An optimum strategy for detection in the presence of random transient disturbance and white Gaussian noise

Detection of a deterministic signal is considered Because of the presence of the transient disturbance, the traditional totally probabilistic criteria are no longer appropriate, since they cannot be related to the physical reality, as in the case of stationary ergodic noise only. A mixed strategy is proposed for the detection where the disturbance is treated as a semideterministic object while white Gaussian noise is treated as a genuinely random object. Specifically, the author uses as the detection statistic the log-likelihood ratio of two conditional probability measures (corresponding to the signal-presence and the signal-absence hypotheses), given the disturbance, in which the disturbance is replaced by its maximum a posteriori likelihood estimate. The detection statistic takes the generalized (in function space) form of a soft-limiter or a blanker followed by the matched filter. It is an explicit detection algorithm, though improvement in computational efficiency is much desired