The minimum positional error incurred by any connectivity-based positioning algorithm for mobile wireless systems

A very important problem in many wireless ad-hoc networks, including wireless sensor networks, is positioning or the determination of geographical locations of the wireless nodes. Positioning is used both in infrastructural aspects of sensor networks, like geographic routing and topology maintenance, and in applications like wildlife tracking. Connectivity-based positioning algorithms in mobile wireless systems are studied in this work. These algorithms compute node positions based only on the connectivity, i.e. the neighborhood information of each node. Many algorithms have been proposed for positioning in stationary node systems and bounds on positional error of algorithms have been derived. The design and analysis of positioning algorithms for mobile node systems is a more challenging problem. Node mobility increases the amount of positional information available to a positioning algorithm. The work in this paper establishes a bound on the positional error for connectivity-based algorithms in mobile systems. The formulation from the analysis is used to investigate the benefit of this additional positional information on reducing positional error. There is a limit to the usefulness of positional information from previous node positions due to movement. This captures an important performance tradeoff: historical positional information can yield reduced positional error but requires more connectivity information from the network which requires greater computational resources.

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

[2]  Jiannong Cao,et al.  Accurate and Energy-Efficient Range-Free Localization for Mobile Sensor Networks , 2010, IEEE Transactions on Mobile Computing.

[3]  Jiannong Cao,et al.  Locating Nodes in Mobile Sensor Networks More Accurately and Faster , 2008, 2008 5th Annual IEEE Communications Society Conference on Sensor, Mesh and Ad Hoc Communications and Networks.

[4]  P. Noble,et al.  A two-dimensional random-walk analysis of human granulocyte movement. , 1972, Biophysical journal.

[5]  Edward A. Codling,et al.  Random walk models in biology , 2008, Journal of The Royal Society Interface.

[6]  Xenofon D. Koutsoukos,et al.  A Survey on Localization for Mobile Wireless Sensor Networks , 2009, MELT.

[7]  R. Serfozo.  Basics of Applied Stochastic Processes , 2012 .

[8]  Nitin H. Vaidya,et al.  Location-aided routing (LAR) in mobile ad hoc networks , 1998, MobiCom '98.

[9]  Radhika Nagpal,et al.  Organizing a Global Coordinate System from Local Information on an Ad Hoc Sensor Network , 2003, IPSN.

[10]  Adam Wolisz,et al.  Analytical investigation of intersection based range-free localization , 2008, Ann. des Télécommunications.

[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]  Xue Liu,et al.  EUL: An Efficient and Universal Localization Method for Wireless Sensor Network , 2009, 2009 29th IEEE International Conference on Distributed Computing Systems.

[13]  Kaveh Pahlavan,et al.  Location awareness for everyday smart computing , 2009, 2009 International Conference on Telecommunications.

[14]  Suprakash Datta,et al.  Localization in wireless sensor networks , 2007, IPSN.

[15]  Jacques Dutka,et al.  On the problem of random flights , 1985 .

[16]  Mehdi Dehghan,et al.  Monte Carlo Localization of Mobile Sensor Networks Using the Position Information of Neighbor Nodes , 2009, ADHOC-NOW.

[17]  Charles J. Colbourn,et al.  Unit disk graphs , 1991, Discret. Math..

[18]  John Anderson,et al.  Wireless sensor networks for habitat monitoring , 2002, WSNA '02.

[19]  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.

[20]  Tracy Camp,et al.  A survey of mobility models for ad hoc network research , 2002, Wirel. Commun. Mob. Comput..

[21]  David G. Kirkpatrick,et al.  Unit disk graph recognition is NP-hard , 1998, Comput. Geom..

[22]  Martin Vetterli,et al.  Proceedings of the 4th international symposium on Information processing in sensor networks , 2005 .

[23]  M. Eisen,et al.  Probability and its applications , 1975 .

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

[25]  Roger Wattenhofer,et al.  Unit disk graph approximation , 2004, DIALM-POMC '04.

[26]  S. MacLean,et al.  A lower bound on range-free node localization algorithms , 2008, 2008 IEEE International Symposium on Wireless Communication Systems.

[27]  David Evans,et al.  Localization for mobile sensor networks , 2004, MobiCom '04.

[28]  Eric W. Weisstein,et al.  The CRC concise encyclopedia of mathematics , 1999 .

[29]  Yong Wang,et al.  Energy-efficient computing for wildlife tracking: design tradeoffs and early experiences with ZebraNet , 2002, ASPLOS X.

[30]  Moshe Sidi,et al.  The Expected Uncertainty of Range Free Localization Protocols in Sensor Networks , 2004, ALGOSENSORS.

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

[32]  Krishna M. Sivalingam,et al.  Proceedings of the 1st ACM international workshop on Wireless sensor networks and applications , 2002 .

[33]  Roger Wattenhofer,et al.  Theoretical aspects of connectivity-based multi-hop positioning , 2005, Theor. Comput. Sci..

[34]  Koen Langendoen,et al.  Monte Carlo localization for mobile wireless sensor networks , 2008, Ad Hoc Networks.