Well-Conditioned Sensor Placement for Range-Only Localization

This paper addresses the optimality of Network topology for localization purposes when measurements are range-only. Localization procedures based on TOA and TDOA range measurements are considered in this paper. As of now, the optimal placement of fixed terminals to locate mobile terminals has been studied based on Cramer-Rao Lower Bound (CRLB). CRLB is a universal bound on the variance of a general unbiased estimator and therefore is not dependent to the estimator and methods of localization. Here we introduce another algorithm dependent criterion, based on perturbation theory of linear equations. Different optimal topologies are presented using the new criterion. These optimal topologies, called well-conditioned topologies, lead to better location estimation. Some simulations have been conducted to verify the theoretical results.