On optimum distributed detection and robustness of system performance

In this paper we consider some theoretical and practical issues regarding optimum distributed detection systems. The detection systems considered here are parallel distributed detection systems, with each sensor allowed to produce multi-bit output, and the performance optimization criterion is the Neyman-Pearson criterion. For conditionally independent sensor observations, it is shown that the optimum sensor quantizers are likelihood ratio quantizers, and the necessary conditions for optimum quantizer thresholds are obtained. For dependent sensor observations, since the optimum sensor quantizers are not likelihood ratio quantizers and therefore quite difficult to obtain, a suboptimal detection scheme is presented instead. In order to obtain the optimum quantizer thresholds, the conditional densities of sensor observations must be complete known. However in real applications, these densities are rarely known and must be estimated from finite samples. Thus, there exist some differences or variations between the true but unknown densities and the estimated densities that are used to design the optimal systems. Since such variations will certainly cause degradation of system performance, it is necessary to test the system performance in the presence of such variations. The system performance and its robustness with respect to the variations of densities or density parameters are tested in this paper and it is shown that the system performance is quite stable or robust, with respect to such variations.