OPTIMUM DISTRIBUTED DETECTION OF WEAK SIGNALS IN DEPENDENT SENSORS

Locally optimum (LO) distributed detection is considered for observations that are dependent from sensor to sensor. LO detection has been extensively studied for classical detection scenarios but general results for LO distributed detection, specifically for dependent sensor observations, have been lacking. The necessary conditions are presented for the LO distributed sensor detector designs and fusion rule for an N sensor parallel distributed detection system with dependent sensor observations, and specific solutions are obtained for a random signal in additive noise detection problem with two sensors. These solutions indicate that the LO sensor detector nonlinearities, in general, contain a term proportional to f'/f, where f is the noise probability density function (pdf). The importance of this term varies with the additive noise pdf and the false alarm probability. For some non-Gaussian pdfs, the new term is significant and causes the LO sensor detector nonlinearities to be nonsymmetric even for symmetric pdfs. LO solutions are presented for finite sample sizes and the LO solutions are discussed in the asymptotic case. These results are extended to yield the form of the solutions for the N sensor LO random signal distributed detection problem, that yields expected generalizations of the two sensor results.