Noise Estimation in Long-Range Matched-Filter Envelope Sonar Data

In sonar signal processing when selecting a threshold for detection, it is necessary to consider the noise in the signal to achieve the desired rates of detection and false alarm. The clutter component of this noise, caused by scattering from environmental features, is often a limiting factor. This is particularly the case when active sonar systems operate in shallow water. Therefore, suitable modeling of clutter-limited data is vital for accurate detection in such environments. This paper investigates the $K$-distribution, the Weibull distribution, and the log-normal distribution as models for clutter-limited matched-filter envelope sonar data, obtained using FM chirp pulses in a shallow-water environment. The models are evaluated using modified Kolmogorov–Smirnov (KS) and Anderson–Darling (AD) tests. Critical values for the upper tail AD statistic applied to the $K$ -distribution are estimated by Monte Carlo simulation and tabulated here. Results show that the $K$ -distribution and the Weibull distribution provide a good model of noise in clutter-limited environments. However, the $K$-distribution provides a better fit in the tails, which is important for target detection. The Kolmogorov–Smirnov test is shown to be an unsuitable method of evaluating fit when the tail of a distribution is of greatest interest. We also show that the estimated shape parameter of the $K$ -distribution does provide a simple means of identifying regions dominated by clutter.