Algorithm for optimal filtering of random Markov signals with pulse-disturbance-amplitude estimation

Optimal filtering problem of random Markov signals with simultaneous estimation of pulse disturbance amplitudes is considered. Linear models of stochastic difference equations in discrete time are used to describe signals, observed processes, and pulse disturbances. Pulse disturbances occur at random times with random amplitudes. A real-time calculation procedure is obtained for the joint a posteriori probability density function of random signals and pulse disturbance amplitudes. A quasioptimal filtering algorithm is derived in the case of scalar signals and scalar observed processes by a partition method. Computer simulation results are presented.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 39, No. 4, pp. 496–513, April, 1996.