RSS Localization Under Gaussian Distributed Path Loss Exponent Model

We consider localization from the received signal strength (RSS) when the transmit power and the log-distance pathloss exponent (PLE) are unknown. The unknown transmit power problem is handled by working with the difference of RSS (DRSS) from a reference node. The unknown PLE is statistically modelled as a Gaussian distributed random variable. A maximum-likelihood estimation procedure is firstly proposed to obtain the ratio-of-distances in closed-form. Next, in order to obtain the source location from the ratio-of-distance estimates, we propose a two-step linear least squares (TLLS) estimator which exploits the known relation between the source coordinates and the range variable. Finally, we propose a maximum-a-posteriori (MAP) estimator which jointly estimates the source location and the PLE by maximizing the posterior likelihood of the DRSS values, given the distribution of the PLE. Numerical studies validate the improved localization accuracy of the proposed estimators over the state-of-the-art.