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

[2]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

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

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

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

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

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

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

[9]  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).

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

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

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

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

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

[15]  J. J. Moré,et al.  Global continuation for distance geometry problems , 1995 .

[16]  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).

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

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

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

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