Semidefinite programming for ad hoc wireless sensor network localization

We describe an SDP relaxation based method for the position estimation problem in wireless sensor networks. The optimization problem is set up so as to minimize the error in sensor positions to fit distance measures. Observable gauges are developed to check the quality of the point estimation of sensors or to detect erroneous sensors. The performance of this technique is highly satisfactory compared to other techniques. Very few anchor nodes are required to accurately estimate the position of all the unknown nodes in a network. Also the estimation errors are minimal even when the anchor nodes are not suitably placed within the network or the distance measurements are noisy.

[1]  Y. Ye,et al.  A Distributed Method for Solving Semidefinite Programs Arising from Ad Hoc Wireless Sensor Network Localization , 2006 .

[2]  Ying Zhang,et al.  Localization from mere connectivity , 2003, MobiHoc '03.

[3]  Joakim Nivre.  AN EFFICIENT ALGORITHM , 2003 .

[4]  Mani B. Srivastava,et al.  The bits and flops of the n-hop multilateration primitive for node localization problems , 2002, WSNA '02.

[5]  Jan M. Rabaey,et al.  Robust Positioning Algorithms for Distributed Ad-Hoc Wireless Sensor Networks , 2002, USENIX Annual Technical Conference, General Track.

[6]  Deborah Estrin,et al.  An Empirical Study of Epidemic Algorithms in Large Scale Multihop Wireless Networks , 2002 .

[7]  B. R. Badrinath,et al.  Ad hoc positioning system (APS) , 2001, GLOBECOM'01. IEEE Global Telecommunications Conference (Cat. No.01CH37270).

[8]  Gaurav S. Sukhatme,et al.  Relaxation on a mesh: a formalism for generalized localization , 2001, Proceedings 2001 IEEE/RSJ International Conference on Intelligent Robots and Systems. Expanding the Societal Role of Robotics in the the Next Millennium (Cat. No.01CH37180).

[9]  Gaetano Borriello,et al.  Location Systems for Ubiquitous Computing , 2001, Computer.

[10]  Mani B. Srivastava,et al.  Dynamic fine-grained localization in Ad-Hoc networks of sensors , 2001, MobiCom '01.

[11]  L. El Ghaoui,et al.  Convex position estimation in wireless sensor networks , 2001, Proceedings IEEE INFOCOM 2001. Conference on Computer Communications. Twentieth Annual Joint Conference of the IEEE Computer and Communications Society (Cat. No.01CH37213).

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

[13]  Xiong Zhang,et al.  Solving Large-Scale Sparse Semidefinite Programs for Combinatorial Optimization , 1999, SIAM J. Optim..

[14]  Henry Wolkowicz,et al.  Solving Euclidean Distance Matrix Completion Problems Via Semidefinite Programming , 1999, Comput. Optim. Appl..

[15]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[16]  Y. Ye,et al.  Semidefinite Relaxations, Multivariate Normal Distributions, and Order Statistics , 1998 .

[17]  Yinyu Ye,et al.  An Efficient Algorithm for Minimizing a Sum of Euclidean Norms with Applications , 1997, SIAM J. Optim..

[18]  Jorge J. Moré,et al.  Global Continuation for Distance Geometry Problems , 1995, SIAM J. Optim..