On Minimax Detection of Gaussian Stochastic Sequences and Gaussian Stationary Signals

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.