Conditionally optimal linear estimation of normal processes in Volterra stochastic systems

On the basis of Pugachev's conditionally optimal estimation (filtering and extrapolation) and previous investigations of the present authors, two estimation approximate conditionally optimal methods for normal stochastic processes in Volterra stochastic systems (VStS) reducible to linear StS with additive and parametric noises are developed. Some approaches for synthesis of Pugachev's filters and extrapolators by replacing parametric noises with equivalent corresponding additive noises are given. Test examples for one-dimensional VStS are presented. The given theory and test examples may be simply generalized to VStS with autocorrelated noises and VStS with hereditary and nonlinear interaction functions.