Anchor placement in TOA based wireless localization networks via convex relaxation

A wireless source localization network consisting of synchronized target and anchor nodes is considered. An anchor placement problem is formulated to minimize the Cramér-Rao lower bound (CRLB) on estimation of target node positions by anchor nodes. First, it is shown that the anchor placement problem can be approximated as a minimization problem of the ratio of two supermodular functions. Due to the lack of a polynomial time algorithm for such problems, an anchor selection problem is proposed to solve the anchor placement problem. Via relaxation of integer constraints, the anchor selection problem is approximated by a convex optimization problem, which is used to propose two algorithms for anchor selection. Furthermore, extensions to quasi-synchronous wireless localization networks are discussed. To examine the performance of the proposed algorithms, various simulation results are presented.