A Theoretical Analysis of the Conditions for Unambiguous Node Localization in Sensor Networks

In this paper we provide a theoretical foundation for the problem of network localization in which some nodes know their locations and other nodes determine their locations by measuring distances or bearings to their neighbors. Distance information is the separation between two nodes connected by a sensing/communication link. Bearing is the angle between a sensing/communication link and the x-axis of a node’s local coordinate system. We construct grounded graphs to model network localization and apply graph rigidity theory and parallel drawings to test the conditions for unique localizability and to construct uniquely localizable networks. We further investigate partially localizable networks.

[1]  Robert E. Tarjan,et al.  Dividing a Graph into Triconnected Components , 1973, SIAM J. Comput..

[2]  Ian F. Akyildiz,et al.  Sensor Networks , 2002, Encyclopedia of GIS.

[3]  Walter Whiteley,et al.  Constraining Plane Configurations in Computer-Aided Design: Combinatorics of Directions and Lengths , 1999, SIAM J. Discret. Math..

[4]  G. Laman.  On graphs and rigidity of plane skeletal structures , 1970 .

[5]  Seth J. Teller,et al.  The cricket compass for context-aware mobile applications , 2001, MobiCom '01.

[6]  Bill Jackson,et al.  Egerváry Research Group on Combinatorial Optimization Connected Rigidity Matroids and Unique Realizations of Graphs Connected Rigidity Matroids and Unique Realizations of Graphs , 2022 .

[7]  Deborah Estrin,et al.  GPS-less low-cost outdoor localization for very small devices , 2000, IEEE Wirel. Commun..

[8]  A. Stephen Morse,et al.  Operations on Rigid Formations of Autonomous Agents , 2003, Commun. Inf. Syst..

[9]  B. Anderson,et al.  Sensor and network topologies of formations with direction, bearing, and angle information between agents , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[10]  Brian D. O. Anderson,et al.  Rigidity, computation, and randomization in network localization , 2004, IEEE INFOCOM 2004.

[11]  B. R. Badrinath,et al.  Ad hoc positioning system (APS) using AOA , 2003, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428).

[12]  Walter Whiteley,et al.  Rigidity and scene analysis , 2004, Handbook of Discrete and Computational Geometry, 2nd Ed..

[13]  Mark Weiser,et al.  Some Computer Science Problems in Ubiquitous Computing , 1993 .

[14]  Brian D. O. Anderson,et al.  Merging globally rigid formations of mobile autonomous agents , 2004, Proceedings of the Third International Joint Conference on Autonomous Agents and Multiagent Systems, 2004. AAMAS 2004..

[15]  Walter Whiteley,et al.  Some matroids from discrete applied geometry , 1996 .

[16]  Bruce Hendrickson,et al.  Conditions for Unique Graph Realizations , 1992, SIAM J. Comput..

[17]  Anthony Man-Cho So,et al.  Theory of semidefinite programming for Sensor Network Localization , 2005, SODA '05.