Wireless Sensor Network Localization with Spatially Correlated Shadowing

The problem of estimating the positions of the sensors in a wireless sensor network is commonly known as the wireless sensor localization problem and has been formulated as a relaxed semidefinite programming problem assuming inter-sensor distance measures corrupted by additive Gaussian noise. In this paper, we assume received signal strength measurements under a spatially correlated lognormal shadowing pathloss model and formulate the corresponding non-convex maximum likelihood distance estimator. We apply a Taylor approximation to the objective function, and then relax the problem to a semidefinite program. The localization performance of the approximation is analyzed and is shown to be satisfactory in the case the shadowing covariance is unknown, and excellent when known.