OPTIMIZATION OF DETECTION NETWORKS .2. TREE-STRUCTURES

A distributed binary detection problem with multimessage (greater-than -or-equal-to 1 bit) communications is considered, wherein the nodes (s ensors, decision makers (DMs)) of the system are organized in the form of a tree with multiple root nodes. A numerical algorithm is develope d for determining the optimal decision rule at each node assuming mono tone cost functions imposed only on the root nodes. It is assumed that the observations of each node are conditionally independent of those of the other nodes. It is shown that the problem is equivalent to solv ing a nonlinear optimal control problem, and the necessary conditions of optimality using Bayes' risk as the optimization criterion are deri ved. The optimal control approach provides an interpretation of certai n functions of the co-state variables in terms of thresholds, and lead s to a computationally efficient min-H algorithm to solve for the opti mal decision rule at each node. The numerical algorithm provides a too l to investigate the organizational issues of adaptation, structure, a nd robustness.