Detection of random transient signals via hyperparameter estimation

Difficulties arise with the generalized likelihood ratio test (GLRT) in situations where one or more of the unknown signal parameters requires an enumeration that is computationally intractable. In the transient signal detection problem, the frequency characteristics of the signal are typically unknown; therefore, even if an aggregate signal bandwidth is assumed, the estimation problem intrinsic to the GLRT requires an enumeration of all possible sets of signal locations within the monitored band. In this paper, a prior distribution is imposed over those portions of the signal parameter space that traditionally require enumeration. By replacing intractable enumeration over possible signal characteristics with an a priori signal distribution and by estimating the “hyperparameters” (of the prior distribution) jointly with other signal parameters, it is possible to obtain a new formulation of the GLRT that avoids enumeration and is computationally feasible. The GLRT philosophy is not changed by this approach—what is different from the original GLRT is the underlying signal model. The performance of this new approach appears to be competitive with that of a scheme of emerging acceptance: the “power-law” detector.