Least-squares adjustment taking into account the errors in variables

In this article, we discuss the procedure for computing the values of the unknowns under the condition of the minimum sum of squares of the observation residuals (least-squares method), taking into account the errors in the unknowns. Many authors have already presented the problem, especially in the field of regression analysis and computations of transformation parameters. We present an overview of the theoretical foundations of the least-squares method and extensions of this method by considering the errors in unknowns in the model matrix. The method, which can be called ‘the total least-squares method’, is presented in the paper for the case of fitting the regression line to a set of points and for the case of calculating transformation parameters for the transition between the old and the new Slovenian national coordinate systems. With the results based on relevant statistics, we confirm the suitability of the considered method for solving such tasks.

Development of Parameter Transformation of Indonesian Geospatial Reference System 2013

DGN95 is a static geospatial reference system, in which the change in the value of coordinates towards time as a result of tectonic plate movement and deformation of the earth’s crust, is not considered. Changes in the value of coordinates towards time need to be considered in defining a geospatial reference system for the territory of Indonesia. This is because the territory of Indonesia is located between several tectonic plates which are very dynamic and active. This area of IndoneFor this reason, SRGI2013 was born, a national coordinate system that was consistent and compatible with the global coordinate system. SRGI considers changes in coordinates based on time functions. Problems arise when the coordinates of the old pillar still use the DGN95 datum reference system. Many published maps or geodetic control network use the old coordinate system, then the mapping user has difficulty getting the conversion of coordinates change aforesaid. The purpose of this study is to produce coordinate transformation parameters to change the coordinates of the old datum (DGN95) into coordinates in the SRGI2013 datum. The results of the transformation parameters resulted are used to change coordinates that are still in the old datum. In addition to making it easier for users to transform coordinates. The coordinate transformation method used uses the 3-dimensional coordinate transformation of the Bursa-Wolf model (7 parameters) and the Affinity model (10 parameters).

Determination of the relationship between Vietnam national coordinate reference system (VN-2000) and ITRS, WGS84 and PZ-90

In July 2000, Hanoi-72 reference system was replaced by the Vietnam reference system, namely as VN-2000 as an official geodetic background system in Vietnam. Ministry of Natural Resources and Environment of Vietnam has reported the transformation parameters between VN-2000 and WGS84. Nevertheless, there is a need to estimate a new transformation parameter set between VN-2000 and WGS84 because WGS84 has been updated. In addition, there is now a lack of an accurate published set of parameters for transformation from VN-2000 to not only the International Terrestrial Reference System ITRS but also PZ-90. In this study, coordinate transformation parameters between ITRS and VN-2000 are estimated through the use of a least square approach and the common points with known coordinates in both systems. These set of parameters was then deployed to determine the link between VN-2000 and WGS84 as well as PZ-90. The results denoted that the derived transformation parameters, on the basis of the results at the checkpoints, could generated station positions with the accuracy at several cm level for transformation from VN-2000 to the new realizations of ITRS, WGS84 and PZ90 and reversely. These achievements reveals that the set of parameters is great significance for many applications related to positioning in Vietnam.

TRANSFORMATION PARAMETERS BETWEEN UCS-2000 AND WGS-84

According to the Order of the Ministry of Agrarian Policy of Ukraine, published in 2016, about the procedure for using the national coordinate system UCS-2000, this was the first time officially presented parameters of the Helmert transformation from the UCS-2000 system to the ITRF-2000 system. However, all software products are used for communication between various coordinate systems as the main coordinate system, WGS-84. The Helmert transformation parameters between the UCS-2000 and WGS-84 systems are found for the new realization of WGS-84 (G1762) based on GPS data and the old realization of the WGS-84, based on the US Satellite Navigation System, known as DOPPLER Transit. It is shown that the use of the transformation parameters of the old realization WGS-84 for the processing of present GPS measurements will result in a systematic error of the order of 0.6 m. Obtained transformation parameters can be used as the first approximation to obtain accurate Helmert transformations based on GPS measurements at points with known coordinates in the UCS-2000 system. The described procedure for determining the parameters will be especially useful in the case when a more accurate connection will be established between the systems ITRFyy and WGS-84, than the current one.

Application of the Undifferenced GNSS Precise Positioning in Determining Coordinates in National Reference Frames

In high-accuracy positioning using GNSS, the most common solution is still relative positioning using double-difference observations of dual-frequency measurements. An increasingly popular alternative to relative positioning are undifferenced approaches, which are designed to make full use of modern satellite systems and signals. Positions referenced to global International Terrestrial Reference Frame (ITRF2008) obtained from Precise Point Positioning (PPP) or Undifferenced (UD) network solutions have to be transformed to national (regional) reference frame, which introduces additional bases related to the transformation process. In this paper, satellite observations from two test networks using different observation time series were processed. The first test concerns the positioning accuracy from processing one year of dual-frequency GPS observations from 14 EUREF Permanent Network (EPN) stations using NAPEOS 3.3.1 software. The results were transformed into a national reference frame (PL-ETRF2000) and compared to positions from an EPN cumulative solution, which was adopted as the true coordinates. Daily observations were processed using PPP and UD multi-station solutions to determine the final accuracy resulting from satellite positioning, the transformation to national coordinate systems and Eurasian intraplate plate velocities. The second numerical test involved similar processing strategies of post-processing carried out using different observation time series (30 min., 1 hour, 2 hours, daily) and different classes of GNSS receivers. The centimeter accuracy of results presented in the national coordinate system satisfies the requirements of many surveying and engineering applications.

State borders in ETRS89 coordinates – reality or fiction ?

<p>Common unique ETRS89 coordinates of the state boundaries are crucial for cross-border data harmonization for international projects. In the frame of European Location Framework (ELF) project Czech Office for Surveying, Mapping and Cadastre (ČÚZK) cooperates with Poland on egde-matching on the state border. During the preliminary phase of the project was some difficulty identified. If the state boundary is measured and administered in the national coordinate system, the accuracy of the transformation into the ETRS89 is influenced by discrepancies of the local trigonometric network, which results in two slightly different state boundaries. Final solution for Europe – international treaties on the state borders based on the ETRS89 coordinates – is necessary, but it will take years.</p>

Controlling Length Deformation Caused by Elevation According to Coordinate Transformation

Because of the influence of elevation, Surface observation distance and reference ellipsoid distance is not equal, Resulting in length deformation, The size of the deformation is caused by elevation, In order to meet the requirements of measurement accuracy, It must be controlled within a certain range. In this paper, through establishing measuring reference, realized coordinates transformation in the national reference, it is very effective to control length deformation which is caused by elevation, at the same time, The relative position of survey area is unchanged in the national coordinate system