Joint PDF construction for sensor fusion and distributed detection

A novel method of constructing a joint PDF under H
₁
, when the joint PDF under H
₀
is known, is developed. It has direct application in distributed detection systems. The construction is based on the exponential family and it is shown that asymptotically the constructed PDF is optimal. The generalized likelihood ratio test (GLRT) is derived based on this method for the partially observed linear model. Interestingly, the test statistic is equivalent to the clairvoyant GLRT, which uses the true PDF under H
₁
, even if the noise is non-Gaussian.