Performance and geometric interpretation for decision fusion with memory

A binary distributed detection system comprises a bank of local decision makers (LDMs) and a central information processor or data fusion center (DFC). All LDMs survey a common volume for a binary {H₀, H₁} phenomenon. Each LDM forms a binary decision: it either accepts H₁ (target-present) or H₀ (target-absent). The LDM is fully characterized by its performance probabilities. The decisions are transmitted to the DFC through noiseless communication channels. The DFC then optimally combines the local decisions to obtain a global decision which minimizes a Bayesian objective function. The DFC remembers and uses its most recent decision in synthesizing each new decision. When operating in a stationary environment, our architecture converges to a steady-state decision LDM in finite time with probability one, and its detection performance during convergence and in steady state is strictly determined. Once convergence is proven, we apply the results to the detection of signals with random phase and amplitude. We further provide a geometric interpretation for the behaviour of the system