Accurate localization of low-level radioactive source under noise and measurement errors

ABSTRACT

The localization of a radioactive source can be solved in closed-form using 4 ideal sensors and the Apollonius circle in a noise- and error-free environment. When measurement errors and noise such as background radiation are considered, a larger number of sensors is needed to produce accurate results, particularly for extremely low source intensities. In this paper, we present an efficient fusion algorithm that can exploit measurements from n sensors to improve the localization accuracy, and show how the accuracy scales with n. We report testbed results for a 0.911 μCi source to illustrate the effectiveness of our algorithm, in particular performance comparisons with state-of-the-art fusion algorithms based on Mean of Estimates (MoE) and Maximum Likelihood Estimation (MLE). We show that ITP is more accurate than MoE, whereas the choice between ITP and MLE is generally a tradeoff between accuracy and run time efficiency. Higher-intensity radioactive sources are not safe for actual experiments. In this case, we present simulation results based on a validated simulation model. We show that a low-intensity 400 μCi source, similar to the radioactivity of a concealed dirty bomb, can be localized to within 32.5 m using a sensor density of about 1 per 1100 m² in a surveillance area.

REFERENCES

• 1: http://www. rftrax. com/radczt. html.
• 2: X. Cheng, A. Thaeler, G. Xue, and D. Chen. Tps:a time-based positioning scheme for outdoor wireless sensor networks. In INFOCOM 2004: Proceedings of the 23rd Annual Joint Conference of the IEEE Computer and Communications Societies, volume 4, pages 2685--2696, 7--11 March 2004.
• 3: J. Cox and M. B. Partensky. Spatial Localization Problem and the Circle of Apollonius. ArXiv Physics e-prints, Jan. 2007.
• 4: M. Ester, H. -P. Kriegel, J. Sander, and X. Xu. A density-based algorithm for discovering clusters in large spatial databases with noise. In Proc. of 2nd International Conference on Knowledge Discovery and Data Mining (KDD-96), pages 226--231, 1996.
• 5: Sudipto Guha , Rajeev Rastogi , Kyuseok Shim, CURE: an efficient clustering algorithm for large databases, Proceedings of the 1998 ACM SIGMOD international conference on Management of data, p.73-84, June 01-04, 1998, Seattle, Washington, United States
• 6: A. Gunatilaka, B. Ristic, and R. Gailis. On localisation of a radiological point source. IDC'07: Information, Decision and Control, 2007.
• 7: John A. Hartigan, Clustering Algorithms, John Wiley & Sons, Inc., New York, NY, 1975
• 8: Tian He , Chengdu Huang , Brian M. Blum , John A. Stankovic , Tarek Abdelzaher, Range-free localization schemes for large scale sensor networks, Proceedings of the 9th annual international conference on Mobile computing and networking, September 14-19, 2003, San Diego, CA, USA [doi>10.1145/938985.938995]
• 9: L. J. Heyer, S. Kruglyak, and S. Yooseph. Exploring expression data:Identification and analysis of coexpressed genes. Genome Research, 9:1106--1115, 1999.
• 10: G. F. Knoll. Radiation Detection and Measurement. John Wiley, 2000.
• 11: D. Mihalas and B. W. Mihalas. Foundations of Radiation Hydrodynamics. Courier Dover Publications, 2000.
• 12: D. Niculescu and B. Nath. Ad hoc positioning system (aps)using aoa. In INFOCOM 2003: Proceedings of the 22nd Annual Joint Conference of the IEEE Computer and Communications Societies, pages 1734--1743 vol. 3, 2003.
• 13: C. S. Ogilvy. Excursions in Geometry. Dover Publications, 1990.
• 14: N. S. V. Rao. Identification of simple product-form plumes using networks of sensors with random errors. In International Conference on Information Fusion, 2006.
• 15: Nageswara S. V. Rao , Mallikarjun Shankar , Jren-Chit Chin , David K. Y. Yau , Srinivasagopalan Srivathsan , S. Sitharama Iyengar , Yong Yang , Jennifer C. Hou, Identification of Low-Level Point Radiation Sources Using a Sensor Network, Proceedings of the 7th international conference on Information processing in sensor networks, p.493-504, April 22-24, 2008 [doi>10.1109/IPSN.2008.19]
• 16: N. S. V. Rao, M. Shankar, J.-C. Chin, D. K. Y. Yau, Y. Yang, J. C. Hou, X. Xu, and S. Sahni. Localization under random measurements with application to radiation sources. In International Conference on Information Fusion, 2008.
• 17: N. S. V. Rao, X. Xu, and S. Sahni. A computational geometry method for dtoa triangulation. In International Conference on Information Fusion, 2007.
• 18: Andreas Savvides , Chih-Chieh Han , Mani B. Strivastava, Dynamic fine-grained localization in Ad-Hoc networks of sensors, Proceedings of the 7th annual international conference on Mobile computing and networking, p.166-179, July 2001, Rome, Italy [doi>10.1145/381677.381693]
• 19: Gyula Simon , Miklós Maróti , Ákos Lédeczi , György Balogh , Branislav Kusy , András Nádas , Gábor Pap , János Sallai , Ken Frampton, Sensor network-based countersniper system, Proceedings of the 2nd international conference on Embedded networked sensor systems, November 03-05, 2004, Baltimore, MD, USA [doi>10.1145/1031495.1031497]
• 20: A. Sundaresan, P. K. Varshney, and N. S. V. Rao. Distributed detection of a nuclear radioactive source using fusion of correlated decisions. In International Conference on Information Fusion, 2007.
• 21: Andrew Thaeler , Min Ding , Xiuzhen Cheng, iTPS: an improved location discovery scheme for sensor networks with long-range beacons, Journal of Parallel and Distributed Computing, v.65 n.2, p.98-106, February 2005 [doi>10.1016/j.jpdc.2004.09.002]
• 22: X. Xu, N. S. V. Rao, and S. Sahni. A computational geometry method for localization using difference of distances. IEEE Transactions on Sensor Networks, 2008. to appear.

INDEX TERMS

Primary Classification:
  C. Computer Systems Organization
  C.2 COMPUTER-COMMUNICATION NETWORKS
      C.2.1 Network Architecture and Design

General Terms:
Algorithms, Design, Experimentation, Performance

Keywords:
iterative pruning, noise and error management, radioactive source localization, sensor data fusion, sensor network