Detection-Threshold Approximation for Non-Gaussian Backgrounds

Abstract

Abstract-The detection threshold (DT) term in the sonar equation describes the signal-to-noise ratio (SNR) required to achieve a specified probability of detection (P d ) for a given probability of false alarm (P f a ). Direct evaluation of DT requires obtaining the detector threshold (h) as a function of P f a and then using h while inverting the often complicated relationship between SNR and P d . However, easily evaluated approximations to DT exist when the background additive noise or reverberation is Gaussian (i.e., has a Rayleigh-distributed envelope). While these approximations are extremely accurate for Gaussian backgrounds, they are erroneously low when the background has a heavy-tailed probability density function. In this paper it is shown that by obtaining h appropriately from the non-Gaussian background while approximating P d for a target in the non-Gaussian background by that for a Gaussian background, the easily evaluated approximations to DT extend to non-Gaussian backgrounds with minimal loss in accuracy. Both fluctuating and non-fluctuating targets are considered in Weibulland K-distributed backgrounds. While the P d approximation for fluctuating targets is very accurate, it is coarser for nonfluctuating targets, necessitating a correction factor to the DT approximations.

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