Transformation of spatial coordinates (3D) is a common computational task in photogrammetry, engineering geodesy, geographical information systems or computer vision. In the most frequently used variant, transformation of point coordinates requires knowledge of seven transformation parameters, of which three determine translation, another three rotation and one change in scale. As these parameters are commonly determined through iterative methods, it is essential to know their initial approximation. While determining approximate values of the parameters describing translation or scale change is relatively easy, determination of rotation requires more advanced methods. This study proposes an original, two-step procedure of estimating transformation parameters. In the initial step, a modified version of simulated annealing algorithm is used for identifying the approximate value of the rotation parameter. In the second stage, traditional least squares method is applied to obtain the most probable values of transformation parameters. The way the algorithm works was checked on two numerical examples. The computational experiments proved that proposed algorithm is efficient even in cases characterised by very disadvantageous configuration of common points.

Geodetic measurements are commonly used in displacement analysis to determine the absolute values of displacements of points of interest. In order to properly determine the displacement values, it is necessary to correctly identify a subgroup of mutually stable points constituting a reference system. The complexity of this task depends on the spatial size of the network, the timespan of measurements and geological conditions affecting the type of changes in the location of points. As a consequence of the abovementioned factors, the task of stable identification in a longer timespan for a subgroup of points may produce equivocal results. In particular, it is likely that alternative subgroups of reference points meeting the mutual stability criteria will be selected, sometimes without common reference points. The proposed method of reference system identification utilises optimisation algorithms. Two such algorithms were tested, i.e., simulated annealing (SA) and Hooke-Jeeves (HJ) method. Two numerical examples were used to test the proposed method. Although in the first example both methods delivered a positive result, the second example showed the superiority of the SA method over the HJ. The proposed method can be considered a tool supporting the person analysing and making calculations in reaching the ultimate decision on reference points.

This paper presents the accuracy investigation results and functionality of Ubisense RTLS positioning system. Three kinds of studies were conducted: test of calibration accuracy, analysis of theoretical accuracy of the coordinates determination as well as accuracy measurements in field conditions. Test of calibration accuracy was made with several different geometric constellation of reference points (tag positions). We determined changes of orientation parameters of receivers and disturbance of positioning points coordinates against chosen reference points constellations. Analysis of theoretical accuracy was made for several receivers spatial positions and their orientations. It allowed to indicate favourable and unfavourable measurement area considering accuracy and reliability. Real positioning accuracy of the Ubisense system was determined by comparison with coordinates measured using precise tacheometer TCRP1201+. Results of conducted experiments and accuracy analysis of test measurement were presented in figures and diagrams.

Precise information of railway tracks geometry is necessary to design alignment project. Geodetic measurements are the most common method of determining this information and sags of arch direct measurement are the traditional and still popular measurement method. Development of geodetic measurements techniques made possible to use another methods such as tacheometry, GNSS, and new methods based on mobile measurement devices. Series of experiments were conducted to set the practical usability of selected modern measurement methods to design track alignment project. The experimental measurements were performed on the 3 km long two-track railway fragment. Following methods were used during the test measurements: sags of arch direct measurement, tacheometry with total station, GNSS, automated methods with the use of a trolley system. Above mentioned measurement methods were compared taking into account time and labour consumption, range of geometric data, measurement equipment cost, reliability and accuracy of surveying procedure. Because of different data types are delivered with various methods, sags of arch were used for comparison of accuracy. Comparison of geometrical data obtained with analysed methods allowed to formulate conclusions concerning practical usability those methods for track alignment project development.

Monitoring systems using automated electronic total stations are an important element of safety control of many engineering objects. In order to ensure the appropriate credibility of acquired data, it is necessary that instruments (total stations in most of the cases) used for measurements meet requirements of measurement accuracy, as well as the stability of instrument axis system geometry. With regards to the above, it is expedient to conduct quality control of data acquired using electronic total stations in the context of performed measurement procedures. This paper presents results of research conducted at the Faculty of Geodesy and Cartography at Warsaw University of Technology investigating the stability of “basic” error values (collimation, zero location for V circle, inclination), for two types of automatic total stations: TDA 5005 and TCRP 1201+. Research provided also information concerning the influence of temperature changes upon the stability of investigated instrument’s optical parameters. Results are presented in graphical analytic technique. Final conclusions propose methods, which allow avoiding negative results of measuring tool-set geometry changes during conducting precise deformation monitoring measurements.