On the Joint Estimation of the RSS-Based Location and Path-loss Exponent

Due to its straightforward implementation, the received signal strength (RSS) has been an advantageous approach for low cost localization systems. Although the propagation model is difficult to characterize in uncertain environments, the majority of current studies assume to have exact knowledge of the path-loss exponent (PLE). This letter deals with RSS based localization in an unknown path-loss model. First, we derive an analytical expression for the mean square error on location estimates for incorrect PLE assumption and examine, via simulation, the effects of error in the PLE on the location accuracy. Second, we enhance a previously proposed RSS-PLE joint estimator (JE) by reducing its complexity. We also propose a maximum a posteriori (MAP) estimator by considering the PLE as an unknown random variable. Finally, we derive the Hybrid Cramer Rao Bound (HCRB) as a benchmark for the MAP estimator. Error analysis results predict large error due to incorrect PLE assumption which are in agreement with the simulation results. Further simulations show that the MAP estimator exhibits better performance at low signal to noise ratio (SNR) and that the relation between the HCRB and CRB depends on the network geometry.