des Instituts für Geodäsie

Heft 19/1986

The Basic Observation Equations
of Carrier Phase Measurements
to the Global Positioning System
Including General Orbit Modelling


In: LANDAU, Herbert / EISSFELLER, Bernd / HEIN, Günter W. [1986]:
GPS Research 1985 at the Institute of Astronomical and Physical Geodesy
Schriftenreihe Universitärer Studiengang Vermessungswesen, Universität der Bundeswehr München, Heft 19, Neubiberg, S. 7-45.


Starting with the physics of microwave propagation the non-linear observation equations of carrier phase (difference) observations to the Global Positioning System (GPS) are derived. A possible orbit model and its parameters are described for the GPS satellites and inserted in the observation equations following the principle of integrated geodesy. The treatment of tropospheric and ionospheric effects on the observations is presented as well as the complete linearization of the final observation equations. The general estimation model for multi-baseline vectors including orbit modelling is outlined.

The paper intends to present the mathematical beckground of the use of GPS phase observations for surveying in a general operational way. It does not discuss details of the numerical realization. Rather, it is devoted to show the different functional relationship of the basic parameters and assumptions inherent in any approach.

A short summary of the paper was presented at the First International Symposium on Precise Positioning with the Global Positioning System, Rockville, Md., April 15-19, 1985, under the title "Integrated Modelling of GPS-Orbits and Multi-Basline Components".

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