Research on performance of the Page Test independent of unknown signal length

Abstract

The change of the probability distribution function (PDF), or related parameters, is one of the basic changes of the statistical characteristics when the sonar target signal emerges or disappears. The Page Test can detect transients effectively based on this principle. It is more difficult for the Page Test to detect passive sonar signals because of unknown signal parameters. Generally based on Newman-Pearson criterion, given the certain transient length, the Page Test works well with these parameters which are calculated with the detection performance model, such as the threshold and the bias. When the real signal length mismatches the designed one, those parameters are no longer accurate and performance of the detector decreases remarkably. In this paper the time-varying-threshold Page Test (VPT) insensitive to the signal length is researched. The theoretical detection probability (Pd) model of the VPT is more complicated than the routine Page Test because the threshold changes with the length of continuous nonzero detection results. The methods to calculate the normal and latent Pd of nonzero initial state are deduced in this paper. The theoretical analyses and the simulated results of Pd are compared between the VPT and the routine Page Test (PT) on two cases of matched transient signal length and mismatched one. The sea trial data of certain bearing channel after beam-forming are used to test these two methods. The results indicate that the former is better than the mismatched PT, but inferior to the matched one. In fact the signal length matched detection can not be realized because the signal length can not be obtained.