Semidefinite Programming-Based Localization Algorithm in Networks with Inhomogeneous Media

Abstract

In this paper, we study the asymptotic properties of a semidefinite programming (SDP) based localization algorithm in a network with inhomogeneous RF transmission medium given incomplete and inaccurate pairwise distance measurements between sensors-sensors and sensors-anchors. We proposed a novel relaxed SDP approach based on a graph realization problem with noisy time-of-arrival (TOA) measurements with additive Gaussian noise and inaccurate transmission permittivity and permeability coefficients both with additive standard Gaussian noise (varying dielectric constant). Modeling the inhomogeneous RF transmission medium as a series of homogeneous transmission mediums between any two given points and given the true distances between a pair of sensors and the set of known pair-wise distances between sensors-sensors and sensors-anchors, an upper bound for the expected value of the optimal objective relaxed SDP problem is obtained, showing that its asymptotic properties potentially grows as fast as the summation of true distances between the pair of sensors-sensors and sensor-anchors and the TOA noisy measurements mean and standard deviation.