Threshold optimization according to the restricted Bayes criterion in decentralized detection problems

Abstract

Abstract:In this paper, the restricted Bayes approach is studied in a decentralized detection problem. All decisions on which the hypothesis is true are made by local sensors through conditionally independent observations. Then these decisions are transmitted to the fusion center for the final decision. In the conventional approach, all thresholds of local sensors and the fusion center are considered as deterministic variables and optimized according to the given criterion for given test statistics of local sensors and the fusion center. In this paper, it is shown that setting thresholds as random variables instead of deterministic ones can improve the performance according to the restricted Bayes criterion. It is proved that optimal random thresholds are dependent on each other, and the probability density function of each one consists of at most two point masses. Two methods for the implementation of this scheme are proposed. A necessary and sufficient condition for improvability of the conventional approach through replacing optimal deterministic thresholds by optimal random ones is derived. Finally, theoretical results are investigated through simulations.