Distributed detection with common observations

Distributed detection with dependent observations is always a challenging problem. In this paper, we consider a special dependent case where sensors share some common information. Specifically, we investigate a tandem network with sensor 1 sending a one-bit decision to sensor 2 where the final decision is made. Along with their common observation X₂, sensors 1 and 2 possess their conditionally independent measurements X₁ and X₃, respectively. After obtaining the relationship between the optimal sensor 1 rule and sensor 2 fusion rule, we derive the necessary condition for the optimal sensor decision rules for both sensors. We compare the optimal rules with two suboptimal rules for distributed detection of a constant DC signal in Gaussian noise with various of signal-to-noise ratios.