Thomas Artz

Consistent adjustment of combined terrestrial and celestial reference frames

Today, the realization of the International Terrestrial Reference System (ITRS) and the International Celestial Reference System (ICRS) is performed separately. Consequently, the two realizations are not fully consistent and show differences in the network geometry and the realized scale of the terrestrial reference frame (TRF) and in the simultaneously estimated Earth Orientation Parameter (EOP) series. The paper deals with the common adjustment of the Terrestrial Reference Frame (TRF), the Celestial Reference Frame (CRF) and the linking EOP. It presents a computation strategy, which is based on the combination of normal equations. The main focus of the paper is on the impact of a combination of different space geodetic techniques on the CRF, which was not in detail studied so far. The influence of the local tie handling as well as the impact of the EOP combination are studied. The results show, that the combination leads only to small but partly systematic changes of the CRF. The maximum systematic effect is about 0.5 mas for source positions derived in regional networks only.

GGOS-D Consistent, High-Accuracy Technique-Specific Solutions

Consistent and homogeneous long-time series of the space geodetic techniquesGlobal Positioning System (GPS), Satellite Laser Ranging (SLR), andVery Long Baseline Interferometry (VLBI) provide the basis for thecombination efforts of GGOS-D. For a consistent combination, thedefinition of common standards for parameterization and modeling isessential. These standards and the technique-specific processingoptions of all individual GPS, SLR, and VLBI solutions as well asthe combined SLR and VLBI solutions are discussed.

Using an atmospheric turbulence model for the stochastic model of geodetic VLBI data analysis

Space-geodetic techniques at radio wavelength, such as global navigation satellite systems and very long baseline interferometry (VLBI), suffer from refractivity of the Earth’s atmosphere. These highly dynamic processes, particularly refractivity variations in the neutral atmosphere, contribute considerably to the error budget of these space-geodetic techniques. Here, microscale fluctuations in refractivity lead to elevation-dependent uncertainties and induce physical correlations between the observations. However, up to now such correlations are not considered routinely in the stochastic model of space-geodetic observations, which leads to very optimistic standard deviations of the derived target parameters, such as Earth orientation parameters and station positions. In this study, the standard stochastic model of VLBI observations, which only includes, almost exclusively, the uncertainties from the VLBI correlation process, is now augmented by a variance–covariance matrix derived from an atmospheric turbulence model. Thus, atmospheric refractivity fluctuations in space and time can be quantified. One of the main objectives is to realize a suitable stochastic model of VLBI observations in an operational way. In order to validate the new approach, the turbulence model is applied to several VLBI observation campaigns consisting of different network geometries leading the path for the next-generation VLBI campaigns. It is shown that the stochastic model of VLBI observations can be improved by using high-frequency atmospheric variations and, thus, refining the stochastic model leads to far more realistic standard deviations of the target parameters. The baseline length repeatabilities as a general measure of accuracy of baseline length determinations improve for the turbulence-based solution. Further, this method is well suited for routine VLBI data analysis with limited computational costs.

Numerical Issues in Space-Geodetic Data Analysis and Their Impact on Earth Orientation Parameters

Space-Geodetic techniques are used to provide fundamental scientific products like the terrestrial and celestial reference frame or the Earth orientation parameters (EOPs). These parameters are typically determined in a least squares adjustment of redundant observations. Within this process, numerical issues materializing in the condition of the equation system as well as in insufficient stability of the solution play an important role. While bad condition numbers are an indicator of numerical problems having no connection to the solution strategy i.e., the algorithms used for solving the equation system, numerical stability refers to the algorithms which are used. This paper focuses on the impact of numerical conditioning on EOPs.

Improved Parameter Estimation of Zenith Wet Delays Using an Inequality Constrained Least Squares Method

The path of signals from space geodetic techniques, such as Very Long Baseline Interferometry (VLBI) or Global Navigation Satellite Systems (GNSS), is affected by refractivity variations in the neutral atmosphere. This tropospheric delay, which represents a major contribution to the error budget of space geodetic observations, is generally considered by applying an adequate model (hydrostatic component) and by additionally estimating tropospheric parameters (wet component). Sometimes, the standard approach may lead to negative tropospheric parameters. Due to the fact, that there is nothing like negative water vapour, these negative estimates do not reflect the meteorological conditions in a plausible way.In this paper, we introduce an Inequality Constrained Least Squares (ICLS) method from the field of convex optimization to constrain the tropospheric parameters to non-negative values. We applied this new methodology to 17 years of VLBI sessions. For about 20% of these sessions the method automatically applied inequality constraints. For many sessions the procedure is successful. However, deficiencies in the hydrostatic modeling also lead to worse results for a few sessions. Thus, the methodology is applicable to VLBI data analyses if the a priori modeling is correct which is not always the case for the data set available at the moment.

Development of a Combination Procedure for Celestial Reference Frame Determination

The currently existing realizations of the International Celestial Reference System (ICRS), the International Celestial Reference Frame 1 (ICRF1) and ICRF2, are based on solutions estimated by one VLBI group. In contrast, the International Terrestrial Reference Frame (ITRF) is based on a multi-technique combination with contributions from different geodetic space techniques. Furthermore, these individual technique-specific solutions are generated in an intra-technique combination. To overcome the shortcomings of the past ICRF determination, one of the main goals for the upcoming realizations of the ICRS and ITRS is an entirely consistent and simultaneous computation of both frames. This includes inter- as well as intra-technique combinations.

Scheduling Scenarios for VLBI Observations of Satellites

In this paper, a methodology for automatic scheduling of Very Long Baseline Interferometry (VLBI) observations of satellites is presented and first scheduling approaches are investigated. For this investigation the orbit of a geostationary satellite has been chosen, but, the methodology has also been successfully applied to an orbit of a Global Navigation Satellite Systems satellite. A scheduling procedure based on covariance optimization is developed and observations are simulated. In contrast to other simulation studies for a dedicated VLBI satellite mission, we are performing a scheduling process where observations of quasars and satellites are considered being equally important. Thus, the satellites are consistently included into a VLBI experiment. To validate the individual schedules, simplistic daily constant orbit shifts are estimated and analyzed. In this way, the necessary time between two subsequent satellite observations and the geometry of the observing network are investigated. Taking into account all circumstances, large global networks are the best option for estimating orbit shifts. Such a configuration leads to a large number of observations and a good observing geometry for the orbit. For a geostationary satellite, it is sufficient to carry out only one observation per hour or even longer. However, the presented results are only valid for the estimation of orbit shifts. Various improvements of these initial investigations are imaginable, e.g., considering orbit parameters within the scheduling process or estimating realistic orbit parameters.

GGOS-D Consistent and Combined Time Series of Geodetic/Geophyical Parameters

The generation of the GGOS-D global terrestrial reference frame is based on VLBI, SLR, and GPS observations. The respective observation blocks, analysed as individual units, depend on the technique and cover either full weeks, full days (GPS and SLR) or observing sessions of 24 h duration (VLBI). From these observation units, time series of parameters have been inferred and studies of the quality of the results have been carried out for the identification of deficits in the analyses. In this paper, we describe examples of time series of site coordinates, Earth orientation, and atmosphere parameters as well as peculiarities in the behaviour of these parameters.