Two mutually orthogonal radiating antennas each transmit electromagnetic radiation to three mutually orthogonal receiving antennas. The transmitted electromagnetic radiation carries data characterizing the phase and magnetic moment of the electromagnetic radiation. Measurement of the two transmitted signals as received by the set of three orthogonal receiving antennas produces information which, in combination with two known position or orientation parameters, is sufficient to determine in a noniterative manner the six position and orientation parameters of the receiving antennas with respect to the radiating antennas. Use of only two radiating antennas increases the speed of the system and simplifies the transmitter. Alternatively, three radiating antennas and two receiving antennas may be provided to simplify the receiver.