Optimal Fusion Rule and Design of Network Communication Structures

In chapter 4, we have derived a number of results on the optimal sensor rules with a fixed fusion rule for general multisensor m-ary network decision systems. To achieve globally optimal performance, the previous results are obviously not enough because the number of all possible fusion rules are very large and exhaustive searching for the optimal fusion rule is computationally intractable. Therefore, in Sections 5.3-5.7, we are going to extend the results on the optimal fusion rule and some related interesting properties derived in Section 3.5 to more general network decision systems discussed in Chapter 4. On the other hand, in terms of the two-level optimization strategy in the distributed decision system, a local sensor may first need a locally optimal sensor rule based on its own information for its own local goal, and then send its decision result to the fusion center. Finally, the fusion center fuses all received local decision results to get an optimal final decision. When all sensor rules (not only sensor outputs) are well known, the optimal final fusion can reduce to the conventional decision problem at the second level. We will formulate and solve it thoroughly in Section 5.1. If only the sensor outputs can be known, some results on reducing the number of valuable fusion rules are presented in Section 5.2 in both two-level optimization and global optimization senses. Here, by valuable fusion rules we mean that they must contain an optimal fusion rule.