On the Epsilon Most Stringent Test Between Two Vector Lines in Gaussian Noise

This paper addresses the problem of distinguishing between two vector lines observed through noisy measurements. This is a hypothesis testing problem where the two hypotheses are composite since the signal amplitudes are deterministic and not known. An ideal criterion of optimality, namely the most stringent test, consists in minimizing the maximum shortcoming of the test subject to a constrained false alarm probability. The maximum shortcoming corresponds to the maximum gap between the power function of the test and the envelope power function which is defined as the supremum of the power over all tests satisfying the prescribed false alarm probability. The most stringent test is unfortunately intractable. Hence, a suboptimal test, called the epsilon most stringent test, is proposed. This test has a very simple form and its statistical properties are expressed in closed-form. It is numerically shown that the proposed test has a small loss of optimality and that it outperforms the generalized likelihood ratio test.