Reference point determination with a new mathematical model at the 20 m VLBI radio telescope in Wettzell

A new mathematical model to estimate the International VLBI Service (IVS) reference point and additional parameters of a Very Long Baseline Interferometry (VLBI) radio telescope was developed by Lösler and Hennes (2008). To verify this analysis procedure a reference point determination was carried out on the 20m radio telescope at the “Fundamentalstation Wettzell” (Germany) from April to May 2008. This paper describes the terrestrial local survey, the analysis methodology and the results obtained, in particular the accuracy of the determination of the IVS reference point

Multiple Outlier Detection: Hypothesis Tests versus Model Selection by Information Criteria

The detection of multiple outliers can be interpreted as a model selection problem. Models that can be selected are the null model, which indicates an outlier free set of observations, or a class of alternative models, which contain a set of additional bias parameters. A common way to select the right model is by using a statistical hypothesis test. In geodesy data snooping is most popular. Another approach arises from information theory. Here, the Akaike information criterion (AIC) is used to select an appropriate model for a given set of observations. The AIC is based on the Kullback-Leibler divergence, which describes the discrepancy between the model candidates. Both approaches are discussed and applied to test problems: the fitting of a straight line and a geodetic network. Some relationships between data snooping and information criteria are discussed. When compared, it turns out that the information criteria approach is more simple and elegant. Along with AIC there are many alternative information criteria for selecting different outliers, and it is not clear which one is optimal

An innovative mathematical solution for a time-efficient IVS reference point determination

The improvement of the local ties between different observation methods (GPS, VLBI, etc.) improves the quality of the ITRF considerably. The IVS reference point of a VLBI radio telescope is defined as the intersection between the azimuth- and elevation-axis or, if they do not intersect, the intersection of the right-angle projection from the elevation-axis onto the azimuth-axis. In the past, these axes have been estimated by fitting 3D circles, e.g. (Eschelbach et al., 2003) or (Dawson et al., 2006). The data acquisition for the determination of the circles requires that the telescope has to be moved into clearly defined positions; therefore, the basic station process (data gathering for the intrinsic telescope task) is disturbed. In this paper we present an alternative mathematical model, which computes the reference point without circle fitting. This algorithm does not need observations from predefined telescope positions and therefore the station\u27s downtime can be reduced. The parameter estimation of this non-linear problem is implemented in two steps. At first we are using the Levenberg-Marquardt-Algorithm for a pre-evaluation to find stable approximate values (Madsen et al., 2004), which we use for the main least-square-model in a second step

Evolution and obtained expertise in reference point determination at the GIK

The International Terrestrial Reference System (ITRS) is realized by geodetic space techniques, which are linked by local-ties at the observation stations. Therefore, reliability and high accuracy are the main requirements for the determination of the different reference points in the corresponding local reference frame. At the Geodetic Institute of the University of Karlsruhe several scientific studies have been carried out to determine the reference point of radio telescopes at different observation stations and with different calculation models. Starting in 2002 the IVS reference point at Onsala Space Observatory was determined by 3D-circle fits with error propagation using full covariance information, which is custom procedure nowadays. In 2008 a completely new mathematical model was established able to fulfill future requirements as for example minimizing downtime of the telescope. Geodetic measurements with a tacheometer respectively a lasertracker at the Fundamentalstation Wettzell and the Onsala Space Observatory yielded a good verification of the model. This contribution shows the evolution and obtained expertise in reference point determination at the Geodetic Institute of the University of Karlsruhe by comparing the results of different campaigns at the Onsala Space Observatory

How to account for temporal correlations with a diagonal correlation model in a nonlinear functional model : A plane fitting with simulated and real TLS measurements

To avoid computational burden, diagonal variance covariance matrices (VCM) are preferred to describe the stochasticity of terrestrial laser scanner (TLS) measurements. This simplification neglects correlations and affects least-squares (LS) estimates that are trustworthy with minimal variance, if the correct stochastic model is used. When a linearization of the LS functional model is performed, a bias of the parameters to be estimated and their dispersions occur, which can be investigated using a second-order Taylor expansion. Both the computation of the second-order solution and the account for correlations are linked to computational burden. In this contribution, we study the impact of an enhanced stochastic model on that bias to weight the corresponding benefits against the improvements. To that aim, we model the temporal correlations of TLS measurements using the Matérn covariance function, combined with an intensity model for the variance. We study further how the scanning configuration influences the solution. Because neglecting correlations may be tempting to avoid VCM inversions and multiplications, we quantify the impact of such a reduction and propose an innovative yet simple way to account for correlations with a “diagonal VCM.” Originally developed for GPS measurements and linear LS, this model is extended and validated for TLS range and called the diagonal correlation model (DCM). © 2020, The Author(s)

Bestimmung des lokalen Verbindungsvektors zwischen IVS- und IGS-Referenzrahmen am Raumobservatorium Onsala (Schweden)

Für die Bildung des International Terrestrial Reference Frame (ITRF) müssen Ergebnisse von verschiedenen Raumverfahren wie beispielsweise Very Long Baseline Interferometry (VLBI), SLR/LLR (Satellite/Lunar Laser Ranging) oder Global Navigation Satellite System (GNSS) genutzt und miteinander kombiniert werden. Die Kombination dieser Raumverfahren wird jedoch erst durch so genannte Kollokationsstationen möglich. Dies sind Stationen, an denen mindestens zwei Raumverfahren betrieben werden. Der Verbindungsvektor (local-tie), der die räumlichen Beziehungen zwischen den betriebenen Raumverfahren beschreibt, wird durch präzise, lokale, terrestrische Vermessung der Referenzpunkte abgeleitet. Die im Herbst dieses Jahres durchgeführten Vermessungsarbeiten mit einem Lasertracker an der Fundamentalstation in Onsala (Schweden) zur Bestimmung des Verbindungsvektors zwischen dem GPS- und dem VLBI-Referenzpunkt sowie die erzielten Ergebnisse sollen im Folgenden dargestellt werden

Terrestrial monitoring of a radio telescope reference point using comprehensive uncertainty budgeting

During the 15-day-long global very long baseline interferometry campaign CONT14, a terrestrial monitoring campaign was carried out at the Onsala Space Observatory. The goal of these efforts was to monitor the reference point of the Onsala 20 m radio telescope during normal telescope operations. Parts of the local site network as well as a number of reflectors that were mounted on the 20 m radio telescope were observed in an automated and continual way using the in-house-developed software package HEIMDALL. The analysis of the observed data was performed using a new concept for a coordinate-based network adjustment to allow the full adjustment process in a true Cartesian global reference frame. The Akaike Information Criterion was used to select the preferable functional model for the network adjustment. The comprehensive stochastic model of this network adjustment process considers over 25 parameters, and, to describe the persistence of the observations performed during the monitoring with a very high measurement frequency, includes also time-dependent covariances. In total 15 individual solutions for the radio telescope reference point were derived, based on monitoring observations during the normal operation of the radio telescope. Since the radio telescope was moving continually, the influence of timing errors was studied and considered in the adjustment process. Finally, recursive filter techniques were introduced to combine the 15 individual solutions. Accuracies at the sub-millimeter level could be achieved for the radio telescope reference point. Thus, the presented monitoring concept fulfills the requirement proposed by the global geodetic observing system

The variance inflation factor to account for correlations in likelihood ratio tests: deformation analysis with terrestrial laser scanners

The measurement noise of a terrestrial laser scanner (TLS) is correlated. Neglecting those correlations affects the dispersion of the parameters when the TLS point clouds are mathematically modelled: statistical tests for the detection of outliers or deformation become misleading. The account for correlations is, thus, mandatory to avoid unfavourable decisions. Unfortunately, fully populated variance covariance matrices (VCM) are often associated with computational burden. To face that challenge, one answer is to rescale a diagonal VCM with a simple und physically justifiable variance inflation factor (VIF). Originally developed for a short-range correlation model, we extend the VIF to account for long-range dependence coming from, for example, atmospheric turbulent effects. The validation of the VIF is performed for the congruency test for deformation with Monte Carlo simulations. Our real application uses data from a bridge under load

Permanent monitoring of the reference point at the 20m radio telescope Wettzell

To achieve the aims of the VLBI2010 agenda and of the Global Geodetic Observing System (GGOS) an automated monitoring of the reference points of different geodetic space techniques, such as Very Long Baseline Interferometry (VLBI), is desirable. The resulting permanent monitoring of the local-tie vectors at co-location stations are essential to obtain the sub-millimeter level in the combinations. For this reason a monitoring system was installed by the Geodetic institute of the University of Karlsruhe (GIK) to observe the 20m radio telescope for VLBI at the Geodetic Observatory Wettzell from May to August. A specially developed software from the Geodetic Institute of the university collected data from automated total station measurements, meteorological sensors, and sensors in the telescope monument (e.g., Invar cable data). A real-time visualization directly offered a live view of the measurements during the regular observation operations. Additional scintillometer measurements allowed refraction corrections during the post-processing. This project is one of the first feasibility studies aimed at determining significant deformations of the VLBI antenna due to, for instance, changes in temperature

Bestimmung der Parameter einer Regressionsellipse in allgemeiner Raumlage

Dreidimensionale Koordinaten von diskreten Punkten eines zu untersuchenden Objektes können mit verschiedenen geodätischen Messsystemen erfasst werden. Um jedoch eine qualitative Aussage bezüglich der Größe, Form oder Lage dieses Objektes treffen zu können, werden Algorithmen zur Schätzung von Approximationsformen benötigt. Das Ableiten von Formmaßen mithilfe der Methode der kleinesten Quadrate bildet die Grundlage bei der Qualitätsüberwachung und -analyse z.B. im Anlagen- und Maschinenbau. Am Beispiel der Ellipsenausgleichung werden in diesem Beitrag zunächst Bestimmungsverfahren in der Ebene beschrieben, die anschließend auf den allgemeinen räumlichen Fall übertragen werden und in einem einfach zu implementierenden funktionalen Modell zur Parameterschätzung münden