The three-dimensional coordinate’s transformation from one system to another, and more specifically, the Helmert transformation problem, is one of the most well-known transformations in the field of engineering. In this paper, its solution, in reverse problem, was investigated for specific data using three different methods. It is presented by solving it with the method of Euler angles as well as with the use of quaternion and dual-quaternion algebra, after first giving some basic mathematical theory. After research, not only were three artificial sets of data used, which were structured in a specific way and forced into specific transformations to be solved, but also a real geodesy problem was tested, in order to identify the sensitivity and problems of each method. Statistical analysis of the results was performed by each method, while it was found that there were significant deviations in rotations and translations in the method of Euler angles and dual quaternions, respectively.

The National Technical University of Athens undertook the compilation of an "Integrated Diagnostic Research Project and Strategic Planning for Materials, Interventions Conservation and Rehabilitation of the Holy Aedicule of the Church of the Holy Sepulchre in Jerusalem". This paper focuses on the work merging the geometric documentation with the characterization of materials, the identification of building phases and the diagnosis of decay and pathology through the use of analytical and non-destructive techniques. Through this integrated approach, i.e. through the documentation and characterization of the building materials, through the diagnosis of decay and pathology, through the accurate geometric documentation of the building and through the non-destructive prospection of its internal structure, it was feasible to identify the construction phases of the Holy Aedicule, identifying the remnants of the preserved earlier constructions and the original monolithic Tomb. This work, thus, demonstrates that the adoption of an interdisciplinary approach for integrated documentation is a powerful tool for a better understanding of monuments, both in terms of its structural integrity, as well as in terms of its state of preservation, both prerequisites for effective rehabilitation.

Reflectorless distance measurement provides the ability to easily make quick measurements saving time and labor for surveyors. The precision and accuracy of these types of measurements are under discussion because of the variety of parameters that can affect these measurements that are not well-understood. This paper attempts to answer some of the questions that have arisen about the credibility of reflectorless distance measurements ranging up to 50 m. An experiment was carried out using 26 different materials as the reflecting surface (these materials were also of differing colors). Additionally, the experiment used three different angles of incidence of the incoming electromagnetic energy with three different types of reflectorless total stations over a variety of ranges. A further experiment was conducted with an additional total station using 11 different materials at different ranges. To properly evaluate the results, a special supporting base was manufactured for holding the reflecting surface to e...

Forecasting is one of the most growing areas in most sciences attracting the attention of many researchers for more extensive study. Therefore, the goal of this study is to develop an integrated forecasting methodology based on an Artificial Neural Network (ANN), which is a modern and attractive intelligent technique. The final result is to provide short-term and long-term forecasts for point position changing, i.e., the displacement or deformation of the surface they belong to. The motivation was the combination of two thoughts, the insertion of the forecasting concept in Geodesy as in the most scientific disciplines (e.g., Economics, Medicine) and the desire to know the future position of any point on a construction or on the earth’s crustal. This methodology was designed to be accurate, stable and general for different kind of geodetic data. The basic procedure consists of the definition of the forecasting problem, the preliminary data analysis (data pre-processing), the definition of the most suitable ANN, its evaluation using the proper criteria and finally the production of forecasts. The methodology gives particular emphasis on the stages of the pre-processing and the evaluation. Additionally, the importance of the prediction intervals (PI) is emphasized. A case study, which includes geodetic data from the year 2003 to the year 2016—namely X, Y, Z coordinates—is implemented. The data were acquired by 1000 permanent Global Navigation Satellite System (GNSS) stations. During this case study, 2016 ANNs—with different hyper-parameters—are trained and tested for short-term forecasting and 2016 for long-term forecasting, for each of the GNSS stations. In addition, other conventional statistical forecasting methods are used for the same purpose using the same data set. Finally the most appropriate Non-linear Autoregressive Recurrent network (NAR) or Non-linear Autoregressive with eXogenous inputs (NARX) for the forecasting of 3D point position changing is presented and evaluated. It is proved that the use of ANNs, in order to make short-term and long-term forecasts, provides forecasting changes of the order of 2 mm with Mean Absolute Error (MAE) of the order of 0.5 mm.