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 info...

Geodetic deformation analysis can be interpreted as a model selection problem. The null model indicates that no deformation has occurred. It is opposed to a number of alternative models, which stipulate different deformation patterns. A common way to select the right model is the usage of a statistical hypothesis test. However, since we have to test a series of deformation patterns, this must be a multiple test. As an alternative solution for the test problem, we propose the p-value approach. Another approach arises from information theory. Here, the Akaike information criterion (AIC) or some alternative is used to select an appropriate model for a given set of observations. Both approaches are discussed and applied to two test scenarios: A synthetic levelling network and the Delft test data set. It is demonstrated that they work but behave differently, sometimes even producing different results. Hypothesis tests are well-established in geodesy, but may suffer from an unfavourable choice of the decision error rates. The multiple test also suffers from statistical dependencies between the test statistics, which are neglected. Both problems are overcome by applying information criterions like AIC.

The observations of geodetic very long baseline interferometry (VLBI) measurements refer to an invariant point of the radio telescope. This point is often called the reference point. For the interpretation of VLBI results it is necessary to know the position of this invariant point and its possible variation with time. Only the knowledge of the reference point makes it possible to combine VLBI results with results from other colocated techniques and in the framework of the global geodetic observing system (GGOS). Within the GGOS an automated monitoring of the reference points and therefore of the local-tie vectors at colocation stations is discussed earlier in other studies. In this paper a new mathematical model is described to allow such an automated monitoring of the reference point of an azimuth-elevation type radio telescope.

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.

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.