UPGRADED OPTIMAL ROBUST MULTIDIMENSIONAL FILTERING OF STATIONARY RANDOM USEFUL SIGNALS

Abstract

A characteristic feature of the devices, wich serves for measuring parameters of motion, is the presence of instrumental and methodological errors, which form a random broadband noise. One of the most effective ways to reduce the effects of noise on the measurement results is optimal filtration. Existing methods of optimal filters synthesis do not fully solve the problem of providing high precision stationary random selection of useful signals. To solve this problem we have used the idea of a modernized Wiener filtering. Then the problem of optimal filter synthesis reduces to finding the structure and parameters of the matrix of transfer functions W₁ and W₂, which would ensure a minimum quality of the selected criteria. To solve the problem the sensor matrix of transfer functions is presented in the form of polynomial matrices of complex argument s of dimension n × n. Using this notation, the next step was the introduction of the quality criterion in the frequency domain. In order to minimize the resulting functional introduced a single matrix variable transfer functions G, which allowed to find the equations needed to calculate the optimal filter transfer function matrix W. Thanks to the special way a certain block matrix factorization, achieved a significant simplification of the synthesis algorithm with respect to the known methods of optimal filtering. Thus, a new method of synthesis of optimal multivariate upgraded vinerovskogo correction filter noise in the frequency domain. Its distinguishing feature is a special selection of variruemoy matrix, which greatly simplifies the process of synthesis by bringing to the trivial factorization of the procedures.