Low Complexity Joint Estimation of Location and Path-Loss Exponent

Localization of wireless devices via the received signal strength (RSS) has become very popular in recent years owing to its economical and uncomplicated implementation. The performance of RSS based location systems is highly dependent on the knowledge of the propagation channel. An unrealistic assumption in many current studies is the possession of the exact knowledge of the path-loss exponent (PLE). This letter deals with the estimation of location coordinates in unknown path-loss model. First, the non-linear path-loss equations are linearized and the solution is obtained using linear least square (LLS) solution. Second, in order to underline the effects of inaccurate PLE assumption in noisy channels on location coordinates, error analysis is done when incorrect PLE is assumed, hence a closed form expression is derived for mean square error (MSE) and bias. Next, we transform the LLS problem into a single variable minimization problem to estimate jointly the location and PLE. Simulation results show that incorrect PLE assumption has superlative impact on MSE and bias of location estimates. Further simulation shows that the proposed technique exhibits acceptable performance while estimating the PLE however the estimates are biased. In order to achieve higher accuracy, the obtained estimates are used as an initial estimate to our previously proposed iterative algorithm [1]. The resultant MSE is then compared with the Cramer-Rao bound and the improved convergence is demonstrated.