×

Source detection algorithms for dynamic contaminants based on the analysis of a hydrodynamic limit. (English) Zbl 1409.60137

Summary: In this work we propose and numerically analyze an algorithm for detection of a contaminant source using a dynamic sensor network. The algorithm is motivated using a global probabilistic optimization problem and is based on the analysis of the hydrodynamic limit of a discrete time evolution equation on the lattice under a suitable scaling of time and space. Numerical results illustrating the effectiveness of the algorithm are presented.

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
65C35 Stochastic particle methods
86A22 Inverse problems in geophysics
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] P. Billingsley, Convergence of Probability Measures, 2nd ed., Wiley Series in Probability and Statistics: Probability and Statistics, John Wiley & Sons, New York, 1999. · Zbl 0944.60003
[2] S. M. Brennan, A. M. Mielke, D. C. Torney, and A. B. Maccabe, Radiation detection with distributed sensor networks, Computer, 37 (2004), pp. 57–59.
[3] N. Burch, E. K. Chong, D. Estep, and J. Hannig, Analysis of routing protocols and interference-limited communication in large wireless networks via continuum modeling, J. Engrg. Math., (2013), pp. 1–17. · Zbl 1294.68037
[4] E. Cator and L. Pimentel, Hydrodynamical Methods in Last Passage Percolation Models, Publicaço͂es matemáticas, 2011, .
[5] Y. Chen, K. Moore, and Z. Song, Diffusion boundary determination and zone control via mobile actuator-sensor networks (MAS-NET): Challenges and opportunities, Proc. SPIE Intelligent Comput. Theory Appli., 5421 (2004), pp. 102–113.
[6] E. K. Chong, D. Estep, and J. Hannig, Continuum modeling of large networks, Int. J. Numer. Model. Electron. Netw. Devices Fields, 21 (2008), pp. 169–186. · Zbl 1138.90342
[7] V. N. Christopoulos and S. Roumeliotis, Adaptive sensing for instantaneous gas release parameter estimation, in ICRA 2005, Proceedings of the 2005 IEEE International Conference on Robotics and Automation, Piscataway, NJ, IEEE, 2005, pp. 4450–4456.
[8] F. Golse, Hydrodynamic limits, in European Congress of Mathematics, European Mathematical Society, Zürich, 2005, pp. 699–717. · Zbl 1115.82028
[9] J. Gravner and J. Quastel, Internal DLA and the Stefan problem, Annals Probab., 28 (2000), pp. 1528–1562. · Zbl 1108.60318
[10] A. Hazart, J.-F. Giovannelli, S. Dubost, and L. Chatellier, Inverse transport problem of estimating point-like source using a Bayesian parametric method with MCMC, Signal Process., 96 (2014), pp. 346–361.
[11] W. Hoeffding, Probability inequalities for sums of bounded random variables, J. Ameri. Statist. Assoc., 58 (1963), pp. 13–30. · Zbl 0127.10602
[12] C. Huang, T. Hsing, N. Cressie, A. R. Ganguly, V. A. Protopopescu, and N. S. Rao, Bayesian source detection and parameter estimation of a plume model based on sensor network measurements, Appl. Stoch. Models Bus. Ind., 26 (2010), pp. 360–361.
[13] H. Ishida, T. Nakamoto, T. Moriizumi, T. Kikas, and J. Janata, Plume-tracking robots: A new application of chemical sensors, Biol. Bull., 200 (2001), pp. 222–226.
[14] W. Li, J. A. Farrell, and R. T. Card, Tracking of fluid-advected odor plumes: Strategies inspired by insect orientation to pheromone, Adapt. Behav., 9 (2001), pp. 143–170.
[15] R. J. Nemzek, J. S. Dreicer, D. C. Torney, and T. T. Warnock, Distributed sensor networks for detection of mobile radioactive sources, IEEE Trans. Nucl. Sci., 51 (2004), pp. 1693–1700.
[16] J. Quastel, Introduction to KPZ, Curr. Dev. Math., 2011 (2011), pp. 125–194. · Zbl 1316.60019
[17] S. S. Ram and V. V. Veeravalli, Localization and intensity tracking of diffusing point sources using sensor networks, in Global Telecommunications Conference, 2007, GLOBECOM’07, IEEE, Piscataway, NJ, 2007, pp. 3107–3111.
[18] N. Rao, Identification of a class of simple product-form plumes using sensor networks, in Innovations and Commercial Applications of Distributed Sensor Networks Symposium, Bethesda, MD, 2005.
[19] R. Sykes, W. Lewellen, and S. Parker, A Gaussian plume model of atmospheric dispersion based on second-order closure, J. Clim. Appl. Meteorol., 25 (1986), pp. 322–331.
[20] M. Takaoka, M. Uchida, K. Ohnishi, and Y. Oie, A generalised diffusion-based file replication scheme for load balancing in p2p file-sharing networks, Int. J. Grid Utility Comput., 3 (2012), pp. 242–252.
[21] E. Yee, Bayesian probabilistic approach for inverse source determination from limited and noisy chemical or biological sensor concentration measurements, Proc. SPIE, 6554 (2007), p. 65540W–1.
[22] Y. Zhang, Continuum Limits of Markov Chains with Application to Wireless Network Modeling and Control, Ph.D. thesis, Colorado State University, Fort Collins, 2014.
[23] Y. Zhang, E. K. Chong, J. Hannig, and D. Estep, Approximating extremely large networks via continuum limits, IEEE Access, 1 (2013), pp. 577–595.
[24] Y. Zhang, E. K. Chong, J. Hannig, and D. Estep, Continuum modeling and control of large nonuniform wireless networks via nonlinear partial differential equations, Abstr. Appl. Anal., 2013 (2013), 16 pp., . · Zbl 1273.35280
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.