wise) basis by the IVS (Bachmann et al. 2016). Each per-technique time series is already a combination of the individual Analysis Center solutions of that technique. ...
Article
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Constructing and maintaining a stable terrestrial reference frame (TRF) is one of the key objectives of fundamental astronomy and geodesy. The datumrealization for all the global TRF versions, such as ITRF2014 and its predecessor ITRF2008, assumes linear time evolution for transformation parameters and then imposes some conditions on these Helmert transformation parameters. In this paper, we investigate a new approach, which is based on weekly estimation of station positions and Helmert transformation parameters from a combination of the solutions of four space-geodetic techniques, i.e., Satellite Laser Ranging (SLR), Very Long Baseline Interferometry (VLBI), Global Positioning System (GPS) and Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS). For this study, an interval of one week is chosen because the arc length of the SLR solutions is seven days. The major advantage of this weekly estimated reference frame is that both the non-linear station motions and the non-linear origin motion are implicitly taken into account. In order to study the non-linear behavior of station motions and physical parameters, ITRF2008 is used as a reference. As for datum definition of weekly reference frame, on one hand SLR is the unique technique to realize the origin and determine the scale together with VLBI, and on the other hand the orientation is realized via no net rotation with respect to ITRF2005 on a subset of core stations. Given the fact that without enough collocations an inter-technique combined TRF could not exist, the selection and relative weight of local ties surveyed at co-location sites are critical issues. To get stable results, we first assume that, if there were no events such as equipment changes between the measurement epoch of the local tie and that of the space-geodetic solution, the relative position between the two co-located stations should be invariant and this local tie could be used for computing the inter-technique combined reference frame in those weeks during the stable period of this tie. The resulting time series of both station positions and transformation parameters are studied in detail and are compared with ITRF2008. The residual station positions in the weekly combined reference frame are usually in the range of two millimeters without any periodic characteristic, but the residual station positions, when subtracting the regularized station position in ITRF2008, may reach a magnitude of a few centimeters and seem to have a significant annual signal. The physical parameter series between the weekly reference frame and ITRF2008 also show the obvious existence of an annual signal and reach a magnitude of one centimeter for origin motion and two parts per billion (ppb) for scale. © 2018 National Astronomical Observatories, CAS and IOP Publishing Ltd..
... The single session analysis followed the IERS 2010 conventions (Petit and Luzum 2010), the involved a-prioris and the models are given in Table 5. The terrestrial datum was realized with nonet-rotation/no-net-translation (NNR/NNT) conditions on the stations contained in the VTRF2014 catalog (Bachmann et al. 2016), the celestial one with a NNR condition on the ICRF2 defining sources. ...
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... The denominator of Eq. (40) is indeed dependent on the degrees of freedom r j involved in the modelling of local effects, consistent with Lucas and Dillinger (1998). The numerator of Eq. (40) may also be written on the form (Bachmann et al. 2016) ...
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... The space geodetic solutions used here were provided on a weekly basis by the IAG International Services of satellite techniques: ILRS [11], IGS [12] and IDS [13] and on a daily (VLBI sessionwise) basis by the IVS [14]. Each per-technique time series was already a combination of the individual Analysis Center (AC) solutions of that technique. ...
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Based on four intra-technique combined solutions in SINEX format, we tried at first to assess the accuracy of each single-technique Earth Orientation Parameters (EOPs) series over a past time interval of at least15 years by comparison with IERS EOP 08C04 combined solution as the reference in this paper. The EOPs studied here mainly consist of four elements, i.e. polar motion (XPO, YPO), Universal Time (UT1-UTC) and length-of-day (LOD). We combined these intra-technique EOP series, each of them associated with a given space geodetic technique by taking advantage of the relationship of the first three EOP components and three rotational parameters which carry the orientation of technique-related reference frame with respect to the estimated weekly inter-technique combined reference frame. Results indicated that the discrepancy between the pole coordinates (XPO, YPO) series, extracted from the intra-SLR combined loose-constraint solutions and the IERS EOP 08C04, seemed to be clearly characterized by systematic errors. Although both the XPO and YPO series determined by intra-VLBI combination had no significant characteristic of system error, they had relatively large difference values at some point with respect to the IERS EOP 08C04, which may be limited by the quantity of observation stations. Since the number of GPS stations is on the increase aimed at better global coverage, the accuracy of pole coordinates provided by IGS was superior to that derived from other space-geodetic techniques. As for DORIS XPO and YPO series from intra-DORIS combined minimal-constraint solutions, the discrepancy range of the former with respect to IERS EOP 08C04 was a little smaller than that of the latter. The objective of this study is twofold: on the one hand to analysis individual EOP series derived from the various space-geodetic techniques, on the other hand to present the new inter-technique combined EOP solution consistent with weekly inter-technique combined reference frame.
... The single session analysis followed the IERS 2010 conventions (Petit and Luzum 2010), the involved a-prioris and the models are given in Table 5. The terrestrial datum was realized with nonet-rotation/no-net-translation (NNR/NNT) conditions on the stations contained in the VTRF2014 catalog (Bachmann et al. 2016), the celestial one with a NNR condition on the ICRF2 defining sources. ...
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Recent improvements in the development of VLBI (very long baseline interferometry) and other space geodetic techniques such as the global navigation satellite systems (GNSS) require very precise a-priori information of short-period (daily and sub-daily) Earth rotation variations. One significant contribution to Earth rotation is caused by the diurnal and semi-diurnal ocean tides. Within this work, we developed a new model for the short-period ocean tidal variations in Earth rotation, where the ocean tidal angular momentum model and the Earth rotation variation have been setup jointly. Besides the model of the short-period variation of the Earth’s rotation parameters (ERP), based on the empirical ocean tide model EOT11a, we developed also ERP models, that are based on the hydrodynamic ocean tide models FES2012 and HAMTIDE. Furthermore, we have assessed the effect of uncertainties in the elastic Earth model on the resulting ERP models. Our proposed alternative ERP model to the IERS 2010 conventional model considers the elastic model PREM and 260 partial tides. The choice of the ocean tide model and the determination of the tidal velocities have been identified as the main uncertainties. However, in the VLBI analysis all models perform on the same level of accuracy. From these findings, we conclude that the models presented here, which are based on a re-examined theoretical description and long-term satellite altimetry observation only, are an alternative for the IERS conventional model but do not improve the geodetic results.
... Compared to Global Navigation Satellite Systems (GNSS), Satellite Laser Ranging (SLR) or Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS), geodetic VLBI is the only space-geodetic technique which allows to simultaneously determine all Earth Orientation Parameters (EOP; Sovers et al. 1998) and uniquely provides the Earth rotational phase (UT1-UTC). Geodetic VLBI is also important for the realization and the maintenance of the International Terrestrial Reference Frame (ITRF; Altamimi et al. 2016;Bachmann et al. 2016). ...
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We perform extensive simulations in order to assess the accuracy with which the position of a radio transmitter on the surface of the Moon can be determined by geodetic VLBI. We study how the quality and quantity of geodetic VLBI observations influence these position estimates and investigate how observations of such near-field objects affect classical geodetic parameters like VLBI station coordinates and Earth rotation parameters. Our studies are based on today’s global geodetic VLBI schedules as well as on those designed for the next-generation geodetic VLBI system. We use Monte Carlo simulations including realistic stochastic models of troposphere, station clocks, and observational noise. Our results indicate that it is possible to position a radio transmitter on the Moon using today’s geodetic VLBI with a two-dimensional horizontal accuracy of better than one meter. Moreover, we show that the next-generation geodetic VLBI has the potential to improve the two-dimensional accuracy to better than 5 cm. Thus, our results lay the base for novel observing concepts to improve both lunar research and geodetic VLBI.
... The main characteristics of three solutions analyzed in the present work, (namely IDS, IGS and IVS time series) are summarized in Table 1, other details can be found in paragraphs 5.1, 5.2 and 5.3. Moreaux et al. (2016), Bachmann et al. (2016) and Rebischung et al. (2015). ...
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The accuracy and stability of Very Long Baseline Interferometry (VLBI) systems are essential for maintaining global geodetic reference frames such as the International Terrestrial Reference Frame (ITRF). This study focuses on the precise determination of the VLBI Invariant Point (IVP) and the detection of antenna axis offset. Ground-based surveys were conducted at the Sejong Space Geodetic Observatory using high-precision instruments, including total station, to measure slant distances, as well as horizontal and vertical angles from fixed pillars to reflectors attached to the VLBI instrument. The reflectors comprised both prisms and reflective sheets to enhance redundancy and data reliability. A detailed stochastic model incorporating variance component estimation was employed to manage the varying precision of the observations. The analysis revealed significant measurement variability, particularly in slant distance measurements involving prisms. Iterative refinement of the variance components improved the reliability of the IVP and antenna axis offset estimates. The study identified an antenna axis offset of 5.6 mm, which was statistically validated through hypothesis testing, confirming its significance at a 0.01 significance level. This is a significance level corresponding to approximately a 2.576 sigma threshold, which represents a 99% confidence level. This study highlights the importance of accurate stochastic modeling in ensuring the precision and reliability of the estimated VLBI IVP and antenna axis offset. Additionally, the results can serve as a priori information for VLBI data analysis.
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High-precision Polar motion prediction is of great significance for deep space exploration and satellite navigation. Polar motion is affected by a variety of excitation factors, and nonlinear prediction methods are more suitable for Polar motion prediction. In order to explore the effect of deep learning in Polar motion prediction, This paper proposes a combined model based on empirical wavelet transform (EWT), Convolutional Neural Networks (CNN) and Long Short Term Memory (LSTM). By training and forecasting EOP 20C04 data, the effectiveness of the algorithm is verified, and the performance of two forecasting strategies in deep learning for Polar motion prediction is explored. The results indicate that recursive multi-step prediction performs better than direct multi-step prediction for short-term forecasts within 15 days, while direct multi-step prediction is more suitable for medium and long-term forecasts. In the 365-day forecast, the mean absolute error (MAE) of EWT-CNN-LSTM in the X direction and Y direction is 18.25mas and 15.78mas, respectively, which is 23.5\% and 16.2\% higher than the accuracy of Bulletin A. The results show that the algorithm has a good effect in medium and long term PM prediction.
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The time evolution of station positions has historically been described by piece-wise linear models in the International Terrestrial Reference Frame (ITRF). Although those models were extended with exponential and logarithmic functions in the ITRF2014 and with annual and semiannual sine waves in the ITRF2020, part of the Earth’s surface deformation is still not captured by such deterministic functions. Taking into account additional aperiodic ground deformation in the reference frame could in principle provide a better description of the shape of the Earth. This would, however, require the aperiodic displacements of the different space geodetic techniques to be tied into a common frame by means of co-motion constraints. The relevance of applying co-motion constraints to the measured aperiodic displacements raises questions because of the presence of technique-specific errors in the station position time series. In this article, we investigate whether common aperiodic displacements, other than post-seismic deformation, can be detected at ITRF co-location sites. We use for that purpose station position time series extracted from the solutions provided by the four technique services for ITRF2014 and carefully aligned to a common reference frame in order to minimize differential network effect. The time series are then cleaned from linear, post-seismic and periodic signals (including seasonal deformation and technique systematic errors). The residual time series are finally compared within ITRF co-location sites. Modest correlations are observed between Global Navigation Satellite Systems residual time series and the other space geodetic techniques, mostly in the vertical component, pointing to a domination of technique errors over common aperiodic displacements. The pertinence of applying co-motion constraints to measured aperiodic displacements is finally discussed in light of these results.
Chapter
The ITRF2020 is the upcoming official solution of the International Terrestrial Reference Frame and is the successor to the currently used ITRF2014. The global ITRF2020 solution is based on an inter-technique combination of the four space-geodetic techniques VLBI, GNSS, SLR, and DORIS. In this context, the Combination Centre of the IVS (International VLBI Service for Geodesy and Astrometry) operated by the Federal Agency for Cartography and Geodesy (BKG, Germany) in close cooperation with the Deutsches Geodätisches Forschungsinstitut at TUM (DGFI-TUM, Germany) generates the final VLBI contribution of the IVS. This is achieved by an intra-technique combination utilizing the individual contributions of multiple IVS Analysis Centres (ACs). For the IVS contribution to the ITRF2020, sessions containing 24 h VLBI observations from 1979 until the end of 2020 were re-processed by 11 different ACs and submitted to the IVS Combination Centre. As a result, datum-free normal equations containing station coordinates and source positions as well as full sets of Earth Orientation Parameters (EOP) are delivered. In order to ensure consistency of the combined solution, time series of EOP and station coordinates were generated and further investigated for validation. Finally, the IVS contribution to the ITRF2020 comprises session-wise normal equations including EOP and station coordinates provided in SINEX format. In order to assess the quality of the contributions by the individual IVS ACs, internal as well as external comparisons of the estimated EOP are carried out, with the combined solution as well as external time series (e.g., IERS Bulletin A) serving as a reference. Additionally, the scale of the IVS contribution is investigated as VLBI is one of the space geodetic techniques realizing the scale of the ITRF. The evaluation of the contributions by the ACs, the combination procedure, and the results of the combined solution for station coordinates and EOP will be presented.
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The DTRF2014 solution is the latest ITRS realization of DGFI-TUM computed in the framework of ITRF2014. It is mainly characterized by two innovations: it is the first secular ITRS realization considering non-tidal loading corrections derived from geophysical models. Secondly, the DTRF2014 release includes all information necessary to approximate the observed instantaneous station positions at any epoch of the observation time span. Therefore, besides the classical SINEX and EOP files, the applied non-tidal loading corrections, the residual time series of station positions as well as the translation time series of the DTRF2014 origin are provided. The DTRF2014 is computed from the same input as ITRF2014 comprising the full history of observation data of the four space geodetic techniques Very Long Baseline Interferometry (VLBI), Satellite Laser Ranging (SLR), Global Navigation Satellite System (GNSS), and Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS). The DTRF2014 solution is computed using the DGFI-TUM approach based on the combination of normal equation systems. With reference to the IERS Conventions, the origin of DTRF2014 is realized from SLR input data only. The scale of the DTRF2014 solution is assumed to be statistically equal for SLR and VLBI. This assumption is based on tests performed in the framework of the DTRF2014 computation showing a range for the scale offset at epoch 2000.0 of ±3.3 mm. For the GNSS and the DORIS subnetwork of the DTRF2014 solution, a weighted mean scale of SLR and VLBI is realized. Cross-validations performed between DTRF2014 and ITRF2014 show the high consistency of present ITRS realizations. For GNSS, VLBI and SLR the obtained transformation parameters range within ±1.7 mm for positions (except for the VLBI and SLR scale and the VLBI z-translation) and ±0.3 mm/yr for the velocities, the parameters for DORIS are all below 4.2 mm and 0.25 mm/yr (except for the scale rate). The RMS of the transformations, reflecting the agreement of network geometry, range between 0.55 mm for VLBI and 2.25 mm for DORIS. The RMS of station velocities is between 0.08 and 0.62 mm/yr. The DTRF2014 solution provides a high precision and reliability confirmed by various validations performed internally and by external groups. For instance, applications of DTRF2014 for a precise orbit determination (POD) of the altimetry satellite TOPEX and Jason-2 show small radial crossfit residuals between SLR and DORIS and indicate a good performance of DTRF2014.
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We present results from observation, correlation and analysis of interferometric measurements between the three geodetic very long baseline interferometry (VLBI) stations at the Onsala Space Observatory. In total, 25 sessions were observed in 2019 and 2020, most of them 24 h long, all using X band only. These involved the legacy VLBI station ONSALA60 and the Onsala twin telescopes, ONSA13NE and ONSA13SW, two broadband stations for the next-generation geodetic VLBI global observing system (VGOS). We used two analysis packages: ν Solve to pre-process the data and solve ambiguities, and ASCOT to solve for station positions, including modelling gravitational deformation of the radio telescopes and other significant effects. We obtained weighted root mean square post-fit residuals for each session on the order of 10-15 ps using group-delays and 2-5 ps using phase-delays. The best performance was achieved on the (rather short) baseline between the VGOS stations. As the main result of this work, we determined the coordinates of the Onsala twin telescopes in VTRF2020b with sub-millimetre precision. This new set of coordinates should be used from now on for scheduling, correlation, as a priori for data analyses, and for comparison with classical local-tie techniques. Finally, we find that positions estimated from phase-delays are offset ∼ + 3 mm in the up-component with respect to group-delays. Additional modelling of (elevation dependent) effects may contribute to the future understanding of this offset.
Thesis
Die Erde befindet sich in einem kontinuierlichen Wandel, der aus verschiedenen variierenden dynamischen Prozessen und einwirkenden Kräften resultiert. Die globale Erderwärmung, der Anstieg des Meeresspiegels oder tektonische Verschiebungen sind einige der globalen Phänomene, die diesen Veränderungsprozess sichtbar machen. Um diese Veränderungen besser zu verstehen, deren Ursachen zu analysieren und um geeignete Präventivmaßnahmen abzuleiten, ist ein eindeutiger Raumbezug zwingend notwendig. Der International Terrestrial Reference Frame (ITRF) als globales erdfestes kartesisches Koordinatensystem bildet hierbei die fundamentale Basis für einen eindeutigen Raumbezug, zur Bestimmung von präzisen Satellitenorbits oder zum Detektieren von Verformungen der Erdkruste. Die 2015 verabschiedete Resolution „A global geodetic reference frame for sustainable development“ (A/RES/69/266) der Vereinten Nationen (UN) verdeutlicht den hohen Stellenwert und die Notwendigkeit eines solchen globalen geodätischen Bezugssystems. Das Global Geodetic Observing System (GGOS) wurde 2003 durch die International Association of Geodesy (IAG) gegründet. „Advancing our understanding of the dynamic Earth system by quantifying our planet’s changes in space and time“ lautet die 2011 formulierte Zielsetzung, auf die alle Arbeiten von GGOS ausgerichtet sind, um die metrologische Plattform für sämtliche Erdbeobachtungen zu realisieren. Die Bestimmung eines globalen geodätischen Bezugsrahmens, der weltweit eine Positionsgenauigkeit von 1mm ermöglicht, ist eine der großen Herausforderungen von GGOS. Das Erreichen dieses Ziels setzt neben der technischen Weiterentwicklung und dem infrastrukturellen Ausbau geodätischer Raumverfahren das Identifizieren und Quantifizieren von systematischen Abweichungen sowohl im lokalen als auch im globalen Kontext voraus. Die Bestimmung eines globalen geodätischen Bezugsrahmens erfolgt durch eine kombinierte Auswertung aller geodätischen Raumverfahren. Da diese untereinander nur eine geringe physische Verknüpfung aufweisen, stellen lokal bestimmte Verbindungsvektoren, die auch als Local-Ties bezeichnet werden, eine der wesentlichen Schlüsselkomponenten bei der Kombination dar. Ungenaue, fehlerbehaftete und inaktuelle Local-Ties limitieren die Zuverlässigkeit des globalen geodätischen Bezugssystems. In der vorliegenden Arbeit werden ein Modell sowie verschiedene Lösungsverfahren entwickelt, die eine Verknüpfung der geometrischen Referenzpunkte von Radioteleskopen bzw. Laserteleskopen mit anderen geodätischen Raumverfahren durch prozessbegleitende lokale terrestrische Messungen erlauben. Während Radioteleskope zur Interferometrie auf langen Basislinien (VLBI) verwendet werden, ermöglichen Laserteleskope Entfernungsmessungen zu Erdsatelliten (SLR) oder zum Mond (LLR). Die Bestimmung des geometrischen Referenzpunktes von Laser- und Radioteleskopen ist messtechnisch herausfordernd und erfordert eine indirekte Bestimmungsmethode. Bestehende geometrische Methoden sind entweder auf eine bestimmte Teleskopkonstruktion beschränkt oder erfordern ein spezielles Messkonzept, welches ein gezieltes Verfahren des Teleskops voraussetzt. Die in dieser Arbeit hergeleitete Methode weist keine konstruktionsbedingten Restriktionen auf und erfüllt zusätzlich alle Kriterien der durch das GGOS angeregten prozessintegrierten in-situ Referenzpunktbestimmung. Hierdurch wird es möglich, den Referenzpunkt kontinuierlich und automatisiert zu bestimmen bzw. zu überwachen. Um die Zuverlässigkeit von VLBI-Daten zu erhöhen und um die Zielsetzung von 1mm Positionsgenauigkeit im globalen Kontext zu erreichen, wird das bestehende VLBI-Netz gegenwärtig durch zusätzliche Radioteleskope unter dem Namen VLBI2010 Global Observing System (VGOS) erweitert. Die hierbei entstehenden VGOS-Radioteleskope zeichnen sich u. a. durch eine sehr kompakte Bauweise und hohe Rotationsgeschwindigkeiten aus. Weitgehend ununtersucht ist das Eigenverformungsverhalten dieser Teleskope. Während für konventionelle Radioteleskope bspw. Signalwegänderungen von z. T. mehreren Zentimetern dokumentiert sind, existieren nur wenige vergleichbare Studien für VGOS-Radioteleskope. Hauptgründe sind zum einen die erhöhten Genauigkeitsanforderungen und zum anderen fehlende Modelle zur Beschreibung der Reflektorgeometrien, wodurch eine direkte Übertragung bisheriger Mess- und Analyseverfahren erschwert wird. In dieser Arbeit werden für VGOS-spezifizierte Radioteleskope Modelle erarbeitet, die eine geometrische Beschreibung der Form des Haupt- und Subreflektors ermöglichen. Basierend auf diesen Modellen lassen sich u. a. Änderungen der Brennweite oder Variationen der Strahllänge infolge von lastfallabhängigen Deformationen geometrisch modellieren. Hierdurch ist es möglich, wesentliche Einflussfaktoren zu quantifizieren, die eine Variation des Signalweges hervorrufen und unkompensiert vor allem zu einer systematischen Verfälschung der vertikalen Komponente der Stationskoordinate führen. Die Wahl eines geeigneten Schätzverfahrens, um unbekannte Modellparameter aus überschüssigen Beobachtungen abzuleiten, wird häufig als trivial und gelöst angesehen. Im Rahmen dieser Arbeit wird gezeigt, dass neben messprozessbedingten systematischen Abweichungen auch systematische Abweichungen durch das gewählte Schätzverfahren entstehen können. So resultieren aus der Anwendung eines Schätzverfahrens, welches ausschließlich in linearen Modellen Gültigkeit besitzt, i.A. keine erwartungstreuen Schätzwerte bei nichtlinearen Problemstellungen. Insbesondere in der Formanalyse des Hauptreflektors eines VLBI-Radioteleskops zeigt sich, dass die resultierenden Schätzwerte verzerrt sind, und diese Verzerrungen Größenordnungen erreichen, die als kritisch zu bewerten sind.
Chapter
This chapter describes the theory and the individual operational steps and components needed to carry out geodetic and astrometric Very Long Baseline Interferometry (VLBI) measurements. Pairs of radio telescopes are employed to observe far distant compact radio galaxies for the determination of the differences of the arrival times at the telescopes. From multiple observations of time delays of different radio sources, geodetic parameters of interest such as telescope coordinates, Earth orientation parameters, and radio source positions are inferred. The VLBI operation’s scheme generally consists of scheduling, observing session, correlation, and data analysis. In diesem Kapitel werden die Theorie und die einzelnen operationellen Schritte und Komponenten beschrieben, die erforderlich sind, um mit dem Verfahren der Radiointerferometrie auf langen Basislinien (im Englischen Very Long Baseline Interferometry [VLBI]) geodätische und astrometrische Messungen durchzuführen. Bei diesem Verfahren werden jeweils Paare von Radioteleskopen genutzt, um die Differenzen der Ankunftszeiten der Signale von Quasaren als primäre Observable zu gewinnen. Aus einer Vielzahl dieser Laufzeitdifferenzen von verschiedenen Radioquellen können dann die relevanten Zielparameter wie Teleskopkoordinaten, Erdorientierungsparameter und Radioquellenpositionen ermittelt werden. Der gesamte VLBI-Prozess besteht in der Regel aus den Schritten Erstellung des Beobachtungsplans, Durchführung der Beobachtungen, Korrelation und Datenanalyse.
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This investigation implements a least-squares methodology to fit a triaxial ellipsoid to a set of three-dimensional Cartesian coordinates obtained from present-day geospatial techniques, materializing the terrestrial frame ITRF2014. To approximate, as much as possible previous research on this topic, the original spatial values of the station coordinates were "reduced" to the surface of the EGM2008 geoid model by introducing a simple and straightforward procedure. The mathematical model adopted in all LS solutions is the standard quadric surface polynomial equation parameterizing a triaxial ellipsoid. Functionally related to these polynomial coefficients are nine geometric parameters: the three ellipsoid semi-axes, its origin location with respect to the current conventional geocentric terrestrial frame, and the three rotations defining its spatial orientation. The final results are compatible with the pioneering work started by Burša in 1970 and, lately, by a recent publication by Panou and colleagues in that incorporates updated geoid models.
Article
We review the main concepts underlying the determination of terrestrial reference frames (TRFs) through a recursive algorithm based on Kalman Filtering and Rauch-Tung-Striebel (RTS) smoothing which is currently adopted at Jet Propulsion Laboratory (JPL) to compute sub-secular frame products (JTRFs). We contextualize the TRF determination in the state-space framework and we emphasize connections between frame state, its observability through space-geodetic frame inputs and the similarity transformation which is central to frame definition. We elaborate on the notion of sub-secular frame, enabled by our approach, in constrast to standard TRF products which, secular by construction, are designed to represent the long-term mean physical properties of the frame. Comparisons of JTRF solutions to standard products such as the International Terrestrial Reference Frame (ITRF) suggest high-level consistency in a long-term sense with time derivatives of the Helmert transformation parameters connecting the two TRFs below 0.18 mm/yr. We discuss advantages and limitations of JPL approach to TRF determination and outline lines of inquiries that are currently being researched as part of JTRF development plan.
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Die Kombination von geodätischen Raumtechniken ist essentiell für die Bestimmung eines globalen geodätischen Referenzrahmens sowie von Erdrotationsparametern. Eine direkte Verknüpfung der unterschiedlichen Raumtechniken ist aufgrund der geringen physischen Verknüpfungen nicht ohne Zusatzinformationen sinnvoll möglich. Eine Schlüsselrolle spielen hierbei lokale Verbindungsvektoren (Local-Ties), die zwischen den geometrischen Referenzpunkten der Raumtechniken definiert sind. Diese Verbindungsvektoren lassen sich an Forschungseinrichtungen wie dem Geodätischen Observatorium Wettzell durch präzise terrestrische Vermessung bestimmen. Eine besondere Herausforderung stellen hierbei die Referenzpunkte von VLBI-Radio- und SLR-Laserteleskopen dar, da diese nicht materialisiert und direkt taktil bestimmt werden können. In diesem Beitrag wird eine indirekte Methode zur Bestimmung des geometrischen Referenzpunktes eines VLBI-Radio- bzw. SLR-Laserteleskopes vorgestellt. Das entwickelte Modell erlaubt eine automatisierte und prozessbegleitende messtechnische Erfassung aller relevanten Größen. Der neue Modellansatz erfordert darüber hinaus keine Synchronisation zwischen dem Messinstrument und dem Teleskop, sodass Messunsicherheiten minimiert werden. Eine erfolgreiche Validierung erfolgte 2018 am Satellite Observing System Wettzell, bei der die Datenerhebung vollständig automatisiert mit dem Lasertracker AT401 durchgeführt wurde, und der Referenzpunkt mit einer Unsicherheit von 50 µm bestimmt werden konnte.
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In this paper we investigate the impact of using the three ITRS realizations DTRF2014, ITRF2014, and JTRF2014 as a priori TRF for the VLBI combination on EOP and scale. The scale factor between the IVS routine combined solution and DTRF2014, ITRF2014, and JTRF2014 shows a significant offset of −0.59 ppb with respect to ITRF2014 and of 0.19 ppb with respect to JTRF2014. No significant offset was found for the DTRF2014-based solution. The investigation of the EOP of all four TRF-based solutions (DTRF2014-, ITRF2014-, JTRF2014- and VTRF2015q2-based) shows specific effects when comparing to the reference time series IERS 14C04, IGS, and ILRS. Relative to the VTRF2015q2-based solution, x-pole differences with respect to the DTRF2014-based solution (positive trend) and JTRF2014-based solution (scatter and negative trend), as well as an offset concerning the y-pole for all three TRF-based solutions with an additional scatter for the JTRF2014-based solution are recognized. No significant differences were found for pole rates, nutation, and LOD, but using ITRF2014 or JTRF2014 leads to marginal larger scatter with respect to the VTRF-based EOP series for LOD. In addition, a significant impact was found when comparing dUT1. All three TRF-based solutions show a significant offset comparing to IERS 14C04, whereas no offset is detected for the VTRF2015q2-based solution.
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The Vienna VLBI and Satellite Software (VieVS) is state-of-the-art Very Long Baseline Interferometry (VLBI) analysis software for geodesy and astrometry. VieVS has been developed at Technische Universität Wien (TU Wien) since 2008, where it is used for research purposes and for teaching space geodetic techniques. In the past decade, it has been successfully applied on Very Long Baseline Interferometry (VLBI) observations for the determination of celestial and terrestrial reference frames as well as for the estimation of celestial pole offsets, universal Time (UT1-UTC), and polar motion based on least-squares adjustment. Furthermore, VieVS is equipped with tools for scheduling and simulating VLBI observations to extragalactic radio sources as well as to satellites and spacecraft, features which proved to be very useful for a variety of applications. VieVS is now available as version 3.0 and we do provide the software to all interested persons and institutions. A wiki with more information about VieVS is available at http://vievswiki.geo.tuwien.ac.at/.
Article
We present and discuss JTRF2014, the Terrestrial Reference Frame (TRF) the Jet Propulsion Laboratory constructed by combining space-geodetic inputs from Very Long Baseline Interferometry (VLBI), Satellite Laser Ranging (SLR), Global Navigation Satellite Systems (GNSS) and Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS) submitted for the realization of ITRF2014. Determined through a Kalman filter and Rauch-Tung-Striebel smoother assimilating position observations, Earth Orientation Parameters (EOPs), and local ties, JTRF2014 is a sub-secular, time series-based TRF whose origin is at the quasi-instantaneous Center of Mass (CM) as sensed by SLR and whose scale is determined by the quasi-instantaneous VLBI and SLR scales. The dynamical evolution of the positions accounts for a secular motion term, annual, and semi-annual periodic modes. Site-dependent variances based on the analysis of loading displacements induced by mass redistributions of terrestrial fluids have been used to control the extent of random walk adopted in the combination. With differences in the amplitude of the annual signal within the range 0.5-0.8 mm, JTRF2014-derived Center of Network-to-Center of Mass (CM-CN) is in remarkable agreement with the geocenter motion obtained via spectral inversion of GNSS, Gravity Recovery and Climate Experiment (GRACE) observations and modeled Ocean Bottom Pressure (OBP) from Estimating the Circulation and Climate of the Ocean (ECCO). Comparisons of JTRF2014 to ITRF2014 suggest high-level consistency with time derivatives of the Helmert transformation parameters connecting the two frames below 0.18 mm/yr and WRMS differences of the polar motion (polar motion rate) in the order of 30 μas (17 μas/d).
Article
This paper studies the connection between the subdaily model for polar motion used in the processing of very long baseline interferometry (VLBI) observations and the estimated nutation offsets. By convention accepted by the International Earth Rotation Service, the subdaily model for polar motion recommended for routine processing of geodetic observations does not contain any daily retrograde terms due to their one-to-one correlation with the nutation. Nevertheless, for a 24-h VLBI solution a part of the signal contained in the polar motion given by the used subdaily model is numerically mistaken for a retrograde daily sidereal signal. This fictitious retrograde daily signal contributes to the estimated nutation, leading to systematic differences between the nutation offsets from VLBI solutions computed with different subdaily polar motion models. We demonstrate this effect using solutions for all suitable 24-h VLBI sessions over a time span of 11 years (2000–2011). By changing the amplitudes of one tidal term in the underlying subdaily model for polar motion and comparing the estimated parameters to the solutions computed with the unchanged subdaily model, the paper shows and explains theoretically the effects produced by the individual subdaily terms on the VLBI nutation estimates.
Article
The consistent estimation of terrestrial reference frames (TRF), celestial reference frames (CRF) and Earth orientation parameters (EOP) is still an open subject and offers a large field of investigations. Until now, source positions resulting from Very Long Baseline Interferometry (VLBI) observations are not routinely combined on the level of normal equations in the same way as it is a common process for station coordinates and EOPs. The combination of source positions based on VLBI observations is now integrated in the IVS combination process. We present the studies carried out to evaluate the benefit of the combination compared to individual solutions. On the level of source time series, improved statistics regarding weighted root mean square have been found for the combination in comparison with the individual contributions. In total, 67 stations and 907 sources (including 291 ICRF2 defining sources) are included in the consistently generated CRF and TRF covering 30 years of VLBI contributions. The rotation angles A1A_1, A2A_2 and A3A_3 relative to ICRF2 are −12.7, 51.7 and 1.8 {\upmu } as, the drifts DαD_\alpha and DδD_\delta are −67.2 and 19.1 \upmu as/rad and the bias BδB_\delta is 26.1 \upmu as. The comparison of the TRF solution with the IVS routinely combined quarterly TRF solution shows no significant impact on the TRF, when the CRF is estimated consistently with the TRF. The root mean square value of the post-fit station coordinate residuals is 0.9 cm.
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Very Long Baseline Interferometry (VLBI) is a primary space-geodetic technique for determining precise coordinates on the Earth, for monitoring the variable Earth rotation and orientation with highest precision, and for deriving many other parameters of the Earth system. The International VLBI Service for Geodesy and Astrometry (IVS, http://ivscc.gsfc.nasa.gov/) is a service of the International Association of Geodesy (IAG) and the International Astronomical Union (IAU). The datasets published here are the results of individual Very Long Baseline Interferometry (VLBI) sessions in the form of normal equations in SINEX 2.0 format (http://www.iers.org/IERS/EN/Organization/AnalysisCoordinator/SinexFormat/sinex.html, the SINEX 2.0 description is attached as pdf) provided by IVS as the input for the next release of the International Terrestrial Reference System (ITRF): ITRF2014. This is a new version of the ITRF2008 release (Böckmann et al., 2009). For each session/ file, the normal equation systems contain elements for the coordinate components of all stations having participated in the respective session as well as for the Earth orientation parameters (x-pole, y-pole, UT1 and its time derivatives plus offset to the IAU2006 precession-nutation components dX, dY (https://www.iau.org/static/resolutions/IAU2006_Resol1.pdf). The terrestrial part is free of datum. The data sets are the result of a weighted combination of the input of several IVS Analysis Centers.
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Altimetric data from the TOPEX/POSEIDON mission will be used for studies of global ocean circulation and marine geophysics. However, it is first necessary to remove the ocean tides, which are aliased in the raw data. The tides are constrained by two distinct types of information: the hydrodynamic equations which the tidal fields of elevations and velocities must satify, and direct observational data from tide gauges and satellite altimetry. The authors develop and apply a generalized inverse method, which allows them to combine rationally all of this information into global tidal fields best fitting both the data and the dynamics, in a least square sense. The resulting inverse solution is a sum of the direct solution to the astronomically forced Laplace tidal equations and a linear combination of the representers for the data functionals. With the representers calcuated they can easily update the model as additional TOPEX/POSEIDON data become available. -from Authors
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The increasing accuracy and growing time span of Very Long Baseline Interferometry (VLBI) observations allow the determination of seasonal signals in station positions which still remain unmodelled in conventional analysis approaches. In this study we focus on the impact of the neglected seasonal signals in the station displacement on the celestial reference frame and Earth orientation parameters. We estimate empirical harmonic models for selected stations within a global solution of all suitable VLBI sessions and create mean annual models by stacking yearly time series of station positions which are then entered a priori in the analysis of VLBI observations. Our results reveal that there is no systematic propagation of the seasonal signal into the orientation of celestial reference frame but position changes occur for radio sources observed non-evenly over the year. On the other hand, the omitted seasonal harmonic signal in horizontal station coordinates propagates directly into the Earth rotation parameters causing differences of several tens of microarcseconds.
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We present the second realization of the International Celestial Reference Frame (ICRF2) at radio wavelengths using nearly 30 years of Very Long Baseline Interferometry observations. ICRF2 contains precise positions of 3414 compact radio astronomical objects and has a positional noise floor of ~40 μas and a directional stability of the frame axes of ~10 μas. A set of 295 new "defining" sources was selected on the basis of positional stability and the lack of extensive intrinsic source structure. The positional stability of these 295 defining sources and their more uniform sky distribution eliminates the two greatest weaknesses of the first realization of the International Celestial Reference Frame (ICRF1). Alignment of ICRF2 with the International Celestial Reference System was made using 138 positionally stable sources common to both ICRF2 and ICRF1. The resulting ICRF2 was adopted by the International Astronomical Union as the new fundamental celestial reference frame, replacing ICRF1 as of 2010 January 1.
Article
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We present the second realization of the International Celestial Reference Frame (ICRF2) at radio wavelengths using nearly 30 years of Very Long Baseline Interferometry observations. ICRF2 contains precise positions of 3414 compact radio astronomical objects and has a positional noise floor of ~40 μas and a directional stability of the frame axes of ~10 μas. A set of 295 new "defining" sources was selected on the basis of positional stability and the lack of extensive intrinsic source structure. The positional stability of these 295 defining sources and their more uniform sky distribution eliminates the two greatest weaknesses of the first realization of the International Celestial Reference Frame (ICRF1). Alignment of ICRF2 with the International Celestial Reference System was made using 138 positionally stable sources common to both ICRF2 and ICRF1. The resulting ICRF2 was adopted by the International Astronomical Union as the new fundamental celestial reference frame, replacing ICRF1 as of 2010 January 1.
Conference Paper
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Precise measurements of the shape, the gravity field and the rotation of the Earth are important for many fields of geosciences. Beside high quality sensors an accurate, stable and global reference frame is required to get reliable results. In the scientific community the International Terrestrial Reference Frame (ITRF) is commonly used, where point positions are modeled linearly as coordinates and velocities. Additionally, a sum of time dependent variations have to be considered. These variations are often caused by tidal and non-tidal mass redistributions in the atmosphere, the ocean and the hydrology, the so-called geophysical fluids. On the one hand the point displacement has to be considered, on the other hand the gravity field variations have to be taken into account for precise orbit determination. Special data sets to model the non-tidal effects are available at the Global Geophysical Fluids Centre (GGFC) of the IERS. Model tests and comparisons are necessary due to the fact that a broad variety of models with different parameters (e.g. the spatial resolution) are provided. We performed extensive model comparisons for specific ITRF stations and for the entire grids. Additionally, the impact on the space geodetic techniques SLR, VLBI and GNSS was studied. We calculated several global solutions with different model combinations and analyzed the impact on the estimated station coordinates and other parameters, e.g. the Earth rotation parameters and the geocenter.
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New VLBI (Very Long Baseline Interferometry) data analysis software (called Vienna VLBI Software, VieVS) is being developed at the Institute of Geodesy and Geophysics in Vienna taking into consideration all present and future VLBI2010 requirements. The programming language MATLAB is used, which considerably eases the programming efforts because of many built-in functions and tools. MATLAB is the high-end programming language of the students at the Vienna University of Technology and at many other institutes worldwide. VieVS is equipped with the most recent models recommended by the IERS Conventions. The parameterization with piece-wise linear offsets at integer hours in the least-squares adjustment provides flexibility for the combination with other space geodetic techniques. First comparisons with other VLBI software packages show a very good agreement, and there are plans to add further features to VieVS, e.g. capabilities for Kalman filtering, phase delay solutions, and spacecraft tracking.
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The paper describes the determination of horizontal and vertical movements of the Adriatic microplate on the basis of GPS measurements carried out in the period between 1994 and 2005 within the frame of the 21 measuring campaigns organized at the research territory. The role of geodetic measurement methods particularly GPS method is essential in applications that requires high accuracy and precision as in the velocity field estimation of tectonic plates. The processing of GPS data as well as computation of the coordinates of points and their velocities was performed by Bernese GPS Software Ver. 5.0 based on 140 daily solutions. The mean standard deviations of estimated coordinates from repeatability of daily solutions and combined solution are σϕ=2.0 mm, σλ=2.2 mm and σh=5.6 mm. In purpose to determine and present the trend of height component the comparison of the data obtained by monitoring the change of sea level and the results of GPS measurement data was investigated. On the basis of the computed relative velocities of points as related to the Euro-Asian plate, the parameters of Euler rotation vector and Euler pole of the Adriatic microplate have been calculated and compared with other solutions. Also, the kinematic research area model has been determined on the basis of the combined solution results and compared with global kinematic models NNR-NUVEL-1A and APKIM2000.
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The detection and elimination of outliers in VLBI observations is an impor-tant pre-processing step for VLBI parameter estimation. A common technique to handle this problem is based on a so-called 3-sigma rejection criterion. It starts with an initial least-squares adjustment. Afterwards, all observations are eliminated from the data whose residuals exceed their respective standard deviations (sigma) by a factor greater than three. The final parameters are estimated in a second step. This technique which is also implemented in the VLBI processing software OCCAM LSM 5.0 is compared in this study with several robust estimators which are less restrictive regarding data elimination. From a methodological point of view all considered techniques are least-squares estima-tions using iterative reweighting. Data from more than 2000 VLBI sessions over a time span of 20 years were used for performance tests. The following results can be given: The 3-sigma criterion is rather fast but usually too simplistic since it tends to wrongly elimi-nate correct observations. Among the robust estimators the BIBER by Wicki performed best. It proved to be both efficient and reliable.
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Within almost all space-geodetic techniques, contributions of different analysis centers (ACs) are combined in order to improve the robustness of the final product. So far, the contributing series are assumed to be independent as each AC processes the observations in different ways. However, the series cannot be completely independent as each analyst uses the same set of original observations and many applied models are subject to conventions used by each AC. In this paper, it is shown that neglecting correlations between the contributing series yields too optimistic formal errors and small, but insignificant, errors in the estimated parameters derived from the adjustment of the combined solution.
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Theoretical modeling of the station displacements produced by tidal deformations of the Earth due to lunisolar gravitational forces is a necessary part of the analysis of space geodetic data. To attain the accuracies demanded by the precision of the data, a generalized version of the Love number formalism has to be used wherein the classical Love and Shida numbers are replaced by sets of Love number parameters with values that depend on the frequency of the tidal excitation. This paper presents theoretical expressions for the contributions from the various Love number parameters to the station displacement vector and a scheme for efficient computation of these contributions, taking into account the frequency dependence of these parameters as well as the imaginary parts that are present when the effects of mantle anelasticity are taken into account. A brief discussion of the permanent tide which arises from the zero frequency component of the tide-generating potential is included.
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Classical least squares regression consists of minimizing the sum of the squared residuals. Many authors have produced more robust versions of this estimator by replacing the square by something else, such as the absolute value. In this article a different approach is introduced in which the sum is replaced by the median of the squared residuals. The resulting estimator can resist the effect of nearly 50% of contamination in the data. In the special case of simple regression, it corresponds to finding the narrowest strip covering half of the observations. Generalizations are possible to multivariate location, orthogonal regression, and hypothesis testing in linear models.
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A new realization of the International Terrestrial System was computed at the ITRS Combination Centre at DGFI as a contribution to ITRF2008. The solution is labelled DTRF2008. In the same way as in the DGFI computation for ITRF2005 it is based on either normal equation systems or estimated parameters derived from VLBI, SLR, GPS and DORIS observations by weekly or session-wise processing. The parameter space of the ITRS realization comprises station positions and velocities and daily resolved Earth Orientation Parameters (EOP), whereby for the first time also nutation parameters are included. The advantage of starting from time series of input data is that the temporal behaviour of geophysical parameters can be investigated to decide whether the parameters can contribute to the datum realization of the ITRF. In the same way, a standardized analysis of station position time series can be performed to detect and remove discontinuities. The advantage of including EOP in the ITRS realization is twofold: (1) the combination of the coordinates of the terrestrial pole—estimated from all contributing techniques—links the technique networks in two components of the orientation, leading to an improvement of consistency of the Terrestrial Reference Frame (TRF) and (2) in their capacity as parameters common to all techniques, the terrestrial pole coordinates enhance the selection of local ties as they provide a measure for the consistency of the combined frame. The computation strategy of DGFI is based on the combination of normal equation systems while at the ITRS Combination Centre at IGN solutions are combined. The two independent ITRS realizations provide the possibility to assess the accuracy of ITRF by comparison of the two frames. The accuracy evaluation was done separately for the datum parameters (origin, orientation and scale) and the network geometry. The accuracy of the datum parameters, assessed from the comparison of DTRF2008 and ITRF2008, is between 2–5 mm and 0.1–0.8 mm/year depending on the technique. The network geometry (station positions and velocities) agrees within 3.2 mm and 1.0 mm/year. A comparison of DTRF2008 and ITRF2005 provides similar results for the datum parameters, but there are larger differences for the network geometry. The internal accuracy of DTRF2008—that means the level of conservation of datum information and network geometry within the combination—was derived from comparisons with the technique-only multi-year solutions. From this an internal accuracy of 0.32 mm for the VLBI up to 3.3 mm for the DORIS part of the network is found. The internal accuracy of velocities ranges from 0.05 mm/year for VLBI to 0.83 mm/year for DORIS. The internal consistency of DTRF2008 for orientation can be derived from the analysis of the terrestrial pole coordinates. It is estimated at 1.5–2.5 mm for the GPS, VLBI and SLR parts of the network. The consistency of these three and the DORIS network part is within 6.5 mm.
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ITRF2008 is a refined version of the International Terrestrial Reference Frame based on reprocessed solutions of the four space geodetic techniques: VLBI, SLR, GPS and DORIS, spanning 29, 26, 12.5 and 16years of observations, respectively. The input data used in its elaboration are time series (weekly from satellite techniques and 24-h session-wise from VLBI) of station positions and daily Earth Orientation Parameters (EOPs). The ITRF2008 origin is defined in such a way that it has zero translations and translation rates with respect to the mean Earth center of mass, averaged by the SLR time series. Its scale is defined by nullifying the scale factor and its rate with respect to the mean of VLBI and SLR long-term solutions as obtained by stacking their respective time series. The scale agreement between these two technique solutions is estimated to be 1.05 ± 0.13 ppb at epoch 2005.0 and 0.049 ± 0.010ppb/yr. The ITRF2008 orientation (at epoch 2005.0) and its rate are aligned to the ITRF2005 using 179 stations of high geodetic quality. An estimate of the origin components from ITRF2008 to ITRF2005 (both origins are defined by SLR) indicates differences at epoch 2005.0, namely: −0.5, −0.9 and −4.7mm along X, Y and Z-axis, respectively. The translation rate differences between the two frames are zero for Y and Z, while we observe an X-translation rate of 0.3mm/yr. The estimated formal errors of these parameters are 0.2mm and 0.2mm/yr, respectively. The high level of origin agreement between ITRF2008 and ITRF2005 is an indication of an imprecise ITRF2000 origin that exhibits a Z-translation drift of 1.8mm/yr with respect to ITRF2005. An evaluation of the ITRF2008 origin accuracy based on the level of its agreement with ITRF2005 is believed to be at the level of 1cm over the time-span of the SLR observations. Considering the level of scale consistency between VLBI and SLR, the ITRF2008 scale accuracy is evaluated to be at the level of 1.2ppb (8mm at the equator) over the common time-span of the observations of both techniques. Although the performance of the ITRF2008 is demonstrated to be higher than ITRF2005, future ITRF improvement resides in improving the consistency between local ties in co-location sites and space geodesy estimates. KeywordsReference systems–Reference frames–ITRF–Earth rotation
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During the 1990s, a large number of new tidal atlases were developed, primarily to provide accurate tidal corrections for satellite altimetry applications. During this decade, the French tidal group (FTG), led by C. Le Provost, produced a series of finite element solutions (FES) tidal atlases, among which FES2004 is the latest release, computed from the tidal hydrodynamic equations and data assimilation. The aim of this paper is to review the state of the art of tidal modelling and the progress achieved during this past decade. The first sections summarise the general FTG approach to modelling the global tides. In the following sections, we introduce the FES2004 tidal atlas and validate the model against in situ and satellite data. We demonstrate the higher accuracy of the FES2004 release compared to earlier FES tidal atlases, and we recommend its use in tidal applications. The final section focuses on the new dissipation term added to the equations, which aims to account for the conversion of barotropic energy into internal tidal energy. There is a huge improvement in the hydrodynamic tidal solution and energy budget obtained when this term is taken into account.
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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.
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Sind in den Eingangsdaten für eine Parameterschätzung derartige Werte enthalten, für die das angesetzte Modell nicht zutreffend ist (z.B. grobe Fehler), so besteht die grundsätzliche Aufgabe, die maximale Untergruppe konsistenter Daten aus den Eingangsdaten herauszufinden. In dieser Arbeit werden hierzu zwei neue Methoden vorgestellt. Zum einen wird die von PETROVIC (1991, 2002) entwickelte Ausgleichung nach maximaler Korrelation (MCA) erweitert, zum anderen wird eine neue Methode mit der Bezeichnung „MSS - Die Methode der maximalen Untergruppe“ entwickelt, bei der die maximale Untergruppe konsistenter Daten mit Hilfe einer kombinatorischen Suche gefunden werden kann. Die Diskussion bestehender und die Entwicklung neuer Methoden erfolgt anhand der Kongruenzuntersuchung geodätischer Netze. Als Spezialfall der generellen Problematik besteht hierbei die Aufgabe, aus der Menge aller Netzpunkte (bzw. aller Stützpunkte) die maximale Untergruppe stabiler Punkte zu lokalisieren. Im Hinblick auf diese Aufgabenstellung wird gezeigt, wie Koordinaten aus einer freien Netzausgleichung mit ihren singulären Kofaktorenmatrizen in einer ebenen oder räumlichen Helmerttransformation verarbeitet werden können. Zudem wird gezeigt, daß die Koordinatentransformation ohne Näherungswerte für die Parameter Translation und Rotation erfolgen kann. An einem Anwendungsbeispiel der Kongruenzuntersuchung wird gezeigt, daß die falsche Lokalisierung verschobener Punkte nicht in der Wahl der verwendeten Zielfunktion für die Ausgleichung begründet liegt, sondern Vielmehr in der Strategie der sukzessiven Analyse einzelner Punkte. Nach der Entwicklung der generellen Methodik des „MSS - Verfahrens“ erfolgt die Anwendung in der Kongruenzuntersuchung, wobei die kongruente Punktgruppe in dem untersuchten numerischen Beispiel gefunden wird. Da die kombinatorische Suche auch in den Fällen zu einer Lösung führen kann, in denen die bestehenden Verfahren (z.B. „data snooping, Einsatz resistenter und robuster Schätzverfahren) versagen, wird die Anwendung der „MSS - Methode“ auch bei anderen Aufgabenstellungen motiviert.
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From October 2003 to September 2005, the International VLBI Service for Geodesy and Astrometry (IVS) examined current and future requirements for geodetic VLBI, including all components from antennas to analysis. IVS Working Group 3 ‘VLBI 2010', which was tasked with this effort, concluded with recommendations for a new generation of VLBI systems. These recommendations were based on the goals of achieving 1 mm measurement accuracy on global baselines, performing continuous measurements for time series of station positions and Earth orientation parameters, and reaching a turnaround time from measurement to initial geodetic results of less than 24 hours. To realize these recommendations and goals, along with the need for low cost of construction and operation, requires a complete examination of all aspects of geodetic VLBI including equipment, processes, and observational strategies. Hence, in October 2005, the IVS VLBI2010 Committee (V2C) commenced work on defining the VLBI2010 system specifications. In this paper we give a summary of the recent progress of the VLBI2010 project.
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Altimetric data from the TOPEX/POSEIDON mission will be used for studies of global ocean circulation and marine geophysics. However, it is first necessary to remove the ocean tides, which are aliased in the raw data. The tides are constrained by the two distinct types of information: the hydrodynamic equations which the tidal fields of elevations and velocities must satisfy, and direct observational data from tide gauges and satellite altimetry. Here we develop and apply a generalized inverse method, which allows us to combine rationally all of this information into global tidal fields best fitting both the data and the dynamics, in a least squares sense. The resulting inverse solution is a sum of the direct solution to the astronomically forced Laplace tidal equations and a linear combination of the representers for the data functionals. The representer functions (one for each datum) are determined by the dynamical equations, and by our prior estimates of the statistics or errors in these equations. Our major task is a direct numerical calculation of these representers. This task is computationally intensive, but well suited to massively parallel processing. By calculating the representers we reduce the full (infinite dimensional) problem to a relatively low-dimensional problem at the outset, allowing full control over the conditioning and hence the stability of the inverse solution. With the representers calculated we can easily update our model as additional TOPEX/POSEIDON data become available. As an initial illustration we invert harmonic constants from a set of 80 open-ocean tide gauges. We then present a practical scheme for direct inversion of TOPEX/POSEIDON crossover data. We apply this method to 38 cycles of geophysical data records (GDR) data, computing preliminary global estimates of the four principal tidal constituents, M(sub 2), S(sub 2), K(sub 1) and O(sub 1). The inverse solution yields tidal fields which are simultaneously smoother, and in better agreement with altimetric and ground truth data, than previously proposed tidal models. Relative to the 'default' tidal corrections provided with the TOPEX/POSEIDON GDR, the inverse solution reduces crossover difference variances significantly (approximately 20-30%), even though only a small number of free parameters (approximately equal to 1000) are actually fit to the crossover data.
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Analysis of very long baseline interferometry data indicates that systematic errors in prior estimates of baseline length, of order 5 cm for approximately 8000-km baselines, were due primarily to mismodeling of the electrical path length of the troposphere and mesosphere ('atmospheric delay'). Here observational evidence for the existence of such errors in the previously used models for the atmospheric delay is discussed, and a new 'mapping' function for the elevation angle dependence of this delay is developed. The delay predicted by this new mapping function differs from ray trace results by less than approximately 5 mm, at all elevations down to 5 deg elevation, and introduces errors into the estimates of baseline length of less than about 1 cm, for the multistation intercontinental experiment analyzed here.
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Precise measurements of the Earth’s shape, gravity field, and rotation provide critical data for many geoscientific disciplines. In order to obtain reliable data, an accurate, stable, and global reference frame is required. The International Terrestrial Reference Frame, where station positions are modeled linearly, is commonly used throughout the geoscientific community for this purpose. Mass redistribution in the geophysical fluids, namely atmosphere, oceanic, and continental hydrology, cause time dependent variations in station coordinates, and other parameters such as the geocenter coordinates. Tidally-induced loading is described in the IERS Conventions. Models for non-tidal loading are available through the Global Geophysical Fluid Center. An overview of these models is given and comparisons were carried out. Within these comparisons, the best agreement was observed between the two atmospheric models, whereas the biggest discrepancies were found between the hydrology models. The processing setup for the Very Long Baseline Interferometry (VLBI), Satellite Laser Ranging (SLR) and Global Navigation Satellite Systems (GNSS) solutions is described, with loading displacement values introduced at the observation level. By using of non-tidal loading models the RMS of the height is reduced for 93% of the GNSS stations, with a max. reduction of 50%. The model impact on the station height in Wettzell derived by GNSS, SLR and VLBI shows a good agreement. In SLR results the Blue-Sky effect is visible. Applying the loading models reduced the seasonal variations visible in the geocenter time series derived by SLR almost completely.
Article
The analysis coordinator of the International VLBI Service for Geodesy and Astrometry (IVS) regularly disseminates the official IVS products of Earth orientation parameters (EOPs). For 2 years now, these parameters have been produced by combining datum-free normal equations of up to six IVS analysis centers. In this paper we document the combination methodology, discuss critical issues, and report on the quality of the products. The agreement of the very long baseline interferometry results with the International Global Navigation Satellite Systems (GNSS) Service GPS EOPs is of the order of 18 mus for length of day and 100 muas (microarc seconds) and 300 muas/d for the polar motion components and their rates, respectively.
Article
In the analyses of geodetic very long baseline interferometry (VLBI) and GPS data the analytic form used for mapping of the atmosphere delay from zenith to the line of site is most often a three-parameter continued fraction in 1/sin(elevation). Using the 40 years reanalysis (ERA-40) data of the European Centre for Medium-Range Weather Forecasts for the year 2001, the b and c coefficients of the continued fraction form for the hydrostatic mapping functions have been redetermined. Unlike previous mapping functions based on data from numerical weather models (isobaric mapping functions (Niell, 2000) and Vienna mapping functions (VMF) (Boehm and Schuh, 2004)), the new c coefficients are dependent on the day of the year, and unlike the Niell mapping functions (Niell, 1996) they are no longer symmetric with respect to the equator (apart from the opposite phase for the two hemispheres). Compared to VMF, this causes an effect on the VLBI or GPS station heights that is constant and as large as 2 mm at the equator and that varies seasonally between 4 mm and 0 mm at the poles. The updated VMF, based on these new coefficients and called VMF1 hereinafter, yields slightly better baseline length repeatabilities for VLBI data. The hydrostatic and wet mapping functions are applied in various combinations with different kinds of a priori zenith delays in the analyses of all VLBI International VLBI Service for Geodesy and Astrometry (IVS)-R1 and IVS-R4 24-hour sessions of 2002 and 2003; the investigations concentrate on baseline length repeatabilities, as well as on absolute changes of station heights.
Article
We develop a formalism for parameterizing and evaluating the effects of lateral variations in the properties of Earth's atmosphere on the propagation of microwave signals. A parametric form is incorporated into our analysis of very long baseline interferometry (VLBI) data, and the estimated atmospheric delay gradients are compared with those calculated from three-dimensional weather analysis fields from the National Center for Environmental Prediction (NCEP). For a 12-day series of experiments in January 1994, the VLBI and the NCEP analyses show common atmospheric gradient delays with amplitudes of up to 30 mm at 10° elevation angle. Comparison of the characteristics over a longer period of time reveals common mean north-south gradients with amplitudes up to ~10mm at 10° elevation at midlatitudes. No discernible mean east-west gradients were found in either data set. The root-mean-square (RMS) variations of the gradient effects, determined from the NCEP analysis, are similar in the north-south and east-west directions, with a typical RMS scatter of 6-10 mm at 10° elevation. After accounting for gradients, detailed analysis of the January 1994 VLBI data shows clearly that the residual station height variations of ~10mm at Westford, Massachusetts, are almost totally explained by the effects of atmospheric pressure loading.
Article
Gradients in the atmospheric refractive index can lead to errors in estimated vertical and horizontal station coordinates. These errors produce systematic errors in the terrestrial and celestial reference frames determined from our very long baseline interferometry (VLBI) measurements. Estimation of gradients for our global VLBI data set changes the terrestrial reference frame length scale by −0.7 ppb and produces station position adjustments that vary approximately monotonically with latitude. Estimating gradients reduces the radio source declinations by an amount that peaks at about 0.5 mas near the equator and decreases toward the poles. VLBI gradient estimates are consistent with gradients derived from a global three-dimensional model of assimilated meteorological data. Both indicate that mean atmospheric delay gradients point toward the equator in both the northern and southern hemispheres. The correlation coefficient between VLBI and meteorological model gradients for VLBI sessions for the VLBI antenna at Westford, Massachusetts was 0.56.
Article
The Data Assimilation Office at NASA's Goddard Space Flight Center is currently producing a multiyear gridded global atmospheric dataset for use in climate research, including tropospheric chemistry applications. The data, which are being made available to the scientific community, are well suited for climate research since they are produced by a fixed assimilation system designed to minimize the spinup in the hydrological cycle. By using nonvarying system, the variability due to algorithm change is eliminated and geophysical variability can be more confidently isolated. The analysis incorporates rawinsonde reports, satellite retrievals of geopotential thickness, cloud-motion winds, and aircraft, ship, and rocketsonde reports. At the lower boundary, the assimilating atmospheric general circulation model is constrained by the observed sea surface temperature and soil moisture derived from observed surface air temperature and precipitation fields. The available output data include all prognostic variables and a large number of diagnostic quantities such as heating rates, precipitation, surface fluxes, cloud fraction, and the height of the planetary boundary layer. These variables were chosen to assure a complete budget of the energy and moisture cycles. The assimilated data should also be useful for estimating transport by cumulus processes. The analysis increments (observation minus first guess) and the estimated analysis errors are provided to help the user assess the quality of the data. All quantities are made available every 6 h at the full resolution of the assimilating general circulation model. Selected surface quantities are made available every 3 h. 33 refs., 10 figs.
Article
In late 2008, the Product Center for the International Terrestrial Reference Frame (ITRF) of the International Earth Rotation and Reference Systems Service (IERS) issued a call for contributions to the next realization of the International Terrestrial Reference System, ITRF2008. The official contribution of the International VLBI Service for Geodesy and Astrometry (IVS) to ITRF2008 consists of session-wise datum-free normal equations of altogether 4,539 daily Very Long Baseline Interferometry (VLBI) sessions from 1979.7 to 2009.0 including data of 115 different VLBI sites. It is the result of a combination of individual series of session-wise datum-free normal equations provided by seven analysis centers (ACs) of the IVS. All series are completely reprocessed following homogeneous analysis options according to the IERS Conventions 2003 and IVS Analysis Conventions. Altogether, nine IVS ACs analyzed the full history of VLBI observations with four different software packages. Unfortunately, the contributions of two ACs, Institute of Applied Astronomy (IAA) and Geoscience Australia (AUS), had to be excluded from the combination process. This was mostly done because the IAA series exhibits a clear scale offset while the solution computed from normal equations contained in the AUS SINEX files yielded unreliable results. Based on the experience gathered since the combination efforts for ITRF2005, some discrepancies between the individual series were discovered and overcome. Thus, the consistency of the individual VLBI solutions has improved considerably. The agreement in terms of WRMS of the Terrestrial Reference Frame (TRF) horizontal components is 1 mm, of the height component 2 mm. Comparisons between ITRF2005 and the combined TRF solution for ITRF2008 yielded systematic height differences of up to 5 mm with a zonal signature. These differences can be related to a pole tide correction referenced to a zero mean pole used by four of five IVS ACs in the ITRF2005 contribution instead of a linear mean pole path as recommended in the IERS Conventions. Furthermore, these systematics are the reason for an offset in the scale of 0.4 ppb between the IVS’ contribution to ITRF2008 and ITRF2005. The Earth orientation parameters of seven series used as input for the IVS combined series are consistent to a huge amount with about 50 μas WRMS in polar motion and 3 μs in dUT1.
Article
Very Long Baseline Interferometry (VLBI) plays a unique and fundamental role in the maintenance of the global (terrestrial and celestial) reference frames, which are required for precise positioning in many research areas such as the understanding and monitoring of global changes, and for space missions. The International VLBI Service for Geodesy and Astrometry (IVS) coordinates the global VLBI components and resources on an international basis. The service is tasked by the International Association of Geodesy (IAG) and International Astronomical Union (IAU) to provide products for the realization of the Celestial Reference Frame (CRF) through the positions of quasars, to deliver products for the maintenance of the terrestrial reference frame (TRF), such as station positions and their changes with time, and to generate products describing the rotation and orientation of the Earth. In particular, VLBI uniquely provides direct observations of nutation parameters and of the time difference UT1-UTC. This paper summarizes the evolution and current status of the IVS. It points out the activities to improve further on the product quality to meet future service requirements.
Article
The contribution of the International VLBI Service for Geodesy and Astrometry (IVS) to the ITRF2005 (International Terrestrial Reference Frame 2005) has been computed by the IVS Analysis Coordinator’s office at the Geodetic Institute of the University of Bonn, Germany. For this purpose the IVS Analysis Centres (ACs) provided datum-free normal equation matrices in Solution INdependent EXchange (SINEX) format for each 24h observing session to be combined on a session-by-session basis by a stacking procedure. In this process, common sets of parameters, transformed to identical reference epochs and a prioris, and especially representative relative weights have been taken into account for each session. In order to assess the quality of the combined IVS files, Earth orientation parameters (EOPs) and scaling factors have been derived from the combined normal equation matrices. The agreement of the EOPs of the combined normal equation matrices with those of the individual ACs in terms of weighted root mean square (WRMS) is in the range of 50–60μas for the two polar motion components and about 3μs for UT1−UTC. External comparisons with International GNSS Serive (IGS) polar motion components is at the level of 130–170μas and 21μs/day for length of day (LOD). The scale of the terrestrial reference frame realized through the IVS SINEX files agrees with ITRF2000at the level of 0.2ppb.
Article
Thermal expansion of radio telescopes has long been recognized as an effect which cannot be neglected in geodetic and astrometric VLBI data analysis if millimeter accuracy is desired. In this article, the author documents the conventions which are being set by the International VLBI Service for Geodesy and Astrometry (IVS) for a consistent modelling of this effect in its routine product generation. For the largest telescopes, the annual cycle of thermal expansion may change the height of the VLBI reference point by as much as 20mm. However, for telescopes which are used in present-day IVS operations, the variations rather range from 4 to 6mm.
Article
The first part of this paper compares homogeneously reprocessed Very Long Baseline Interferometry (VLBI) and Global Positioning System (GPS) long-term height series from 1994 to 2007. The data analysis used fully adapted state-of-the-art models (like VMF1 and a priori zenith delays from ECMWF) for the GPS and VLBI processing. The series are compared in terms of long-term non-linear behaviour, harmonic and mean annual signals (not necessarily of harmonic nature). The similarity between both techniques is very good (especially the mean annual signals), which is assumed to be due to the adapted models and consistent reprocessing of both series. As two almost independent observing techniques see the same annually recurring signals at almost all co-located sites, we expect a good geophysical interpretability as integral vertical deformation. For the second part of this paper, the height time series of 161 suitable GPS sites (of the same solution as before) are used to determine a harmonic and a mean annual signal for each of them. Comparing the annual signals for this big dataset visually to GRACE-determined load deformations described in other publications, we find good agreement. This puts emphasis to the assumption that our height data have a lot of potential to be interpreted as geophysical signals. Out of these 161, 131 are grouped to 55 clusters, if at least two nearby (some thousand kilometres) sites show similar mean annual signals, which are thus confirmed to be real regional deformation, not local or technical artefacts. These 55 signals are presented on a “world map” of regional average mean annual height signals, as easy-to-handle tool to validate geophysical models. The data of these measured regional mean annual signals can be downloaded from a web-page for numerical analysis.
Article
This paper investigates whether in very long baseline interferometry (VLBI) analysis atmospheric loading corrections should be applied a priori at the observation level or whether it is sufficient to correct for atmospheric loading effects a posteriori by adding constant values per session to the estimated station coordinates. Simulated observations at single stations corresponding to the precise point positioning approach of global navigation satellite systems show that the atmospheric loading effect can be fully recovered by a posteriori corrections, i.e., the height differences between both approaches stay well below 1mm. However, real global VLBI network solutions with sessions from 1984 to 2008 reveal that the effect of neglected atmospheric loading corrections at the stations is distributed to the other stations in the network, thus resulting in station height differences between solutions with observation level and with a posteriori corrections which can be as large as 10mm and a ‘damping’ effect of the corrections. As soon as the terrestrial reference frame and the corresponding coordinate time series are determined, it would be conceptually wrong to apply atmospheric loading corrections at the VLBI stations. We recommend the rigorous application of atmospheric loading corrections at the observation level to all stations of a VLBI network because the seven parameters for translation, rotation, and in particular the network-scale of VLBI networks are significantly affected.
Article
Azimuthal asymmetries in the atmospheric refractive index can lead to errors in estimated vertical and horizontal station coordinates. Daily average gradient effects can be as large as 50 mm of delay at a 7 deg elevation. To model gradients, the constrained estimation of gradient paramters was added to the standard VLBI solution procedure. Here the analysis of two sets of data is summarized: the set of all geodetic VLBI experiments from 1990-1993 and a series of 12 state-of-the-art R&D experiments run on consecutive days in January 1994. In both cases, when the gradient parameters are estimated, the overall fit of the geodetic solution is improved at greater than the 99% confidence level. Repeatabilities of baseline lengths ranging up to 11,000 km are improved by 1 to 8 mm in a root-sum-square sense. This varies from about 20% to 40% of the total baseline length scatter without gradient modeling for the 1990-1993 series and 40% to 50% for the January series. Gradients estimated independently for each day as a piecewise linear function are mostly continuous from day to day within their formal uncertainties.
IVS combination center at BKG-robust outlier detection and weighting strategies
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Recent progress in the VLBI2010 development Observing our changing Earth, international association of geodesy symposia
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Make it citable: data in IVS
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Geodesy for planet Earth-the new Vienna VLBI software VieVS. International association of geodesy symposia
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Konzeption und Entwicklung neuer interaktiver multimedialer Lern- und Arbeitsmethoden für die geodätische Ausgleichungsrechnung
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IERS conventions 2003. IERS technical note no. 32
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IERS conventions 2010. IERS technical note no. 36. Verlag des Bundesamtes für Kartographie und Geodäsie, Frankfurt am Main
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Klassische und robuste Ausgleichungsverfahren
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Robust parameter estimation of the spatial Helmert-transformation
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