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Distributed Sensing

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Poisson Point Processes
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Abstract

PPPs make several important, albeit somewhat disjointed, contributions to distributed sensor network detection, tracking, and communication connectivity. The focus in this chapter is on detection and communication since tracking problems are specialized forms of the multisensor intensity filter presented in Section 6.5. Communication path lengths of a randomly distributed sensor field are characterized by distance distributions. Distance distributions are obtained for sensors located at the points of a nonhomogeneous PPP realization. Both sensor-to-target and sensor-to-sensor distances are discussed. Communication diversity, that is, the number of communication paths between sensors in a distributed sensor field is discussed as a threshold phenomenon a geometric random graph and related to the abrupt transition phenomenon of such graphs. Detection coverage is discussed for both stationary and drifting sensor fields using Boolean models. These problems relate to classical problems in stochastic geometry and geometric probability. The connection between stereology and distributed sensor fields is presented as a final topic.

How can I tell what I think till I see what I say?

E.M. Forster, Aspects of the Novel, 1927

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Notes

  1. 1.

    The importance of invariance was not recognized in early discussions of the concept of a random line. Bertrand’s paradox (1888) involves three different answers to a question about the length of a random chord of a circle. The history is reviewed in [61, Chapter 1].

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Correspondence to Roy L. Streit .

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Streit, R.L. (2010). Distributed Sensing. In: Poisson Point Processes. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-6923-1_7

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  • DOI: https://doi.org/10.1007/978-1-4419-6923-1_7

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