Conditionally optimal filtering in stochastic systems with random parameters and unsolved derivatives

For observable differential Gaussian stochastic systems (StS) with random parameters in the form of multicomponent integral canonical expansions (MC ICE) and StS with unsolved derivatives (USD), methodological support for synthesis of conditionally optimal filters is presented. A survey in the fields of analytical modeling and sub- and conditionally optimal filtering, extrapolation, and identification is presented. Necessary information concerning MC ICE is given. Special attention is paid to mean square regressive linearization including MC ICE. The stochastic systems with USD reducible to differential are considered. Basic results in normal conditionally optimal filtering (COF) are presented for StS USD reducible to differential. The theory of COF application to StS USD with multiplicative noises is developed. An illustrative example for scalar StS USD reducible to differential is given. For future COF generalization, ($i$) methods of moments, quasi-moments, and one- and multidimensional densities of orthogonal expansions and ($ii$) development for stochastic inclusions are recommended.