Least Squared Relative Error Estimator for RSS Based Localization With Unknown Transmit Power

Research on received signal strength (RSS) based localization has received a lot of attention from both academia and industry because of its low complexity and high efficiency. In this letter, the RSS based localization problem when the transmit power is unknown, is addressed based on the least squared relative error (LSRE) estimation. By taking exponential transformation, the original log-normal RSS measurement model is transformed into a multiplicative model, which is used to formulate a non-convex LSRE estimation problem with the source location and the transmit power as variables. We then apply semidefinite relaxation (SDR) to the non-convex LSRE problem to obtain a convex semidefinite programming (SDP) problem. To facilitate SDR, we introduce two compound variables constructed by the source location and the transmit power, and then estimate the two compound variables instead of directly estimating the source location and the transmit power. The source location estimate is recovered according to its relation with the compound variable. Both simulations and real field test demonstrate the superior performance of the proposed method over several existing methods.