Multisensor Binary Decision

Abstract

In this chapter, we will not limit the number of sensors to two and not limit sensors transmission to a single binary number as done in the last chapter. In fact, to improve the decision accuracy, if additional communication bandwidth is available, from each sensor more than one binary number could be transmitted out. In the first six sections of this chapter, we will suggest a discretized iterative algorithm to approximate the optimal local (sensor) compression rules under a fixed fusion rule for the distributed multisensor Bayes binary decision problem. First, we will show that any general fusion rule can be formulated as a bi-valued polynomial function of the local compression rules. Then, under a given fusion rule, we will present a fixed point type necessary condition for the optimal local compression rules and propose an efficient discretized iterative algorithm and prove its finite convergence. After this, we will consider the optimal fusion rule problem for a class of the systems with a specific communication pattern. For such a system, namely an /-sensor system, suppose that the total number of bits transmitted by l —1 sensors are fixed, we can change the number of bits transmitted by the l sensor to a certain number, which is determined completely by the total number of bits transmitted by other l —1 sensors. For those systems with the modified communication pattern, we will present an optimal fusion rule, and prove that this fusion rule is not only superior to all possible fusion rules under the original communication pattern, but also an optimal fusion rule for the modified communication pattern. Furthermore, we will prove that even if the lth sensor now can transmit uncompressed observational data to the fusion center, the performance cannot be better than that achieved by the aforementioned optimal fusion rule. Moreover, this optimal fusion rule does not depend on the statistical properties of the observational data, or even on the decision criteria. It only depend on the total number of bits transmitted by other l — 1 sensors. Numerical examples support the above results and give