The probability of false alarm (P/sub fa/) in active sonar systems is an important system performance measure. This measure is typically estimated by the proportion of alarms to opportunities over some finite window, essentially forming the sample exceedance distribution function (EDF). It is common for sonar systems to be 'over-sampled'; that is, to have a sampling rate higher than the minimum required for representing the bandwidth of the received signal, resulting in reverberation data that are correlated from sample to sample. The performance of the sample EDF in P/sub fa/ estimation under such conditions is of interest. It is easily shown that the estimator remains unbiased with correlated data. However, it is shown in this paper that the variance of the estimator may be reduced from that for independent data by oversampling. Further, the variance is seen to fall between the Cramer-Rao lower bound based on independent thresholded (binary) data and that based on the complex matched filter output data.

Page's (1954) test is optimal for detecting a permanent change in distribution, in the sense that it minimizes the worst case average delay to detection given an average distance between false alarms. When used to detect transient signals, however, it in fact becomes the generalized likelihood ratio test (GLRT). Since a GLRT is in almost all cases ad hoc, Page's test used as such cannot be said to be optimal in any explicit sense. This article discusses the development of the min-max test, via the new ideas of Baygun and Hero (see ibid., vol.41, p.688-703, 1995) for the detection of a transient.

The performance of Page's (1954) test for the detection of a permanent change in distribution is reasonably well understood. However, there are few parallel results on its application to the detection of a temporary (i.e., transient) change, and this is the paper's subject. Specifically, a lower bound on detectability is developed using a quantization approach; and a pair of approximations are presented, one based on a Brownian motion analogy, which yields an upper bound in the Gaussian case, and the other again on quantisation. The correspondence between these and simulation appears good in both Gaussian and non-Gaussian cases with heavier tail probability.