Inter-technique combination based on homogeneous normal equation systems including station coordinates, earth orientation and troposphere parameters

<p>The current realisation of the ITRF2014, features the estimation of polar motion (x-pole and y-pole) based on the combination of the four space geodetic techniques, whereas polar motion rates are based on two techniques, and UT1-UTC and LOD are taken only from the solution of a single technique (VLBI). Moreover,the combination of troposphere parameters (from VLBI and GNSS) with tropospheric ties and the combination of common clocks at the fundamental sites are not yet exploited in this combination strategy. Therefore, a rigorous combination of all common parameter types, with consistent Earth Orientation Parameters (EOPs) and with appropriate inter-technique tropospheric and clock ties, is still a considerable way to go.</p><p>The guiding principle for a rigorous combination is that all parameter types common to more than one space geodetic observation technique should be combined, including their full variance-covariance information as well as the corresponding ties. Based on this fact, and keeping in mind that both, GNSS and geodetic VLBI are based on microwave frequencies, and that their physical models and their parameter types (site coordinates and velocities, troposphere estimates, EOPs and -possibly- clock estimates) are closely related, we used data from the CONT17 campaign to study the benefits to be expected from a more rigorous combination approach, and we developed a processing scheme, based on a tailored version of the Bernese V5.2 software, for the consistent estimation of all EOPs, with daily and sub-daily resolution of polar motion and UT1-UTC, and for realising inter-technique tropospheric ties. We discuss the challenges and results of this rigorous inter-technique combination of VLBI and GNSS observations, and provide evidence of the need of such an approach.</p>

This paper presents how Very Long Baseline Interferometry (VLBI) realizes the Earth Orientation Parameters (EOP) and which accuracy can be theoretically reached depending on the involved reference frames. The definition of EOP is based on the transformation between the Geocentric Celestial Reference System (GCRS) and the International Terrestrial Reference System (ITRS). The ITRS part is in common for all the space geodetic techniques. The method applied here utilizes the uncertainty of the orientation of the actual set of radio sources of a VLBI observing session related to GCRS and the uncertainty of the orientation of the set of terrestrial network stations related to ITRS for the assessment of the uncertainty of the EOP. The uncertainty of the initial orientation of the GCRS is about 35 μas and the uncertainty of the orientation stability is about 0.7 μas∕year. In addition small systematics are present due to the aberration caused by the rotation of our galaxy at the level of 5 μas∕year. The uncertainty of the initial orientation of the ITRS of about 800 μas is about 20 times larger, while the uncertainty of the orientation rate of about 80 μas∕year is about 100 times larger compared to the corresponding celestial values. The initial orientation and the orientation stability of ITRS could be much more precisely defined by constraining it to the GCRS via the EOP.

Satellite Laser Ranging (SLR) is currently the unique technique to determine station coordinates, Earth Orientation Parameters (EOPs) and Stokes coefficients of the Earth’s gravity field from one observation equation with a high accuracy. These parameters form the so-called ‘three pillars’ (Plag and Pearlman, 2009) of the Global Geodetic Observing System (GGOS). In its function as an official analysis center of the International Laser Ranging Service (ILRS) (Pearlman et al., 2002), DGFI is developing and maintaining software to process SLR observations called ‘DGFI Orbit and Geodetic parameter estimation Software’ (DOGS). The software is used to analyze SLR observations and to compute multi-satellite solutions. In this study, up to 10 satellites (ETALON1/2, LAGEOS1/2, STELLA, STARLETTE, AJISAI, LARETS, LARES and BLITS) with different orbit characteristics (e.g., inclination and altitude) are combined. The relative weighting of the satellites is done using a variance component estimation. The diverse orbits allow to decrease the correlation of parameters such as gravity field coefficients (GFCs) and EOPs. Beside the Earth’s gravity field (weekly GFCs with degree and order ≤ 6 and monthly GFCs with degree and order ≤ 20) and rotation (terrestrial pole coordinates, UT1-UTC extrapolated with LOD), 3-D station coordinates are estimated weekly or monthly. Different combined solutions are compared to LAGEOS-only solutions. If LARES is combined with LAGEOS1/2, a significant improvement in the GFCs, the EOP and the TRF can be achieved. If more satellites are combined, the variation of the pole coordinates w.r.t. the IERS 08 C04 time series can be reduced up to 56%. Furthermore, systematics in LOD are nearly completely eliminated. The variation of the station coordinates w.r.t. SLRF2008 (http://www.ilrs.gsfc.nasa.gov/science/awg/SLRF2008.html, 2013) can be reduced by about 30%.

The determination of the temporal variations of the Earth orientation parameters (EOP) and spherical harmonic coefficients of the gravity field are geodetic contributions to the analysis of global geodynamic processes. As the Earth’s tensor of inertia is functionally related both to the EOP via the Euler-Liouville equations and directly to the gravity field coefficients of degree 2 it allows the mutual validation of these two sets of parameters.This paper proposes a statistically founded method of combining the temporal variations of the EOP and of the gravity field coefficients of degree 2 by a least-squares estimation based on the Gauss-Helmert model (condition equations with unknowns). Thereby statistically founded values for the unknown parameters can be derived, together with residuals for the observations, checkability and accuracy measures.The EOP and gravity field coefficients of degree 2 are introduced as observations together with correction terms such as excitation functions of atmosphere and ocean. The results of the Gauss-Helmert model computed with gravity field coefficients from GRACE and the C04 series from the International Earth Rotation and Reference Systems Service are shown in this paper. If given standard deviations are taken into account and covariances are neglected the following results are obtained: Δlod is coupled with C20 and vice versa, C21 and S21 are coupled with the polar motion, but the polar motion itself and the gravity field coefficients C22 and S22 are not checked by any other parameterKeywordsEarth orientation parametersGravity field coefficients Temporal variationsValidation

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

The Earth Orientation Parameters (EOP) connect the International Terrestrial Reference System (ITRS) to the Geocentric Celestial Reference System (GCRS). These parameters, i.e., Universal Time, UT1, and pole coordinates in the ITRS and in the GCRS, describe the irregularities of the Earth’s rotation. They are mainly determined by two modern astro-geodetic techniques, VLBI (Very Long Baseline Radio Interferometry) on extragalactic radio sources, which is used to realize and maintain the International Celestial Reference System (ICRS), and Global Navigation Satellite System (GNSS), especially GPS (Global Positioning System), which has an important contribution to the realization of the ITRS. The aim of this presentation is twofold: to present the modern bases for the consideration of Earth orientation and to discuss how the principles of VLBI and GPS give access to the measure of different components of the EOP variations, especially UT1. The accuracy that can be achieved is based on the improved concepts, definitions, and models that have been adopted by IAU/IUGG resolutions on reference systems and Earth’s rotation, as well as on the refined strategy of the observations.

This paper generalizes the results of investigations on the instabilities of the Earth's rotation and related geophysical processes. Long series of observations of the Earth's orientation parameters are demonstrated. The tidal variations in the length of the day are described. The temporal variations in the atmospheric angular momentum and their contribution to the instabilities of the Earth's rotation are studied. The mechanisms of seasonal variations in the length of the day and polar motion are discussed. The probable geophysical processes responsible for the decades-long (2–100 years) instability of the Earth's rotation are discussed.

<p>The ITRF2020 is the upcoming realization of the International Terrestrial Reference Frame. As the successor of the ITRF2014, it is based on an inter-technique combination of all four space-geodetic techniques, i.e., VLBI, GNSS, SLR and DORIS, and it is based on contributions from different institutions around the world. In this context, the Combination Centre of the International VLBI Service for Geodesy and Astrometry (IVS) – operated by the Federal Agency for Cartography and Geodesy (BKG, Germany) and the Deutsches Geodätisches Forschungsinstitut (DGFI-TUM, Germany) – generates the VLBI intra-technique combination for ITRF2020 utilizing the individual contributions of multiple IVS Analysis Centres (AC).</p><p>For the contribution to the ITRF2020 solution, sessions containing 24h VLBI observations from 1979 until the end of 2020 are reprocessed by 11 ACs and submitted to the IVS Combination Centre. All individual sessions include datum-free normal equations containing station coordinates and source positions as well as full sets of Earth Orientation Parameters (EOP) in the required SINEX format. For ensuring consistently combined solutions, time series of EOP and station coordinates, as well as a VLBI-only Terrestrial Reference Frame (VTRF), have been investigated.</p><p>This contribution focuses on detailed investigations concerning the session-dependency of the scale and the impact of the individual AC contributions to the combination. Thereby significant differences of the scale estimates from the different session types are investigated. Also, the evaluation of the ACs’ contributions to the combined solution will be presented.</p>

<p>Precise positioning and navigation on the Earth’s surface and in space require accurate Earth Orientation Parameters (EOP) data and predictions. In the last few decades, the problem of EOP prediction has become a subject of increased attention within the international geodetic community, and many research centres from around the world have developed their own methods of forecasting the EOP. It is not surprising that those various predictions differ in many aspects such as accuracy and the length of the forecast horizon.</p><p>A re-assessment of the various EOP prediction capabilities is currently pursued in the frame of the 2<sup>nd</sup> EOP PCC, which started in September 2021. The new campaign was prepared by the EOP PCC office run by the Space Research Centre of the Polish Academy of Sciences (CBK PAN) in cooperation with GeoForschungsZentrum (GFZ) and under the auspices of the International Earth Rotation and Reference Systems Service (IERS). The campaign will be continued until the end of the year 2022 and all interested scientists are invited to contribute with new predictions at any time.</p><p>In this presentation, we provide preliminary results of the 2<sup>nd</sup> EOP PCC by focusing on the quality of EOP predictions up to 10 days into the future. The quality assessment includes metrics such as mean absolute error (MAE) and root mean square error (RMSE) for the ensemble of all predictions, but also more detailed assessments of individual predictions. The accuracy of EOP forecasts is determined using IERS 14 C04 solution as a reference. We will pay special attention to the impact of input data exploited by participants, including the Effective Angular Momentum functions.</p>

Time series of Earth Orientation Parameters (EOP) have been obtained from independent parallel Very Long Baseline Interferometry (VLBI) networks NEOS-A and CORE-A using OCCAM 5.0 software.

The article aims to present the results obtain from the scheduling and simulation of VLBI measurements in October 2010 for a period of three days for 24 hour continuous observations. To be sure that we will obtain good VLBI observation we have to do an optimization of the network. This can be done quite accurately by using the new modules that are part of the VLBI processing software’s, the modules scheduling and simulation. This can be considered the first step in preparation of the VLBI experiment. Very Long Baseline Interferometry (VLBI) it is a primary space-geodetic technique that it is able to determine precise coordinates on the Earth, by monitoring the variable of Earth orientation parameters (EOP) with high precision. Also Very Long Baseline Interferometry plays an important role for determination of celestial and terrestrial reference frame. It is also a technique that each year is more developed form a software and hardware point of view. To obtain the scans we used a set of eight different VLBI antennas and as a source we used different quasars. In the scheduling we used the source based strategy contrary to the station based approach and the radio sources where from updated catalogues according to the requirements of the VLBI2010 system, which means that we are able to obtain a best coverage of the celestial sphere. The results show that scheduling and simulation are very good tools in preparing real VLBI experiments.

The difference UT1-UTC is the most variable quantity among the Earth Orientation Parameters (EOP) with significant unpredictable variation. It can be measured only with the quasi-space-fixed technique VLBI. The IVS organizes two different VLBI observation campaigns: The bi-weekly 24-hour Rapid campaigns and the daily 1-hour Intensive sessions. As a result, two independent UT1-UTC time series are estimated and published as official IVS EOP-S and EOP-I products. These have different strengths and weaknesses in terms of continuity and accuracy, but both are characterized by irregular temporal resolution. We present the current activities of BKG towards a combined processing of VLBI Intensive and Rapid data in one common adjustment. In this way, we unify the strengths of both sessions and generate a UT1-UTC time series characterized by a daily, continuous and temporally regular resolution, e.g., at 12:00 UTC. We achieved a significant improvement in accuracy of 35% lower WRMS values compared to the regular session-wise Intensive-only solution. By using a continuous EOP parameterization, the accuracy is almost at a constant level and less dependent on the irregularity of the VLBI observation period. The processing is based on homogenized, datum-free NEQs which allow a rigorous combination on the normal equation level instead of the observation level. Based on the improved combination method, we intend to set up a new operational VLBI EOP product at BKG. Its characteristics make it suitable as an input for EOP prediction algorithms.

The International Terrestrial Reference Frame (ITRF), the Earth Orientation Parameter (EOP) time series, and the International Celestial Reference Frame are obtained separately and may thus present inconsistencies. To solve this problem, a first step has been made with the latest ITRF realization (ITRF2005), which has been computed, for the first time, with consistent EOP time series. Another approach to better understand this issue is to directly estimate, in the same process, station positions and EOP time series, from all the space-geodetic measurements.

The International GPS Service (IGS): An interdisciplinary service in support of Earth sciences

Systematic errors at harmonics of the GPS draconitic year have been found in diverse GPS-derived geodetic products like the geocenter \(Z\)-component, station coordinates, \(Y\)-pole rate and orbits (i.e. orbit overlaps). The GPS draconitic year is the repeat period of the GPS constellation w.r.t. the Sun which is about 351 days. Different error sources have been proposed which could generate these spurious signals at the draconitic harmonics. In this study, we focus on one of these error sources, namely the radiation pressure orbit modeling deficiencies. For this purpose, three GPS+GLONASS solutions of 8 years (2004–2011) were computed which differ only in the solar radiation pressure (SRP) and satellite attitude models. The models employed in the solutions are: (1) the CODE (5-parameter) radiation pressure model widely used within the International GNSS Service community, (2) the adjustable box-wing model for SRP impacting GPS (and GLONASS) satellites, and (3) the adjustable box-wing model upgraded to use non-nominal yaw attitude, specially for satellites in eclipse seasons. When comparing the first solution with the third one we achieved the following in the GNSS geodetic products. Orbits: the draconitic errors in the orbit overlaps are reduced for the GPS satellites in all the harmonics on average 46, 38 and 57 % for the radial, along-track and cross-track components, while for GLONASS satellites they are mainly reduced in the cross-track component by 39 %. Geocenter \(Z\)-component: all the odd draconitic harmonics found when the CODE model is used show a very important reduction (almost disappearing with a 92 % average reduction) with the new radiation pressure models. Earth orientation parameters: the draconitic errors are reduced for the \(X\)-pole rate and especially for the \(Y\)-pole rate by 24 and 50 % respectively. Station coordinates: all the draconitic harmonics (except the 2nd harmonic in the North component) are reduced in the North, East and Height components, with average reductions of 41, 39 and 35 % respectively. This shows, that part of the draconitic errors currently found in GNSS geodetic products are definitely induced by the CODE radiation pressure orbit modeling deficiencies.