Adjustment of geodetic measurements in geodetic reference system

Geodetske mreže predstavljajo pomemben segment geodezije, saj nam zagotavljajo materializacijo referenčnih koordinatnih sistemov za številne praktične geodetske naloge. Geodetsko mrežo je mogoče izravnati v več koordinatnih sistemih, vendar moramo meritve zato reducirati v ustrezen koordinatni sistem. Zato predstavimo lokalni astronomski koordinatni sistem, lokalni geodetski koordinatni sistem, geodetski koordinatni sistem in koordinatni sistem kartografske projekcije. Predstavimo tudi transformacije med njimi in redukcijo merjenih količin v različne koordinatne sisteme. Nadaljujemo z izravnavo geodetske mreže, kjer začnemo z redukcijo meritev iz fizične realnosti (fizičnega prostora) v eno, dvo in trodimenzionalni geodetski koordinatni sistem. Meritve reduciramo tudi v dvodimenzionalni koordinatni sistem kartografske projekcije. Na podlagi reduciranih meritev predstavimo proces izravnave geodetske mreže po metodi najmanjših kvadratov. Na praktičnem primeru predstavimo proces izravnave geodetske mreže. Primerjamo rezultate izravnave geodetske mreže v različnih koordinatnih sistemih. Na podlagi rezultatov dokažemo, da je izravnava geodetske mreže neodvisna od koordinatnega sistema, če ustrezno reduciramo meritve v ustrezni koordinatni sistem. Izravnane koordinate točk v geodetski mreži so torej identične ne glede na to, ali so izravnane v geodetskem koordinatnem sistemu ali v koordinatnem sistemu kartografske projekcije.Geodetic networks are an important field of research in geodetic and surveying science. They provide the materialization of reference coordinate systems for many practical geodetic and surveying applications. Geodetic network can be adjusted in multiple coordinate systems, but we must reduce measurements to the appropriate coordinate system. We present local astronomic, local geodetic, geodetic and projected coordinate systems, transformations between them and the reduction of measured quantities to the different coordinate systems. We continue with the geodetic network adjustment, where we start with the reduction of typical surveying measurements from the physical reality (physical space) to three, two and one-dimensional geodetic coordinate systems. We also reduce measurements into the two-dimensional projected coordinate system. Based on reduced measurements we present the process of the geodetic network adjustment with least squares method. We also illustrate the geodetic network adjustment process on a practical example. We compare the result of geodetic network adjustments in different coordinate systems. Based on these results we prove that the geodetic network adjustment is independent of a coordinate system if we properly reduce measurements to the appropriate coordinate system. The adjusted point coordinates in the geodetic network are, therefore, identical even when adjusted in a geodetic or in a projected coordinate system