A New Perspective on Range and Directional Localization Problem

This work studies the problem of target localization based on received signal strength (RSS) and angle of arrival (AOA) observations. In contrast to the existing solutions which base their derivations on separate manipulations of each of the measurement models and rely on additional quantity of information available through measurement fusion to boost their performance, we take a different approach here. Rather than treating the measurements individually, we combine them together in order to study the problem from a geometrical perspective. By exploiting the fact that the measurements are noise-corrupted, a fictitious sensor is introduced by each reference point in the network, which allows for application of law of cosines (LC) to fabricated triangles whose last vertex lies at the true target location. Based on weighted central mass of all fictitious sensors, additional side length of the triangles is estimated, which, together with the available angle information, enables straightforward conversion of the problem into a generalized trust region sub-problem (GTRS), which is solved exactly by a bisection method. Both cases of known and unknown transmit power are considered. The proposed algorithm has significantly inferior computational burden than the state-of-the-art approaches, and it not only matches their localization accuracy, but it outperforms them considerably for low number of reference points.