Semidefinite Programming for Wireless Cooperative Localization Using Biased RSS Measurements

Abstract

Cooperative localization in wireless sensor network (WSN) using biased received signal strength (RSS) measurements is investigated in this letter. In the existing work on cooperative RSS localization, measurements of sensor nodes (including both target-anchor and target-target measurements) are generally assumed bias-free. However, in practice, they may be subject to biases, which directly affect localization accuracy. As a result, the existing localization methods are not applicable any more. In this letter, RSS observation biases are considered as the extra parameters to be estimated as well as locations of target nodes. To overcome the nonconvexity of the maximum likelihood (ML) estimator, semidefinite programming (SDP) is applied with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l_{1}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l_{2}$ </tex-math></inline-formula> norms, respectively. Then, the locations of multiple target nodes and observation biases are simultaneously estimated through convex optimization. Numerical examples demonstrate the performance superiority of the proposed methods compared to the existing bias-free SDP methods for wireless cooperative localization.