Polynomial-Based Methods for Localization in Multiagent Systems

This chapter reviews a series of results obtained in the field of localization that are based on polynomial optimization. It provides a review of a set of polynomial function optimization tools, including sum of squares (SOS). The chapter presents several applications of these tools in various sensor network localization tasks. As the first application, it proposes a method based on SOS relaxation for node localization using noisy measurements and describes the solution through semidefinite programming (SDP). The chapter applies the method to address the problems of target localization in the presence of noise and relative reference frame determination based on range and bearing measurements. Some simulation and experiment results are also provided to show the applicability of the method. The chapter provides a condition for having exact global optimums for polynomial functions using SOS relaxation and establishes that, for generic polynomials, the condition is satisfied.