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Developing algorithms of optimal forecasting and filtering for some classes of nonstationary random sequences
(НТУ "ХПІ", 2018) Cheremskaya, Nadezhda Valentinovna
The problem of forecasting and filtering non-stationary random sequences is solved in the article. Optimal forecasting and filtering are performed using linear estimates and minimizing the mean squared error. For non-stationary random sequences, even with the correlation functions of the simplest form, such studies were not conducted. In this work, on the examples of non-stationary sequences, the problem of forecasting and filtering is solved explicitly. The correlation function image is obtained using the Hilbert approach, which allows one to calculate correlation functions as scalar products in a corresponding Hilbert space. The solution of the extrapolation problem with particular correlation function considered in the article can be used to simulate filtration and forecasting processes in real systems in the case of non-stationary random signals.