Метод синтезу оптимального багатовимірного фільтру для виділення регулярного сигналу на фоні випадкових перешкод

Abstract

In terms of [1] we formulate the problem of synthesis of a complex system of allocation of a useful regular signal. Suppose that a multidimensional stationary filter best processes the input information about the same regular signal r(t), which is obtained by several "non-ideal" meters, and the result is transmitted to the evaluation system. In this article, a multi-channel measurement system, which is connected to the input of a multidimensional data transmission system, the dynamics of which is described by a system of linear differential equations. The input of the measuring system receives an n-dimensional vector of measured signals r (t), the components of which are deterministic functions. The vector r (t) belongs to the main group of "non-ideal" meters. Measurements are accompanied by interference, which is a random stationary process with zero mathematical expectation and a known fractional-rational matrix of spectral densities. An integral indicator of the quality of the system is the sum of the weighted integral quadratic error of the regular signal estimation and the variance of the random component of the error. Thus, a new algorithm for the synthesis of a complete optimal regular signal extraction system against the background of a multidimensional stationary random interference is obtained, which allows to find the structure and parameters of a multidimensional optimal filter taking into account the dynamics of the information transmission system.