Real-time pulse arrival detection in the presence of white Gaussian noise

A stochastic model is considered in which the observable signal is a stochastic process defined as the additive combination of a pulse with a random arrival time and a white Gaussian process. It is assumed that the probability density function of the arrival time is known. The concern is to detect the arrival of the pulse based on an observation set which terminates as soon as the arrival of the pulse is announced. A technique for achieving this goal is to apply the observed signal to an appropriate nonlinear filter and monitor its output until a certain criterion is met. Two such criteria are proposed and expressions for their associated filtering schemes are determined. In general, it is difficult to obtain exact implementable filters to recursively determine these expressions, thus under certain assumptions, an approximate filtering scheme is proposed.