  Minimax detection of Gaussian stochastic sequences (signals) with unknown
covariance matrices is studied. For a fixed false alarm probability (1-st kind
error probability), the performance of the minimax detection is being
characterized by the best exponential decay rate of the miss probability (2-nd
kind error probability) as the length of the observation interval tends to
infinity. Our goal is to find the largest set of covariance matrices such that
the minimax robust testing of this set (composite hypothesis) can be replaced
with testing of only one specific covariance matrix (simple hypothesis) without
any loss in detection characteristics. In this paper, we completely describe
this maximal set of covariance matrices. Some corollaries address minimax
detection of the Gaussian stochastic signals embedded in the White Gaussian
noise and detection of the Gaussian stationary signals.
