Maximum Likelihood localization of wireless networks using biased range measurements

Localization of ad-hoc wireless networks is useful for services, management and routing. Localization is frequently based on station-to-station range measurements and a few reference sensors. We address the localization problem in the case of incomplete set of noisy range measurements with unknown bias. A statistically efficient, maximum likelihood algorithm, inspired by the Gerchberg-Saxton procedure for phase retrieval, is presented. In addition, a compact explicit expression for the Fisher Information matrix is provided. A set of numerical examples demonstrates the bias effect on the localization accuracy. As expected, the localization accuracy improves when the unknown bias is estimated.