Short delay detection of a transient in additive Gaussian noise via higher order statistic test

In the context of electromagnetic surveillance, our aim is to detect a transient in a non-stationary Gaussian noise by a higher order statistic test. We prove that the higher order statistic detection test provides a very short delay detection and a good estimation of the transient arrival time. We develop the theoretical ground and use a new formalism (an extension of Gardner's (1988) work) that enables us to evaluate theoretically the response of higher order statistic test for detection. The theory is applied on a simple and typical example: the kurtosis. We then compare the theoretical results to simulation results.