Distributed Wireless Sensor Network Localization Via Sequential Greedy Optimization Algorithm

Node localization is essential to most applications of wireless sensor networks (WSNs). In this paper, we consider both range-based node localization and range-free node localization with uncertainties in range measurements, radio range, and anchor positions. First, a greedy optimization algorithm, named sequential greedy optimization (SGO) algorithm, is presented, which is more suitable for distributed optimization in networks than the classical nonlinear Gauss-Seidel algorithm. Then a unified optimization framework is proposed for both range-based localization and range-free localization, and two convex localization formulations are obtained based on semidefinite programming (SDP) relaxation techniques. By applying the SGO algorithm to the edge-based SDP relaxation formulation, we propose a second-order cone programming (SOCP)-based distributed node localization algorithm. Two distributed refinement algorithms are also proposed by using the SGO algorithm to nonconvex localization formulations. The proposed localization algorithms all can be implemented partially asynchronously in networks. Finally, extensive simulations are conducted to demonstrate the efficiency and accuracy of the proposed distributed localization algorithms.

[1]  Kim-Chuan Toh,et al.  Semidefinite Programming Approaches for Sensor Network Localization With Noisy Distance Measurements , 2006, IEEE Transactions on Automation Science and Engineering.

[2]  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).

[3]  Wing-Kin Ma,et al.  Semi-Definite Programming Algorithms for Sensor Network Node Localization With Uncertainties in Anchor Positions and/or Propagation Speed , 2009, IEEE Transactions on Signal Processing.

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

[5]  Chen He,et al.  Normalized Incremental Subgradient Algorithm and Its Application , 2009, IEEE Transactions on Signal Processing.

[6]  Yinyu Ye,et al.  Semidefinite programming based algorithms for sensor network localization , 2006, TOSN.

[7]  Ying Zhang,et al.  Robust distributed node localization with error management , 2006, MobiHoc '06.

[8]  John C. Platt,et al.  Fast training of support vector machines using sequential minimal optimization, advances in kernel methods , 1999 .

[9]  John N. Tsitsiklis,et al.  Parallel and distributed computation , 1989 .

[10]  Stephen P. Boyd,et al.  Further Relaxations of the Semidefinite Programming Approach to Sensor Network Localization , 2008, SIAM J. Optim..

[11]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[12]  Neal Patwari,et al.  Distributed Multidimensional Scaling with Adaptive Weighting for Node Localization in Sensor Networks , 2004 .

[13]  Ying Zhang,et al.  Localization from connectivity in sensor networks , 2004, IEEE Transactions on Parallel and Distributed Systems.

[14]  Brian D. O. Anderson,et al.  Wireless sensor network localization techniques , 2007, Comput. Networks.

[15]  Jos F. Sturm,et al.  A Matlab toolbox for optimization over symmetric cones , 1999 .

[16]  P. Tseng,et al.  On the convergence of the coordinate descent method for convex differentiable minimization , 1992 .

[17]  Ian F. Akyildiz,et al.  Wireless sensor networks: a survey , 2002, Comput. Networks.

[19]  T. Abatzoglou,et al.  Minimization by coordinate descent , 1982 .

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

[21]  Alfred O. Hero,et al.  Distributed weighted-multidimensional scaling for node localization in sensor networks , 2006, TOSN.

[22]  Tarek F. Abdelzaher,et al.  Range-free localization schemes for large scale sensor networks , 2003, MobiCom '03.

[23]  Yinyu Ye,et al.  Semidefinite programming for ad hoc wireless sensor network localization , 2004, Third International Symposium on Information Processing in Sensor Networks, 2004. IPSN 2004.

[24]  Chen He,et al.  A SDP Approach for Range-Free Localization in Wireless Sensor Networks , 2008, 2008 IEEE International Conference on Communications.

[25]  P. P. Vaidyanathan,et al.  Iterative greedy algorithm for solving the FIR paraunitary approximation problem , 2006, IEEE Transactions on Signal Processing.

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

[27]  Alfred O. Hero,et al.  Relative location estimation in wireless sensor networks , 2003, IEEE Trans. Signal Process..

[28]  Paul Tseng,et al.  Second-Order Cone Programming Relaxation of Sensor Network Localization , 2007, SIAM J. Optim..

[29]  Jun Luo,et al.  Sensor Network Localization via Nondifferentiable Optimization , 2008, IEEE GLOBECOM 2008 - 2008 IEEE Global Telecommunications Conference.

[30]  John E. Dennis,et al.  Numerical methods for unconstrained optimization and nonlinear equations , 1983, Prentice Hall series in computational mathematics.

[31]  Zhi-Quan Luo,et al.  Distributed sensor network localization using SOCP relaxation , 2008, IEEE Transactions on Wireless Communications.

[32]  Kim-Chuan Toh,et al.  SDPT3 -- A Matlab Software Package for Semidefinite Programming , 1996 .

[33]  Jyh-Chin Juang,et al.  On the application of alternating projection under the constraint of linear matrix inequalities , 1999 .