Reliable parameter estimation for generalised gaussian pdf models: application to signal detection in non-gaussian noisy environment

In this paper, a new analytical approximated expression for the sharpness parameter of a Generalised Gaussian pdf model as a function of a higher-order statistic, namely normalised kurtosis is proposed. The approximation is based on some mathematical considerations concerning the Gamma function, and provides a very precise sharpness evaluation for a wide range of normalised kurtosis values. As a result, it allows the exploitation of the parametric Generalised Gaussian pdf model in advanced signal processing applications, e.g. detection of weak signals in non-Gaussian noise, where an accurate evaluation of noise distribution is required.