A geometrical closed form solution for RSS based far-field localization: Direction of Exponent Uncertainty

Abstract

In this study, a new powerful geometrical closed-form solution called Direction of Exponent Uncertainty (DEU) is proposed for received signal strength (RSS) based far-field localization when path loss exponent (PLE) and transmit power are both unknown. The uncertainty in the PLE due to environmental factors is a significant challenge for RSS based localization. DEU is built after careful investigation of geometrical behaviors of differential received signal strength circles, i.e. the locus of possible location of the emitter when transmit power is unknown. It is shown that the uncertainty in the PLE corresponds to a linear uncertainty for the location of the emitter in two dimensional space. This critical observation creates a basis for the sensor to move towards the emitter without estimating the emitter location after only three measurements. Furthermore, with only four different measurements, it is possible to effectively estimate the location of the emitter as well as the PLE by means of intersection of DEUs. Intersection of DEUs attains Cramer Rao Lower Bound with a dramatically reduced execution time compared to nonlinear least squares estimator. DEU is also proposed as an efficient route planning tool for moving sensors such as unmanned aerial vehicles.