Linear local data fusion for sequential test

This paper studies local data fusion for sequential detection. Let a sensor network monitor a Gaussian phenomenon in Gaussian background noise, and let the observation of each sensor be a vector r. In order to reduce the communication burden, each sensor reports a linearly fused scalar x=w^T r instead of the raw data r to a processing center, which executes sequential detection. The aim of this paper is how to design the fusion vector w so as to minimize the average expected sample size (AESS) of the detector. Two typically hypothetical cases - equal variance and equal mean - are analyzed, and their optimal fusion vectors are derived.