Second order cone programming for sensor network localization with anchor position uncertainty

We consider the problem of node localization in sensor networks, and we focus on networks in which the ranging measurements are subject to errors and anchor positions are subject to uncertainty. We consider a statistical model for the uncertainty in the anchor positions and formulate the robust localization problem that finds a maximum likelihood estimation of the node positions. To overcome the non-convexity of the resulting optimization problem, we obtain a convex relaxation that is based on the second order cone programming (SOCP). We also propose a possible distributed implementation using the SOCP convex relaxation. We present numerical studies that compare the presented approach to other existing convex relaxations for the robust localization problem in terms of positioning error and computational complexity.

[1]  Stephen J. Wright,et al.  Numerical Optimization , 2018, Fundamental Statistical Inference.

[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]  James Aspnes,et al.  On the Computational Complexity of Sensor Network Localization , 2004, ALGOSENSORS.

[4]  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.

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

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

[7]  Yunhao Liu,et al.  Beyond Trilateration: On the Localizability of Wireless Ad-Hoc Networks , 2009, INFOCOM 2009.

[8]  Jean-Yves Le Boudec,et al.  A location-based routing method for mobile ad hoc networks , 2005, IEEE Transactions on Mobile Computing.

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

[10]  Anthony Man-Cho So,et al.  Universal Rigidity: Towards Accurate and Efficient Localization of Wireless Networks , 2010, 2010 Proceedings IEEE INFOCOM.

[11]  Ting Kei Pong Edge-based semidefinite programming relaxation of sensor network localization with lower bound constraints , 2012, Comput. Optim. Appl..

[12]  Paul Tseng,et al.  (Robust) Edge-based semidefinite programming relaxation of sensor network localization , 2011, Math. Program..

[13]  K. C. Ho,et al.  An Approximately Efficient TDOA Localization Algorithm in Closed-Form for Locating Multiple Disjoint Sources With Erroneous Sensor Positions , 2009, IEEE Transactions on Signal Processing.

[14]  Brian D. O. Anderson,et al.  A Theory of Network Localization , 2006, IEEE Transactions on Mobile Computing.

[15]  Joseph Shmuel Picard,et al.  Bounds on the Number of Identifiable Outliers in Source Localization by Linear Programming , 2010, IEEE Transactions on Signal Processing.

[16]  Chris Hide,et al.  Adaptive Kalman Filtering for Low-cost INS/GPS , 2002, Journal of Navigation.

[17]  Yik-Chung Wu,et al.  Robust joint localization and time synchronization in wireless sensor networks with bounded anchor uncertainties , 2009, 2009 IEEE International Conference on Acoustics, Speech and Signal Processing.

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

[19]  Hongyang Chen,et al.  Distributed Wireless Sensor Network Localization Via Sequential Greedy Optimization Algorithm , 2010, IEEE Transactions on Signal Processing.

[20]  Xiuzhen Cheng,et al.  TPS: a time-based positioning scheme for outdoor wireless sensor networks , 2004, IEEE INFOCOM 2004.

[21]  Zhiguo Ding,et al.  A simple approach of range-based positioning with low computational complexity , 2009, IEEE Transactions on Wireless Communications.

[22]  Paramvir Bahl,et al.  RADAR: an in-building RF-based user location and tracking system , 2000, Proceedings IEEE INFOCOM 2000. Conference on Computer Communications. Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies (Cat. No.00CH37064).

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

[24]  Rong Peng,et al.  Angle of Arrival Localization for Wireless Sensor Networks , 2006, 2006 3rd Annual IEEE Communications Society on Sensor and Ad Hoc Communications and Networks.

[25]  Ian Oppermann,et al.  UWB location and tracking for wireless embedded networks , 2006, Signal Process..

[26]  P. Tseng Convergence of a Block Coordinate Descent Method for Nondifferentiable Minimization , 2001 .

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

[28]  Shahrokh Valaee,et al.  Compressive Sensing Based Positioning Using RSS of WLAN Access Points , 2010, 2010 Proceedings IEEE INFOCOM.

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

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

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

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

[33]  R.L. Moses,et al.  Locating the nodes: cooperative localization in wireless sensor networks , 2005, IEEE Signal Processing Magazine.

[34]  Deborah Estrin,et al.  Habitat monitoring with sensor networks , 2004, CACM.

[35]  Vikram Krishnamurthy,et al.  Expectation maximization algorithms for MAP estimation of jump Markov linear systems , 1999, IEEE Trans. Signal Process..

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

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