- Research Article
- Open access
- Published:
Autonomous Positioning Techniques Based on Cramér-Rao Lower Bound Analysis
EURASIP Journal on Advances in Signal Processing volume 2006, Article number: 093043 (2006)
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
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
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
Kay SM: Fundamentals of Statistical Signal Processing: Estimation Theory. Prentice-Hall PTR, Upper Saddle River, NJ, USA; 1993.
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.
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.
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.
Qi Y: Wireless geolocation in a non-line-of-sight environment, M.S. thesis. Princeton University, Princeton, NJ, USA; 2003.
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
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
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.
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.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
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.
About this article
Cite this article
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
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1155/ASP/2006/93043