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Stochastic Optimization of Sensor Placement for Diver Detection

Author

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  • Anton Molyboha

    (Department of Mathematical Sciences, Stevens Institute of Technology, Hoboken, New Jersey 07030)

  • Michael Zabarankin

    (Department of Mathematical Sciences, Stevens Institute of Technology, Hoboken, New Jersey 07030)

Abstract

A comprehensive framework for diver detection by a hydrophone network in an urban harbor is presented. It includes a signal processing algorithm and a diver detection test and formulates optimal hydrophone placement as a two-stage stochastic optimization problem with respect to different scenarios of underwater noise. The signal processing algorithm identifies sound intensity peaks associated with diver breathing and outputs a diver number measuring the likelihood of diver presence, whereas the diver detection test aggregates the diver numbers obtained from the hydrophones in a linear statistic and optimizes the statistic's coefficients and a detection threshold for each noise scenario. The serial dependence of the diver numbers on a short time scale (several detection periods) is modeled by a hidden Markov chain, and finding the worst-case diver's trajectory for each hydrophone placement and noise scenario is reduced to a linear programming problem. The framework is tested in numerical experiments with real-life data for circular and elliptic hydrophone placements and is shown to be superior to a deterministic energy-based approach.

Suggested Citation

  • Anton Molyboha & Michael Zabarankin, 2012. "Stochastic Optimization of Sensor Placement for Diver Detection," Operations Research, INFORMS, vol. 60(2), pages 292-312, April.
    • Handle: RePEc:inm:oropre:v:60:y:2012:i:2:p:292-312
    DOI: 10.1287/opre.1110.1032
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    References listed on IDEAS

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    1. Leroux, Brian G., 1992. "Maximum-likelihood estimation for hidden Markov models," Stochastic Processes and their Applications, Elsevier, vol. 40(1), pages 127-143, February.
    2. Sergei Pashko & Anton Molyboha & Michael Zabarankin & Sergei Gorovyy, 2008. "Optimal sensor placement for underwater threat detection," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(7), pages 684-699, October.
    3. G. Hanoch & H. Levy, 1969. "The Efficiency Analysis of Choices Involving Risk," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 36(3), pages 335-346.
    4. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, December.
    5. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
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    Cited by:

    1. Fang Lu & John J. Hasenbein & David P. Morton, 2016. "Modeling and Optimization of a Spatial Detection System," INFORMS Journal on Computing, INFORMS, vol. 28(3), pages 512-526, August.
    2. Oleg Burdakov & Jonas Kvarnström & Patrick Doherty, 2017. "Optimal scheduling for replacing perimeter guarding unmanned aerial vehicles," Annals of Operations Research, Springer, vol. 249(1), pages 163-174, February.

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