Filtering of an Interrupted Signal on Approximation by Gamma Distribution Under the Influence of Additive Multiplicative Interference

The problem of constructing an algorithm for recognizing and filtering a continuous-valued Markov process measured in a mixture with random additive and multiplicative interference under conditions of random information interruptions is considered. The Bayes principle and the well-known two-stage filtering method “forecast-correction” are applied, supplemented by procedures for identifying the number of the structure, in which the system is located in the current and next time intervals. At the forecast stage, identification is based on calculating the probabilities of the future state of the system based on a priori information about the probabilities of its transitions from structure to structure, as well as on the current values of estimates of these probabilities. At the correction stage, identification is based on the use of probability prediction results and a priori known information about the reliability of the information of the system status indicator. In addition, the values of the probability densities of the measuring information in each structure are used, the expressions for which are obtained on the basis of a priori known laws of distribution of additive and multiplicative interference, as well as the predicted probability density of the Markov process in each structure at the next step of calculations. To obtain a practically realizable algorithm, expressions for the predicted and a posteriori densities of the Markov process probabilities are obtained based on their approximation by the probability density of the gamma distribution, completely determined by the first two initial moments. This made it possible to obtain a closed system of recurrent equations for estimating the probability of information interruption, mathematical expectations and variances of the Markov process in each structure.