Optimal Distributed Detection of Multiple Hypotheses Using Blind Algorithms

Abstract

In a parallel distributed detection system each local detector makes a decision based on its own observations and transmits its local decision to a fusion center, where a global decision is made. Given fixed local decision rules, in order to design the optimal fusion rule, the fusion center needs to have perfect knowledge of the performance of the local detectors as well as the prior probabilities of the hypotheses. Such knowledge is not available in most practical cases. In this thesis, we propose a blind technique for the general distributed detection problem with multiple hypotheses. We start by formulating the optimal M-ary fusion rule in the sense of minimizing the overall error probability when the local decision rules are fixed. The optimality can only be achieved if the prior probabilities of hypotheses and parameters describing the local detector performance are known. Next, we propose a blind technique to estimate the parameters aforementioned as in most cases they are unknown. The occurrence numbers of possible decision combinations at all local detectors are multinomially distributed with occurrence probabilities being nonlinear functions of the prior probabilities of hypotheses and the parameters describing the performance of local detectors. We derive nonlinear Least Squares (LS) and Maximum Likelihood (ML) estimates of unknown parameters respectively. The ML estimator accounts for the known parametric form of the likelihood function of the local decision combinations, hence has a better estimation accuracy. Finally, we present the closed-form expression of the overall detection performance for both binary and M-ary distributed detection and show that the overall detection performance using estimated values of unknown parameters approaches quickly to that using their true values. We also investigate various impacts to the overall detection. The simulation results show that the blind algorithm proposed in this thesis provides an efficient way to solve distributed detection problems.