A nonparametric Page test applied to active sonar detection

A nonparametric Page test (NPT) is proposed for active sonar detection in shallow water when the received reverberation and background noise is not expected to produce the traditional Rayleigh distributed matched filter amplitude. When the reverberation and background noise is heavy-tailed, the false alarm performance of a detector designed under the Rayleigh assumption will degrade. The NPT has constant false alarm performance irrespective of the statistical distribution of the reverberation and background noise assuming adequate normalization produces a stationary sequence. Greater control of the false alarm performance is obtained at the expense of a reduction in detection performance. The standard Wald and Siegmund based approximations for the Page test performance measures are derived; the average time between false alarms and the average delay before detection. The quality of these approximations is examined through comparison with simulation results where it is seen that the Siegmund based approximations are adequate for detector implementation and performance prediction. The detection algorithm is applied to reverberation data where it is seen to perform favorably against the thresholded matched filter and exhibits an expected loss in detection performance compared to the standard Page test