Detection of Multiple Sonar Sine Waves of Unknown Frequency

A study of the use of a passive omnidirectional hydrophone to detect sonar targets. Examination of optimum target detectors reveals that only the total signal energy is significant in evaluating detectability; thus, in theory, a detector should make use of even very small amplitude components. The number of possible combinations of frequencies is also important, since the false-alarm probability is approximately proportional to this number. For the suboptimum detectors considered, where the detection of two or more sine waves individually is required, the dependent frequency case is shown to be always more detectable than the independent frequency case, although the difference becomes very small as amplitude ratios increase. Other findings are that the EFAR (equal false alarm) detector stresses discrimination at the cost of detectability, while the MOD (maximum over-all detectability) detector loses all discrimination to maximize detectability; and that, while these devices are identical when the two sine wave amplitudes (in the two-out-of-two case) are equal, they diverge rapidly in opposite directions when the amplitudes become different. (See also RM-4809-ARPA, RM-4578-ARPA)