In Doppler satellite positioning techniques the receiver is often equipped with a monopole antenna. The location of the phase center of this antenna is needed if high accuracy positioning is to be achieved. The phase center, however, changes with the direction of incidence of the received electromagnetic wave. In this paper the phase center is calculated for the idealized model of a monopole antenna with an infinitely large, perfectly conducting ground plane. The analysis is carried out by using the boundary integral equation method for determining the surface current density on the conducting parts of the configuration.