Application of Least Squares with Conditional Equations Method for Railway Track Inventory Using GNSS Observations.

Satellite geodetic networks are commonly used in surveying tasks, but they can also be used in mobile surveys. Mobile satellite surveys can be used for trackage inventory, diagnostics and design. The combination of modern technological solutions with the adaptation of research methods known in other fields of science offers an opportunity to acquire highly accurate solutions for railway track inventory. This article presents the effects of work carried out using a mobile surveying platform on which Global Navigation Satellite System (GNSS) receivers were mounted. The satellite observations (surveys) obtained were aligned using one of the methods known from classical land surveying. The records obtained during the surveying campaign on a 246th km railway track section were subjected to alignment. This article provides a description of the surveying campaign necessary to obtain measurement data and a theoretical description of the method employed to align observation results as well as their visualisation.

Estimation and Prediction of Vertical Deformations of Random Surfaces, Applying the Total Least Squares Collocation Method.

This paper proposes a method for determining the vertical deformations treated as random fields. It is assumed that the monitored surfaces are subject not only to deterministic deformations, but also to random fluctuations. Furthermore, the existence of random noise coming from surface's vibrations is also assumed. Such noise disturbs the deformation's functional models. Surface monitoring with the use of the geodetic levelling network of a free control network class is carried out. Assuming that, in some cases, the control networks are insufficient in surface's deformation analysis, additional and non-measurable reference points have been provided. The prediction of these points' displacements and estimation of the free control network points' displacement are carried out using the collocation method applying the total least squares adjustment. The proposed theoretical solutions were verified by the simulation methods and on the example of a real control network.

Efficacy of Msplit Estimation in Displacement Analysis.

Sets of geodetic observations often contain groups of observations that differ from each other in the functional model (or at least in the values of its parameters). Sets of observations obtained at various measurement epochs is a practical example in such a context. From the conventional point of view, for example, in the least squares estimation, subsets in question should be separated before the parameter estimation. Another option would be application of Msplit estimation, which is based on a fundamental assumption that each observation is related to several competitive functional models. The optimal assignment of every observation to the respective functional model is automatic during the estimation process. Considering deformation analysis, each observation is assigned to several functional models, each of which is related to one measurement epoch. This paper focuses on the efficacy of the method in detecting point displacements. The research is based on example observation sets and the application of Monte Carlo simulations. The results were compared with the classical deformation analysis, which shows that the Msplit estimation seems to be an interesting alternative for conventional methods. The most promising are results obtained for disordered observation sets where the Msplit estimation reveals its natural advantage over the conventional approach.