Performance and geometric interpretation for decision fusion with memory

A binary distributed detection system comprises a bank of local decision ma kers (LDM's) and a central information processor (the data fusion center, D FC), All LDM's survey a common volume for a binary {H-0, H-1} phenomenon. E ach LDM forms a binary decision: it either accepts H-1 ("target-present") o r H-0 ("target-absent"). The LDM is fully characterized by its performance probabilities (probability of false alarm and probability of detection). Th e decisions are transmitted to the DFC through noiseless communication chan nels. The DFC then optimally combines the local decisions to obtain a globa l decision ("target-present" or "target-absent") which minimizes a Bayesian objective function. Along with the local decisions, the DFC in our archite cture remembers and uses its most recent decision in synthesizing each new decision. When operating in a stationary environment, our architecture conv erges to a steady-state decision in finite time with probability one, and i ts detection performance during convergence and in steady state is strictly determined, Once convergence is proven, we apply the results to the detect ion of signals with random phase and amplitude. We further provide a geomet ric interpretation for the behavior of the system: the unit square of the c urrent (P-f, P-d) known to the DFC is partitioned into polygons, one of whi ch defines a "stopping set" of values. If the current (P-f, P-d) falls into this region, there is no way to leave it, and hence there is no reason to continue testing.