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SOME REMARKS ON DISTRIBUTED SENSING WITH COSTS

Published online by Cambridge University Press:  11 February 2014

Allan Gut
Allan Gut*
Affiliation:
Department of Mathematics, Uppsala University, Box 480, SE-751 06 Uppsala, Sweden. E-mail: allan.gut@math.uu.se
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Abstract

A recent paper by Pozdnyakov and Steele [6] is devoted to distributed sensor networks in which the sensors send summarized information to some remotely located fusion agents. Main focus is on sensors that send their information according to a so-called binary-plus-passive design. Some exact relations in a sequential approach, aimed at making decisions before a given budget is exhausted are presented. In this paper, we provide asymptotic results in the case of more general sensors for increasing budgets. The essential ingredient is the observation that the setting can be modeled within the framework of certain stopped two-dimensional random walks. We also provide asymptotics for the cost for large decision boundaries, and, finally, some comments on the probability of a positive/negative decision as well as on the duration of the process until a decision is made in the binary-plus-passive design.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 28 , Issue 2 , April 2014 , pp. 271 - 277
Copyright
Copyright © Cambridge University Press 2014 

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References

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6.Pozdnyakov, V. & Steele, M. (2010). Bugs on a budget: distributed sensing with cost for reporting and nonreporting. Probability in the Engineering and Informational Sciences, 24: 525–534.Google Scholar