μ Robust Stable Extrapolation of a Stationary Random Process with Interval Limited Variance

A method for synthesizing μ robust stable linear minimax extrapolator of a stationary random process under conditions of interval uncertainty of the parameters of the measured signal is presented. A robust and stable minimax extrapolation is shown in a constructive form of μ, both in terms of the result and the solution. The theorems of determinization and reduction on the existence and uniqueness of a consistent interval saddle point in the problem of extrapolation with small indistinct interval deviations in the right parts of the restrictions on the spectral power density of the perturbation of the measured signal in the form of a consistent interval Lagrange function are formulated and proved. In a constructive form, a 4-step algorithm is proposed for determinizing the search for the optimum of an imperfectly defined functional of the variance of the estimation error to find the optimum of the same name for two fully defined (deterministic) functionals. This approach, unlike others (for example, probabilistic), always ensures the existence of a stable result and solution of a single optimum in the problem of interval minimax extrapolation due to regularization by a small parameter with a derivative of the eigenfunction of a singularly perturbed integro-differential equation of the first order with an integral operator of the Voltaire type of the second kind, defined by a symmetric, closed real the core. Unlike classical forecasting and estimation methods, the proposed method allows us to obtain guaranteed interval-stable robust estimates of the state with some deviations of the actual probabilistic characteristics of the initial data from the hypothetical ones.