FILTERING OF SIGNALS WITH UNKNOWN INTERFERENCE POWER AND RANDOM JUMPING PERTURBATION

Abstract

A linear stochastic dynamic system under the influence of random disturbances and interference is considered. The perturbation is a sequence of uncorrelated random variables with a distribution in the range [–1, 1]. This sequence is modeled by a random binary signal with values 1 and 0 and is described by a Markov chain with known probabilities of transitions from one state to another. The modulated signal is fed to the input of the linear control unit. The output signal of the control object is measured with an error, which is a sequence of uncorrelated random variables with an unknown distribution in the range [–1, 1].The problem under consideration differs from the optimal linear filtration problems based on the application of the Kalman filter and its modifications. Its novelty consists in the following: 1) the input signal is a random jumping process – uncorrelated noise modulated by a random binary signal; 2) the variances of random processes – the input signal and the interference characterizing their power are unknown. А posteriori mathematical expectation and the a posteriori variance of the filtering error are determined by the methods of Bayesian estimation and the theory of systems with a random jump structure. The optimal estimation algorithm is described by a system of recurrent equations. It consists of five interconnected blocks: 1) a meter of mathematical expectation and dispersion of an additive mixture of an output signal with interference; 2) an indicator of a random structure; 3) a classifier of a random structure; 4) a dispersiometer; 5) a filter.