Polynomial-Based Linear Programming Relaxation of Sensor Network Localization Problem

One important task in the deployment of a wireless sensor network is solving the sensor network localization problem to assure location awareness of each sensor node in the network. The sensor network localization can be formulated as a global optimization problem that aims to minimize the squared inter-sensor distances under the constraint that such distances equal to some given numbers. The corresponding optimization formulation is generally nonsmooth, nonconvex, and NP-hard problem, and thus prior works have proposed approximate solution using relaxation methods such as semidefinite or conic programming. In this paper, a linear programming relaxation approach is proposed to solve such an optimization problem using the concept of Handelman's representation of nonnegative polynomial functions over polytopic set. Numerical simulation results are given to illustrate the promising potential of the proposed approach.