A new approach to the geometry of TOA location

Positioning a transmitter via measured times of arrival (TOAs), or range measurements, is a familiar technique that has received much attention in the literature. In the traditional geometric interpretation, TOAs generate circles whose intersections provide the estimate of the transmitter. In this paper a new geometrical interpretation is presented in which straight lines of position (LOPs), rather than the circular LOPs, are used to determine the position of the transmitter. The straight LOPs come from a simple observation regarding the geometry of the system and are not obtained from linearization. Two methods using the straight LOPs are given and their performance is analyzed and compared to methods which employ linearization.