A greedy algorithm for decentralized Bayesian detection with feedback

We consider a decentralized binary detection architecture comprised of n local detectors (LDs) communicating their decisions to a Data Fusion Center (DFC). Each local detector (LD) declares preference for one of two hypotheses (H₀ or H₁) and transmits it to the DFC. The decision of the k^th LD at time step t is u^t_k. The DFC develops a global preference u^t₀ for one of hypotheses based on the vector of local decisions U^t while minimizing a Bayesian cost. The input to the k^th LD at time step t is the observation y^t_k collected from the surveyed environment, and the previous global decision u^t-1₀. Alhakeem and Varshney developed a person-by-person optimal (PBPO) solution to this problem, namely a PBPO procedure to calculate the global fusion rule and the local decision rules. However, their solution requires that at each time step 2ⁿ fusion rule equations and 2n local threshold equations be solved simultaneously. In this paper we suggest a suboptimal solution to the problem, based on independent local minimizations of similar Bayesian cost by each LD and by the DFC. To assess the cost of decentralization, the performance of this solution is compared to that of an architecture that processes all observations in one central location.