Orientation and velocity effects in the global positioning system

We present a simple model of the signals transmitted by global positioning system (GPS) satellites and of the reception of these signals by a GPS receiver, neglecting atmospheric effects. The model idealizes the receiver and transmitter as electric dipole antennas. We derive the open-circuit voltage induced in the antenna of the receiver as a function of time, position, velocity, and orientation of the respective antenna. As an application of this model, we show that by using a single dipole antenna, a user of the GPS can compute his position, time, and two angles of attitude, by tracking the phases of the open-circuit antenna voltages for six GPS satellites.