Optimization of detection networks. I. Tandem structures

A distributed binary detection problem with binary communications is considered, wherein the nodes (sensors and decision-makers) of the system are organized in a series configuration. It is shown that this problem can be reformulated as a deterministic multistage nonlinear optimal control problem. The necessary and sufficient conditions of optimality using Bayes´ risk as the optimization criterion are then derived, and a physical interpretation of how the costates relate to the decision threshold at each node is provided. Using the min-H method of optimal control theory, a computationally efficient algorithm with linear complexity in the number of nodes per iteration is proposed to solve for the optimal decision strategy. The algorithm is then extended to solve a Neyman-Pearson version of the problem to obtain the optimal team (network) receiver operating characteristic curve. Two easily implemented suboptimal decision rules termed the asymptotic decision strategy and the constant control strategy are proposed and their properties are investigated