Detection-Threshold Approximation for Non-Gaussian Backgrounds

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-fa). Direct evaluation of DT requires obtaining the detector threshold (h) as a function of and then using 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 targets (FTs) and nonfluctuating targets (NFTs) are considered in Weibull- and K-distributed backgrounds. While the approximation for FTs is very accurate, it is coarser for NFTs, necessitating a correction factor to the DT approximations.