Abstract
The effect of amplitude fluctuation on sonar detection can be expressed quantitatively by means of receiver operating characteristic (ROC) curves having a fluctuation index k as a parameter. The fluctuation-modified ROCs are found to be similar to conventional ROCs for non-fluctuating signals (k = 1), but on double-probability paper have a slope that depends on the value of k. A simple example with Gaussian statistics is developed where the time mean of a signal fluctuates Gaussianly about the ensemble mean. From this idea, the analytical expressions for the “tilted” ROCs, as well as their plots, are derived. Two extremes of slow and fast fluctuations are discussed.
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