Baseline-dependent clock offsets in VLBI data analysis

The primary goal of the geodetic Very Long Baseline Interferometry (VLBI) technique is to provide highly accurate terrestrial and celestial reference frames as well as Earth orientation parameters. In compliance with the concept of VLBI, additional parameters reflecting relative offsets and variations of the atomic clocks of the radio telescopes have to be estimated. In addition, reality shows that in many cases significant offsets appear in the observed group delays for individual baselines which have to be compensated for by estimating so-called baseline-dependent clock offsets (BCOs). For the first time, we systematically investigate the impact of BCOs to stress their importance for all kinds of VLBI data analyses. For our investigations, we concentrate on analyzing data from both legacy networks of the CONT17 campaign. Various aspects of BCOs including their impact on the estimates of geodetically important parameters, such as station coordinates and Earth orientation parameters, are investigated. In addition, some of the theory behind the BCO determination, e.g., the impact of changing the reference clock in the observing network on the BCO estimate is introduced together with the relationship between BCOs and triangle delay closures. In conclusion, missing channels, and here in particular at S band, affecting the ionospheric delay calibration, are identified to be the dominant cause for the occurrence of significant BCOs in VLBI data analysis.

The use of astronomy VLBA campaign MOJAVE for geodesy

We investigated the suitability of the astronomical 15 GHz Very Long Baseline Array (VLBA) observing program MOJAVE-5 for estimation of geodetic parameters, such as station coordinates and Earth orientation parameters. We processed a concurrent dedicated VLBA geodesy program observed at 2.3 GHz and 8.6 GHz starting on September 2016 through July 2020 as reference dataset. We showed that the baseline length repeatability from MOJAVE-5 experiments is only a factor of 1.5 greater than from the dedicated geodetic dataset and still below 1 ppb. The wrms of the difference of estimated Earth orientation parameters with respect to the reference IERS C04 time series are a factor of 1.3 to 1.8 worse. We isolated three major differences between the datasets in terms of their possible impact on the geodetic results, i.e. the scheduling approach, treatment of the ionospheric delay, and selection of target radio sources. We showed that the major factor causing discrepancies in the estimated geodetic parameters is the different scheduling approach of the datasets. We conclude that systematic errors in MOJAVE-5 dataset are low enough for these data to be used as an excellent testbed for further investigations on the radio source structure effects in geodesy and astrometry.

The space–time references of BeiDou Navigation Satellite System

The BeiDou Navigation Satellite System (BDS) is essentially a precise time measurement and time synchronization system for a large-scale space near the Earth. General relativity is the basic theoretical framework for the information processing in the master control station of BDS. Having introduced the basic conceptions of relativistic space–time reference systems, the space–time references of BDS are analyzed and the function and acquisition method of the Earth Orientation Parameters (EOP) are briefly discussed. The basic space reference of BDS is BeiDou Coordinate System (BDCS), and the time standard is the BDS Time (BDT). BDCS and BDT are the realizations of the Geocentric Terrestrial Reference System (GTRS) and the Terrestrial Time (TT) for BDS, respectively. The station coordinates in the BDCS are consistent with those in International Terrestrial Reference Frame (ITRF)2014 at the cm–level and the difference in scale is about $$1.1 \times 10^{ - 8}$$ 1.1 × 10 - 8 . The time deviation of BDT relative to International Atomic Time (TAI) is less than 50 ns and the frequency deviation is less than $$2 \times 10^{ - 14}$$ 2 × 10 - 14 . The Geocentric Celestial Reference System (GCRS) and the solar Barycentric Celestial Reference System (BCRS) are also involved in the operation of BDS. The observation models for time synchronization and precise orbit determination are established within the GCRS framework. The coordinate transformation between BDCS and GCRS is consistent with the International Earth Rotation and Reference Systems Service (IERS). In the autonomous operation mode without the support of the ground master control station, Earth Orientation Parameters (EOP) is obtained by means of long-term prediction and on-board observation. The observation models for the on-board astrometry should be established within the BCRS framework.

Kriging-based prediction of the Earth’s pole coordinates

Coordinates of the Earth’s pole represent two out of five Earth orientation parameters describing Earth’s rotation. They are necessary in transformation between celestial reference frame and terrestrial reference frame and what goes further in precise positioning and navigation, applications in astronomy, communication with outer space objects. Complexity of measuring techniques and data processing involved in the pole coordinates determination make it impossible to obtain them in real-time mode, hence a prediction problem of the polar motion emerges. In this study, geostatistical prediction methods, i. e., simple and ordinary kriging are applied. Millions of predictions have been performed to draw reasonable conclusions on prediction capabilities of applied kriging variants. The study is intended in ultra-short-term prediction (up to 15 days into the future) using the IERS EOP 14 C04 (IAU2000A) and IERS EOP 05 C04 (IAU2000A) series as a reference. Mean absolute prediction errors (for days 1–15) with respect to IERS 14 C04 are ranging 0.66–5.25 mas for PMx and 0.47–3.59 mas for PMy. On the other hand, for IERS 05 C04 the values are 0.60–4.95 mas and 0.44–3.29 mas for PMx and PMy; respectively. The results indicate competitiveness of the introduced methods with existing ones.

VLBI and GPS inter- and intra-technique combinations on the observation level for evaluation of TRF and EOP

We study the effects of combination on the observation level (COL) of different space-geodetic techniques and of networks of the same technique and present the corresponding improvement for the determination of station positions and earth orientation parameters. Data from the continuous geodetic very long baseline interferometry (VLBI) campaign CONT17 are used in a batch least-squares (LSQ) estimator. This campaign includes 15 days of observations with two legacy S/X networks, namely Legacy-1 (L1) and Legacy-2 (L2). For this study the VLBI L1 network is used as the base and reference solution. Data from the L1 network are combined first with data from co-located Global Positioning System (GPS) stations by estimating common tropospheric parameters. The derived station positions repeatabilities of the VLBI and GPS networks are evaluated with respect to single-technique solutions. In terms of precision, we find a 25% improvement for the vertical repeatability of the L1 network, and a 10% improvement for the horizontal one. The GPS network also benefits by 20% and 10% in the horizontal and vertical components, respectively. Furthermore, a combined solution using data of the L1 and L2 network is performed by estimating common earth orientation parameters. The combined L1&GPS and L1&L2 solutions are compared to the reference solution by investigating UT1 and polar motion estimates. UT1 is evaluated in terms of mean bias and formal errors with respect to the International Earth Rotation Service (IERS) C04 products which were used as a priori values. The L1&GPS solution has the lowest formal error and mean bias for UT1 with a 30% improvement. The weighted root mean square (WRMS) and weighted mean offset (WMO) differences between the obtained polar motion estimates and the ones derived by the International GNSS Service (IGS) are also compared. We find that the L1&GPS solution gives the lowest WRMS and WMO, exhibiting an average 40% improvement with respect to the reference solution. The presented results highlight the potential of COL for ongoing transition to multi-space geodetic analysis, e.g., Global Navigation Satellite Systems (GNSS) with the next-generation VLBI system. Graphic Abstract

Effect of non-tidal station loading on Lunar Laser Ranging observatories and on the estimation of Earth orientation parameters

<p>The distance between the observatories on Earth and the retro-reflectors on the Moon has been regularly observed by the Lunar Laser Ranging (LLR) experiment since 1970. In the recent years, observations with bigger telescopes (APOLLO) and at infra-red wavelength (OCA) are carried out, resulting in a better distribution of precise LLR data over the lunar orbit and the observed retro-reflectors on the Moon, and a higher number of LLR observations in total. Providing the longest time series of any space geodetic technique for studying the Earth-Moon dynamics, LLR can also support the estimation of Earth orientation parameters (EOP), like UT1. The increased number of highly accurate LLR observations enables a more accurate estimation of the EOP. In this study, we add the effect of non-tidal station loading (NTSL) in the analysis of the LLR data, and determine post-fit residuals and EOP. The non-tidal loading datasets provided by the German Research Centre for Geosciences (GFZ), the International Mass Loading Service (IMLS), and the EOST loading service of University of Strasbourg in France are included as corrections to the coordinates of the LLR observatories, in addition to the standard corrections suggested by the International Earth Rotation and Reference Systems Service (IERS) 2010 conventions. The Earth surface deforms up to the centimetre level due to the effect of NTSL. By considering this effect in the Institute of Geodesy (IfE) LLR model (called ‘LUNAR’), we obtain a change in the uncertainties of the estimated station coordinates resulting in an up to 1% improvement, an improvement in the post-fit LLR residuals of up to 9%, and a decrease in the power of the annual signal in the LLR post-fit residuals of up to 57%. In a second part of the study, we investigate whether the modelling of NTSL leads to an improvement in the determination of EOP from LLR data. Recent results will be presented.</p>

ESA’s efforts for more consistent geodetic products

<p>The importance of an accurate global geodetic reference frame and associated Earth orientation parameters is undisputed and has been recognised by the UN resolution 69/266. Given the importance of global geodetic references,  ESA is actively contributing to the IAG services: IGS, ILRS, IDS and the contribution to the IVS is in preparation.</p><p>ESA’s activities can be divided into four main areas: the operation of Ground Infrastructure (ESTRACK, EGON, …), the establishment and improvement of inter-technique ties, the operation of a scientific data archive (GSSC) and the generation of geodetic products and services.</p><p>This presentation will focus on the activities performed by the Navigation Support Office. The Navigation Support Office at ESA/ESOC is responsible for providing the Geodetic Reference Frame for all ESA missions and is also the Consortium Coordinator of the Galileo Geodetic Service Provider (GGSP) that generates the Galileo Geodetic Reference Frame (GTRF). Within its responsibilities, the Navigation Support Office is continuously working on improving the consistency of its geodetic products. The possibility to perform a Combination On the Observation Level (CoOL) for all geodetic observations is an excellent tool to identify inconsistencies. Over the recent years, significant improvements have been implemented in the data processing in order to enhance the consistency of the delivered products. As the status of the inter-technique ties remains a limiting factor in this context, ESA is currently investigating the possibility of using space ties, e.g. combining GNSS, SLR, DORIS and VLBI in space.</p><p>This presentation will give an overview of the geodetic products and services generated by ESA’s Navigation Support Office and outline the associated processing setup. In particular, it will report on the analysis performed to improve the consistency of the results provided by the different observation techniques and outline the recent improvements and ongoing activities.</p>

A preliminary assessment of the accuracy of the VGOS geodetic products: implications for the terrestrial reference frame and Earth orientation parameters

<p>The next-generation VLBI system called VGOS (VLBI Global Observing System) has been designed and built as a significant improvement over the legacy geodetic VLBI system to meet the accuracy and stability goals set by the Global Geodetic Observing System (GGOS). Improved geodetic products are expected as the VGOS technique transitions from demonstration to operational status, which is underway. Since 2019, a network of nine VGOS stations has been observing bi-weekly under the auspices of the International VLBI Service for Geodesy and Astrometry (IVS) to generate standard geodetic products. These products, together with the mixed-mode VLBI observations that tie the VGOS and legacy networks together will be contributions to the next realization of the International Terrestrial Reference Frame (ITRF2020). Moreover, since 2020 a subset of 2 to 4 VGOS stations has also been observing in a VLBI Intensive-like mode to assess the feasibility of Earth rotation (UT1) estimation using VGOS. Intensives are daily legacy VLBI observations that are run on a daily basis using a single baseline between Kokee Park Geophysical Observatory, Hawaii, and Wettzell Observatory, Germany, made with the goal of near-real-time monitoring of UT1. In this presentation, we will describe the VGOS observations, correlation, post-processing, and preliminary geodetic results, including UT1. We will also compare the VGOS estimates to estimates from legacy VLBI, including estimates from mixed-mode observations, to explore the precision and accuracy of the VGOS products.</p>

Towards Inter-Technique Co-Location of GNSS and VLBI Observations

<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>