Optimizing the geodetic networks based on the distances between the net points and the project border

Geodetic networks are important for most engineering projects. Generally, a geodetic network is designed according to precision, reliability, and cost criteria. This paper provides a new criterion considering the distances between the Net Points (NPs) and the Project Border (PB) in terms of Neighboring (N). Optimization based on the N criterion seeks to relocate the NPs as close as possible to PB, which leads to creating shorter distances between NPs or those distances linking NPs with Target Points (TPs) to be measured inside PB. These short distances can improve the precision of NPs and increase the accuracy of observations and transportation costs between NPs themselves or between NPs and TPs (in real applications). Three normalized N objective functions based on L1, L2, and L∞‒norms were formulated to build the corresponding N optimization models, NL1; NL2; and NL∞ and to determine the best solution. Each model is subjected to safety, precision, reliability, and cost constraints. The feasibility of the N criterion is demonstrated by a simulated example. The results showed the ability of NL∞ to determine the safest positions for the NPs near PB. These new positions led to improving the precision of the network and preserving the initial reliability and observations cost, due to contradiction problems. Also, N results created by all N models demonstrate their theoretical feasibility in improving the accuracy of the observations and transportation cost between points. It is recommended to use multi-objective optimization models to overcome the contradiction problem and consider the real application to generalize the benefits of N models in designing the networks.

The method of detection and localization of configuration defects in geodetic networks by means of Tikhonov regularization

In adjusted geodetic networks, cases of local configuration defects (defects in the geometric structure of the network due to missing data or errors in point numbering) can be encountered, which lead to the singularity of the normal equation system in the least-squares procedure. Numbering errors in observation sets cause the computer program to define the network geometry incorrectly. Another cause of a defect may be accidental omission of certain data records, causing local indeterminacy or lowering of local reliability rates in a network. Obviously, the problem of a configuration defect may be easily detectable in networks with a small number of points. However, it becomes a real problem in large networks, where manual checking of all data becomes a very expensive task. The paper presents a new strategy for the detection of configuration defects with the use of the Tikhonov regularization method. The method was implemented in 1992 in the GEONET system (www.geonet.net.pl).

The PPP data processing algorithm to create geodetic networks

The article deals with determination of coordinates using global navigation systems, and application of the PPP data processing algorithm to obtain coordinates. The authors conducted an experiment illustrating the algorithm accuracy.

GNSS Networks for Geodynamics in the Caribbean, Northwestern South America, and Central America

For several years, under the framework of national and international projects, the number of GNSS geodetic stations has been increasing in countries located in the area comprised by the Caribbean, northwestern South America and Central America. Data from these geodetic stations have made it possible not only to meet the needs for geospatial information in each of the countries, but also to get a better understanding about the geodynamic interaction of the Caribbean, South American, Nazca and Cocos plates, as well as tectonic blocks wedged in between these plates. This article presents a brief description of the tectonic framework, the existing geodetic networks and the results obtained using data from some stations in the study area.

Research of technical characteristics of wall leveling signs in the context of the ethymology of terms

The aim is to clarify the etymology of the terms “wall leveling mark” and “wall leveling benchmark” in the context of the historical sequence of the appearance of leveling networks in the Ukrainian lands to present the author’s view on these definitions in scientific reference and encyclopedic geodetic literature. To conduct a chronological study of the phenomenon of leveling wall signs of different structures and the corresponding technologies of binding to them in leveling networks, which were created in the Ukrainian lands during the XIX–XXI centuries. Pay attention to the fact that level marks and wall frames, which are valid (working) independent geodetic signs in leveling networks, due to long-term operation are carriers of important geodetic information. Method. To study the results of the analysis of historical sources, standards, reference, encyclopedic and scientific literature in the context of the analysis of the definitions of “level mark” and “wall benchmark” was used analysis of patterns of functioning of the relevant geodetic terminological units. Results. On the territory of Ukraine during the XIX–XXI centuries. Created a leveling (height) network [State Geodetic Network, experimental operation], which operates to this day. The functioning of the leveling (height) network is regulated by legislative acts and regulations. Thanks to the geo-portal of the DGM of Ukraine created by NDIGK, it is possible to obtain information about the preserved level signs. The peculiarity of the leveling (height) network is that it was created by different departments of different countries [Glushkov V.V., 2003] with different height systems and taking into account the access of Ukrainian lands to the Black Sea. All this led to the use of different designs of wall leveling signs and, accordingly, their interpretation, which is not sufficiently reflected in the geodetic reference and regulatory literature. Scientific novelty. The performed comprehensive analysis of information sources can serve as a basis for development of scientific and technical recommendations formonitoring of level signs ofDGMofUkraine and will allow to reveal weaknesses of their functioning which are caused by changes in vital activity of the city environment. The practical value of the work is to solve the problem of distinguishing the production characteristics of the wall leveling mark and wall leveling benchmark, which are fixed leveling signs in geodetic networks of thickening and leveling networks to develop technical developments for inspection and updating points II, leveling networks classes and geodetic networks of thickening in the context of monitoring of geodetic points of DGM of Ukraine and their corresponding representation in the scientific and reference geodetic literature.

Different Approaches to Coordinate Transformation Parameters Determination of Nonhomogeneous Coordinate Systems

During reconstruction and restoration of city geodetic networks, there is quite a common problem that is related to the nonhomogeneity of existing geodetic networks. In any city, local authorities operate with their coordinate systems. Such conditions lead to inconsistency between data of different services. There is only one way how to overcome the problem that lies in the creation and deployment of the new common coordinate system for the whole city. But such an approach has a lack connected with the necessity of transformation parameters acquisition for the latest and old coordinate systems. Insofar as old coordinate systems had been created with different accuracy, using various equipment, and measuring technologies, it is not possible to consider them as homogeneous. It means that we cannot use a classical conformal Helmert transformation to link different coordinate systems. In the presented paper were studied the different approaches for transformation parameters acquisition. A case study of the Almaty city coordinate system was researched and compared the following methods: Helmert transformation, bilinear transformation, the second and third-order regression transformation, and the fourth-order conformal polynomial transformation. It was found out that neither of the considered methods maintains the necessary transformation accuracy (>5 cm). That is why the creation of the transformation field using the finite element method (FEM) was suggested. The whole city was divided into triangles using Delaunay triangulation. For each triangle, the transformation parameters were found using affine transformation with the necessary accuracy.

THE ISSUE OF LS-OPTIMIZATION SATELLITE GEODETIC NETWORKS IN THE TERRESTRIAL COORDINATE SYSTEM

The issue of processing GNSS measurements performed to add a new item into a "hard" network is discussed. Two variants of this add: «beam» and «network» are compared. A fragment of the satellite network, which includes five "hard" points of the main network and one defined, acted as the object on which the computational experiment was carried out, testing the theory of this question. The processing of observational materials is implemented in to Excel electronic computational table using an algorithm synthesized version of the parametric version of LS-optimization of spatial data. The «insert» coordinates obtained as a result of this processing and their average square errors were identical for both variants, which is what follows from the theory of LS-optimization of measurement results taking into account of the errors of the coordinates of «hard» points.