Distributed hypothesis testing with a fusion center: The conditionally dependent case

Kien C. Nguyen, Tansu Alpcan, Tamer Başar

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The paper deals with decentralized Bayesian detection with M hypotheses, and N sensors making conditionally correlated measurements regarding these hypotheses. Each sensor sends to a fusion center an integer from {0, 1, D - 1}, and the fusion center makes a decision on the actual hypothesis based on the messages it receives from the sensors so as to minimize the average probability of error. Such conditionally dependent scenarios arise in several applications of decentralized detection such as sensor networks and network security. Conditional dependence leads to a non-standard distributed decision problem where threshold based policies (on likelihood ratios) are no longer optimal, which results in a challenging distributed optimization/decision making problem. We show that, in this case, the minimum average probability of error cannot be expressed as a function of the marginal distributions of the sensor messages. Instead, we characterize this probability based on the joint distributions of these messages. We also provide some numerical results for the case where the sensors' measurements follow bivariate normal distributions.

Original languageEnglish (US)
Title of host publicationProceedings of the 47th IEEE Conference on Decision and Control, CDC 2008
Pages4164-4169
Number of pages6
DOIs
StatePublished - 2008
Event47th IEEE Conference on Decision and Control, CDC 2008 - Cancun, Mexico
Duration: Dec 9 2008Dec 11 2008

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0191-2216

Other

Other47th IEEE Conference on Decision and Control, CDC 2008
CountryMexico
CityCancun
Period12/9/0812/11/08

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

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  • Cite this

    Nguyen, K. C., Alpcan, T., & Başar, T. (2008). Distributed hypothesis testing with a fusion center: The conditionally dependent case. In Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008 (pp. 4164-4169). [4739150] (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2008.4739150