Optimal detection of a random envelope of pulsed signals

The optimal detection of an envelope of random pulsed signals on a background of white Gaussian noise is considered. It is assumed that the shape of the pulsed signals in the envelope is known along with the a priori probability densities of the amplitudes and moments of appearance of individual pulses. Algorithms are obtained for the formation of the likelihood ratio in real time. Equations are derived which represent a set of Kalman-Bucy filters with additional components depending on particular likelihood ratios.