Accurate Distance Estimation for RSS Localization With Statistical Path Loss Exponent Model

We study the ratio-of-distance estimation from the difference of received signal strength (DRSS) when the source transmission power is unknown. Due to fluctuations in the wireless medium, the path loss exponent is also considered unknown and is modelled statistically as a uniformly distributed random variable. When maximum-likelihood estimation is employed, we are required to solve a highly non-linear function which contains a summation of exponential and Q-function terms in the log-ratio-of-distances. In the state-of-the-art [8], the Q-function terms are ignored in order to derive an approximate but erroneous solution in closed-form. In this work, we firstly expose the adverse impact of ignoring the Q-function terms on the estimation performance. Next, we propose a uniform search root finder (USRF) method which solves the original non-linear function without ignoring any of the underlying terms. Numerical studies reveal that the proposed method not only provides much more accurate ratio-of-distance estimates than the state-of-the-art, but also provides significantly better localization accuracy.