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.     

STUDY OF ALGORITHMS FOR ESTIMATING SIGNALS WITH A PULSED-DISTURBANCE FLOW

Using the methods of the Markov theory of optimal nonlinear filtering, we derive equations of the algorithm for estimating random signals described by linear difference equations in discrete time in the case of a pulsed-disturbance flow. Optimal estimates of signals are represented as the sum of auxiliary estimates allowing for the influence of pulsed disturbances spaced apart by a multiple number of pulses. The results of mathematical simulation are given and the algorithm structure is discussed.