Localization of networks using various ranging bias models

Given a network of stations with incomplete and possibly imprecise inter-station range measurements, it is required to find the relative positions of the stations. Several models for the bias in the range estimates are discussed. We present a set of iterative algorithms that cope successfully with the various bias models and provide Maximum Likelihood position estimates. Proof of convergence is provided. A procedure, albeit designed for precise measurements, is also proposed for the initialization of the iterative algorithms. We also present compact, matrix form expression for the Cramer—Rao Bound (CRB). Numerical examples are provided to corroborate the results. Copyright © 2007 John Wiley & Sons, Ltd.

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

[2]  J R Fienup,et al.  Phase retrieval algorithms: a comparison. , 1982, Applied optics.

[3]  H. Koorapaty.  Cramer-Rao bounds for time of arrival estimation in cellular systems , 2004, 2004 IEEE 59th Vehicular Technology Conference. VTC 2004-Spring (IEEE Cat. No.04CH37514).

[4]  Arogyaswami Paulraj,et al.  An analytical constant modulus algorithm , 1996, IEEE Trans. Signal Process..

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

[6]  A. Savvides,et al.  Network localization in partially localizable networks , 2005, Proceedings IEEE 24th Annual Joint Conference of the IEEE Computer and Communications Societies..

[7]  J. Holtzman,et al.  The non-line of sight problem in mobile location estimation , 1996, Proceedings of ICUPC - 5th International Conference on Universal Personal Communications.

[8]  Koen Langendoen,et al.  Distributed localization in wireless sensor networks: a quantitative compariso , 2003, Comput. Networks.

[9]  R. Gerchberg.  A practical algorithm for the determination of phase from image and diffraction plane pictures , 1972 .

[10]  Bodhi Priyantha,et al.  The Cricket indoor location system , 2005 .

[11]  B. Friedlander.  A passive localization algorithm and its accuracy analysis , 1987 .

[12]  A.J. Weiss,et al.  Maximum Likelihood Positioning of Network Nodes Using Range Measurements , 2006, 2006 3rd International Symposium on Wireless Communication Systems.

[13]  H.V. Poor,et al.  Nonparametric nonline-of-sight identification , 2003, 2003 IEEE 58th Vehicular Technology Conference. VTC 2003-Fall (IEEE Cat. No.03CH37484).

[14]  Gul Agha,et al.  Resilient Localization for Sensor Networks in Outdoor Environments , 2005, ICDCS.

[15]  Anthony J. Weiss,et al.  On the accuracy of a cellular location system based on RSS measurements , 2003, IEEE Trans. Veh. Technol..

[16]  Lixia Zhang,et al.  Recursive position estimation in sensor networks , 2001, Proceedings Ninth International Conference on Network Protocols. ICNP 2001.

[17]  J. Smith,et al.  The spherical interpolation method of source localization , 1987 .

[18]  John W. Fisher,et al.  Nonparametric belief propagation for self-localization of sensor networks , 2005, IEEE Journal on Selected Areas in Communications.

[19]  N.B. Mandayam,et al.  Decision theoretic framework for NLOS identification , 1998, VTC '98. 48th IEEE Vehicular Technology Conference. Pathway to Global Wireless Revolution (Cat. No.98CH36151).

[20]  Hisashi Kobayashi,et al.  Cramér-Rao Lower bound for geolocation in non-line-of-sight environment , 2002, 2002 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[21]  Arogyaswami Paulraj,et al.  Estimation of multipath parameters in wireless communications , 1998, IEEE Trans. Signal Process..

[22]  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.

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

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

[25]  David C. Moore,et al.  Robust distributed network localization with noisy range measurements , 2004, SenSys '04.

[26]  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).