Understanding and solving flip-ambiguity in network localization via semidefinite programming

Authors:
Stefano Severi;Giuseppe Abreu;Giuseppe Destino;Davide Dardari
Affiliations:
Università degli Studi di Bologna, Cesena, Italy;University of Oulu, Finland;University of Oulu, Finland;Università degli Studi di Bologna, Cesena, Italy
Venue:
GLOBECOM'09 Proceedings of the 28th IEEE conference on Global telecommunications
Year:
2009

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Abstract

We employ the semidefine programming (SDP) framework to first analyze, and then solve, the problem of flip-ambiguity afflicting range-based network localization algorithms with incomplete ranging information. First, we study the occurrence of flip-ambiguous nodes and errors due to flip ambiguity by considering random network topologies with successively smaller connectivity ranges RMax RMax - ΔR . . . RU RL, and employing an SDP-based unique localizability test to detect the limiting connectivity ranges RU and RL that are respectively sufficient and un-sufficient to ensure unique localizability. Then, we utilize this information to construct an SDP formulation of the localization problem with Genie-aided constraints, which is shown to resolve flip-ambiguities. Finally, we derive a flip-ambiguity-robust network localization algorithm by relaxing the Genie-aided constraints onto feasible alternatives. Finally, the performance of the so-obtained localization algorithm is studied by Monte-Carlo simulations, which reveal a substantial improvement over the conventional SDP-based algorithm.