1st International Workshop Control over Communication Channels

Research Article

A Sequential Problem in Decentralized Detection with Communication

  • @INPROCEEDINGS{10.1109/WIOPT.2009.5291561,
        author={Demosthenis Teneketzis and ashutosh nayyar},
        title={A Sequential Problem in Decentralized Detection with Communication},
        proceedings={1st International Workshop Control over Communication Channels},
        publisher={IEEE},
        proceedings_a={CONCOM},
        year={2009},
        month={10},
        keywords={Decentralized Detection stopping time stopping rule sensor network},
        doi={10.1109/WIOPT.2009.5291561}
    }
    
  • Demosthenis Teneketzis
    ashutosh nayyar
    Year: 2009
    A Sequential Problem in Decentralized Detection with Communication
    CONCOM
    IEEE
    DOI: 10.1109/WIOPT.2009.5291561
Demosthenis Teneketzis1,*, ashutosh nayyar1,*
  • 1: Department of Electrical Engineering and Computer Science University of Michigan
*Contact email: teneket@eecs.umich.edu, anayyar@umich.edu

Abstract

We consider a sequential problem in decentralized detection. Two observers can make repeated noisy observations of a binary hypothesis on the state of the environment. At any time, observer 1 can stop and send a final message to observer 2 or it may continue to take more measurements. Every time observer 1 postpones its final message to observer 2, it incurs a penalty. We consider observer 2’s operation under two different scenarios. In the first scenario, observer 2 waits to receive the final message from observer 1 and then starts taking measurements of its own. It is then faced with a stopping problem on whether to stop and declare a decision on the hypothesis or to continue taking measurements. In the second scenario, observer 2 starts taking measurements from the beginning. It is then faced with a different stopping problem. At any time, observer 2 can decide whether to stop and declare a decision on the hypothesis or to continue to take more measurements and wait for observer 1 to send its final message. We obtain parametric characterization of optimal policies for the two observers under both scenarios. We then extend these characterizations to a problem with multiple peripheral sensors that each send a single final message to a coordinating sensor who makes the final decision on the hypothesis.