An RKHS approach to detection and estimation problems--II: Gaussian signal detection

The theory of reproducing kernel Hilbert spaces is used to obtain a simple but formal expression for the likelihood ratio (LR) for discriminating between two Gaussian processes with unequal covariances, and to develop a test by which the formal expression can be checked for validity. This LR formula can be evaluated by working separately with each covariance, thus reducing the calculations for the random signal case to those for the simpler known signal problem. In contrast, all previous LR formulas for the unequal covariance problem seem to require calculations involving both covariances simultaneously.