Relativnostni vplivi na GPS opazovanja : diplomska naloga

Jelenc, Blaž (author), Stopar, Bojan (mentor), Lakner, Mitja (comentor)

Diplomsko delo obravnava relativnostne vplive na GPS opazovanja. Na začetku sta na kratko predstavljeni posebna in splošna teorija relativnosti. V poglavju posebne relativnosti sta predstavljena pojma Lorentzove transformacije in lastnega časa. V poglavju o splošni relativnosti sta definirana in na kratko predstavljena pojma tenzorja in mnogoterosti, v nadaljevanju pa še slavne Einsteinove enačbe polja ter oris fizikalnega ozadja teh enačb. Sledi podrobna izpeljava enačb za Dopplerjev pojav in lastni čas v Schwartzschildovi metriki, ki jih nato uporabim na relaciji satelit-sprejemnik, kjer se sprejemnik nahaja na geoidu. V nadaljevanju si ogledamo postopke sinhronizacije ur, ki so bistveni pri vzpostavitvi koordinatnega časa. Zadnje poglavje vse dotedanje ugotovitve uporabi pri obravnavi kodnih in faznih opazovanj, kjer nekoliko presenetljivo (a pričakovano) odkrijemo, da so relativnostni vplivi na obe vrsti opazovanj praktično enaki.

• Language: Slovenian
• Keywords: geodezija, diplomska dela, UNI, splošna relativnost, GPS opazovanja
• Work type: Undergraduate thesis
• Typology: 2.11 - Undergraduate Thesis
• Organization: FGG - Faculty of Civil and Geodetic Engineering
• Place of publishing: Ljubljana
• Publisher: [B. Jelenc]
• Year: 2006
• Number of pages: IX, 58 str.
• PID: 20.500.12556/RUL-32070
• UDC: 528.28:(043.2)
• COBISS.SI-ID: 3185249
• Publication date in RUL: 10.07.2015

JELENC, Blaž, 2006, Relativnostni vplivi na GPS opazovanja : diplomska naloga [online]. Bachelor’s thesis. Ljubljana : B. Jelenc. [Accessed 17 April 2025]. Retrieved from: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=eng&id=32070

Secondary language

• Language: English
• Title: Relativistic effects on GPS observations : graduation thesis

Abstract

Diploma presents relativistic effects on GPS observations. First and second chapter are a short introduction to special and general theory of relativity, where notions of proper time, Lorentz transform, tensor and manifold are presented. Famous Einstein field equations follow and I give a brief explanation of physical backgroung. A detailed derivation of Doppler effect and proper time equations in Schwartzschild metric follows, which are then used in connection with satellite and reciver, where the reciver is supposed to be placed on geoid. An important chapter on clock synchronisation is also included, methods described there are important in construction of coordinate time. Last chapter deals with code and phase observations, and an important conclusion is that relativistic effects on these two different types of observations are basically the same.

• Keywords: general relativity, GPS observations