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Autonomous Positioning Techniques Based on Cramér-Rao Lower Bound Analysis

Abstract

We consider the problem of autonomously locating a number of asynchronous sensor nodes in a wireless network. A strong focus lies on reducing the processing resources needed to solve the relative positioning problem, an issue of great interest in resource-constrained wireless sensor networks. In the first part of the paper, based on a well-known derivation of the Cramér-Rao lower bound for the asynchronous sensor positioning problem, we are able to construct optimal preprocessing methods for sensor clock-offset cancellation. A cancellation of unknown clock-offsets from the asynchronous positioning problem reduces processing requirements, and, under certain reasonable assumptions, allows for statistically efficient distributed positioning algorithms. Cramér-Rao lower bound theory may also be used for estimating the performance of a positioning algorithm. In the second part of this paper, we exploit this property in developing a distributed algorithm, where the global positioning problem is solved suboptimally, using a divide-and-conquer approach of low complexity. The performance of this suboptimal algorithm is evaluated through computer simulation, and compared to previously published algorithms.

References

  1. Moses RL, Krishnamurthy D, Patterson RM: A self-localization method for wireless sensor networks. EURASIP Journal on Applied Signal Processing 2003, 2003(4):348–358. 10.1155/S1110865703212063

    MATH  Google Scholar 

  2. Patwari N, Hero AO III, Perkins M, Correal NS, O'Dea RJ: Relative location estimation in wireless sensor networks. IEEE Transactions on Signal Processing 2003, 51(8):2137–2148. 10.1109/TSP.2003.814469

    Article  Google Scholar 

  3. Kay SM: Fundamentals of Statistical Signal Processing: Estimation Theory. Prentice-Hall PTR, Upper Saddle River, NJ, USA; 1993.

    MATH  Google Scholar 

  4. Rydström M, Ström EG, Svensson A: Clock-offset cancellation methods for positioning in asynchronous sensor networks. Proceedings of IEEE International Conference on Wireless Networks, Communications, and Mobile Computing (WirelessCom '05), June 2005, Maui, Hawaii, USA 2: 981–986.

    Google Scholar 

  5. Rydström M, Urruela A, Ström EG, Svensson A: A low complexity algorithm for distributed sensor localization. Proceedings of the 11th European Wireless Conference (EW~'05), April 2005, Nicosia, Cyprus 2: 714–718.

    Google Scholar 

  6. Scharf LL, McWhorter LT: Geometry of the Cramer-Rao bound. Proceedings of IEEE 6th SP Workshop on Statistical Signal and Array Processing, October 1992, Victoria, BC, Canada 5–8.

    Google Scholar 

  7. Qi Y: Wireless geolocation in a non-line-of-sight environment, M.S. thesis. Princeton University, Princeton, NJ, USA; 2003.

    Google Scholar 

  8. Bhapkar VP:Estimating functions, partial sufficiency and-sufficiency in the presence of nuissance parameters. Selected Proceedings of the Symposium on Estimating Functions, March 1996, Athens, Ga, USA

    Google Scholar 

  9. Fang BT: Simple solutions for hyperbolic and related position fixes. IEEE Transactions on Aerospace and Electronic Systems 1990, 26(5):748–753. 10.1109/7.102710

    Article  Google Scholar 

  10. Urruela A, Riba J: Novel closed-form ML position estimator for hyperbolic location. Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '04), May 2004, Montreal, Quebec, Canada 2: 149–152.

    Google Scholar 

  11. Rydström M: Positioning and tracking in asynchronous wireless sensor networks. In Tech. Rep. R027/2005. Department of Signals and Systems, Chalmers University of Technology, Göteborg, Sweden; October 2005.

    Google Scholar 

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Correspondence to Mats Rydström.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Rydström, M., Urruela, A., Ström, E.G. et al. Autonomous Positioning Techniques Based on Cramér-Rao Lower Bound Analysis. EURASIP J. Adv. Signal Process. 2006, 093043 (2006). https://doi.org/10.1155/ASP/2006/93043

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  • DOI: https://doi.org/10.1155/ASP/2006/93043

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