Sources of Probability in Predicting Passive Sonar Performance

Abstract

There are three sources of probabilistic statements found in predicting passive sonar performance. These are (1) the detection process for a single observation time T; (2) the sequence of multiple observations carried out by a sonar operator resulting in N independent observations; and (3) the availability of a given level of input signal to noise (S/N) ratio. The first two considerations result in a conditional detection and false-alarm probability given a fixed value of input S/N ratio. Recognition differential is seen not as the value of input S/N ratio required for detection probability 50% but rather the minimum value of S/N ratio that will trigger the sequential observation process and lead to a detection probability near unity and false-alarm probability near zero. The third consideration results in a probability density distribution for input S/N ratio because one wishes to predict detection for an ensemble of targets, propagation loss conditions, sea states, and sonar operators. The probability of detection for a given variance and expected value of input S/N ratio and given value of recognition differential is seen to be the integrated product of the first two probabilities times the third. The probability of a false alarm in passive sonar operation is negligibly low because of the sequential observation process. A sample problem for aural detection and for detection by time-bearing plot will be presented.