A mathematical model for a polarisation based orientation measurement principle in time of arrival radio localisation systems

The determination of orientation within time of arrival radio localisation systems is a widely discussed matter within the scientific world. In most cases, this goal is reached by using additional navigation sensors. Some other techniques exist, which are utilising only carrier phase measurements. For that purpose, the antenna configuration has to be chosen adequately. In the case considered here, a freely rotating and moving transmitter is equipped with a linearly polarised antenna. Two opposed circularly polarised antennas are used at the receiver. A general mathematical model for this basic measurement system is presented here. The electromagnetic field theory is deployed for the complete transmission chain up to the point where carrier phase measurements are obtained. As input to the model serve position and orientation of each of the transmitter and receiver antennas. The theory is verified by measurements with a rotating transmitter. The comparison of measured and calculated carrier phase values delivers a good match of theory and praxis.