Source Localization Using RSS Measurements with Sensor Position Uncertainty

Received signal strength- (RSS-) based localization has attracted considerable attention for its low cost and easy implementation. In plenty of existing work, sensor positions, which play an important role in source localization, are usually assumed perfectly known. Unfortunately, they are often subject to uncertainties, which directly leads to effect on localization result. To tackle this problem, we study the RSS-based source localization with sensor position uncertainty. Sensor position uncertainty will be modeled as two types: Gaussian random variable and unknown nonrandom variable. For either of the models, two semidefinite programming (SDP) methods are proposed, i.e., SDP-1 and SDP-2. The SDP-1 method proceeds from the nonconvex problem with respect to the maximum likelihood (ML) estimation and then obtains an SDP problem using proper approximation and relaxation. The SDP-2 method first transfers the sensor position uncertainties to the source position and then obtains an SDP formulation following a similar idea as in SDP-1 method. Numerical examples demonstrate the performance superiority of the proposed methods, compared to some existing methods assuming perfect sensor position information.