Volume 15, Issue 2

The paper presents M split estimation as an alternative to methods in the class of robust M-estimation. The analysis conducted showed that M split estimation is highly efficient in the identification of observations encumbered by gross errors, especially those of small or moderate values. The classical methods of robust estimation provide then unsatisfactory results. M split estimation also shows high robustness to single gross errors of large values. The presented analysis of M split estimators’ robustness is of a chiefly empirical nature and is based on the example of a simulated levelling network and a real angular-linear network. Using the Monte Carlo method, mean success rates for outlier identification were determined and the courses of empirical influence functions were specified. The outcomes of the analysis were compared with the relevant values achieved via selected methods of robust M-estimation.

The CORS network is a volunteer-based network of Global Positioning System reference stations located mainly in the US and its territories. We discuss the most recent comprehensive reprocessing of all GPS data collected via this network since 1996. Daily data for GPS weeks 834 through 1933 were reprocessed leading to epoch 2010.0 coordinates and velocities of 3049 stations aligned to IGS14. The updated realization of the US National Spatial Reference System derived in this work has been in use since late 2019. As a validation of the results, the derived velocity field is compared to several other solutions and to three regional geophysical and geodetic velocity models. These comparisons uncovered unstable stations which move differently than the regional kinematics around them. Once these are ignored, we estimate the horizontal and vertical stability of this updated realization to be better than ∼0.3 and ∼0.6 mm/year, respectively. We use the position residuals and estimated uncertainties from this reprocessing to derive long-term stability measures for all active stations serving longer than 3 years. These measures exposed ∼60 CORS with the poorest long-term stability, which have been consequently excluded from serving as mapping control.

The goal of classical geodetic data analysis is often to estimate distributional parameters like expected values and variances based on measurements that are subject to uncertainty due to unpredictable environmental effects and instrument specific noise. Its traditional roots and focus on analytical solutions at times require strong prior assumptions regarding problem specification and underlying probability distributions that preclude successful application in practical cases for which the goal is not regression in presence of Gaussian noise. Machine learning methods are more flexible with respect to assumed regularity of the input and the form of the desired outputs and allow for nonparametric stochastic models at the cost of substituting easily analyzable closed form solutions by numerical schemes. This article aims at examining common grounds of geodetic data analysis and machine learning and showcases applications of algorithms for supervised and unsupervised learning to tasks concerned with optimal estimation, signal separation, danger assessment and design of measurement strategies that occur frequently and naturally in geodesy.

To survey the pipe’s axis used in the installation of the cable-stayed bridge, a reflectorless total station and a proposed surveying observation technique were used. The approach includes a new method for observation and a graphical solution for the pipe’s axis determination. The technique shown in this paper can be applied for vertical and semi-vertical cylindrical pipes. A field test with real data and results is also presented.

As crustal structure models based on seismic and other data are frequently used as a-priori information for further geophysical and geological studies and interpretations (e. g., for gravity inversion), it is important to accurately document their qualities. For instance, the uncertainties in published crustal structures deeply affect the accuracies of produced Moho contour maps. The qualities in seismic crustal models arise from several factors such as the survey method, the spatial resolution of the survey (for example the spacing of the shot points and the recording stations), and the analytical techniques utilized to process the data. It is difficult to determine the uncertainties associated with seismic based crustal depth/Moho depth (MD) models, and even more difficult to use such data for estimating the Moho density contrast (MDC) and its accuracy. However, there is another important observable available today, namely global satellite gravitational data, which are fairly homogeneous v. r. t. accuracy and distribution over the planet. For instance, we find by simple error propagation, using the error covariance matrix of the GOCE TIM5 gravitational model, that this model can determine the MD to a global RMS error of 0.8 km with a resolution of about 1° for a known MDC of 200 kg/m3\text{kg}/{\text{m}^{3}}. However, the uncertainty in the MDC will further deteriorate the result. We present a new method for estimating the MD and MDC uncertainties of one model by comparing it with another (correlated or uncorrelated) model with known uncertainty. The method is applied in estimating the uncertainty for the CRUST1.0 MD model from four global models (CRUST19, MDN07, GEMMA1.0, KTH15C), yielding mean standard errors varying between 2 and 4.9 km in ocean regions and between 3.2 and 6.0 km on land regions with overall means of 3.8±0.4 and 4.8±0.6km4.8\pm 0.6\hspace{0.1667em}\text{km}, respectively. Also, starting from the KTH15C MDC model, the mean standard error of CRUST1.0 MDC was estimated to 47.4 and 48.3 kg/m3\text{kg}/{\text{m}^{3}} for ocean and land regions, respectively.

Simultaneous use of data repeated levelling measurements and continuous GNSS observations allows increasing the spatial resolution of geodynamics models. For this purpose, it is necessary to create a single network, a so-called hybrid network. This paper aims at examining the possibility of using scale-free network theory to determine the most relevant common points in hybrid networks using the distance criterion. Used on European network points: UELN (United European Levelling Network) and EPN (European Permanent GPS Network) and the regional network. In the hybrid network (UELN + EPN), 18 pseudo-nodal points with the highest number of links were identified. The accepted distance criterion shows that about 90 % of the EPN points can be used as common points. The application of the scale-free network theory allows determining the significance of points in a hybrid network.